U.S. patent application number 09/848144 was filed with the patent office on 2001-10-11 for optical stress generator and detector.
Invention is credited to Maris, Humphrey J., Stoner, Robert J..
Application Number | 20010028460 09/848144 |
Document ID | / |
Family ID | 46203669 |
Filed Date | 2001-10-11 |
United States Patent
Application |
20010028460 |
Kind Code |
A1 |
Maris, Humphrey J. ; et
al. |
October 11, 2001 |
Optical stress generator and detector
Abstract
Disclosed is a system for the characterization of thin films and
interfaces between thin films through measurements of their
mechanical and thermal properties. In the system light is absorbed
in a thin film or in a structure made up of several thin films, and
the change in optical transmission or reflection is measured and
analyzed. The change in reflection or transmission is used to give
information about the ultrasonic waves that are produced in the
structure. The information that is obtained from the use of the
measurement methods and apparatus of this invention can include:
(a) a determination of the thickness of thin films with a speed and
accuracy that is improved compared to earlier methods; (b) a
determination of the thermal, elastic, and optical properties of
thin films; (c) a determination of the stress in thin films; and
(d) a characterization of the properties of interfaces, including
the presence of roughness and defects.
Inventors: |
Maris, Humphrey J.;
(Barrington, RI) ; Stoner, Robert J.; (Duxbury,
MA) |
Correspondence
Address: |
HARRY F. SMITH, ESQ.
OHLANDT, GREELEY, RUGGIERO & PERLE, L.L.P.
10th FLOOR
ONE LANDMARK SQUARE
STAMFORD
CT
06901-2682
US
|
Family ID: |
46203669 |
Appl. No.: |
09/848144 |
Filed: |
May 3, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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09848144 |
May 3, 2001 |
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09511719 |
Feb 23, 2000 |
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6271921 |
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09511719 |
Feb 23, 2000 |
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09382251 |
Aug 24, 1999 |
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6175416 |
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09382251 |
Aug 24, 1999 |
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08954347 |
Oct 17, 1997 |
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5959735 |
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08954347 |
Oct 17, 1997 |
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08689287 |
Aug 6, 1996 |
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5748318 |
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60010543 |
Jan 23, 1996 |
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Current U.S.
Class: |
356/432 |
Current CPC
Class: |
G01N 21/1702 20130101;
G01N 2291/0427 20130101; G01N 2291/02881 20130101; Y10S 977/901
20130101; G01N 2291/02827 20130101; G01N 29/2418 20130101; G01N
29/0681 20130101; Y10S 977/956 20130101; G01N 2291/0426 20130101;
Y10S 977/834 20130101; Y10S 977/90 20130101; Y10S 977/955
20130101 |
Class at
Publication: |
356/432 |
International
Class: |
G01N 021/00 |
Goverment Interests
[0002] This invention was made with government support under
grant/contract number DEFG02-ER45267 awarded by the Department of
Energy. The government has certain rights in the invention.
Claims
What is claimed is:
1. A method for characterizing a structure, comprising the steps
of: applying first electromagnetic radiation to the structure for
creating propagating stress pulses within the structure; applying
second electromagnetic radiation to the structure at a plurality of
different incidence angles so as to intercept the propagating
stress pulses; sensing a reflection or transmission of the second
electromagnetic radiation from the structure at the plurality of
incidence angles; associating a change in the reflection of the
second electromagnetic radiation over time with a value of an
optical characteristic of the structure, and determining in
accordance with the value of the optical characteristic the
velocities of the propagating stress pulses; and optionally
determining the elastic modulus of the structure in accordance with
the determined velocities of the propagating stress pulses.
2. A method for characterizing a three dimensional sample comprised
of a substrate and possibly one or more films deposited on said
substrate together with at least one structure that is disposed
upon or embedded within the substrate or one or more of the films,
comprising the steps of: simulating a mechanical response of the
sample, at a plurality of discrete time steps, to the application
of pulses of first electromagnetic radiation; applying pulses of
the first electromagnetic radiation to the sample for creating
propagating stress pulses within the sample; applying second
electromagnetic radiation to the sample so as to intercept the
propagating stress pulses; sensing from a reflection of the second
electromagnetic radiation from the sample at least one of a
time-varying change in intensity, position, direction, polarization
state, and optical phase of the second electromagnetic radiation;
and associating the sensed time-varying change with a property of
interest of the sample in accordance with the simulated response of
the sample.
3. A method as set forth in claim 2, wherein the property of
interest includes a dimension that is other than a thickness of the
at least one film.
4. A method for characterizing a structure, comprising the steps
of: simulating at predetermined time step increments, in accordance
with one or more characteristics of the structure, a mechanical
response of a simulated structure over an interval of time to an
application of a first pulse of optical radiation by at least the
steps of, determining an initial stress distribution within the
simulated structure, determining a change over the interval of time
in the stress and strain distribution in the simulated structure
following an application of the first pulse of optical radiation,
and determining the transient optical response of the simulated
structure by application of a second pulse of optical radiation
within the interval of time; applying the first pulse of optical
radiation to the structure; applying, during the interval of time,
the second pulse of optical radiation to the structure; comparing a
measured transient response of the structure to the determined
transient response for the simulated structure; adjusting a value
of the one or more characteristics of the simulated structure so as
to bring the determined transient response into agreement with the
measured transient response; and associating the adjusted value of
the one or more characteristics with a value of one or more actual
characteristics of the structure.
5. A method as set forth in claim 4, wherein the structure further
comprises at least one layer disposed over a substrate, and wherein
the step of determining an initial stress distribution within the
simulated structure includes the steps of: from optical constants
and a thickness of the at least one layer, calculating an electric
field, due to the first optical pulse, in the simulated structure
in terms of an amplitude, angle of incidence, and polarization of
the first pulse on a surface of the structure; from the calculated
electric field distribution, calculating an amount of energy
absorbed in the simulated structure as a function of position;
determining an effect of thermal diffusion on the absorbed energy
distribution; calculating a temperature rise as a function of
position within the simulated structure; and calculating a stress
within the simulated structure from the calculated temperature
rise.
6. A method as set forth in claim 4, wherein the step of
determining a change in stress and strain in the simulated
structure includes the steps of: selecting a time step .tau.; for
each layer of the simulated structure, calculating a bin size b
equal to the time step .tau. multiplied by the sound velocity in
the layer; and dividing each layer into bins of the calculated bin
size or bins smaller than the calculated bin size.
7. A method as set forth in claim 6, wherein the step of
determining a change in stress and strain in the simulated
structure further includes the steps of: decomposing the stress in
each bin into two components, one component initially propagating
towards a free surface of the simulated structure and one component
propagating away from the free surface of the simulated structure;
within each layer, stepping the two components forward from bin to
bin in the appropriate direction, wherein for a bin adjacent to a
boundary between two layers the stress propagating towards the
boundary is stepped partly into the first bin on the other side of
the boundary; repeating the foregoing steps for a sufficient number
of time steps .tau. to determine the stress distribution for a
period at least equal the interval of time; and calculating the
strain from the determined stress by division by an appropriate
elastic coefficient.
8. A method as set forth in claim 4, wherein the structure further
comprises at least one layer disposed over a substrate, and wherein
the step of determining a transient response of the simulated
structure to an application of a second pulse of optical radiation
within the interval of time includes the steps of: calculating
changes .DELTA.n and .DELTA..kappa. in optical constants of each
layer from calculated strain distribution as a function of depth
into the simulated structure; and from the calculated changes
.DELTA.n and .DELTA..kappa. in the optical constants as a function
of depth, and from unperturbed optical constants of the at least
one layer, calculating at least one of the quantities .DELTA.R,
.DELTA.T, .DELTA.P, .DELTA..phi. and .DELTA..delta..
9. A method as set forth in claim 8, wherein the step of comparing
a measured transient response of the structure to the determined
transient response compares the at least one of the calculated
quantities .DELTA.R, .DELTA.T, .DELTA.P, .DELTA..phi. and
.DELTA..delta. with a measured result.
10. A method as set forth in claim 4, wherein said plurality of
discrete time steps are selected to be small compared to a time
required for an acoustic wave to propagate through a thinnest layer
that comprises the structure.
11. A non-destructive system for characterizing a sample,
comprising: means for generating an optical pump pulse and for
focussing the pump pulse relative to a surface of the sample; means
for generating an optical probe pulse and for focussing the probe
pulse relative to the surface of the sample; means for measuring at
least one transient response of the structure to the pump pulse by
detecting a change in a reflected or transmitted portion of the
probe pulse; and detector means for automatically adjusting the
focus of at least one of the pump and probe pulses in response to
reflected portions of at least one of the pump and probe
pulses.
12. A non-destructive system for characterizing a sample as set
forth in claim 11, wherein said means for generating an optical
pump pulse generates a train of pump pulses which are applied to a
single location on the surface of the sample.
13. A non-destructive system for characterizing a sample as set
forth in claim 11, wherein the pump pulse induces a stress pulse in
the sample that propagates normal to the surface.
14. A non-destructive system for characterizing a sample,
comprising: means for generating an optical pump pulse and for
directing the pump pulse to an area of the surface of the sample;
means for generating an optical probe pulse and for directing the
probe pulse to a same or different area of the surface of the
sample so as to arrive after the pump pulse; means for measuring at
least one transient response of the structure to the pump pulse by
detecting a change in a reflected or transmitted portion of the
probe pulse; and means for determining an electrical resistivity of
at least a portion of the sample in accordance with the measured
transient response.
15. A non-destructive system for characterizing a sample,
comprising: means for generating an optical pump pulse and for
directing the pump pulse to an area of the surface of the sample;
means for generating an optical probe pulse and for directing the
probe pulse to a same or different area of the surface of the
sample so as to arrive after the pump pulse; means for measuring at
least one transient response of the structure to the pump pulse by
detecting a change in a characteristic of a reflected or
transmitted portion of the probe pulse; means for varying a
temperature of at least a portion of the structure during the
operation of the measuring means; and means for determining, from
the measured transient response, a derivative of a velocity of an
acoustic wave within the structure with respect to temperature, and
for associating the determined derivative of the velocity with a
static stress within the structure.
16. A method for operating a non-destructive system for
characterizing a sample, comprising the steps of: generating an
optical pump pulse and directing the pump pulse to an area of the
surface of the sample; generating an optical probe pulse and
directing the probe pulse to a same or different area of the
surface of the sample so as to arrive after the pump pulse;
measuring at least one transient response of the structure to the
pump pulse by detecting a change in a characteristic of a reflected
or transmitted portion of the probe pulse; and determining an
electrical resistivity of a portion of the sample in accordance
with the measured transient response.
17. A method for operating a non-destructive system for
characterizing a sample, comprising the steps of: generating an
optical pump pulse and directing the pump pulse to an area of the
surface of the sample; generating an optical probe pulse and
directing the probe pulse to a same or different area of the
surface of the sample so as to arrive after the pump pulse;
measuring at least one transient response of the structure to the
pump pulse by detecting a change in a characteristic of a reflected
or transmitted portion of the probe pulse; varying a temperature of
at least a portion of the structure during the step of measuring;
and determining, from the measured transient response, a derivative
of a velocity of an acoustic wave within the structure with respect
to temperature, and associating the determined derivative of the
velocity with a static stress within the structure.
18. A non-destructive system for characterizing a sample,
comprising: means for a generating a sequence of optical pump
pulses at a frequency f.sub.1 and for directing the sequence of
pump pulses to an area of the surface of the sample; means for
generating a sequence of optical probe pulses at a frequency
f.sub.2 and for directing the sequence of probe pulses to a same or
different area of the surface of the sample, wherein f.sub.1 is not
equal to f.sub.2 for continuously varying a delay between the
generation of a pump pulse and the generation of a probe pulse; and
means for measuring, at a rate given by one of (f.sub.1-f.sub.2) or
(f.sub.1+f.sub.2), at least one transient response of the structure
to the sequence of pump pulses by detecting a change in a
characteristic of a reflected or transmitted portion of the
sequence of probe pulses.
19. A non-destructive system for characterizing a sample,
comprising: means for a generating a sequence of optical pump
pulses and for directing the sequence of pump pulses to an area of
the surface of the sample; means for generating a sequence of
optical probe pulses, wherein a delay between individual ones of
the probe pulses, with respect to an individual one of the pump
pulses, is modulated at a frequency f and for directing the
sequence of probe pulses to a same or different area of the surface
of the sample; and means for measuring, at a rate given by f, at
least one transient response of the structure to the sequence of
pump pulses by detecting a change in a characteristic of a
reflected or transmitted portion of the sequence of probe
pulses.
20. A non-destructive system for characterizing a sample,
comprising: means for a generating a sequence of optical pump
pulses that are intensity modulated at a frequency f.sub.1 and for
directing the sequence of pump pulses to an area of the surface of
the sample; means for generating a sequence of optical probe
pulses, wherein a delay between individual ones of the probe
pulses, with respect to an individual one of the pump pulses, is
modulated at a frequency f.sub.2, and for directing the sequence of
probe pulses to a same or different area of the surface of the
sample, wherein f is not equal to f.sub.2; and means for measuring,
at a rate given by one of (f.sub.1-f.sub.2) or (f.sub.1+f.sub.2),
at least one transient response of the structure to the sequence of
pump pulses by detecting a change in a characteristic of a
reflected or transmitted portion of the sequence of probe
pulses.
21. A non-destructive system for characterizing a sample,
comprising: means for generating an optical pump pulse having a
first wavelength and for directing the pump pulse to an area of the
surface of the sample; means for generating an optical probe pulse
from the optical pump pulse and for directing the probe pulse to a
same or different area of the surface of the sample so as to arrive
after the pump pulse, the optical probe pulse being generated to
have a second wavelength that is a harmonic of the first
wavelength; and means for measuring at least one transient response
of the structure to the pump pulse by detecting a change in a
characteristic of the reflected or transmitted portion of the probe
pulse.
22. A non-destructive system for characterizing a sample,
comprising: means for generating an optical pump pulse and an
optical probe pulse from an input pulse having a first wavelength,
wherein the pump pulse has a wavelength that is a harmonic of the
first wavelength and the probe pulse has a wavelength that is equal
to the first wavelength; means for directing the pump pulse to an
area of the surface of the sample and for directing the probe pulse
to a same or different area of the surface of the sample so as to
arrive after the pump pulse; and means for measuring at least one
transient response of the structure to the pump pulse by detecting
a change in a characteristic of the reflected or transmitted
portion of the probe pulse.
23. A method for operating a non-destructive system for
characterizing a sample, comprising the steps of: generating an
optical pump pulse and directing the pump pulse to an area of the
surface of the sample; generating an optical probe pulse and
directing the probe pulse to a same or different area of the
surface of the sample so as to arrive after the pump pulse;
measuring at least one transient response of the structure to the
pump pulse by detecting a change in a reflected portion of the
probe pulse; and detecting at least one acoustic echo in the
reflected portion of the probe pulse, the step of detecting
including a step of determining a time of arrival of the acoustic
echo by convolving the detected acoustic echo with a predetermined
function.
24. A method for operating a non-destructive system for
characterizing a sample, comprising the steps of: generating an
optical pump pulse and directing the pump pulse to an area of the
surface of the sample; for each generated optical pump pulse,
generating an optical probe pulse and directing the probe pulse to
the surface of the sample so as to arrive after the pump pulse,
wherein some of the probe pulses are directed to the surface at a
first angle relative to the surface, and others of the probe pulses
are directed to the surface at a second angle relative to the
surface; and measuring at least one transient response of the
structure to the pump pulses by detecting a change in a reflected
portion of the probe pulses at each of the first and second
angles.
25. A method for characterizing a structure comprised of a
substrate and at least one layer that is an intentionally or a
non-intentionally formed layer that is disposed over the substrate,
comprising the steps of: generating a reference data set of a
transient optical response of the structure to an optical pump
pulse, the reference data set being generated from at least one of
(a) at least one reference sample or (b) a simulation of a
mechanical motion of a simulated structure at predetermined time
step increments selected to have a duration of less than one half
of a time required for an acoustic pulse to propagate through a
thinnest layer of the structure; applying a sequence of optical
pump pulses and optical probe pulses to the structure; comparing a
measured transient response of the structure to the reference data
set; adjusting a value of the one or more characteristics of the
structure so as to bring the reference data set into agreement with
the measured transient response; and associating the adjusted value
of the one or more characteristics with a value of one or more
actual characteristics of the structure.
26. A non-destructive system for characterizing a sample,
comprising: means for generating an optical pump pulse and for
directing the pump pulse to an area of the surface of the sample;
means for generating an optical probe pulse and for directing the
probe pulse to a same or different area of the surface of the
sample so as to arrive after the pump pulse, wherein the pump pulse
has the same wavelength as the probe pulse or a wavelength that is
different than the wavelength of the probe pulse; means for
automatically controlling a focusing of the pump and probe pulses
on the surface of the sample; means for measuring at least one
transient response of the structure to the pump pulse, the measured
transient response comprising a measurement of at least one of a
modulated change .DELTA.R in an intensity of a reflected portion of
the probe pulse, a change .DELTA.T in an intensity of a transmitted
portion of the probe pulse, a change .DELTA.P in a polarization of
the reflected probe pulse, a change .DELTA..phi. in an optical
phase of the reflected probe pulse, and a change in an angle of
reflection .DELTA..delta. of the probe pulse; means for calibrating
the measurement system for a determination of an amplitude of the
transient optical response of the sample; and means for associating
an output of said means for measuring with at least one
characteristic of interest of the structure.
27. A non-destructive system for characterizing a sample as set
forth in claim 26, and further comprising means for measuring a
derivative of the transient response as a function of at least one
of an incident angle of the pump or probe pulses and as a function
of a wavelength of at least one of the pump and probe pulses.
28. A non-destructive system for characterizing a sample as set
forth in claim 26, and further comprising means for measuring at
least one static response of the sample to the pump pulse, the
static response measurement comprising at least one of a
measurement of the optical reflectivity in accordance with an
incident and a reflected average intensity of at least one of the
pump and probe pulses, an average phase change of at least one of
the pump and probe pulses upon reflection from the structure; and
an average polarization and optical phase of at least one of the
incident and reflected pump and probe pulses.
29. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said characteristic of interest includes
a thickness of at least one layer of the sample, a mechanical
property of the at least one layer, and a characteristic of an
interface between the at least one layer and at least one of
another layer or the substrate.
30. A non-destructive system for characterizing a sample as set
forth in claim 26, and further comprising means for varying a
location of said sample relative to at least one of said pump and
probe pulses.
31. A non-destructive system for characterizing a sample as set
forth in claim 26, and further comprising means for varying a
temperature of said sample during an operation of said measuring
means, and for measuring a derivative of a velocity of an acoustic
wave in said sample with respect to temperature, and for
correlating the measured derivative with a static stress within
said sample.
32. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said pump and probe pulses are applied
along parallel optical paths to a focussing objective that is
disposed for focussing said pump and probe pulses on said
sample.
33. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said pump and probe pulses are applied
along parallel optical paths to a focussing objective that is
disposed for focussing said pump and probe pulses on said sample,
and are applied with one of a normal or oblique incidence angle to
said sample.
34. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein one of said pump and probe pulses is
applied to said surface of said sample with a normal incidence
angle, and wherein the other one of said pump and probe pulses is
applied to said surface of said sample with an oblique incidence
angle.
35. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said pump and probe pulses are derived
from a single laser pulse.
36. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said pump and probe pulses are each
derived from a separate laser pulse.
37. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said pump and probe pulses are derived
from a single laser pulse, and further comprising means for
converting a wavelength of said single laser pulse to a harmonic of
the wavelength such that one of the pump and probe pulses has a
wavelength that differs from the wavelength of the other pulse.
38. A non-destructive system for characterizing a sample as set
forth in claim 26, and further comprising means for impressing an
intensity modulation on at least one of said pump and probe
pulses.
39. A non-destructive system for characterizing a sample as set
forth in claim 38, wherein said means for impressing is
synchronized to a pulse repetition rate of a laser that generates
said pump or probe pulses.
40. A non-destructive system for characterizing a sample as set
forth in claim 38, wherein said means for impressing impresses a
first intensity modulation frequency on said pump pulse and a
second, different intensity modulation frequency on said probe
pulse.
41. A non-destructive system for characterizing a sample as set
forth in claim 26, and further comprising: a continuous wave laser
source for illuminating a portion of a surface of said sample with
cw light; and means, responsive to reflected cw light, for
performing an ellipsometric measurement of said sample.
42. A non-destructive system for characterizing a sample as set
forth in claim 26, and further comprising: a light source for
illuminating a portion of a surface of said sample; and means for
imaging said illuminated portion and for providing the image to one
of an operator or a pattern recognition software.
43. A non-destructive system for characterizing a sample as set
forth in claim 26, and further comprising a thermal source for
illuminating a portion of a surface of said sample with thermal
radiation for controllably varying a temperature of said sample
during the operation of the system.
44. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said measuring means directly measures a
derivative of said at least one transient response of the sample
with respect to a time delay between said pump pulse and said probe
pulse.
45. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein one of the pump and probe pulses has a
wavelength that differs from the wavelength of the other pulse, and
further comprising a wavelength selective filter in an optical path
of the probe pulse for passing the probe pulse while blocking any
scattered portion of the pump pulse.
46. A non-destructive system for characterizing a sample as set
forth in claim 26, and further comprising means for changing a
spatial relationship between a location where the probe pulse is
incident on the sample to a location wherein the pump pulse is
incident on the sample.
47. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said pump and probe pulses are derived
from first and second pulsed laser sources, respectively, and
wherein a pulse repetition rate of said first laser source differs
from a pulse repetition rate of said second laser source.
48. A non-destructive system for characterizing a sample as set
forth in claim 26, and further comprising means for automatically
varying a ratio of pump pulse energy to probe pulse energy.
49. A non-destructive system for characterizing a sample as set
forth in claim 26, and further comprising means for automatically
maintaining a substantially constant location, shape and size of
the probe pulse on the sample for a range of temporal offsets
between the probe pulse and the pump pulse.
50. A non-destructive system for characterizing a sample as set
forth in claim 26, and further comprising means for focussing and
translating said probe pulse on a surface of said sample
independent of said pump pulse.
51. A non-destructive system for characterizing a sample as set
forth in claim 50, wherein said focussing and translating means is
comprised of a fiber optic having a tapered end diameter for
performing near field focussing of said probe pulse, and means for
translating said tapered end of said fiber optic relative to a
focal spot of said pump pulse.
52. A non-destructive system for characterizing a sample as set
forth in claim 50, wherein said focussing and translating means is
comprised of a fiber optic having an end disposed for collecting
reflected probe light, and means for translating said fiber optic
relative to a surface of said sample.
53. A non-destructive system for characterizing a sample as set
forth in claim 26, and further comprising a plurality of fiber
optics each having an end disposed relative to a surface of said
sample for directing said pump and probe pulses to said sample.
54. A non-destructive system for characterizing a sample as set
forth in claim 53, and further comprising a further fiber optic
having an end disposed relative to the surface for collecting
reflected probe light.
55. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said sample is comprised of a plurality
of patterned sub-structures having dimensions less than a focal
spot diameter of either said pump or probe pulses, and wherein a
plurality of said sub-structures are simultaneously illuminated by
said pump and probe pulses.
56. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said sample is comprised of a plurality
of sub-structures that are arranged periodically, and further
comprising means for determining at least one characteristic of
said sub-structures by comparing an optical response of said
sub-structures to simulations of a vibrational response of said
sub-structures to the pump pulse.
57. A non-destructive system for characterizing a sample as set
forth in claim 26, and further comprising means for detecting a
presence of at least one acoustic echo in the reflected portion of
the probe pulse.
58. A non-destructive system for characterizing a sample as set
forth in claim 57, wherein said detecting means determines a time
of arrival of the acoustic echo by detecting a location in time of
a feature of interest of the acoustic echo.
59. A non-destructive system for characterizing a sample as set
forth in claim 57, wherein said detecting means determines a time
of arrival of the acoustic echo by convolving the detected acoustic
echo with a predetermined function.
60. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said measuring means measures the
transient response at at least two different angles of incidence of
said probe pulse.
61. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said sample is further comprised of one
of a transparent layer and a partially absorbing layer.
62. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said sample is further comprised of at
least one first layer disposed beneath at least one second layer,
and wherein at least said probe pulse passes through said at least
one second layer to reach said at least one first layer.
63. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said associating means comprises means
for comparing an output of said measuring means with at least one
of a simulation of the sample to an application of the pump and
probe pulses or to a result of an application of the pump and probe
pulses to a reference sample.
64. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said pump pulse is applied at a first
location on a surface of the sample, wherein said probe pulse is
applied at a second location on the same or a different surface of
the sample, and wherein said associating means determines a
characteristic of interest for a portion of the sample that lies
between the first and second locations.
65. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said sample is patterned into at least
one three-dimensional multilayered sub-structure, and wherein said
associating means comprises means for comparing an output of said
measuring means with a three-dimensional simulation of the at least
one multilayered sub-structure to an application of the pump and
probe pulses.
66. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said characteristic of interest includes
a characteristic of an interlayer between at least one layer and at
least one of another layer or the substrate.
67. A non-destructive system for characterizing a sample as set
forth in claim 66, wherein said characteristic of the interlayer
includes at least one of a thickness of the interlayer, a
structural phase of the interlayer, and a chemical species that is
located within the interlayer.
68. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said characteristic of interest includes
an adhesion property of at least, one layer to another adjacent
layer or to the substrate.
69. A non-destructive system for characterizing a sample as set
forth in claim 26, wherein said characteristic of interest includes
at least one of a derivative of an index of refraction or a
derivative of an extinction coefficient with respect to stress or
strain induced by the pump pulse.
70. A method for characterizing a structure comprised of a
substrate and at least one layer disposed on the substrate,
comprising the steps of: simulating a response of a model of the
structure to an application of a first pulse of optical radiation
followed by a transient response of the structure to an application
of a second pulse of optical radiation within an interval of time;
applying the first pulse of optical radiation to the structure;
applying, during the interval of time, the second pulse of optical
radiation to the structure; comparing a measured transient response
of the structure to the determined transient response; adjusting
one or more characteristics of the model of the structure so as to
bring the determined transient response into agreement with the
measured transient response; and associating the adjusted one or
more characteristics with one or more actual characteristics of the
structure, wherein the step of adjusting adjusts at least one of a
crystal orientation within the at least one layer, an interface
roughness between the at least one layer and another layer or the
substrate, a thermal diffusivity within the at least one layer, an
electronic diffusivity within the at least one layer, optical
constants within the at least one layer, derivatives of optical
constants with respect to stress or strain within the at least one
layer, and a surface roughness of the sample.
71. A method as set forth in claim 70, wherein the step of
adjusting further adjusts a static stress within the at least one
layer.
72. A method as set forth in claim 70, wherein the step of
adjusting further adjusts a presence of or a thickness of a region
of intermixing between two layers or a layer and the substrate.
73. A method for characterizing a structure comprised of a
substrate and at least one layer disposed on the substrate,
comprising the steps of: simulating a mechanical response of a
model of the structure to an application of a first pulse of
optical radiation by the steps of determining an initial stress
distribution within the structure in response to the first pulse of
optical radiation, calculating acoustical normal modes of the
structure, decomposing the determined initial stress distribution
into a sum over the calculated normal modes, and determining a
change in a transient optical response of the structure, at a time
of interest, to a second pulse of optical radiation by summing, for
each calculated normal mode, a change in the transient optical
response due to a spatial stress pattern associated with each
normal mode; applying the first pulse of optical radiation to the
structure; applying, at the time of interest, the second pulse of
optical radiation to the structure; comparing a measured transient
optical response of the structure to the determined transient
optical response; adjusting one or more characteristics of the
structure so as to bring the determined transient optical response
into agreement with the measured transient optical response; and
associating the adjusted one or more characteristics with one or
more actual characteristics of the structure.
74. A method for characterizing a structure comprised of a
substrate and at least one layer disposed on the substrate,
comprising the steps of: simulating a vibrational response of the
at least one layer to an application of a first pulse of optical
radiation, the response being simulated in accordance with a spring
constant parameter per unit area at an interface between the at
least one layer and another layer or the substrate; measuring the
actual response of the at least one layer by applying the first
pulse of optical radiation followed by an application of a second
pulse of optical radiation, and sensing a vibration of the at least
one layer by a change in a reflected portion of the second pulse of
optical radiation; comparing the measured response with the
simulated response; adjusting the spring constant parameter to
bring the simulated response into agreement with the measured
response; and characterizing a strength of the interface from the
adjusted spring constant parameter.
75. A method as set forth in claim 74, wherein the simulated
vibrational response is a simulated damping rate.
76. A non-destructive method for characterizing a sample,
comprising the steps of: generating an optical pump pulse and
directing the pump pulse to an area of the surface of the sample;
for each generated optical pump pulse, generating an optical probe
pulse and directing the probe pulse to the surface of the sample so
as to arrive after the pump pulse; automatically focusing the pump
and probe pulses to achieve predetermined focusing conditions;
measuring at least one transient response of the structure to the
pump pulse, the measured transient responses comprising a
measurement of at least one of a modulated change .DELTA.R in an
intensity of a reflected portion of the probe pulse, a change
.DELTA.T in an intensity of a transmitted portion of the probe
pulse, a change .DELTA.P in a polarization of the reflected probe
pulse, a change .DELTA..phi. in an optical phase of the reflected
probe pulse, and a change in an angle of reflection .DELTA..delta.
of the probe pulse; applying at least one calibration factor to the
at least one transient response; associating an output of said
means for measuring with at least one characteristic of interest of
the structure; adjusting a value of the one or more characteristics
of the structure so as to bring a reference data set into agreement
with the measured transient response; and associating the adjusted
value of the one or more characteristics with a value of one or
more actual characteristics of the structure.
77. A method for characterizing a structure, comprising the steps
of: applying first electromagnetic radiation to the structure for
creating propagating stress pulses within the structure; applying
second electromagnetic radiation to the structure at a
predetermined incidence angle so as to intercept the propagating
stress pulses; sensing a reflection or transmission of the second
electromagnetic radiation from the structure; associating a change
in the reflection of the second electromagnetic radiation over time
with a value of an optical characteristic of the structure for
determining a transient response of the structure; determining an
index of refraction of the structure using an ellipsometric
technique; and determining a velocity of sound in the structure in
accordance with the predetermined angle and the determined
transient response and index of refraction.
Description
CLAIM OF PRIORITY FROM A COPENDING PROVISIONAL PATENT
APPLICATION:
[0001] Priority is herewith claimed under 35 U.S.C. .sctn.119(e)
from copending Provisional Patent Application having application
Ser. No. 60/010,543, filed on Jan. 23, 1996 in the names of
Humphrey Maris and Robert Stoner, and entitled "Improved Optical
Stress Generator and Detector". This Provisional Patent Application
is incorporated by reference herein in its entirety.
FIELD OF THE INVENTION:
[0003] This invention relates to a system for measuring the
properties of thin films, and more particularly to a system which
optically induces stress pulses in a film and which optically
measures the stress pulses propagating within the film.
BACKGROUND OF THE INVENTION:
[0004] Presently, the nondestructive evaluation of thin films and
interfaces is of interest to manufacturers of electrical, optical
and mechanical devices which employ thin films. In one
nondestructive technique a radio frequency pulse is applied to a
piezoelectric transducer mounted on a substrate between the
transducer and the film to be studied. A stress pulse propagates
through the substrate toward the film. At the boundary between the
substrate and the film, part of the pulse is reflected back to the
transducer. The remainder enters the film and is partially
reflected at the opposite side to return through the substrate to
the transducer. The pulses are converted into electrical signals,
amplified electronically, and displayed on an oscilloscope. The
time delay between the two pulses indicates the film thickness, if
the sound velocity in the film is known, or indicates the sound
velocity, if the film thickness is known. Relative amplitudes of
the pulses provide information on the attenuation in the film or
the quality of the bond between the film and the substrate.
[0005] The minimum thickness of films which can be measured and the
sensitivity to film interface conditions using conventional
ultrasonics is limited by the pulse length. The duration of the
stress pulse is normally at least 0.1 .mu.sec corresponding to a
spatial length of at least 3.times.10.sup.-2 cm for an acoustic
velocity of 3.times.10.sup.5 cm/sec. Unless the film is thicker
than the length of the acoustic pulse, the pulses returning to the
transducer will overlap in time. Even if pulses as short in
duration as 0.001 .mu.sec are used, the film thickness must be at
least a few microns.
[0006] Another technique, acoustic microscopy, projects sound
through a rod having a spherical lens at its tip. The tip is
immersed in a liquid covering the film. Sound propagates through
the liquid, reflects off the surface of the sample, and returns
through the rod to the transducer. The amplitude of the signal
returning to the transducer is measured while the sample is moved
horizontally. The amplitudes are converted to a computer-generated
photograph of the sample surface. Sample features below the surface
are observed by raising the sample to bring the focal point beneath
the surface. The lateral and vertical resolution of the acoustic
microscope are approximately equal.
[0007] Resolution is greatest for the acoustic microscope when a
very short wavelength is passed through the coupling liquid. This
requires a liquid with a low sound velocity, such as liquid helium.
An acoustic microscope using liquid helium can resolve surface
features as small as 500 Angstroms, but only when the sample is
cooled to 0.1 K.
[0008] Several additional techniques, not involving generation and
detection of stress pulses, are available for measuring film
thickness. Ellipsometers direct elliptically polarized light at a
film sample and analyze the polarization state of the reflected
light to determine film thickness with an accuracy of 3-10
Angstroms. The elliptically polarized light is resolved into two
components having separate polarization orientations and a relative
phase shift. Changes in polarization state, beam amplitudes, and
phase of the two polarization components are observed after
reflection.
[0009] The ellipsometer technique employs films which are
reasonably transparent. Typically, at least 10% of the polarized
radiation must pass through the film. The thickness of metal sample
films thus cannot exceed a few hundred Angstroms.
[0010] Another technique uses a small stylus to mechanically
measure film thickness. The stylus is moved across the surface of a
substrate and, upon reaching the edge of a sample film, measures
the difference in height between the substrate and the film.
Accuracies of 10-100 Angstroms can be obtained. This method cannot
be used if the film lacks a sharp, distinct edge, or is too soft in
consistency to accurately support the stylus.
[0011] Another non-destructive method, based on Rutherford
Scattering, measures the energy of backscattered helium ions. The
lateral resolution of this method is poor.
[0012] Yet another technique uses resistance measurements to
determine film thickness. For a material of known resistivity, the
film thickness is determined by measuring the electrical resistance
of the film. For films less than 1000 Angstroms, however, this
method is of limited accuracy because the resistivity may be
non-uniformly dependent on the film thickness.
[0013] In yet another technique, the change in the direction of a
reflected light beam off a surface is studied when a stress pulse
arrives at the surface. In a particular application, stress pulses
are generated by a piezoelectric transducer on one side of a film
to be studied. A laser beam focused onto the other side detects the
stress pulses after they traverse the sample. This method is useful
for film thicknesses greater than 10 microns.
[0014] A film may also be examined by striking a surface of the
film with an intense optical pump beam to disrupt the film's
surface. Rather than observe propagation of stress pulses, however,
this method observes destructive excitation of the surface. The
disruption, such as thermal melting, is observed by illuminating
the site of impingement of the pump beam with an optical probe beam
and measuring changes in intensity of the probe beam. The probe
beam's intensity is altered by such destructive, disruptive effects
as boiling of the film's surface, ejection of molten material, and
subsequent cooling of the surface. See Downer, M. C.; Fork, R. L.;
and Shank, C. V., "Imaging with Femtosecond Optical Pulses",
Ultrafast Phenomena IV, Ed. D. H. Auston and K. B. Eisenthal
(Spinger-Verlag, N.Y. 1984), pp. 106-110.
[0015] Other systems measure thickness, composition or
concentration of material by measuring absorption of
suitably-chosen wavelengths of radiation. This method is generally
applicable only if the film is on a transparent substrate.
[0016] In a nondestructive ultrasonic technique described in U.S.
Pat. No. 4,710,030 (Tauc et al.), a very high frequency sound pulse
is generated and detected by means of an ultrafast laser pulse. The
sound pulse is used to probe an interface. The ultrasonic
frequencies used in this technique typically are less than 1 THz,
and the corresponding sonic wavelengths in typical materials are
greater than several hundred Angstroms. It is equivalent to refer
to the high frequency ultrasonic pulses generated in this technique
as coherent longitudinal acoustic phonons.
[0017] In more detail, Tauc et al. teach the use of pump and probe
beams having durations of 0.01 to 100 psec. These beams may impinge
at the same location on a sample's surface, or the point of
impingement of the probe beam may be shifted relative to the point
of impingement of the pump beam. In one embodiment the film being
measured can be translated in relation to the pump and probe beams.
The probe beam may be transmitted or reflected by the sample. In a
method taught by Tauc et al. the pump pulse has at least one
wavelength for non-destructively generating a stress pulse in the
sample. The probe pulse is guided to the sample to intercept the
stress pulse, and the method further detects a change in optical
constants induced by the stress pulse by measuring an intensity of
the probe beam after it intercepts the stress pulse.
[0018] In one embodiment a distance between a mirror and a corner
cube is varied to vary the delay between the impingement of the
pump beam and the probe beam on the sample. In a further embodiment
an opto-acoustically inactive film is studied by using an overlying
film comprised of an opto-acoustically active medium, such as
arsenic telluride. In another embodiment the quality of the bonding
between a film and the substrate can be determined from a
measurement of the reflection coefficient of the stress pulse at
the boundary, and comparing the measured value to a theoretical
value.
[0019] The methods and apparatus of Tauc et al. are not limited to
simple films, but can be extended to obtaining information about
layer thicknesses and interfaces in superlattices, multilayer
thin-film structures, and other inhomogeneous films. Tauc et al.
also provide for scanning the pump and probe beams over an area of
the sample, as small as 1 micron by 1 micron, and plotting the
change in intensity of the reflected or transmitted probe beam.
[0020] While well-suited for use in many measurement applications,
it is an object of this invention to extend and enhance the
teachings of Tauc et al.
OBJECTS OF THE INVENTION:
[0021] It is thus an object of this invention to provide an
improved optical generator and detector of stress pulses.
[0022] It is a further object of this invention to provide an
improved ultrafast optical technique for measuring stress in a thin
film.
[0023] It is still another object of this invention to provide an
improved ultrafast optical technique for determining the elastic
modulus, sound velocity, and refractive index of a thin film.
[0024] It is a still further object of this invention to provide an
improved ultrafast optical technique for characterizing an
interface between two materials, such as an interface between a
substrate and an overlying thin film.
[0025] It is another object of this invention to provide an
ultrafast optical technique for determining a derivative of a
transient response of a sample to a pump pulse, and for correlating
the derivative with a characteristic of interest, such as the
static stress within the sample.
[0026] It is another object of this invention to provide an
ultrafast optical technique for varying a temperature of the sample
and, while varying the temperature, for determining a derivative of
the acoustic velocity within the sample and for subsequently
correlating the derivative of the acoustic velocity with the static
stress within the sample.
[0027] It is another object of this invention to provide an
ultrafast optical technique for determining an electrical
resistivity of a sample.
[0028] It is a further object of this invention to provide
simulation methods for modelling a time-evolved effect of a stress
pulse generated within a sample of interest, and to then employ the
model to characterize the sample.
[0029] t is a further object of this invention to provide an
ultrafast optical technique for measuring a characteristic of
interest in a patterned, periodic, multilayered structure.
[0030] It is one still further object of this invention to provide
an ultrafast optical system and technique wherein optical fibers
are used to advantage for directing and/or focussing at least one
of an incident pump beam, and incident probe beam, or a reflected
or transmitted probe beam.
[0031] It is another object of this invention to provide a
non-destructive system and method for simultaneously measuring at
least two transient responses of a structure to a pump pulse, the
measured transient responses comprising at least two of a
measurement of a modulated change .DELTA.R in an intensity of a
reflected portion of a probe pulse, a change .DELTA.T in an
intensity of a transmitted portion of the probe pulse, a change
.DELTA.P in a polarization of the reflected probe pulse, a change
.DELTA..phi. in an optical phase of the reflected probe pulse, and
a change in an angle of reflection .DELTA..delta. of the probe
pulse.
[0032] It is one further object of this invention to provide a
non-destructive system and method for determining a characteristic
of a sample that includes an automatic control over the focussing
of pump and probe beams at the sample so as to provide a
reproducible intensity variation of the beams during each
measurement.
SUMMARY OF THE INVENTION
[0033] The foregoing and other problems are overcome and the
objects of the invention are realized by methods and apparatus in
accordance with embodiments of this invention.
[0034] This invention relates to a system for the characterization
of thin films and interfaces between thin films through
measurements of their mechanical, optical, and thermal properties.
In the system of this invention incident light is absorbed in a
thin film or in a structure made up of several thin films, and the
change in optical transmission or reflection is measured and
analyzed. The change in reflection or transmission is used to give
information about the ultrasonic waves that are produced in the
structure. The information that is obtained from the use of the
measurement methods and apparatus of this invention can include:
(a) a determination of the thickness of thin films with a speed and
accuracy that is improved compared to earlier methods; (b) a
determination of the thermal, elastic, electrical, and optical
properties of thin films; (c) a determination of the stress in thin
films; and (d) a characterization of the properties of interfaces,
including the presence of roughness and defects.
[0035] The invention features a radiation source for providing a
pump beam and a detection system for non-destructively measuring
the properties of one or more interfaces within a sample. The
radiation source provides the pump beam so as to have short
duration radiation pulses having an intensity and at least one
wavelength selected to non-destructively induce a propagating
stress wave in the sample, a radiation source for providing a probe
beam, a mechanism for directing the pump beam to the sample to
generate the stress wave within the sample, and a mechanism for
guiding the probe beam to a location at the sample to intercept the
stress wave. A suitable optical detector is provided that is
responsive to a reflected or transmitted portion of the probe beam
for detecting a change in the optical constants of the material
induced by the stress wave.
[0036] In one embodiment, the optical detector measures the
intensity of the reflected or transmitted probe beam. The pump and
probe beam may be derived from the same source that generates a
plurality of short duration pulses, and the system further includes
a beam splitter for directing a first portion of the source beam to
form the pump beam, having the plurality of pulses, and directing a
second portion to form the probe beam, also having the plurality of
pulses. The source beam has a single direction of polarization and
the system further includes means for rotating the polarization of
the probe beam and a device, disposed between a sample and the
optical detector, for transmitting only radiation having the
rotated direction of polarization. The system may further include a
temperature detector and a chopper for modulating the pump beam at
a predetermined frequency. The system can further include a
mechanism for establishing a predetermined time delay between the
impingement of a pulse of the pump beam and a pulse of the probe
beam upon the sample. The system can further include circuitry for
averaging the output of the optical detector for a plurality of
pulse detections while the delay between impingements remains set
at the predetermined time delay. The delay setting mechanism may
sequentially change the predetermined time delay and the circuitry
for averaging may successively average the output of the optical
detector during each successive predetermined time delay
setting.
[0037] By example, the pump beam may receive 1% to 99% of the
source beam, and the source beam may have an average power of 10
.mu.W to 10 kW. The source beam may include wavelengths from 100
Angstroms to 100 microns, and the radiation pulses of the source
beam may have a duration of 0.01 psec to 100 psec.
[0038] The sample may include a substrate and at least one thin
film to be examined disposed on the substrate such that interfaces
exist where the films meet, and/or where the film and the substrate
meet. For a sample with an optically opaque substrate, at the pump
wavelength, the pump and probe beams may both impinge from the film
side, or the pump may impinge from the film side and the probe may
impinge from the substrate side. For a sample with a transparent
substrate, both beams may impinge from the film side, or from the
substrate side, or from opposite sides of the sample. The optical
and thermal properties are such that the pump pulse changes the
temperature within at least one film with respect to the substrate.
The temperature within one or more of the thin films disposed on
the substrate may be uniform, and may be equal in several films.
The films may have thicknesses ranging from 1 .ANG. to 100 microns.
At least one film in the sample and/or the substrate has the
property that when a stress wave is present it causes a change in
the intensity, optical phase, polarization state, position, or
direction of the probe beam at the detector. The probe beam source
may provide a continuous radiation beam, and the pump beam source
may provide at least one discrete pump pulse having a duration of
0.01 to 100 psec and an average power of 10 .mu.W to 1 kW.
Alternatively the probe beam source may provide probe beam pulses
having a duration of 0.01 to 100 psec, the pump beam and probe beam
may impinge at the same location on the sample, and the mechanisms
for directing and guiding may include a common lens system for
focusing the pump beam and the probe beam onto the sample. The
position of impingement of the probe beam may be shifted spatially
relative to that of the pump beam, and the probe beam may be
transmitted or reflected by the sample.
[0039] One or more fiber optic elements may be incorporated within
the system. Such fibers may used to guide one or more beams within
the system for reducing the size of the system, and/or to achieve a
desired optical effect such as focussing of one or more beams onto
the surface of the sample. To achieve focussing, the fiber may be
tapered, or may incorporate a small lens at its output. A similar
focussing fiber can be used to gather reflected probe light and
direct it to an optical detector. A fiber may also be used to
modify the beam profile, or as a spatial filter to effect a
constant beam profile under widely varying input beam
conditions.
[0040] This invention advantageously provides a non-destructive
system and method for measuring at least one transient response of
a structure to a pump pulse of optical radiation, the measured
transient response or responses including at least one of a
measurement of a modulated change .DELTA.R in an intensity of a
reflected portion of a probe pulse, a change .DELTA.T in an
intensity of a transmitted portion of the probe pulse, a change
.DELTA.P in a polarization of the reflected probe pulse, a change
.DELTA..phi. in an optical phase of the reflected probe pulse, and
a change in an angle of reflection .DELTA..delta. of the probe
pulse, each of which may be considered as a change in a
characteristic of a reflected or transmitted portion of the probe
pulse. The measured transient response or responses are then
associated with at least one characteristic of interest of the
structure.
[0041] In a presently preferred embodiment the system provides for
automatically focusing the pump and probe pulses to achieve
predetermined focusing conditions, and the application of at least
one calibration factor to the at least one transient response. This
embodiment is especially useful when employed with time-evolved
simulations and models of a structure of interest, which is a
further aspect of this invention.
BRIEF DESCRIPTION OF THE DRAWINGS
[0042] The above set forth and other features of the invention are
made more apparent in the ensuing Detailed Description of the
Invention when read in conjunction with the attached Drawings,
wherein:
[0043] FIGS. 1a-1c depict embodiments of optical sources for use
with the system of this invention;
[0044] FIG. 2 is a block diagram of an embodiment of a sample
characterization system in accordance with this invention;
[0045] FIGS. 3a-3f each depict an embodiment of a pump beam/probe
beam delivery technique to a surface of a sample;
[0046] FIG. 4a is a diagram that illustrates a variability in a
temporal offset between pump and probe beam pulses;
[0047] FIG. 4b is block diagram that illustrates an embodiment of
electro-optical components responsive to the delay between the pump
and probe pulses, as shown in FIG. 4a;
[0048] FIG. 5 is a cross-sectional, enlarged view of a sample
having a substrate, a thin film layer, and an interface between the
substrate and the thin film layer, and that further illustrates a
stress-induced deformation in the thin film wherein constructive
and destructive probe beam interference occurs;
[0049] FIG. 6 illustrates a second embodiment of the interface
characterization system in accordance with this invention;
[0050] FIG. 7 illustrates a fiber optic-based pump and probe beam
delivery and focussing system in accordance with an embodiment of
this invention;
[0051] FIG. 8 illustrates a further embodiment of this invention
wherein a length of fiber optic is employed to compensate for a
change in probe beam profile as a function of delay between the
pump and probe beam pulses;
[0052] FIG. 9 illustrates an embodiment of a delay stage used for
setting a delay between the pump and probe beam pulses; FIG. 10 is
a cross-sectional, enlarged view of the sample having the
substrate, thin film layer, and the interface between the substrate
and the thin film layer, and that further illustrates the
impingement of the probe beam within a focussed spot (FS1) of the
pump beam, and the impingement of the probe beam at a second FS
(FS2) that is displaced from FS1;
[0053] FIG. 11 is an enlarged, cross-sectional view of a
silicon-on-insulator (SOI) sample that is amenable to
characterization in accordance with this invention;
[0054] FIG. 12 is a cross-sectional, enlarged view of the sample
having the substrate, a localized thin film structure disposed on a
surface of the substrate, and the interface between the substrate
and the thin film structure, and that further illustrates various
methods to apply the pump and probe beams;
[0055] FIG. 13 is a cross-sectional, enlarged view of the sample
having the substrate, a localized thin film structure disposed
within a surface of the substrate, and the interface between the
substrate and the thin film structure, and that further illustrates
various methods to apply the pump and probe beams;
[0056] FIG. 14 is a cross-sectional, enlarged view of a sample
having a substrate, a plurality of thin film layers, and interfaces
between the substrate and one of the thin film layers and between
the thin film layers;
[0057] FIGS. 15a-15d each illustrate an optically-induced stress
wave, having a velocity v.sub.s, that propagates in a material, and
the reflection of a portion of the probe beam from the stress
wave;
[0058] FIG. 16 is a block diagram of a first embodiment of a
picosecond ultrasonic system in accordance with this invention,
specifically, a parallel, oblique beam embodiment;
[0059] FIG. 17 is a block diagram of a second embodiment of a
picosecond ultrasonic system in accordance with this invention,
specifically, a normal pump, oblique probe embodiment;
[0060] FIG. 18 is a block diagram of a third, presently preferred
embodiment of a picosecond ultrasonic system in accordance with
this invention, specifically, a single wavelength, normal pump,
oblique probe, combined ellipsometer embodiment;
[0061] FIG. 19 is a block diagram of a fourth embodiment of a
picosecond ultrasonic system in accordance with this invention,
specifically, a dual wavelength, normal pump, oblique probe,
combined ellipsometer embodiment;
[0062] FIG. 20 is a block diagram of a fifth embodiment of a
picosecond ultrasonic system in accordance with this invention,
specifically, a dual wavelength, normal incidence pump and probe,
combined ellipsometer embodiment; and
[0063] FIG. 21 is a logic flow diagram that illustrates a
simulation method in accordance with an aspect of this
invention.
DETAILED DESCRIPTION OF THE INVENTION The
[0064] disclosure of the above-referenced U.S. Pat. No. 4,710,030
(Tauc et al.) is incorporated by reference herein in its
entirety.
[0065] The teaching of this invention is embodied by an optical
generator and detector of a stress wave within a sample. In this
system a first non-destructive pulsed beam of electromagnetic
radiation is directed upon a sample containing at least one film
and possibly also an interface between similar or dissimilar
materials. The first pulsed beam of electromagnetic radiation,
referred to herein as a pump beam 21a, produces a propagating
stress wave within the sample. A second non-destructive pulsed beam
of electromagnetic radiation, referred to herein as a probe beam
21b, is directed upon the sample such that at least one of the
polarization, optical phase, position, direction and intensity of a
reflected portion of the probe beam 21b' or a transmitted portion
of the probe beam 21b" is affected by a change in the optical
constants of the materials comprising the sample, or by a change in
the thickness of one or more layers or sublayers within a thin film
sample due to a propagating stress wave. Physical and chemical
properties of the materials, and possibly also of the interface,
are measured by observing the changes in the reflected or
transmitted probe beam intensity, direction, or state of
polarization as revealed by the time dependence of the changes in
beam intensity, direction or state of polarization. The very short
time scale is particularly important for achieving a high
sensitivity to interfacial and other properties, and for measuring
the properties of films having thicknesses less than several
microns.
[0066] By way of introduction, the arrangement of the pump and
probe beam according to this invention is illustrated in FIG. 10. A
test sample 51 is shown comprised of a film 84 disposed on
substrate 80. An interface 82 is formed between the film 84 and the
substrate 80. By example, the substrate 80 may be comprised of a
semiconductor such as silicon and may form a portion of a
semiconductor wafer, and the film 84 may be an overlying layer of
oxide, polymer, metal, or another semiconductor. In another
exemplary embodiment the sample may be a SOI wafer comprised of a
silicon substrate, a thin layer of silicon oxide, and an overlying
(typically thin) layer of silicon, as is shown in FIG. 11. To test
the sample 51 the pump beam 21a is directed onto a position on the
film 84 (referred to as a focal spot FS1) to generate a stress wave
in the sample due to the absorption of energy in the film 84 or
substrate 80. The pump beam 21a is incident on the sample 51 at an
angle .theta..sub.1 offset from normal. The unabsorbed portion of
the pump beam is reflected as the reflected pump beam 21a'. The
probe beam 21b may be directed to the same spot (FS1) on the sample
at an angle .theta..sub.2 to intercept the stress pulse generated
by the pump beam 21a. In other embodiments of the invention the
probe beam 21b can be directed to another location (FS2). A portion
of the probe beam 21b reflects from the film 84 as the reflected
probe beam 21b'. Any portion of the probe beam 21b that is
transmitted through the sample is referred to as the transmitted
probe beam 21b". The actual values of angles .theta..sub.1 and
.theta..sub.2 can be selected from a wide range of angles. The
intensities of the reflected and transmitted pump and probe beams
depend on the optical constants of the film 84 and substrate 80 and
on the thicknesses of the films.
[0067] FIG. 10 also illustrates probing at points (FS2) at a
distance from the pump beam FS1, which applies to the ultrasonic
and all other applications disclosed herein.
[0068] For a sufficiently thick opaque film disposed on a substrate
the pump light will be absorbed in a surface layer of thickness
small compared to the film thickness. The absorption in the surface
layer generates a stress pulse which propagates back and forth in
the film, giving rise to a series of equally-separated features
("echoes") in the responses measured by the probe beam. The
thickness of a simple film that is thick enough to have distinct
echoes can be determined from the echo time, as described by Tauc
et al. For a thinner film, the echoes become so closely spaced that
they degenerate into vibrational thickness modes of the film,
appearing as damped oscillations in the data, and the thickness can
be deduced from the vibration period. For intermediate thickness
films, or for films composed of multiple layers, the data may be
too complicated to analyze so simply. In such cases it is preferred
to construct a theoretical model for the vibrating structure in
which there may be one or more adjustable unknowns (e.g. film
thicknesses, densities, sound velocities). The theoretical model is
used to simulate the vibrations of the structure over a suitable
time interval (in discrete time steps), and to calculate the
corresponding change in the optical reflectivity of the sample (or
transmission, or polarization state, or optical phase of the
transmitted or reflected beams caused by the stress induced change
in the optical constants of the sample, or by stress induced
displacements of the surface or of interfaces within the
structure). The duration of the time steps are preferably selected
to be small compared to a time required for an acoustic wave to
propagate through a thinnest layer of the structure (e.g., 0.1 psec
to 200 psec). By example, the duration of each time step can be
established at less than one half (e.g., one tenth) of the
propagation time through the thinnest layer. Also by example, the
duration of each time step can be selected to be small compared to
a shortest absorption length (penetration depth) for the pump or
probe light in the structure.
[0069] A method for finding any number of unknowns is to compute a
simulated optical response for a particular set of parameters, and
then to adjust the values of the parameters as needed to achieve a
best-fit to the measured result. Presently preferred methods for
carrying out this modelling and simulation are described in detail
below with reference to FIG. 21.
[0070] The basic equations for the vibrational part of the
simulations are taken from well-known continuum elasticity theory.
The basic equations for the optical part of the simulation are the
Fresnel equations. As an illustration in one dimension (i.e. for a
sample 51 with a stress wave propagating with velocity v.sub.s
along a direction z normal to the surface), the quantity to be
computed in the simulation can be written as follows: 1 R ( t ) = 0
.infin. f ( z ) 33 ( z , t ) z ( 1 )
[0071] In this equation f(z) is the change in the reflectivity with
strain associated with stress .eta..sub.33(z,t) at depth z.
.DELTA.R(t) is the strain induced change in the optical
reflectivity of the sample at a time t. Similar equations can be
written for changes in the transmission or in the polarization
state of the probe beam 21b. The function f(z) includes the effect
of strain on the optical constants within the sample 51, as well as
the effect of displacement of the surface or internal interfaces
(i.e. a time-dependent change in the thickness of one or more
layers) due to the presence of a stress wave.
[0072] In accordance with an aspect of this invention, the physical
properties of the sample 51 which may be determined in this way
include properties which may affect the time dependence of
ultrasonic signals, and/or their amplitudes. These are (among
others) layer thicknesses, sound velocities, interfacial roughness,
interfacial adhesion strength, thermal diffusivities, stress,
strain, optical constants, surface roughness, and interfacial
contaminants.
[0073] FIGS. 1a-1c illustrate various embodiments of optical
sources that are suitable for practicing this invention, while FIG.
2 is a block diagram of an optical generation and detection system
for performing non-destructive picosecond time-scale thin film and
interface characterizations, referred to hereinafter as system
1.
[0074] A first embodiment of an optical source 10 is shown in FIG.
1a, in which the beam from a laser 12 is reflected from a mirror 14
and passes through a polarization rotating device, such as a
half-wave plate 16, to a polarizing beam splitter 18. The beams
emerging from the polarizing beam splitter 18 are orthogonally
polarized, and the ratio of their intensities may be varied through
a wide range by adjusting the orientation of the half-wave plate
16. One beam forms the pump beam 21a, while the probe beam 21b
reflects from a mirror 20.
[0075] An alternative embodiment of an optical source 10' shown in
FIG. 1b includes a frequency doubling crystal 24, such as BBO or
LBO, onto which the laser light is focused by a lens 22 positioned
between it and the laser 12. The coaxial beams of light emerging
from the frequency doubling crystal 24 are separated by means of a
dichroic mirror 26 into the pump and probe beams, each of which is
then collimated by lenses 28 and 30. The polarization of the pump
beam 21a is rotated to be perpendicular to that of the probe beam
21b by means of a half-wave plate 32. The dichroic mirror 26 may be
chosen to pass the fundamental frequency of the laser 12 and
reflect the second harmonic, giving a probe beam at the fundamental
and a pump beam at the second harmonic. Alternatively, the dichroic
mirror 26 may be chosen to pass the second harmonic and reflect the
fundamental, giving the probe beam 21b at the second harmonic and
the pump beam 21a at the fundamental, as shown in FIG. 1b.
[0076] Another embodiment of an optical source 10" is shown in FIG.
1c, in which the pump and probe beams are produced by two different
lasers 12 and 13. In one embodiment, these may be identical pulsed
lasers, in which case the upper beam is passed through the
half-wave plate 16 to rotate its polarization relative to that of
the lower beam by 90 degrees. Alternatively, the lasers 12 and 13
may emit dissimilar wavelengths (two "colors"). Alternatively, the
probe laser 13 may emit a continuous (i.e. non-pulsed) beam.
Alternatively, the pump laser 12 may emit pulses with a repetition
period of .tau..sub.A and the probe laser 13 may emit pulses with a
repetition period .tau..sub.B, as shown in FIG. 4a. Such a scheme
may be used to effect a continuously variable delay between the
pump and probe pulses without the use of a mechanical delay stage
44 of a type depicted in FIG. 2.
[0077] Referring now to FIG. 4b, in this alternative technique the
delay between pairs of A and B pulses increases by a time
.tau..sub.B-.tau..sub.A from one repetition to the next. By
example, .tau..sub.B-.tau..sub.A may be 0.1 psec on average, and
the repetition rate of the pump laser 12 may be 100 MHz. This gives
a time between simultaneous arrivals of the pump and probe pulses
of one millisecond (i.e., the scan time). This embodiment further
includes suitable frequency locking electronics (FLE), mirrors, a
lens, a suitable detector 60, and a fast signal averager (SA). A
measurement of, by example, .DELTA.R(t) may be performed by
applying a signal corresponding to the reflected probe intensity
from the output of the detector 60 to the input of the fast signal
averager (SA), and by triggering sample acquisitions at times
corresponding to the pulsing of the probe laser 13. A large number
(e.g., thousands) of measurements may be averaged in order to
effect a desired signal to noise ratio. It should be noted in
regard to this invention that the delay stage and modulator
described previously in regard to FIG. 2 may be omitted. It should
also be appreciated that any "jitter" in the pulsing of the two
lasers may have the effect of averaging the signals corresponding
to closely spaced delay times, and that this effect may somewhat
attenuate the high frequency components of the measurement.
[0078] Although the pump and probe lasers are depicted in FIG. 1c
separately, they may have one or more optical elements in common,
including the gain medium. Other permutations of pump and probe
color, polarization and pulse rate suggested by the above
description may be used to achieve an improvement in signal
quality, depending on the properties of the materials to be
investigated.
[0079] Examples of the pulsed lasers suitable for use in the system
1 include an Argon ion pumped solid state mode-locked laser, such
as Coherent Inc. Inova (Argon) and Mira (Ti:sapphire); a diode
laser pumped solid state mode locked laser, such as a continuous
wave diode pumped frequency doubled YAG and modelocked Ti:sapphire
laser; and a direct diode pumped mode-locked solid state laser.
[0080] Referring to the embodiment of FIG. 2, a further embodiment
of an optical source 10'" provides both the pump and probe beams
21a and 21b, respectively, in a manner similar to the embodiment of
FIG. 1a. In the FIG. 2 arrangement the linearly polarized beam from
laser 12 passes through the half-wave plate 16, which is used to
rotate its polarization. The polarized beam is then split into pump
and probe beams by a dielectric beam splitter 34. The ratio of pump
to probe may be varied by rotating the incoming polarization. The
lower beam is the pump beam 21a, and the upper beam is the probe
beam 21b. The pump beam 21a passes through a half-wave
plate/polarizer combination 38 which rotates its polarization to be
orthogonal to that of the probe beam 21b, and which also suppresses
any light not polarized along this orthogonal axis.
[0081] The pump and probe beams 21a and 21b are emitted by the
source, and the intensity of the pump beam is modulated at a rate
of about 1 MHz by an acousto-optic modulator (AOM) 40, or by a
photoelastic modulator followed by a polarizer, or by other
intensity modulation means. The probe beam path length is varied by
translating a retroreflector 46 mounted on a computer-controlled
delay stage 44, via a steering mirror combination 110a. Both beams
are then focused by lens 48 onto the sample 51 mounted on a
translatable sample stage 50, and are detected by a photodetector
60. In this embodiment the inputs to the detector 60 include
portions of the input pump and probe beams (inputs c and b,
respectively, via beam splitters 49a and 49b, respectively); and
also include portions of the reflected pump beam 21a' and reflected
probe beam 21b' (inputs d and a, respectively). Outputs from the
detector 60 include signals proportional to the incident pump beam
intensity (e); incident probe beam intensity (f); reflected pump
beam intensity (g); reflected probe beam intensity (h); and probe
modulation intensity (i), i.e. only the modulated part of the
reflected probe intensity. These detector outputs are fed into a
processor 66. The processor 66 calculates from the inputs the
fractional change in the sample's reflectivity R (i.e. .DELTA.R/R),
and normalizes this change by the intensity of the incident pump
beam.
[0082] In the apparatus of this invention the detector input
designated as (a) contains a modulated component which carries the
stress information in addition to a large unmodulated reflected
probe component 21b'. Input (b) is proportional to the unmodulated
portion of the probe signal 21b. The output (i) is a voltage
proportional to only the modulated part of the probe signal, which
is determined by electronically removing the unmodulated component
from the input (a). This output goes to a bandpass filter and
preamplifier 62, then to a synchronous demodulator 64 (e.g. a
lockin amplifier), and finally to the processor 66 where it is
digitized and stored. The inputs (a) and (b) are also used to
determine the reflectivity of the sample corresponding to the probe
beam 21b, and similarly inputs (d) and (c) are used to determine
the reflectivity of the sample corresponding to the pump beam 21a.
These quantities may be used to validate the optical simulation of
the structure, or in some cases to deduce layer properties such as
thickness in accordance with known optical reflectometry
principles. In addition, inputs (a) and (d) are used by the
processor 66 to normalize the reflectivity change output (i). The
energy deposited in the sample 51 by the pump beam 21a may be
determined by comparing the incident and reflected pump and probe
beam intensities (21a', 21b').
[0083] Portions of the pump and probe beams may also be directed
via beam splitter 54 onto one or more position sensitive detectors
(autofocus detector 58) whose output may be used by the processor
66, in conjunction with the sample translation stage 50, to effect
an optimum focus of the pump and probe beams on the sample 51. The
signal to noise ratio may be improved by placing color filters
and/or polarizers between the sample 51 and detector 60 to prevent
light scattered from other parts of the system from impinging one
or more detectors (as an example, to prevent pump light scattered
from the sample 51 from impinging on reflected probe intensity
detector (a)). The signal quality may be further improved by
passing the modulated probe intensity output (i) from the detector
60 through the synchronous demodulator 64 (such as a lockin
amplifier, or signal averager) located before the processor 66. The
signal quality may be further improved for samples 51 tending to
scatter the pump beam 21a into the probe detector by introducing a
second intensity modulator into the probe beam path between the
source 10 and the sample 51. The second intensity modulator has a
modulation frequency differing from the pump beam modulation
frequency by an amount such that the difference frequency is
greater than the input bandwidth of the synchronous demodulator 62.
The detector output (i) corresponding to the reflected probe
intensity may then be synchronously demodulated at the difference
frequency, while the components of (i) at the modulation
frequencies are rejected.
[0084] The pump and probe beams may be focused, as in FIG. 2, onto
the sample through the common lens 48. This arrangement is simple
to practice but is not optimal for all cases, since the pump beam
21a need be scattered through only a small angle by a non-ideal
sample to impinge on the reflected probe detector (a), thereby
introducing noise to the measurement of the modulated probe
intensity. The common lens approach also has the weakness of
achieving non-optimal spot overlap, which may be improved by using
separate lenses, or coaxial beams. The common lens approach is
represented in FIG. 3d in plan view from a location along a normal
to the sample, here a semiconductor wafer 70. Other focusing
geometries may give improved signal quality, depending on the
properties of the sample (e.g. the amount of surface roughness),
and the source (e.g. pump and probe beams having different colors,
versus pump and probe beams having the same color).
[0085] Alternative focusing geometries are also illustrated in FIG.
3, and include:
[0086] (FIG. 3a) pump and probe beams oblique to the sample plane
(i.e., the surface of wafer 70) and not parallel or coaxial to each
other;
[0087] (FIG. 3b) pump and probe beams substantially normal to the
sample plane and parallel, focused through a common lens 98 (as in
FIG. 6);
[0088] (FIG. 3c) pump and probe beams parallel and lying in a plane
orthogonal to the plane of incidence, focused through common lenses
48 and 52;
[0089] (FIG. 3e) (i) pump beam normal and probe beam oblique,
focused independently; or (ii) probe normal and pump oblique;
and
[0090] (FIG. 3f) pump beam and probe beam both normal to the sample
plane and coaxial, focused through a common lens 74.
[0091] The variable delay between the pump and probe beams may be
implemented as shown in FIG. 2 by means of the computer controlled
delay stage 44 in the probe beam path. Alternatively, a similar
delay stage may be inserted within the pump beam path to "advance"
the pump beam pulses in time relative to the probe pulses. An
extremely long delay may be implemented as shown in FIG. 9 by
placing more than one retroreflector 46 on the single translation
stage 44. In this embodiment a plurality of the beam steering
mirrors 110a are employed to direct the probe beam 21b to
individual ones of the retroreflectors 46, thereby significantly
increasing the probe beam path length relative to the pump beam
path length. It is possible to implement a delay which is longer
than the time between successive pulses such that the effects of a
pump pulse arriving at the sample more than one pulse interval
before the probe may be detected.
[0092] The shape and position of the focused probe spot FS on the
surface of the sample 51 may vary systematically, depending on the
position of the delay stage 44 (i.e. the time delay). For example,
the system 1 may exhibit a lack of parallelism between the probe
path in FIG. 2 and the delay stage axis due to misalignment, or as
a result of a flaw in the stage mechanism. This causes a
translation of the probe beam across the focusing lens, and for a
lens exhibiting typical aberrations, can introduce a corresponding
lateral translation of the probe beam 21b relative to the pump beam
21a on the surface of the sample 51, as a function of delay.
[0093] In addition, since all laser beams exhibit some degree of
divergence, varying the path length of one of the beams changes its
diameter at the focusing lens, and this causes a corresponding
change in the diameter of the focused spot (FS) on the sample 51.
The result of all such effects may be to introduce a spurious
dependence of the signal upon delay time. One method to eliminate
such dependencies is shown in FIG. 8, in which a length of optical
fiber 114 is introduced to the path of the delayed probe beam (or
advanced pump beam). The fiber 114 serves as a spatial filter,
preserving a constant spot position, size and profile throughout a
range of input beam conditions. By incorporating such a device into
the probe beam path it is possible to preserve a very stable
overlap of the pump and probe beams on the focus spot FS over a
wide range of delay stage positions. Other types of spatial filters
may also be used to achieve the same effect; for example, any small
aperture (typically smaller than the beam size) such as a pinhole
or narrow slit, followed by a second aperture so chosen as to block
high spatial Fourier components of the beam may be used. A lens may
be used to focus the beam onto the first aperture, and a second
lens may be used to collimate the beam emerging from the second
aperture. In a system employing any of the above techniques it is
preferred to monitor the intensity of the delayed (or advanced)
beam either before or after it impinges on the sample, to properly
normalize the final signal.
[0094] Referring now to FIG. 5, there is illustrated a deflection
through an angle .theta. of the probe beam 21b by a non-uniform
expansion of a region wherein a propagating stress wave exists
(i.e. a bulge 86 in the film 84). The bulge 86 is caused at least
in part by a stress wave which may also have a non-uniform profile
across the spot. The deflection can be detected by a position
sensitive detector such as a split cell 60'. Movement of the
reflected probe beam 21b' can also come about in the absence of the
bulge 86 in transparent and semi-transparent samples due to a
stress induced change in the refractive index. In this case the
beam is displaced by a small amount parallel to the direction along
which it would normally deflect. This displacement can also be
detected by a position sensitive detector. FIG. 5 also illustrates
the lengthening of the path through the sample as a result of the
surface displacement (uniform or non-uniform).
[0095] FIG. 6 illustrates a configuration which is based on FIGS.
1, 2 and 3, and is a preferred implementation of a "normal
incidence, dual wavelength" system. The source 10' (FIG. 1b) is
frequency doubled using the nonlinear crystal 24, such as BBO, KTP
or LBO. The pump and probe beams are separated by the dichroic
mirror 26 such that the doubled wavelength is passed to become the
probe beam 21b, and the undoubted part is reflected to become the
pump beam 21a. The pump beam 21a is modulated by modulator 90 and
is directed at normal incidence onto the sample 51 through
objective 98. The probe beam polarization is rotated by means of a
half wave plate 38 and is then passed through a polarizer 42
oriented to be orthogonal to the pump beam polarization. This
retarder/polarizer combination is also used as a variable
attenuator for the probe beam 21b. The probe beam 21b is then sent
to the variable delay stage 44, and is focused onto the sample 51
through the same normal incidence objective 98 as the probe beam
21a. The reflected probe beam 21b' is directed to the detector 60
by a dichroic mirror 92 which passes the reflected pump beam 21a,
thereby effectively filtering out any reflected probe light. A
filter 94 which passes only the probe beam wavelength is placed
before the detector 60. The detector 60 is followed by the tuned
filter 62, lockin amplifier 64, and processor 66, as in FIG. 2.
[0096] FIG. 7 illustrates an embodiment of this invention wherein
the pump beam 21a and the probe beam 21b are directed to the sample
51 by means of tapered optical fibers 100 and 102, respectively, to
achieve near-field focusing and FS sizes of order 100 nm. The probe
beam 21b is shown having normal incidence, and may have a different
wavelength than the pump beam 21a. In this embodiment a terminal
portion of the pump and/or probe beam delivery fiber 100, 102 is
reduced in diameter, such as by stretching the fiber, so as to
provide a focussed spot FS having a diameter that is less than the
normal range of optical focussing. This enables the pump and/or
probe optical pulse to be repeatably delivered to a very small
region of the sample's surface (e.g., to a spot having a diameter
.ltoreq.one micrometer), regardless of any changes that are
occurring in the optical path length of the pump and/or probe beam.
The pump beam 21a need not be brought in through a fiber, and in
one mode of operation may be much larger than the probe spot size
on the sample. The probe beam 21b may then be scanned by x-axis and
y-axis piezoelectric actuators 102a and 102b on a very small
spatial scale (similar to a Scanning Tunneling Microscope) with the
pump beam location fixed. This embodiment may be used to map
structures patterned in two or more dimensions on a length scale
smaller than can be achieved using conventional lithography.
Therefore, it can be used to map the smallest structures found in
integrated circuits.
[0097] The probe beam 21b can be an expanded beam that is focused
onto the fiber 102 by a lens 104, and the reflected probe beam 21b'
is directed through the fiber 102 and is diverted by a splitter 106
to a filter 108 and then to the detector 60.
[0098] FIG. 12 shows an interface 82 between a patterned structure
84 on top of the substrate 80, and is useful in explaining the use
of this invention when characterizing three dimensional structures
as opposed to planar structures. The patterned structure may be
evaluated by generating a stress wave in the substrate 80 and
detecting the stress wave in the structure 84; or by generating the
stress wave in the structure 84 and detecting the stress wave in
the structure 84; or by generating the stress wave in the structure
84 and detecting the stress wave in the substrate 80.
[0099] FIG. 13 shows an interface 82 surrounding a structure 84
formed within a patterned recess within a surface of substrate 80.
An example of this three dimensional configuration is a tungsten
via formed in a hole in a glass layer by (i) depositing the glass
on a substrate, (ii) patterning and etching the hole, (iii)
depositing a film of tungsten and (iv) polishing the tungsten layer
until the glass is exposed (adhesion promoting layers may be
deposited before the tungsten). The structure may be evaluated by
generating the stress wave in the substrate 80 (not applicable if
the substrate, as in the above tungsten example, is glass) and
detecting it in the embedded structure 84; or by generating the
stress wave in the structure 84 and detecting the stress wave in
the structure 84; or by generating the stress wave in the structure
84 and detecting the stress wave in the substrate 80.
[0100] It should be realized that, in the three dimensional
structures illustrated in FIGS. 12 and 13, the pump beam can also
be employed to excite the normal modes in the structure, which can
in turn affect the transmitted or reflected probe beam.
[0101] When applying the probe beam 21b to the structure 84 it may
be advantageous to use a near-field focussing arrangement, such as
the tapered optical fiber shown in FIG. 7. In this case the pump
beam FS can be significantly larger than the probe beam FS, thereby
enabling the selective probing of small scale structures.
[0102] This capability for spatial imaging can be exploited to
perform measurements of static stress with lateral spatial
resolution to 100 nm scale and below.
[0103] It is also within the scope of this invention to apply a
pump beam FS and a probe beam FS to simultaneously probe a
plurality of patterned structures (e.g., a two-dimensional array of
tungsten vias 0.5 .mu.m in diameter and 1.0 .mu.m apart that are
formed in a substrate). In this case each tungsten via may be
considered a separate, independent oscillator, each of which
contributes to the reflected or transmitted probe beam signal. For
closer spacings between elements, a "superlattice"-type of
vibrational mode can be excited, wherein the reflected or
transmitted probe signal includes coupling effects between the
vias. In either case the probe beam signal can be compared to a
signal obtained from a reference "known good" structure, or to a
simulation of the structure, or from a combination of reference
data and simulations. Any deviation in the probe signal from the
reference and/or simulated signal may indicate that the sample
differs in some way from what was expected.
[0104] FIG. 14 shows that for samples considered in the ultrasonic
technique, a multilayer thin film 84a, 84b may be substituted for a
simple film 84. Such multilayer films may be formed intentionally
by sequential depositions, or unintentionally because the substrate
80 may have been ineffectively cleaned prior to succeeding layer
depositions, or by the (intentional or unintentional) chemical
reaction between two or more layers (for example, following heat
treatment). Such layers may give rise to ultrasonic echoes having
complicated shapes and temporal characteristics. It is possible to
determine the thicknesses and interface characteristics for thin
film structures containing, by example, five or more sublayers.
This is preferably accomplished by comparing the reflectivity or
transmission data with simulations of the ultrasonics and detection
physics to obtain a best fit set of unknowns with the obtained
data.
[0105] In the system configurations which use the AOM 40 to
modulate the pump beam 21a, there may be no relationship between
the modulation rate and the repetition rate of the laser 12. As a
result, the laser pulse train and modulation cycle are
asynchronous. It is possible to make this a synchronous system by
deriving the modulation rate from the pulse repetition rate. The
pulse repetition rate may be obtained from the laser 12 by means of
an optical detector which senses the emitted pulses, or by using
the drive signal from an actively mode-locked laser. To derive the
modulation signal, the pulse rate signal is applied to a counter
which changes the state of the modulator 40 after n laser pulses
are counted. The modulation rate is then 1/2 n times the laser
pulse rate. In such a synchronous scheme the number of pump pulses
impinging on the sample 51 in any period of the modulator 40 is
always the same. This eliminates a potential source of noise in the
modulated probe beam 21b which might arise in an asynchronous
system under conditions in which the laser energy contained within
a single cycle of the modulator 40 varies from period to period of
the modulation.
[0106] A major source of noise is scattered pump light which can
reach the probe beam detector (a) despite having a nominally
orthogonal polarization (polarizers are not perfect, and also the
sample 51 may tend to depolarize the light). As was described
above, one technique to suppress this source of noise is to use
pump and probe beams of different color, so that the pump color may
be blocked by means of a filter before the probe detector.
[0107] Another method is to modulate the probe beam 21b at a
frequency different from the pump beam modulation frequency. By
example, if the pump modulation frequency is f.sub.1 and the probe
modulation frequency is f.sub.2, then the part of the probe beam
modulated by the pump beam at the sample 51 will have a component
at the frequency f.sub.1-f.sub.2. This signal may be passed through
a synchronous demodulator or low pass filter designed to reject
f.sub.1 and f.sub.2 and pass only their difference frequency. Thus,
any pump light scattered by the sample 51 onto the probe detector
(a), which would otherwise appear as noise in the data, is
suppressed. To minimize the introduction of ubiquitous 1/f noise
the difference frequency is preferably not below a few hundred kHz.
Exemplary frequencies are f.sub.1=1 MHz and f.sub.2=500 kHz. For a
sample 51 with the property that the incident light penetrates at
least one wavelength into a layer or layers into which a stress
wave is launched, it is possible to use picosecond ultrasonics to
independently measure the sound velocity and refractive index of
said layer or layers with great precision. The sound velocity may
also be used to determine the elastic modulus. Optical interference
between probe light reflected from the surface of the sample and
probe light reflected from the traveling stress wave gives rise to
oscillations in the intensity of the reflected probe beam 21b' as a
function of delay. The period of these oscillations may be measured
very precisely. For a material having an index of refraction n and
sound velocity v.sub.s the period of the oscillations is given by:
2 = 0 2 nv s cos ( 2 )
[0108] where .lambda..sub.0 is the optical wavelength in free space
and .theta. is the angle between the direction normal to the
surface of the sample 51 and the direction of light propagation in
the sample. Typically one knows .theta. and .lambda..sub.0 in
advance. Thus, from the observed oscillation period, one can deduce
the product nv.sub.s with high precision. The value of v.sub.s
independent of n can be found by measuring .tau. at a second angle
(which yields a value for n), or by using a published value for n.
In addition, from the sound velocity, the elastic modulus
c.sub.11=.rho.v.sub.s.sup.2 of the film may be determined (using a
previously determined value of .rho.).
[0109] In accordance with an aspect of this invention measurements
at two angles are simultaneously made by detecting parts of the
probe beam 21b impinging on the sample 51 within a single focused
beam, which then reflects to two or more closely spaced detectors.
It is also within the scope of the invention to controllably tilt
the sample stage 50, and to thus cause the probe beam 21b to
impinge on the surface of the sample 51 at two or more different
angles of incidence.
[0110] An alternative technique for determining n and v.sub.s has
been described by Grahn et al. (APL 53, no. 21 (Nov. 21, 1988), pp.
2023-2024, and APL. 53, no. 23, (Dec. 5, 1988), pp. 2281-2283).
However, the Grahn et al. technique depends on the use of an
independently-determined thickness for the film.
[0111] Representative samples for which these techniques may be
used are illustrated in FIGS. 15a-15d.
[0112] In FIG. 15a a stress pulse is launched from the film layer
84 by the absorption of the pump beam energy, and propagates within
the substrate 80 with a characteristic velocity v.sub.s. The
application of the probe beam pulse 21b results in two reflections,
one from the surface of the film 84 and another from the stress
pulse. As the stress pulse continues to propagate away from the
film layer 84, the part of the probe pulse reflected at the stress
wave has a changing phase shift relative to the probe pulse
reflecting from the film's surface. One result is that constructive
and destructive interference occurs between the probe pulse
reflected from the surface and that reflected from stress wave,
thereby giving a variation in the intensity of the probe pulse
measured by the detectors as the stress pulse propagates.
[0113] In FIG. 15b the pump pulse launches the stress pulse either
by being applied to the film surface or to the lower surface of the
non-absorbing substrate 80. For the latter case the pump pulse
propagates through the substrate 80 and is absorbed in the film 84,
thereby generating the stress pulse. In either case the probe pulse
is applied to the lower surface of the substrate 80, and gives rise
to three temporally separated reflected probe beams 21b'.
[0114] In FIG. 15c the substrate 80 is assumed to at least weakly
absorb the pump pulse, giving rise to the stress pulse in the
substrate. By example, the substrate 80 may be comprised of
silicon.
[0115] In FIG. 15d a buried film 84 absorbs the pump pulse and
launches a stress pulse that propagates towards the surface of an
overlying transparent film 84'. The resulting reflected probe
pulses 21b' are similar to the case shown in FIG. 21b.
[0116] It should be noted that the teachings of this invention
apply as well to very thin films that essentially vibrate when
excited rather than supporting propagating stress or sound
pulses.
[0117] In accordance with an interface characterization technique
of this invention, amplitude information (i.e., the amplitude of
the change in the reflected or transmitted probe beam intensity) is
used to draw quantitative conclusions about the condition of buried
interfaces or surfaces. The technique has superior sensitivity,
compared to conventional ultrasonic techniques, to very subtle
interfacial defects (contaminants, interlayers, roughness, bonding,
etc.) because the wavelengths of the acoustic phonon comprising the
pulse are much shorter than wavelengths which can be achieved by
other methods. For example, in cases where distinct acoustic echoes
are seen (e.g., for films thicker than few optical absorption
lengths, and thin enough for an acoustic wave to return to the
surface before the delay stage 44 runs out of delay travel), the
echo amplitudes and widths can supply information about the
smoothness of a buried interface from which it has reflected (see,
for example, FIG. 15d).
[0118] An important mechanism determining such distortion of echo
shapes is dephasing at different parts of the stress front reaching
a roughened interface (and reflecting toward the surface) at
different times. By incorporating such mechanisms into a simulation
of a particular structure, it is possible to quantify the degree of
interface roughness.
[0119] As employed herein the roughness of a surface or interlayer
may be taken to be the RMS height and correlation length parallel
to the surface or interlayer.
[0120] It should be noted that the same mechanism can cause echo
broadening if it is the top surface (rather than a buried
interface) which is rough. It is thus believed to be possible to
distinguish between surface roughness-induced echo broadening and
interface roughness-induced echo broadening based, for example, on
the symmetry of the echoes and a comparison with reference echo
shapes and/or simulated echo shapes.
[0121] It should be noted that the use of echoes per se is but one
exemplary technique for characterizing the sample 51. For example,
in some samples distinct echoes are not seen. However, the
characterization of the sample can still be accomplished by
comparing the reflected probe signal to reference data and/or
simulations.
[0122] It is also within the scope of the teaching of this
invention to detect roughness, or to detect variations in film
thickness over small lateral displacements, through the use of a
small area optical generator and detector which are scanned
relative to the sample surface.
[0123] Interfacial layers are another potential cause of echo
distortion. As in the preceding example, a preferred method to
characterize such interfacial layers is to include them in a model
of the sample structure (e.g. as a distinct film having certain
physical properties, some of which may be of interest, and so may
be left as fitting parameters).
[0124] In this regard it should be noted that Tas et al. reported
detecting thin interfacial layers of CF.sub.x between aluminum and
silicon as a particular example of this effect for a situation in
which the aluminum films were very thin (G. Tas et al., Appl. Phys.
Lett. 61(15), Oct. 12, 1992, pp. 1787-1789). Tas et al. did not
observe echoes, but rather the ringing of the aluminum films.
Moreover the result was for a very narrow class of structures in
which the metal films were deposited on top of highly uniform,
ultrathin layers of very soft material.
[0125] Interfacial layers producing much different effects can also
be characterized with the technique of this invention. An important
class of interfacial layers include layers which are formed at
interfaces between two materials which have chemically reacted to
form an intermediate compound. As an example, Ti and Al react to
form TiAl.sub.3; Ti and Si react to form TiSi.sub.2; Co and Si
react to form CoSi.sub.2; Pt and Si react to form PtSi. The
thickness of interfacial layers so formed may be substantial. By
example, in some of the above example pairings the materials may
proceed until one or both of the original materials is completely
consumed by the reaction.
[0126] Interfacial voids, cracks, and regions of poor adhesion may
be detected similarly. Such defects usually give rise to acoustic
reflections, such as but not limited to echoes, having larger
amplitudes than would be seen for a perfect interface. The reason
is that stress pulses exhibit no loss of amplitude when reflected
from a perfectly free surface. As such, the presence of larger than
expected probe signal amplitudes within the data can be indicative
of, by example, a delamination between the film 84 and an
underlying film or substrate.
[0127] This technique is also sensitive to thin film processes that
are intended to enhance adhesion between layers. One such technique
is ion bombardment. It has been found by the inventors that the
rate of damping of ultrasonic ringing of a film deposited on a
substrate, and then implanted with high energy ions, is more slowly
damped for low ion doses than for high ion doses. It is inferred
that the adhesion is greater for samples with higher implant doses
because the acoustic energy in the thin film is able to couple to
the substrate more readily than in samples having lower implant
doses or energies.
[0128] In summary, an ultrashort laser pulse
(.tau..sub..rho..about.0.1 psec) is selectively absorbed in a thin
film or in a more complex nanostructure. The absorption sets up a
thermal stress which generates an ultrashort stress wave impulse.
The propagating stress can affect the optical constants anywhere
within the sample, causing a complex, but calculable, change in the
reflectivity (or transmission, or polarization state, or optical
phase) of the probe beam. Echoes are but one simple case of
temporal features. Other, more complex temporal features may also
be detected, such as those that correspond to ultrasonic vibrations
in nanostructures and multilayer samples. These other temporal
features may not correspond to a stress pulse returning to the
surface. The only requirement for detection is that the stress
generated by the pump is at a depth in the sample where it can
interact with the probe beam.
[0129] A film or a multilayer deposited on a substrate at an
elevated temperature is normally in a state of stress due to
differential thermal expansion. Present techniques for evaluating
the stress have severe practical limitations. Measurements on
several materials have shown how the temperature dependence
.differential.v.sub.s/.differential.T of the sound velocity is
affected by stress. This quantity can be readily measured by the
picosecond ultrasonic methods of this invention and can be used to
give the stress of the film, without the requirement of knowing the
film's precise thickness. The technique has many advantages and is
applicable even for very thin films, multilayers (.about.100
.ANG.), and for submicron lateral dimensions.
[0130] Further in accordance with this invention, the sound
velocity in a film is measured at two temperatures in the film. The
difference between the two sound velocities depends in a
predictable way on the stress within the film, whether the stress
is externally imposed or "built-in". This provides a method for
stress measurement on a lateral scale of the spot size FS, which
may have a diameter of one micron or less. The temperature of the
sample 51 can be changed via a resistively heated stage, an arc
lamp, a CW laser focused onto the measurement spot, or by
modulating the pump power. The sound velocity can be measured by
observing ultrasonic echoes, or oscillatory signals as disclosed in
regard to FIGS. 15a-15d, or the vibrational period of very thin
films.
[0131] The rate of change of the sound velocity with temperature
depends on the stress in the film in a predictable way, as has been
reported in the literature (Salama K. et al., Journal of Applied
Physics vol. 51, page 1505 et seq. (1980); J. Cantrell, Ultrasonics
International 1989 Conference Proceedings, pp. 977 et seq.).
[0132] Picosecond ultrasonics measurements of the sound velocity
may be made in the following ways: echo time (as in Tauc et al.);
ringing period; the oscillation period of oscillations caused by a
travelling stress wave in semitransparent or transparent samples,
or by producing a best fit to picosecond ultrasonic data by varying
a sound velocity parameter in a simulation of one or more
layers.
[0133] The temperature may be changed in the following ways: by a
resistive heater embedded in the sample stage 50; by an inductive
heater; radiatively (i.e. an intense lamp); by varying the pump
beam intensity such that the mean temperature of the sample is
above the ambient; or by introducing a continuous wave heating
laser onto the measurement spot FS through a common or separate
objective.
[0134] The temperature change may be measured in the following
ways: by optical pyrometry; by a calculation of the deposited
heating energy (which requires measurement of the incident and
reflect radiation) and then using the values of the optical and
thermal constants of the sample needed to determine the equilibrium
temperature in the measurement region; with a thermocouple (in
contact with the sample 51); or using the Mirage Effect. In the
Mirage Effect the change in the refractive index in the air above
the heated spot is measured via the deflection of a laser beam
incident at a glancing angle, and the temperature is deduced from
the refractive index change necessary to produce an observed beam
deflection (see, for example, T. R. Anthony et al., Physical Review
B, vol. 42, 1104 (1990)).
[0135] Calibration of the system of this invention can be
accomplished in several manners. By example, films comprised of
several different metals can be deposited on silicon wafers at
different temperatures. In these samples, the stress can be
independently estimated by calculation from differential expansion
and from measurements of film-induced curvature. The calculated
values are then compared with results obtained from the use of the
system of this invention, and calibration factors are determined
accordingly.
[0136] The teaching of this invention also includes methods and
apparatus for measuring the change in the optical constants of a
material with strain. In this technique the system is used to
determine the quantities .differential.n/.differential..eta. and
.differential..sub..kappa./.diffe- rential..eta. in a particular
sample geometry. Samples have a film of glass, or another
transparent material deposited on top of a thin film of opaque or
semi-opaque material (the material of interest may be a metal). The
optical constants of both materials are known. The quantities
.differential.n/.differential..eta. and
.differential..sub..kappa./.diffe- rential..sub..eta. are also
known for the transparent material, and are deduced for the second
material by comparing acoustic data with simulations in which
.differential.n/.differential..eta. and
.differential..sub..kappa./.differential..eta. for the second
material are varied.
[0137] To be able to carry out simulations which enable a
quantitative comparison with data of the magnitude of the change in
the reflectivity or transmissivity of a sample in which a stress
pulse is generated, it is necessary to know in advance by how much
the optical constant n and .kappa. for the subject materials change
in response to stress .sigma.. It is preferable in some embodiments
to carry out simulations in terms of the strain .eta., which may be
related to the stress in a simple way. In terms of the strain, the
foregoing is equivalent to the statement that the quantities
.differential.n/.differential..eta. and
.differential..kappa./.differential..eta. must be known. It is a
feature of this invention that the methods and apparatus described
herein may be used to determine these quantities. In one technique,
.differential.n/.differential..eta. and
.differential..kappa./.differenti- al..eta. may be found for a
material by depositing on top of an optically smooth specimen of
this material a layer of transparent material such as a glass (e.g.
LP-CVD TEOS, or PE-CVD BPSG) having a thickness of at least several
hundred Angstroms, and less than 100 microns. The underlying
specimen of material for which .differential.n/.differential..eta.
and .differential..kappa./.differential..eta. are to be determined
may be a thin film, or a thick substrate. The process of
determining .differential.n/.differential..eta. and
.differential..kappa./.differenti- al..eta. involves two steps
which may be described in relation to FIG. 15d (which shows the
case in which the material of interest is a thin metal film
disposed on top of a substrate which may be silicon. In step (1) a
stress pulse is generated in the material. Part of this stress wave
enters the transparent layer and propagates to the free surface,
then reflects from this surface, then propagates through the
transparent layer, and then part of this stress reenters the metal
film. The stress pulse reflecting from the free surface has the
opposite sign to the incident stress pulse, but identical
amplitude. The fraction of the stress pulse incident from the glass
layer on the metal film which reenters the metal film may be
calculated from the acoustic impedances (i.e. the product of the
sound velocity and density) of the glass and metal (as described in
Tauc et al.). While the stress wave propagates through the glass
layer it gives rise to oscillations as described previously with
regard to FIGS. 15a-15d. The amplitude of these oscillations may be
used to compute the quantity .differential.n/.differe- ntial..eta.
for the glass (which in general will have a different value than
the value corresponding to the metal) either analytically or by
comparison with simulations of the oscillations:
.differential..kappa./.d- ifferential..eta.=0 for the glass. In
step (2) the quantities .differential.n/.differential..eta. and
.differential..kappa./.differenti- al..eta. for the metal layer are
determined by carrying out a simulation of the reflectivity change
which occurs in response to the stress reentering this layer, and
by adjusting .differential.n/.differential..et- a. and
.differential..kappa./.differential..eta. in order to achieve a
best fit to the observed response for times during which the
effects of the stress wave on the reflected probe intensity may be
observed. In these simulations the acoustic impedances and sound
velocities of the glass and metal film are assumed to be known in
advance. In addition, the optical constants n and K for one or both
materials at the pump and probe beam wavelengths may be used as
inputs to the simulations, or alternatively may be used as further
adjustable parameters. An important feature of this procedure is
that simulation parameters so determined should simultaneously fit
the response corresponding to the stress wave propagating in the
metal. In the above procedure it is assumed that the detector 60
and processor 66 are so calibrated as to give the true reflectivity
of the sample as a function of time. An alternative three step
procedure which does not require the detector 60 and processor 66
to be so calibrated is as follows. In step (1) a stress pulse is
generated in the material. Part of this stress wave enters the
transparent layer and propagates to the free surface, then reflects
from this surface, then propagates through the transparent layer,
and then part of this stress reenters the metal film. The stress
pulse reflecting from the free surface has the opposite sign to the
incident stress pulse, but identical amplitude. The fraction of the
stress pulse incident from the glass layer on the metal film which
reenters the metal film may be calculated from the acoustic
impedances (i.e. the product of the sound velocity and density) of
the glass and metal (as described in Tauc et al). While it
propagates through the glass layer the stress wave gives rise to
oscillations as described previously with regard to FIGS. 15a-15d.
In step (2) .differential.n/.differential..eta. for the glass and
.differential.n/.differential..eta. and
.differential..kappa./.differenti- al..eta. for the metal are
allowed to be freely varied in the simulated response in order to
achieve a best fit to the observed response. The values
.differential.n/.differential..eta. and .differential..kappa./.dif-
ferential..eta. so obtained may be scaled by the ratio of the true
value of .differential.n/.differential..eta. for the glass to the
fitted value. Therefore, in Step (3) the true value of
.differential.n/.differential..e- ta. for the glass is determined
(this may be obtained by a number of methods, other than picosecond
ultrasonics, that are applicable to transparent materials), and the
fitted .differential.n/.differential..eta- . and
.differential..kappa./.differential..eta. for the metal are scaled
to obtain their true values.
[0138] It is also within the scope of the teaching of this
invention to use the derivative of the signal versus time to
determine the properties of a sample, rather than the signal
itself. The purpose is to remove some of the background signal,
associated with the cooling of the film, from the data. The
derivative of the signal can also be compared with the derivative
of a simulation to extract parameters.
[0139] In one embodiment of the algorithm used to determine unknown
quantities from the observed reflectivity or transmission of the
sample, the temporal features associated with the propagation of
stress within the sample are compared with a simulation which
includes only the ultrasonic response. Other features, in
particular the slowly varying background associated with diffusion
of heat within the sample, are ignored in such comparisons, or may
be included in the fitting process by introducing one or several
fitting parameters of a slowly varying function (e.g. an
exponential, or a low order polynomial). For some materials the
slowly varying background may have a much greater amplitude than
the features associated with ultrasonic response of the sample. In
order to improve the accuracy and speed of the fitting process in
such situations, it may be convenient to numerically compute the
derivative of the response with respect to delay time. A comparison
may then be made between the derivative so determined and the
derivative of the simulated response, and the values of the
unknowns varied until a best fit is obtained.
[0140] An alternative method is to measure the derivative of the
sample response directly, avoiding the step of numerical
differentiation. This method provides superior signal to noise in
comparison to the numerical procedure. In one embodiment of this
derivative measurement scheme the retroreflector 46 in the probe
path is placed on a mount (such as a piezoelectric actuator) which
is caused to oscillate rapidly (f.sub.2) (i.e. from 10 to 10.sup.6
Hz) along the probe beam axis, thus executing a large number of
oscillations (i.e., greater than 10) for each successive delay
position of the delay mechanism. The signal measured in such a
system may be related to the derivative of the signal versus delay
by a simple proportionality constant, provided that the amplitude
of the oscillations corresponds to a range of delays which are
small compared to the minimum temporal extent of observed
ultrasonic features in an undifferentiated response. In this
embodiment it is also possible to detect at the difference
frequency (f.sub.1-f.sub.2 or f.sub.1+f.sub.2), where f.sub.1 is
the frequency induced by the AOM in the pump beam path (e.g., 1
MHz), and f.sub.2 is the frequency induced by the delay modulator
in the probe beam path.
[0141] Reference is now made to FIG. 16 for illustrating an
embodiment of this invention which is referred to as a parallel,
oblique embodiment.
[0142] This embodiment includes an optical/heat source 120, which
functions as a variable high density illuminator, and which
provides illumination for a video camera 124 and a sample heat
source for temperature-dependent measurements under computer
control. An alternative heating method employs a resistive heater
embedded in the stage sample stage 122. The advantage of the
optical heater is that it makes possible rapid sequential
measurements at two different temperatures, as will be described
below. The video camera 124 provides a displayed image for an
operator, and facilitates the set-up of the measurement system.
Appropriate pattern recognition software can also be used for this
purpose, thereby minimizing or eliminating operator
involvement.
[0143] The sample stage 122 is preferably a multiple-degree of
freedom stage that is adjustable in height (z-axis), position (x
and y-axes), and tilt (.theta.), and allows motor controlled
positioning of a portion of the sample relative to the pump and
probe beams. The z-axis is used to translate the sample vertically
into the focus region of the pump and probe, the x and y-axes
translate the sample parallel to the focal plane, and the tilt axes
adjust the orientation of the stage 122 to establish a desired
angle of incidence for the probe beam. This is achieved via
detectors PDS1 and PDS2 and the local processor, as described
below.
[0144] In an alternative embodiment, the optical head may be moved
relative to a stationary, tiltable stage 122' (not shown). This is
particularly important for scanning large objects (such as 300 mm
diameter wafers, or mechanical structures, etc.) In this embodiment
the pump beam, probe beam, and video are delivered to the
translatable head via optical fibers or fiber bundles.
[0145] BS5 is a broad band beam splitter that directs video and a
small amount of laser light to the video camera 124. The camera 124
and local processor can be used to automatically position the pump
and probe beams on a measurement site.
[0146] The pump-probe beam splitter 126 splits an incident laser
beam pulse (preferably of picosecond or shorter duration) into pump
and probe beams, and includes a rotatable half-wave plate (WP1)
that rotates the polarization of the unsplit beam. WP1 is used in
combination with polarizing beam splitter PBS1 to effect a
continuously variable split between pump and probe power. This
split may be controlled by the computer by means of a motor to
achieve an optimal signal to noise ratio for a particular sample.
The appropriate split depend on factors such as the reflectivity
and roughness of the sample. Adjustment is effected by having a
motorized mount rotate WP1 under computer control.
[0147] A first acousto-optic modulator (AOM1) chops the pump beam
at a frequency of about 1 MHz. A second acousto-optic modulator
(AOM2) chops the probe beam at a frequency that differs by a small
amount from that of the pump modulator AOM1. The use of AOM2 is
optional in the system illustrated in FIG. 16. As will be discussed
below, the AOMs may be synchronized to a common clock source, and
may further be synchronized to the pulse repetition rate (PRR) of
the laser that generates the pump and probe beams.
[0148] A spatial filter 128 is used to preserve at its output a
substantially invariant probe beam profile, diameter, and
propagation direction for an input probe beam which may vary due to
the action of the mechanical delay line shown as the retroreflector
129. The spatial filter 128 includes a pair of apertures A1 and A2,
and a pair of lenses L4 and L5. An alternative embodiment of the
spatial filter incorporates an optical fiber, as described
above.
[0149] WP2 is a second adjustable half wave plate which functions
in a similar manner, with PBS2, to the WP1/PBS1 of the beamsplitter
126. With WP2 the intent is to vary the ratio of the part of the
probe beam impinging on the sample to that of the portion of the
beam used as a reference (input to D5 of the detector 130. WP2 may
be motor controlled in order to achieve a ratio of approximately
unity. The electrical signals produced by the beams are subtracted,
leaving only the modulated part of the probe to be amplified and
processed. PSD2 is used in conjunction with WP2 to achieve any
desired ratio of the intensities of the probe beam and reference
beam. The processor may adjust this ratio by making a rotation of
WP2 prior to a measurement in order to achieve a nulling of the
unmodulated part of the probe and reference beam. This allows the
difference signal (the modulated part of the probe) alone to be
amplified and passed to the electronics.
[0150] The beamsplitter BS2 is used to sample the intensity of the
incident probe beam in combination with detector D2. The linear
polarizer 132 is employed to block scattered pump light
polarization, and to pass the probe beam. Lenses L2 and L3 are pump
and probe beam focusing and collimating objectives respectively.
The beamsplitter BS1 is used to direct a small part of pump and
probe beams onto a first Position Sensitive Detector (PSD1) that is
used for autofocusing, in conjunction with the processor and
movements of the sample stage 122. The PSD1 is employed in
combination with the processor and the computer-controlled stage
122 (tilt and z-axis) to automatically focus the pump and probe
beams onto the sample to achieve a desired focusing condition.
[0151] The detector D1 may be used in common with acoustics,
ellipsometry and reflectometry embodiments of this invention.
However, the resultant signal processing is different for each
application. For acoustics, the DC component of the signal is
suppressed such as by subtracting reference beam input D5, or part
of it as needed, to cancel the unmodulated part of D1, or by
electrically filtering the output of D1 so as to suppress
frequencies other than that of the modulation. The small modulated
part of the signal is then amplified and stored. For ellipsometry,
there is no small modulated part, rather the entire signal is
sampled many times during each rotation of the rotation compensator
(see FIG. 17), and the resulting waveform is analyzed to yield the
ellipsometric parameters. For reflectometry, the change in the
intensity of the entire unmodulated probe beam due to the sample is
determined by using the D1 and D2 output signals (D2 measures a
signal proportional to the intensity of the incident probe).
Similarly, additional reflectometry data can be obtained from the
pump beam using detectors D3 and D4. The analysis of the
reflectometry data from either or both beams may be used to
characterize the sample. The use of two beams is useful for
improving resolution, and for resolving any ambiguities in the
solution of the relevant equations.
[0152] A third beamsplitter BS3 is used to direct a small fraction
of the pump beam onto detector D4, which measures a signal
proportional to the incident pump intensity. A fourth beamsplitter
BS4 is positioned so as to direct a small fraction of the pump beam
onto detector D3, which measures a signal proportional to the
reflected pump intensity.
[0153] FIG. 17 illustrates a normal pump beam, oblique probe beam
embodiment of this invention. Components labelled as in FIG. 16
function in a similar manner, unless indicated differently below.
In FIG. 17 there is provided the above-mentioned rotation
compensator 132, embodied as a linear quarter wave plate on a
motorized rotational mount, and which forms a portion of an
ellipsometer mode of the system. The plate is rotated in the probe
beam at a rate of, by example, a few tens of Hz to continuously
vary the optical phase of the probe beam incident on the sample.
The reflected light passes through an analyzer 134 and the
intensity is measured and transferred to the processor many times
during each rotation. The signals are analyzed according to known
types of ellipsometry methods to determine the characteristics of
the sample (transparent or semitransparent films). This allows the
(pulsed) probe beam to be used to carry out ellipsometry
measurements.
[0154] In accordance with an aspect of this invention the
ellipsometry measurements are carried out using a pulsed laser,
which is disadvantageous under normal conditions, since the
bandwidth of the pulsed laser is much greater than that of a CW
laser of a type normally employed for ellipsometry
measurements.
[0155] When acoustics measurements are being made, the rotation
compensator 132 is oriented such that the probe beam is linearly
polarized orthogonal to the pump beam.
[0156] The analyzer 134 may be embodied as a fixed polarizer, and
also forms a portion of the ellipsometer mode of the system. When
the system is used for acoustics measurements the polarizer 134 is
oriented to block the pump polarization. When used in the
ellipsometer mode, the polarizer 134 is oriented so as to block
light polarized at 45 degrees relative to the plane of the incident
and reflected probe beam.
[0157] Finally, the embodiment of FIG. 17 further includes a
dichroic mirror (DM2), which is highly reflective for light in a
narrow band near the pump wavelength, and is substantially
transparent for other wavelengths.
[0158] It should be noted in FIG. 17 that BS4 is moved to sample
the pump beam in conjunction with BS3, and to reflect a portion of
the pump to D3 and to a second PSD (PSD2). PSD2 (pump PSD) is
employed in combination with the processor, computer controlled
stage 122 (tilt and z-axis), and PSD1 (Probe PSD) to automatically
focus the pump and probe beams onto the sample to achieve a desired
focusing condition. Also, a lens L1 is employed as a pump, video,
and optical heating focussing objective, while an optional lens L6
is used to focus the sampled light from BS5 onto the video camera
124.
[0159] Reference is now made to FIG. 18 for illustrating a further
embodiment of the picosecond ultrasonics system, specifically a
single wavelength, normal pump, oblique probe, combined
ellipsometer embodiment. As before, only those elements not
described previously will be described below.
[0160] Shutter 1 and shutter 2 are computer controlled shutters,
and allow the system to use a He--Ne laser 136 in the ellipsometer
mode, instead of the pulsed probe beam. For acoustics measurements
shutter 1 is open and shutter 2 is closed. For ellipsometer
measurements shutter 1 is closed and shutter 2 is opened. The HeNe
laser 136 is a low power CW laser, and has been found to yield
superior ellipsometer performance for some films.
[0161] FIG. 19 is a dual wavelength embodiment of the system
illustrated in FIG. 18. In this embodiment the beamsplitter 126 is
replaced by a harmonic splitter, an optical harmonic generator that
generates one or more optical harmonics of the incident unsplit
incident laser beam. This is accomplished by means of lenses L7, L8
and a nonlinear optical material (DX) that is suitable for
generating the second harmonic from the incident laser beam. The
pump beam is shown transmitted by the dichroic mirror (DM 138a) to
the AOM1, while the probe beam is reflected to the retroreflector.
The reverse situation is also possible. The shorter wavelength may
be transmitted, and the longer wavelength may be reflected, or vice
versa. In the simplest case the pump beam is the second harmonic of
the probe beam (i.e., the pump beam has one half the wavelength of
the probe beam).
[0162] It should be noted that in this embodiment the AOM2 is
eliminated since rejection of the pump beam is effected by means of
color filter F1, which is simpler and more cost effective than
heterodyning. F1 is a filter having high transmission for the probe
beam and the He--Ne wavelengths, but very low transmission for the
pump wavelength.
[0163] Finally, FIG. 20 illustrates a normal incidence, dual
wavelength, combined ellipsometer embodiment of this invention. In
FIG. 20 the probe beam impinges on PBS2 and is polarized along the
direction which is passed by the PBS2. After the probe beam passes
through WP3, a quarter wave plate, and reflects from the sample, it
returns to PBS2 polarized along the direction which is highly
reflected, and is then directed to a detector D0 in detector block
130. D0 measures the reflected probe beam intensity.
[0164] In greater detail, WP3 causes the incoming plane polarized
probe beam to become circularly polarized. The handedness of the
polarization is reversed on reflection from the sample, and on
emerging from WP3 after reflection, the probe beam is linearly
polarized orthogonal to its original polarization. BS4 reflects a
small fraction of the reflected probe onto an Autofocus Detector
AFD.
[0165] DM3, a dichroic mirror, combines the probe beam onto a
common axis with the illuminator and the pump beam. DM3 is highly
reflective for the probe wavelength, and is substantially
transparent at most other wavelengths.
[0166] D1, a reflected He--Ne laser 136 detector, is used only for
ellipsometric measurements. It
[0167] should be noted that, when contrasting FIG. 20 to FIGS. 18
and 19, that the shutter 1 is relocated so as to intercept the
incident laser beam prior to the harmonic splitter 138.
[0168] Based on the foregoing descriptions of a number of
embodiments of this invention, it can be appreciated that this
invention teaches, in one aspect, a picosecond ultrasonic system
for the characterization of samples in which a short optical pulse
(the pump beam) is directed to an area of the surface of the
sample, and then a second light pulse (the probe beam) is directed
to the same or an adjacent area at a later time. The retroreflector
129 shown in all of the illustrated embodiments 16-20 can be
employed to provide a desired temporal separation of the pump and
probe beams, as was described previously with regard to, by
example, FIG. 9.
[0169] The system measures some or all of the following quantities:
(1) the small modulated change .DELTA.R in the intensity of the
reflected probe beam, (2) the change AT in the intensity of the
transmitted probe beam, (3) the change .DELTA.P in the polarization
of the reflected probe beam, (4) the change .DELTA..phi. in the
optical phase of the reflected probe beam, and/or (5) the change in
the angle of reflection .DELTA..delta. of the probe beam. These
quantities (1)-(5) may all be considered as transient responses of
the sample which are induced by the pump pulse. These measurements
can be made together with one or several of the following: (a)
measurements of any or all of the quantities (1)-(5) just listed as
a function of the incident angle of the pump or probe light, (b)
measurements of any of the quantities (1)-(5) as a function of more
than one wavelength for the pump and/or probe light, (c)
measurements of the optical reflectivity through measurements of
the incident and reflected average intensity of the pump and/or
probe beams; (d) measurements of the average phase change of the
pump and/or probe beams upon reflection; and/or (e) measurements of
the average polarization and optical phase of the incident and
reflected pump and/or probe beams. The quantities (c), (d) and (e)
may be considered to be average or static responses of the sample
to the pump beam.
[0170] One function of the system is to determine the thickness of
the films making up the sample, the mechanical properties of the
films (sound velocities and densities), and the characteristics of
the interfaces (adhesion, roughness, and other interfacial
characteristics).
[0171] The system in accordance with the various embodiments of
this invention thus enables a combination of measurements of the
type listed above so as to enable the determination of properties
of the sample that are not obtainable through the use of
conventional systems.
[0172] By example, consider a sample in which the upper-most film
is transparent. In such a sample the pump pulse will not be
absorbed in this film, but will instead be absorbed in the next
underlying film, assuming that this film is not also transparent.
There will, however, normally be a contribution to the change
.DELTA.R in reflectivity of the probe pulse from the uppermost
transparent film. A stress wave will be generated in the underlying
optically-absorbing film and will propagate into the transparent
film. This will cause a local change .DELTA.n in the refractive
index n of the transparent film, and the location of this change in
the refractive index will propagate towards the free surface of the
transparent film with a speed equal to the sound velocity v in the
film. Probe light which is reflected at this change in n will
interfere constructively or destructively with the probe light
which is reflected at the other interfaces of the sample. As a
consequence there will be a change .DELTA.R in the intensity of the
reflected probe light, which change will amount to an oscillation
of frequency f given by 3 f = 2 nv cos
[0173] where .lambda. is the wavelength in free space of the probe
light and .theta. is the angle between the direction of the probe
light in the sample and the normal to the surface. Hence a
measurement of the frequency of this oscillation can be used to
determine the product nv, but not n and v separately. This
oscillation will suffer an abrupt change in phase when the stress
pulse reaches the free surface of the sample at time .tau..sub.1
and is then reflected back. By a measurement of .tau..sub.1 one can
thus determine the quantity d/v, where d is the film thickness.
These two measurements and their analysis may be obtained using
conventional systems, but do not lead to definite values for the
three quantities of interest n, v, and d. The present invention
overcomes this difficulty as follows.
[0174] If measurements are made of the frequency f as a function of
the angle of incidence .theta. of the probe light outside the
sample the measured f(.theta.) can be analyzed to give both n and
V. This is because the relation between .alpha. and .theta.
involves only n and not v. Then the measurement of the time
.tau..sub.1 can be used to determine d.
[0175] Second, using measurements of the intensity of the reflected
pump or probe light, the phase change or the relative intensities
of the different polarization components of the pump and/or probe
light can also be used in many circumstances to deduce the
refractive index and/or the thickness of the transparent film. For
example, the thickness or optical constants of one or more layers
in a sample may be determined from the measured quantities
according to the principles of optical reflectometry or
ellipsometry. In this case the picosecond light pulses available in
the system of this invention can be used to make such reflectometry
or ellipsometry measurements, and extra light sources may not be
needed. The pulsed nature of the lasers is not relevant to these
measurements. The determination of the optical constants and/or
film thicknesses then enables the sound velocity and/or the
thickness to be deduced from a single measurement of the frequency
f.
[0176] The foregoing example has been described in terms of a
measurement of .DELTA.R(t); clearly the same technique may be
applied to the other transient quantities.
[0177] For many samples of current interest in the semiconductor
circuit fabrication industry it is not practical to measure the
change .DELTA.T in the transmission of the probe light pulse. The
films are normally deposited onto silicon substrates of thickness
around 0.02 cm. Unless light of wavelength of one micron or greater
is used, the light will be heavily absorbed in the substrate making
the measurement of the transmission very difficult. For such
samples conventional methods are thus essentially limited to the
use of the measurement of the change .DELTA.R in the optical
reflectivity induced by the pump pulse. Many samples of interest
include a series of films deposited sequentially onto the
substrate. This type of structure can be referred to as a "stack".
When stress pulses are generated in a stack a very complicated
response (for example, the result of a measurement of .DELTA.R(t))
may be obtained. This complex response results from the generation
of stress pulses in various different parts of the structure, the
propagation of these pulses with partial transmission and partial
reflection across the interfaces into other films, and the change
in the intensity reflection coefficient of the structure due to the
strain-induced change in the optical properties of each film. To
determine the thickness of a number of the films in a stack
requires the determination of the times at which stress pulses
originating at known places in the structure are reflected or
transmitted at the various interfaces. From these times, and using
assumed velocities for the different films, the thicknesses of the
films can be found. The determination of the times just referred to
requires the identification of the different features that appear
in the response .DELTA.R(t). With the arrangement available in
conventional systems the identification of the origin of the
various features may be extremely difficult and/or time-consuming
for a multi-layer structure. It is often necessary to make a guess
that a particular feature arises from a stress pulse which
originates at a particular location and has undergone a certain
sequence of transmissions and reflections at different interfaces.
In addition, it may be the case that a certain feature of interest,
such as the arrival of a stress pulse at one particular interface,
gives a response which happens to be dominated or masked by a
larger response from another stress pulse reaching a different part
of the structure at approximately the same time. The present
invention overcomes these difficulties as follows.
[0178] As mentioned above, in the prior art the primary measured
quantity for most samples of current technical interest is the
change .DELTA.R(t) in optical reflectivity. If the response
.DELTA.R(t) is difficult to analyze, then it is also difficult to
deduce the required information about the structure, for example
the thicknesses of the different films. This difficulty may be
overcome by measurements of .DELTA.P, .DELTA..phi., or
.DELTA..delta.. For example, a particularly important feature may
appear as a very small response in .DELTA.R(t), but may make a
dominant response in .DELTA.P(t), .DELTA..phi.(t), or
.DELTA..delta.t).
[0179] In accordance with an aspect of this invention the
non-destructive system and method is enabled to also simultaneously
measure at least two transient responses of the structure to the
pump pulse. The simultaneously measured transient responses
comprise at least two of a measurement of the modulated change
.DELTA.R in an intensity of a reflected portion of a probe pulse,
the change .DELTA.T in an intensity of a transmitted portion of the
probe pulse, the change .DELTA.P in the polarization of the
reflected probe pulse, the change .DELTA..phi. in optical phase of
the reflected probe pulse, and the change in an angle of reflection
.DELTA..delta. of the probe pulse. The measured transient responses
are then associated with at least one characteristic of interest of
the structure.
[0180] However, even when the measurement of .DELTA.P(t),
.DELTA..phi.(t), or .DELTA..delta.(t) does not show a response in
which the feature of primary interest dominates, it may still be
possible to effectively isolate the response of interest by a
"differential method" (DM). That is, by taking a suitable linear
combination of the different measured responses it may be possible
to enhance the magnitude of the response of interest and reduce the
size of the other competing response or responses.
[0181] The same type of DM procedure as just described can also be
accomplished by making simultaneous or sequential measurements of
one or more of the quantities .DELTA.R(t), etc. at more than one
wavelength of the pump and/or the probe, or angle of incidence of
the pump and/or the robe, or polarization of the pump and/or the
probe beams.
[0182] The same type of DM procedure can also be achieved for some
samples by making measurements at more than one intensity of the
pump and/or probe beams. The point is that the responses, such as
the change in reflectivity .DELTA.R(t), for example, may vary
non-linearly with the intensity and/or the duration of the pump
and/or probe pulses. Thus, again by taking suitable linear
combinations of the responses measured at different intensities or
pulse durations, it may be possible to enhance a portion of the
response arising from one effect at the expense of competing
effects.
[0183] The picosecond ultrasonic system in accordance with the
teaching of this invention can also employ the simultaneous or
sequential measurement of the ellipsometric parameters of the
sample using signals corresponding to one or more suitable
non-pulsed additional light sources (e.g., the He--Ne laser 136)
whose optical path may or may not have some or all optical
components in common with the means for directing the pulsed laser
beams to and from the sample. This overcomes some of the
difficulties of conventional systems in a manner similar to the
methods described above.
[0184] An automatic adjustment of the position and orientation of
the sample to achieve a desired overlap of the pump and probe beams
on the sample surface can also be employed, in conjunction with the
control of the spot size on the sample of one or both of the pump
and probe lasers. This is accomplished, as described in reference
to FIGS. 16-20, with a means for detecting one or both beams after
they impinge on the sample, and a means for adjusting the height
and tilt of the sample with respect to the beams to achieve the
desired focusing conditions. This approach is superior to the
manual adjustment techniques taught by the prior art, in that an
automatic adjustment scheme overcomes the difficulty of a slow and
unreliable manual adjustment which is incompatible with the need to
make rapid and accurate measurements in an industrial environment.
Furthermore, the reproduceability of measurements between samples
is also improved.
[0185] It is also within the scope of this invention to provide a
picosecond ultrasonics system using one or more modulators of the
pump or probe beams in which the modulation drive signal for one or
more of the modulators, and the pulse rate of one or more pulsed
lasers, are derived from a common clock. In addition, it is also
within the scope of the teaching of this invention that the
modulation of the pump or probe beam is derived from the pulse rate
of one or more of the pulsed lasers in the system. This overcomes a
problem in the prior art, wherein the modulation is not
synchronized with the repetition rate of the laser or lasers. Thus,
in each modulation cycle there can be a variation in the number of
probe or pump pulses contained in one modulation cycle according to
the instantaneous phase of the modulator relative to the timing of
the laser pulses. This variation contributes to the noise of the
system, and is advantageously eliminated in the present
invention.
[0186] This invention further teaches a picosecond ultrasonic
system in which measurements for a particular sample are made at at
least two temperatures for the purpose of detecting the change in
the sound velocity in one or more layers in response to the
temperature change. The temperature change may be induced by a heat
lamp directed at the surface of the sample, by a resistive heater
in contact with the rear of the sample, by the average heating of
the sample by the pump light pulses, or by the use of another light
source directed through some of the same optical elements used to
guide the pump and/or probe beams onto the sample (or via some
other optical system). The stress in one or more layers is
determined by relating the observed change in the sound velocity in
one or more layers determined at two or more temperatures to the
stress in the layer or layers.
[0187] As has been described, it has been established
experimentally that the temperature-dependence of the sound
velocity depends on the static stress. This provides the basis for
this aspect of the invention.
[0188] It is important to note that the application of this method
does not require a measurement of the absolute value of the sound
velocity, but only the change of the velocity with temperature.
This is an important point, since to determine the absolute
velocity it would be necessary to have a very precise value for the
film thickness. To determine the temperature-dependence of the
sound velocity, on the other hand, requires only a measurement of
the temperature-dependence of the acoustic transit time. To
determine the temperature-dependence of the sound velocity from
this quantity it is necessary only to apply a correction to allow
for the thermal expansion of the sample.
[0189] This invention further teaches a picosecond ultrasonic
system which directly measures the derivative with respect to time
delay between the pump and probe beams of some or all of the
quantities listed above, i.e., (1) the small modulated change
.DELTA.R in the intensity of the reflected probe beam, (2) the
change .DELTA.T in the intensity of the transmitted probe beam, (3)
the change .DELTA.P in the polarization of the reflected probe
beam, (4) the change .DELTA..phi. in the optical phase of the
reflected probe beam, and/or (5) the change in the angle of
reflection .DELTA..delta. of the probe beam. To achieve the
measurement of the derivative the probe pulse delay is varied
periodically over a small range by means of an oscillating optical
component in the pump or probe path. A frequency range of 10 Hz to
1 MHz is suitable for this purpose.
[0190] One advantage of this method is as follows. In many
applications one is interested in the time of arrival of acoustic
echoes at certain points in the sample. These acoustic echoes
appear as sharp features in the measured reflectivity change
.DELTA.R(t) as a function of time. These echoes can be enhanced
relative to the background if the system directly measures the
derivative of .DELTA.R (or the other quantities listed above) with
respect to time, rather than .DELTA.R itself.
[0191] This invention further teaches a picosecond ultrasonic
system which incorporates an optical fiber or fibers for any of the
following purposes: (a) guiding the laser beam between different
parts of the optical system; (b) guiding the pump and/or probe to
the sample; (c) collecting the reflected or transmitted probe from
the sample; and/or (d) maintaining a constant probe output profile
and position for varying input conditions.
[0192] The picosecond ultrasonic system in accordance with this
invention may incorporate light sources with any of the following
features. A
[0193] first feature employs a pulsed laser with the output
directed to an optical harmonic generator or generators, as in
FIGS. 19 and 20. The outputs of the harmonic generator 138 and/or
the unmodified output of the laser are thus used for the pump
and/or probe beams. This improves on conventional practice in that
it allows for the rejection of the pump light at the detector of
the probe beam so as to improve the signal to noise ratio. Also,
for certain samples the most advantageous wavelength for the
generating pump beam may be different from the optimum wavelength
for the probe beam.
[0194] A second feature employs one or more of the polarizing beam
splitters which are used to continuously vary the ratio of the pump
and probe beams under computer control. The ratio can be controlled
to optimize the signal to noise for a given sample. It may be
advantageous to change the ratio to achieve the best performance
for samples with particular characteristics.
[0195] This invention further teaches a picosecond ultrasonic
system that incorporates different repetition rate lasers to effect
a delay as an alternative approach to a mechanical delay stage.
This has the advantage that a mechanical stage is not required. In
addition, the data can be acquired very quickly, provided that the
signal-to-noise ratio is acceptable.
[0196] This invention further teaches a picosecond ultrasonic
system that employs a multi-element delay stage. This has the
advantage that the delay of the probe pulse is increased for a
given distance moved by the mechanical stage. Thus, the distance
travelled by the stage in order to produce a given delay of the
probe pulse can be decreased.
[0197] Furthermore, the invention teaches the measurement of the
transient optical properties of the sample using a probe pulse that
is derived from an output pulse of the laser that is different from
the output pulse used for the pump. This enables the production of
a large effective delay for the probe, without requiring that a
very long optical path difference be established in the system.
[0198] The invention also teaches a picosecond ultrasonic system
which may include suitable additional optical sources, including
additional lasers as well as white light sources. These sources may
be directed to the sample by a guiding system which may include
some elements in common with the pulsed pump and probe beam paths.
These additional light sources may be used to effect ellipsometry
or reflectometry, or to illuminate the sample for inspection
purposes, or to raise the temperature at a particular location.
[0199] In one aspect the invention provides a picosecond ultrasonic
system that incorporates the color filter F1 in the path of the
probe beam after it has been reflected or transmitted at the sample
for the purpose of suppressing scattered pump light. This
embodiment is employed to advantage when the pump and probe sources
have different wavelengths. The suppression of the pump light
improves the signal to noise ratio when the sample surface is
non-specular, and where the incident pump light is scattered at the
sample surface.
[0200] The invention further provides a picosecond ultrasonic
system that incorporates optical elements for delivering the probe
beam to the sample, and which allows the location, shape and/or
size of the probe spot on the sample to be kept substantially
constant and free from changes due to the variation of the optical
path length of the probe. This is a more general case than the
above-mentioned use of an optical fiber for a similar purpose.
Furthermore, "active" correction schemes can be employed in which
the characteristics of the probe spot are sensed, and in which the
characteristics of probe beam (e.g., profile and location) are
adaptively corrected.
[0201] The invention further teaches a picosecond ultrasonic system
that incorporates an optical guiding system in which the pump and
probe beams are focused separately onto the sample. The pump and
probe beams may be scanned laterally relative to each other. In
particular, a guiding and focusing system can be employed in which
the probe beam is guided through an optical fiber assembly with a
tapered end which effects near field focusing into a spot which is
smaller than the pump beam, and which may be scanned over small
displacements relative while the pump beam is held substantially
stationary. The use of a reduced tip fiber makes it possible to
achieve spots for the pump and probe with dimensions as small as
1000 .ANG..
[0202] It is thus possible to investigate the properties of a
sample through the study of waves propagating across the surface
from one point to another. A second purpose is to generate bulk
waves which travel through the sample from the pumped region to the
probe spot. Other applications pertain to structures that are
laterally patterned. In this case the pump light may be directed so
as to be absorbed in a "dot", i.e. a film which has a very small
area. Stress waves generated in this dot then propagate to the
region of the structure that is sensed by the probe pulse.
[0203] Also disclosed is a picosecond ultrasonic system in which
the results of measurements are compared with computer simulations
of the measured response or responses (1)-(5), for example. To
perform the simulation the following steps are performed. Reference
is also made to the flow chart of FIG. 21.
[0204] (A) Initial stress distribution
[0205] The stress distribution in the sample produced as a result
of the absorption of the pump pulse is calculated using known
values for the optical absorption of the various materials present
in the sample, the specific heats of these materials, the thermal
expansion coefficients, and the elastic constants. To calculate the
stress distribution the effect of thermal diffusion may be taken
into account. For a sample composed of several planar films of
different materials with material properties uniform throughout
each film the following procedure is used.
[0206] From the optical constants and thicknesses of the films the
electric field due to the pump light pulse at all points in the
structure is calculated in terms of the amplitude, angle of
incidence, and polarization of the pump beam incident on the sample
surface. This calculation is most readily performed through the use
of optical transfer matrices. Next, from the calculated electric
field distribution, the energy absorbed in the structure as a
function of position is calculated. Next, the effect of thermal
diffusion on the absorbed energy distribution is considered. Next,
the temperature rise of each part of the sample is calculated. This
temperature rise is the energy deposited per unit volume divided by
the specific heat per unit volume. Next, the stress at all points
in the sample is then calculated from the temperature rise by
multiplying the temperature rise by the thermal expansion
coefficient and the appropriate elastic modulus.
[0207] (B) Change in stress and strain with time
[0208] The change in stress and strain in the sample is next
calculated as a function of time and position using the laws of
physical acoustics. This calculation is effectively performed by
means of a "stepping algorithm", which performs the following
computations.
[0209] First, a time step .tau. is chosen. For each film or layer
that comprises the structure of interest a bin size b equal to the
time .tau. multiplied by the sound velocity in the film is then
calculated. Each film is then divided into bins of this size or
smaller. By example, smaller size bins can be employed at any film
boundary. The time step .tau. is chosen so that each film
preferably contains a large number of bins. The results of the
foregoing give the stress set up by the pump pulse in each bin of
the structure. Next, the stress in each bin is decomposed into two
components, one initially propagating towards the free surface of
the sample and one away from it. Within a given film these two
components are stepped forward from bin to bin in the appropriate
direction. For a bin adjacent to the boundary between two films the
stress propagating towards the boundary is stepped partly into the
first bin on the other side of the boundary and still propagating
in the same direction and partly into the original bin but
propagating in the reverse direction. The fraction of the stress
that is stepped across the interface and the fraction which
reverses direction are calculated from the laws of physical
acoustics. At the top (free) surface of the structure the stress in
the bin adjacent to the surface and propagating towards the surface
remains in the same bin but has its direction reversed, i.e., it
becomes a stress pulse propagating into the interior of the
structure rather than towards the top surface. By applying this
procedure to all bins for a sufficient number of time steps T, the
stress distribution can be calculated for as long a time as is
required for comparison with the measured results. From the
calculated stress the strain is calculated by division by the
appropriate elastic coefficient.
[0210] Samples that are of interest in chip fabrication typically
have a number of thin films deposited on top of a semiconductor
substrate. Presently, the total thickness of these thin films is a
few microns or less, whereas the substrate is typically
approximately 200 microns thick. An important advantage of this
"stepping method" is that it is not necessary to consider stress
propagation throughout the entire substrate. Instead it is normally
sufficient to consider just one bin of the substrate together with
"boundary conditions" specified as follows.
[0211] (1) At each time step r the stress within the single bin of
the substrate and propagating towards the substrate can be
considered to be completely transferred into the remainder of the
substrate so that no part of this stress is reflected. (2) The
stress within the substrate bin and propagating towards the film
structure is taken to be zero. This description of the treatment of
the substrate holds if the amount of light that reaches the
substrate, after passing through whatever films are deposited onto
the substrate, is negligible. This condition holds for the majority
of structures which are of current industrial interest.
[0212] When this condition is not satisfied, and light does reach
the substrate, it is desirable to include in the simulation a
thickness of the substrate sufficient to include the entire depth
over which the pump or the probe light can significantly penetrate.
This depth is typically some number, e.g. five, of absorption
lengths of the pump or probe light. This region of the substrate is
then divided into bins of thickness as specified above. The last
bin of the substrate is then treated according to the following
boundary conditions.
[0213] First, at each time step the stress within the last bin of
the substrate, and propagating towards the interior of the
substrate, can be considered to be completely transferred into the
remainder of the substrate so that no part of this stress is
reflected. Second, the stress within the last bin of the substrate,
and propagating towards the film structure, is taken to be
zero.
[0214] For some samples the above division of the simulation into
the consideration of the calculation of the temperature rise and
the propagation of the stress may not be applicable. It is noted
that, as soon as energy is deposited into any part of the sample, a
stress is set up and mechanical waves are launched into adjacent
regions. If the diffusion of energy is sufficiently large and
continues for a sufficient period of time then the changing
temperature and associated stress distribution in the sample will
continue to generate new stress waves. However, the extension of
the simulation to include this effect is straightforward.
[0215] In some samples, particularly metal films of high electrical
conductivity, a more detailed treatment of the diffusion of energy
is required. The energy in the pump light pulse is initially input
to the conduction electrons, thereby raising their energy
considerably above the Fermi level. These electrons have a very
high diffusion coefficient and may spread a significant distance
through the sample before losing their excess energy as heat to the
lattice. Under these conditions the diffusion of the energy is not
adequately described by Fourier's law for classical heat
conduction. Instead it is preferred to use a more microscopic
approach, taking into account the diffusion rate of the electrons
and the rate at which they lose energy.
[0216] (C) Calculation of the transient response measured by the
probe
[0217] From the calculated strain distribution as a function of
depth into the sample, the changes .DELTA.n and .DELTA..kappa. in
the optical constants are calculated. This step requires knowledge
of the derivatives of the optical constants n and .kappa. with
respect to elastic strain.
[0218] From the calculated changes .DELTA.n and .DELTA..kappa. in
the optical constants as a function of depth, and the unperturbed
optical constants of the films, at least one of the quantities
.DELTA.R, .DELTA.T, .DELTA.P, .DELTA..phi. and .DELTA..delta. is
calculated and compared with the measured results. This calculation
is most conveniently carried out through the use of optical
transfer matrices.
[0219] The above description of the simulation steps A-C is
presented in terms of a one-dimensional model considering only the
variation of the electric field of the probe light, the elastic
stress, the elastic strain, etc., upon the distance along the
direction normal to the surface of the sample. It is within the
scope of this invention to extend the calculations to allow for the
variation in the intensity of the pump and probe beams within the
plane of the surface of the sample. This approach is useful for the
calculation of the change in the propagation angle of the reflected
probe light .DELTA..delta..
[0220] A series of such simulations are performed in which the
assumed thicknesses of the films in the structure are varied. By
comparison of the results of the simulation with some or all of the
measured quantities .DELTA.R, .DELTA.T, .DELTA.P, .DELTA..phi. and
.DELTA..delta. the thicknesses of the films are determined.
[0221] It is also within the scope of this invention to adjust the
film thicknesses so as to be consistent with results of any or all
of: (a) measurements of the optical reflectivity through
measurements of the incident and reflected average intensity of the
pump and/or probe beams; (b) measurements of the average phase
change of the pump and/or probe beams upon reflection; and (c)
measurements of the average polarization and optical phase of the
incident and reflected pump and/or probe beams.
[0222] It is further within the scope of the teaching of this
invention to include simulations which incorporate as adjustable
parameters at least one of the following for one or more films in
order to find a best-fit to measured data.
[0223] A first adjustable parameter is the film thickness, so as to
adjust the thicknesses obtained in accordance with the method
described above.
[0224] In this regard reference can be had to an article entitled
"Time-resolved study of vibrations of .alpha.--Ge:H/.alpha.--Si:
multilayers", Physical Review B, vol. 38, no. 9, Sep. 15, 1988, H.
T. Grahn et al., wherein reference is made to a simulation of a
multilayer structure and a variation in layer thickness (as well as
sound velocities). As was reported in this article, it was not
possible to find parameters such that the simulated response was in
agreement with an experimentally observed .DELTA.R(t). Reference
may also be had, by example, to the following articles that were
also coauthored by one of the inventors of this patent application:
"Sound velocity and index of refraction of AlAs measured by
picosecond ultrasonics", Appl. Phys. Lett. 53 (21), Nov. 21, 1988,
pp. 2023-2024, H. T. Grahn et al.; "Elastic properties of silicon
oxynitride films determined by picosecond acoustics", Appl. Phys.
Lett. 53 (23), Dec. 5, 1988, pp. 2281-2283, H. T. Grahn et al.; and
"Study of vibrational modes of gold nanostructures by picosecond
ultrasonics", Appl. Phys. 73 (1), Jan. 1, 1993, pp. 37-45, H. N.
Lin et al.
[0225] A second adjustable parameter is the sound velocity. An
example of a situation in which one may determine the sound
velocity has been described above. Thus, in this context what is
taught is the determination of the parameters n, d, and v by
comparison of the measured data with simulations, rather than by a
measurement of the frequency f(.theta.) as a function of the angle
.theta..
[0226] A third adjustable parameter is the crystal orientation in a
film. This can be achieved through measurement of the sound
velocity, which is dependent on crystal orientation in all
crystals, even those with cubic symmetry. In non-cubic crystals the
crystal orientation of the film, or the preferential orientation of
crystalline grains, leads to anisotropic optical properties which
can be detected via the measurements of the above described optical
measures of the optical reflectivity by determining the incident
and reflected average intensity of the pump and/or probe beams; the
average phase change of the pump and/or probe beams upon
reflection; and/or the average polarization and optical phase of
the incident and reflected pump and/or probe beams.
[0227] A fourth adjustable parameter is interface roughness. By
example, the interface roughness parameter causes a broadening of a
stress pulse which is transmitted across, or reflected at, the
interface.
[0228] A fifth adjustable parameter is the interface adhesion
strength, as will be described in further detail below. A
[0229] sixth adjustable parameter is the static stress. One
suitable procedure by which this can be determined has been
described previously in the context of measurements made at two or
more temperatures of the sample.
[0230] A seventh adjustable parameter is the thermal diffusivity.
The thermal diffusivity of the different films in the sample
affects the shape and magnitude of the generated stress pulses. By
treating the thermal diffusivity as an adjustable parameter, and
selecting it to give the best agreement between the simulation and
the measured data, the thermal diffusivity of a particular film in
the structure can be determined.
[0231] An eighth adjustable parameter is the electronic
diffusivity. In some samples which contain metal films with high
electrical conductivity the diffusion of the conduction electrons
before they lose the energy that they have received from the pump
pulse has a large effect on the shape and magnitude of the stress
pulses which are generated. By treating the electronic diffusivity
as an adjustable parameter, and adjusting it to give the best
agreement between the simulation and the measured data, the
electronic diffusivity of a particular film in the structure can be
determined.
[0232] It should be appreciated that the seventh and eight
adjustable parameters provide, separately or in conjunction with
one another, a means for the determination of the electrical
resistance of metallic films. A
[0233] ninth adjustable parameter involves the optical constants of
the film(s) and/or substrate.
[0234] A tenth, related adjustable parameter is the derivatives of
the optical constants with respect to stress or strain.
[0235] An eleventh adjustable parameter is the surface roughness.
The surface roughness has the consequence that a stress pulse
reflected at the surface of a sample is broadened. This broadening
may be introduced into the simulation and adjusted until the
simulation gives the best agreement with the measured data. In this
way the surface roughness can be determined.
[0236] A twelfth adjustable parameter is interfacial contamination.
If an interface between two materials A and B is contaminated by
the presence of a thin layer of another material C, the presence of
the layer C affects the reflection and transmission coefficients
for stress waves incident on the interface. For two elastic media
in perfect mechanical contact the reflection and transmission
coefficients are given by well-known formulas from physical
acoustics. The effect of interface adhesion strength on the
coefficients is discussed below. The coefficients may also be
affected by other effects which are unrelated to adhesion strength.
For example, in addition to changing the strength of the coupling
between A and B (i.e., the adhesion strength) the contamination
layer C provides a layer of mass at the interface which affects the
acoustic propagation. The contamination layer C may also lead to
additional optical absorption at the interface. The additional
optical absorption of the pump pulse will in this case result in
additional stress waves to be generated at the interface. The
detection of these additional stress waves provides a means for
detecting the presence of the contamination layer C. This method
can be applied to advantage for detecting contamination on the
surface of optically transparent bulk materials.
[0237] A thirteenth adjustable parameter is related to dimensions
other than thickness and geometrical shape. These parameters are
generally not relevant to measurements on samples consisting solely
of planar films. Instead, these adjustable parameters enter into
the characterization of samples of the type mentioned above with
respect to laterally patterned structures and the like. These
adjustable parameters apply as well to the characterization of an
array of identical structures having dimensions much less than the
pump and probe spot diameter, as described below.
[0238] A further adjustable parameter relates to the presence of
and thickness of a region of intermixing between two adjacent
layers.
[0239] An important aspect of this invention concerns the precise
relation between the computer simulations and the transient optical
responses measured by the system. The following discussion
describes the essential aspects of this relation for the particular
example of a sample containing a number of planar films whose
lateral extent is much greater than their thickness, and also
greater than the linear dimensions of the region of the sample
illuminated by the pump and probe pulses. A generalization of this
discussion to laterally patterned structures will be evident to
workers skilled in the relevant art, when guided by the following
teachings. Similarly, the following discussion will consider, again
as a specific example, a particular one of the transient optical
responses, namely the change .DELTA.R(t) in optical reflectivity.
The generalization of the discussion to a consideration of the
other transient optical responses aforementioned should also become
evident to workers skilled in the relevant art, when guided by the
following teachings.
[0240] In this example the computer simulations calculate the
change in the optical reflectivity .DELTA.R.sub.sim(t) of the
sample when it is illuminated with a pump pulse of unit energy per
unit area of the sample. The simulation also gives a value for the
static reflection coefficient of the pump and probe beams. The
system measures the transient change .DELTA.P.sub.probe-refl in the
power of the reflected probe pulse as determined, for example, by
photodiode D1 in FIG. 18. It also measures the static reflection
coefficients of the pump and probe beams from a ratio of the power
in the incident and reflected beams. The incident probe power is
measured by photodiode D2 in FIG. 18, the reflected probe power is
measured by D1, the incident pump power is measured by D4, and the
reflected pump power is measured by D3.
[0241] To relate the simulation results for the transient change in
the optical reflectivity to the system measurement it is necessary
to know: (a) the power of the pump and probe beams; (b) the
intensity profiles of these beams; and (c) their overlap on the
sample surface.
[0242] Let us suppose first that the pump beam is incident over an
area A and that within this area the pump intensity is uniform.
Then for each applied pump pulse the pump energy absorbed per unit
area is 4 P pump - inc A pump ( 1 - R pump ) f ( 3 )
[0243] where f is the repetition rate of the pump pulse train, and
R.sub.pump is the reflection coefficient for the pump beam. Thus,
the change in optical reflectivity of the each probe light pulse
will be 5 R sim ( t ) P pump - inc A pump ( 1 - R pump ) f ( 4
)
[0244] and the change in power of the reflected probe beam will be
6 P probe - ref1 = P probe - inc R sim ( t ) P pump - inc A pump (
1 - R pump ) f ( 5 )
[0245] In a practical system the illumination of the sample does
not, in fact, produce a uniform intensity of the incident pump
beam. Moreover, the intensity of the probe light will also vary
with position on the sample surface. To account for these
variations the equation for .DELTA.P.sub.probe-refl is modified to
read 7 P probe - ref1 = P probe - inc R sim ( t ) P pump - inc A
effective ( 1 - R pump ) f ( 6 )
[0246] where the effective area A.sub.effective is defined by the
relation where I.sub.probe-inc 8 ( r )
[0247] and I.sub.pump-inc 9 ( r )
[0248] are respectively the 10 A effective = I pump - inc ( r ) A I
probe - inc ( r ) A I pump - inc ( r ) I probe - inc ( r ) ( A ( 7
)
[0249] intensities of the probe and pump beams on the surface of
the sample. One can consider A.sub.effective to be an effective
area of overlap of the pump and probe beams.
[0250] Analogous expressions can be derived for the change in
optical transmission .DELTA.T(t), the change in optical phase
.DELTA..phi.(t), the change in polarization .DELTA.P(t), and the
change .DELTA..delta.(t) in the angle of reflection of the probe
light. The
[0251] following quantities are measured by the system:
.DELTA.P.sub.probe-refl, P.sub.probe-inc, P.sub.pump-inc,
R.sub.pump, R.sub.probe. The computer simulation gives predicted
values for .DELTA..sub.sim(t), R.sub.pump, and R.sub.probe. Thus
the following comparisons can be made between the simulation and
the system measurements in order to determine the characteristics
of the sample.
[0252] (1) A comparison of the simulated and measured reflection
coefficient R.sub.pump.
[0253] (2) A comparison of the simulated and measured reflection
coefficient R.sub.probe.
[0254] (3) A comparison of the simulated and measured transient
change .DELTA.P.sub.probe-refl in the power of the reflected probe
light.
[0255] To make a comparison of the simulated and measured change,
it can be seen from the preceding equation (6) that it is necessary
to know the value of .DELTA..sub.effective. This can be
accomplished by one or more of the following methods.
[0256] (a) A first method directly measures the intensity
variations of the pump and probe beams over the surface of the
sample, i.e, I.sub.probe-inc ({right arrow over (r)}) and
I.sub.pump-inc ({right arrow over (r)}) as a function of position,
and uses the results of these measurements to calculate
.DELTA.effective. This is possible to accomplish but requires very
careful measurements which may be difficult to accomplish in
industrial environment.
[0257] (b) A second method measures the transient response
.DELTA.P.sub.probe-refl for a sample on a system S for which the
area .DELTA..sub.effective is known. This method then measures the
response .DELTA.P.sub.probe-refl of the same sample on the system
S' for which .DELTA..sub.effective is to be determined. The ratio
of the responses on the two systems gives the inverse of the ratio
of the effective areas for the two systems. This can be an
effective method because the system S can be chosen to be a
specially constructed system in which the areas illuminated by the
pump and probe beams are larger than would be desirable for an
instrument with rapid measurement capability. Since the areas are
large for this system it is simpler to measure the intensity
variations of the pump and probe beams over the surface of the
sample, i.e, I.sub.probe-inc ({right arrow over (r)}) and
I.sub.pump-inc ({right arrow over (r)}) as a function of position.
This method is effective even if the quantities which enter into
the calculation of the simulated reflectivity change
.DELTA.R.sub.sim(t) are not known.
[0258] (c) A third method measures the transient response
.DELTA.P.sub.probe-refl for a sample in which all of the quantities
are known which enter into the calculation of the simulated
reflectivity change .DELTA.R.sub.sim(t) of the sample when it is
illuminated with a pump pulse of unit energy per unit area of the
sample. Then by comparison of the measured transient response
.DELTA.P.sub.probe-refl with the response predicted from the Eq. 6
the effective area .DELTA..sub.effective is determined.
[0259] To build a truly effective instrument it is essential that
the effective area .DELTA..sub.effective be stable throughout the
course of a sequence of measurements. To ensure this, the system of
this invention incorporates means for automatically focusing the
pump and probe beams onto the surface of the sample so as to
achieve a reproducible intensity variation of the two beams during
every measurement. The automatic focusing system provides a
mechanism for maintaining the system in a previously determined
state in which the size and relative positions of the beams on the
sample surface are appropriate for effective transient response
measurements.
[0260] It should be noted that for any application in which the
amplitude of an optical transient response is used to draw
quantitative conclusions about a sample (for example, when the
magnitude of a feature that arises from an acoustic echo is
influenced by the condition of a buried interface) a calibration
scheme such as described above must be a feature of the measurement
system.
[0261] The preceding description of the method for the comparison
of the computer simulation results and the system measurements
supposes that the several detectors in the measurement system are
calibrated. It is contemplated that such a system will use
detectors operating in the linear range so that the output voltage
V of each detector is proportional to the incident optical power P.
For each detector there is thus a constant G such that V=GP. The
preceding description assumes that the constant G is known for each
and every detector. In the case that this information is not
available, the individual calibration factors associated with each
of the individual detectors measuring P.sub.probe-inc,
P.sub.pump-inc, and .DELTA.P.sub.probe-refl may be combined with
A.sub.effective and f into a single overall system calibration
constant C. Therefore in terms of a calibration factor C, Eq. 6
could be expressed as
.DELTA.V.sub.probe-refl=CV.sub.probe-inc.DELTA.R.sub.sim(t)V.sub.pump-inc(-
1-R.sub.pump) (8)
[0262] where .DELTA.V.sub.probe-refl is the output voltage from
detector used to measure the change in the power of the reflected
probe light (D1), V.sub.pump-inc is the output voltage from the
detector used to measure the incident pump light (D4), and
V.sub.probe-inc is the output voltage of the detector used to
measure the incident probe light (D2). Thus, to provide an
effective instrument it is sufficient to determine the constant C.
This can be accomplished by either of the following two
methods.
[0263] (a) A first method measures the transient response
.DELTA.V.sub.probe-refl for a sample in which all of the quantities
are known which enter into the calculation of the simulated
reflectivity change .DELTA.R.sub.sim(t) of the sample when it is
illuminated with a pump pulse of unit energy per unit area of the
sample. Next, the method measures V.sub.probe-inc and
V.sub.pump-inc, then determines R.sub.pump either by measurement or
from the computer simulation. The method then finds the value of
the constant C such that Eq. 8 is satisfied.
[0264] (b) A second method measures the transient response
.DELTA.V.sub.probe-refl for a reference sample for which the
transient optical response .DELTA.R(t), when it is illuminated with
a pump pulse of unit energy per unit area of the sample, has been
measured using a system which has been previously calibrated, for
example, by one or more of the methods described above. The method
then measure V.sub.probe-inc and V.sub.pump-inc., determines
R.sub.pump by measurement, and then finds the value of the constant
C such that the following equation is satisfied.
.DELTA.V.sub.probe-refl=CV.sub.probe-inc.DELTA.R(t)V.sub.pump-inc(1-R.sub.-
pump) (9)
[0265] For both of these methods it is important to establish the
autofocus conditions prior to making measurements of
.DELTA.V.sub.probe-refl, since C depends on the value of
A.sub.effective.
[0266] The teaching of this invention furthermore encompasses a
picosecond ultrasonic system in which the results of measurements
are compared with computer simulations of the measured response, as
described above, but using a different method to perform the
simulation. In this case the following steps may be employed.
[0267] First, the initial stress distribution in the structure is
calculated using the method described above.
[0268] Second, the acoustical normal modes of the structure are
calculated through solution of the equations of physical acoustics
together with appropriate boundary conditions at the interfaces
between the films, at the free surface of the sample, and at the
free surface of the substrate. All normal modes up to certain
maximum frequency f.sub.max are calculated. The choice of this
maximum frequency is related to the sharpness of the features, such
as echoes, that appear in the measured data. As an approximate
rule, if it is desired to simulate data for a structure of interest
which has a characteristic time-scale .tau., it is necessary to
choose fmax such that the product of f.sub.max and .tau. is at
least as large as unity. Thus, for example, if the measured data
contains an echo of width 1 psec, then to perform an accurate
simulation it is desirable to calculate all normal modes up to the
frequency 1000 GHz.
[0269] The substrate thickness is typically in the range around 200
microns, whereas often the total thickness of the thin films
deposited onto the substrate is a micron or even less. A
calculation of the normal modes of a sample consisting of films on
a substrate of this thickness is very difficult and time-consuming
because of the very large number of acoustic modes with very
closely-spaced frequencies. However, for the purposes of creating
an accurate simulation of the typical data on this type of sample
it is not necessary to use the actual thickness of the substrate.
Instead it is sufficient to consider the "substrate" to have a
thickness much less than the real physical substrate. The thickness
of this artificial substrate should be sufficiently large such that
the time required for an acoustic wave to propagate through the
substrate from the thin films deposited on the front surface of the
substrate to the far side of the substrate and back again is longer
than the total time span over which the data to be simulated
extends. Thus, for example, if the data extends from zero time
delay of the probe relative to the pump to a time delay of 1000
psecs, and the sound velocity v in the substrate is
5.times.10.sup.5 cm sec.sup.-1, then the artificial substrate can
be taken to have a thickness of as little as 2.5 microns. If the
thickness is at least this great no acoustic echoes can return from
the back of the substrate during the time that measurements are
made, and hence the difference in thickness between the artificial
substrate and the actual substrate is irrelevant.
[0270] Third, the initial stress distribution produced by the pump
beam is decomposed into a sum over the normal modes just
calculated. It is possible to choose a set of amplitudes for the
normal modes such that when the contributions of each normal mode
are added together, taking allowance for the amplitude of each
mode, the initial stress distribution is accurately reproduced. The
initial amplitude of the nth normal mode may be denoted as
A.sub.n.
[0271] Fourth, each normal mode has a characteristic spatial stress
pattern associated with it. This stress pattern gives a change in
the reflection coefficient of the probe light which can be
calculated according to the methods described above. Let this
change when the nth mode has unit amplitude be B.sub.n. This change
is linear in the amplitude of the acoustic normal mode. Hence, the
total change in the reflectivity of the probe light at time zero
is
.DELTA.R(t=0)=sum.sub.nA.sub.nB.sub.n (10)
[0272] Fifth, let the frequency of the nth normal mode be f.sub.n.
Then the total change in reflectivity of the probe light at any
later time t can be calculated as
.DELTA.R(t)=sum.sub.nA.sub.nB.sub.ncos(2.pi.f.sub.nt). (11)
[0273] This simulation method has the advantage that through the
use of the formula just given the change in reflectivity at any
chosen time, or within any chosen time range, may be calculated
without the need to consider the acoustic or optical processes
occurring in the sample for all times intermediate between the
application of the pump pulse and the time of interest. It is
important to note that the amplitudes A.sub.n and the coefficients
B.sub.n need be calculated only once, and can then be used to find
the response at any later time.
[0274] It should be further noted that the above description refers
to the use of this method for the calculation of the change in
reflected intensity of the probe beam. However, completely
analogous methods can be used to simulate the other responses of
interest, i.e. .DELTA.T, .DELTA.P, .DELTA..phi., and
.DELTA..delta..
[0275] As was indicated previously, the teaching of this invention
is also directed to a picosecond ultrasonic system which enables
the measurement of a vibrational response of a sample that
includes, by example, a very thin film on a substrate, or a very
thin film on a significantly thicker film. By example, a substrate
may have a layer of a metal, such as aluminum, and an intervening
layer comprised of a polymer. The measured response is then
analyzed to determine the damping rate of the thickness vibration
of the film. This damping rate is compared with a damping rate
determined for a model based on classical acoustics in which the
interface between the thin film and the substrate (or thicker film)
is characterized by a coupling parameter ("adhesion strength") per
unit area. This coupling parameter, which may be considered to be a
spring constant parameter that is a linear property per unit area,
is the strength of a spring per unit area which connects the
surface of the thin film to the substrate, or to the thicker film.
The adhesion strength is adjusted to give agreement between the
simulation and the measured value of the damping, and is thus used
as a measure of the quality of the interface.
[0276] As was also indicated previously, the teaching of this
invention furthermore pertains to a picosecond ultrasonic system in
which a sample is comprised of an array of identical structures
having dimensions much less than the pump and probe spot diameter.
In this case each structure is simultaneously excited by the pump
beam and then simultaneously examined by the probe beam. The
response of each structure is simulated by the methods described
above. The characteristics of the structures are then deduced by
comparison of the simulation and the measured response.
[0277] Relatedly, this invention also teaches methods for deducing
the dimensions of substantially identical patterned structures
arranged periodically, and for deducing the statistical
distribution of sizes of such structures. This is accomplished by
comparing the observed response of the structures, to a stress
pulse that is induced by the pump pulse, to simulations of the
array of vibrating structures.
[0278] Further in this regard, the teaching of this invention also
pertains to methods for deducing the physical characteristics of
thin films patterned mechanically or by lithographic means into
structures. Steps of the method include simulation of the
mechanical vibrations of a single structure, calculation of the
change in the probe beam after it impinges on the structure, and
adjusting the physical characteristics of the simulated structure
and interfaces in order to obtain a best fit to the observed
response.
[0279] Further in accordance with the teaching of this invention, a
picosecond ultrasonic system employs a method for deducing the
physical characteristics of a sample, and uses an analysis of an
acoustic echo or echoes based on either or both of the following
two methods.
[0280] In a first method a characterization of the time of arrival
of an echo is obtained by means of the location in time of one or
more echo features, such as a point of maximum or minimum amplitude
or inflection point.
[0281] In a second method a characterization of the time of arrival
of the echo as seen in .DELTA.R(t) (or, by example, .DELTA.T(t),
.DELTA.P(t), .DELTA..phi.(t), and .DELTA..delta.(t)) by convolution
of the measured echo with a suitably chosen function f(t) of the
time. Thus, the convolution
C(t.sub.1)=.function..DELTA.R(t)f(t-t.sub.1)dt (12)
[0282] is calculated. The time t.sub.1 is then adjusted so as to
maximize the result of the convolution, i.e. to maximize C. The
resulting value of t.sub.1 is then used as an estimate of the
arrival time of the echo. The function f(t) may be the shape of the
echo measured on a reference sample having known physical
characteristics or determined by simulation. The echo time, or
times, as determined are then used to yield film thicknesses or
interface characteristics.
[0283] In view of the foregoing descriptions, it should thus be
realized that the teaching of this invention also pertains to
methods for deducing the physical characteristics of thin films or
interfaces, in which the steps include the sequential application
of some or all of the above-described methods in order to determine
the physical parameters of a complex sample having more than one
layer or interface.
[0284] The teaching of this invention also pertains to methods for
deducing the sound velocity and refractive index of a film or
substrate in which a stress wave is generated by a light pulse, and
in which an oscillating response is observed in the detected probe
beam as a function of delay, and measurements of the oscillation
period are made corresponding to at least two angles of incidence
of the probe beam on the sample's surface. Measurements at several
angles may be made sequentially or simultaneously. In this case the
film may be partially absorbing, and could be a film which is
underneath (i.e, on the substrate side of) another
partially-absorbing film or films.
[0285] Also encompassed by the teachings of this invention are
methods of relating the quality of a sample to another reference
sample prepared under a particular set of conditions, by comparing
the observed temporal response of the sample with that measured for
the reference sample under similar conditions. The result of the
comparison may or may not ascribe a cause for any observed
differences to a specific physical or chemical property of either
sample. The quality is considered a factor which relates the
similarity or dissimilarity of the optical responses of the several
samples to the generation of a stress wave or pulse by the pump
beam.
[0286] This invention also pertains to the application of the pump
and/or probe beams at different spatial locations on the sample
with the intention of characterizing an intervening part of sample.
The intervening part of the sample may be, by example, an
interface, a crack, or a material in which signals cannot be
directly generated, but which is desired to characterize.
[0287] The teaching of this invention furthermore pertains to
methods and apparatus for exciting modes of one or two dimensional
patterned objects for the purpose of characterizing their shapes,
layer thickness, adhesion, and structural integrity. This aspect of
the invention may be considered as a generalization of the
foregoing features and advantages, and is directed to samples which
are not thin films of uniform thickness and which may be large
compared to their thickness. For these samples the analysis
preferably includes the calculation of the stress, strain, electric
fields due to the pump and probe light pulses, etc., as a function
of two or three spatial coordinates rather than only the distance
from the surface of the sample. While the time-step method
described above may not be applicable to solving this problem,
because it is applicable to one dimension, other numerical
simulation methods may be applied to perform the calculation of how
the stress changes with time. Also, the previously described
simulations employ optical transfer matrices to calculate the
electric field distribution of the pump light and the change in
optical reflectivity (or other changes in the characteristics) of
the probe light. However, the optical transfer matrix method is not
applicable to patterned structures because, again, it is
essentially a one dimensional method. Thus, another more suitable
numerical method is used instead.
[0288] The teaching of this invention also includes methods and
apparatus for exciting stress pulses in one part of a thin film or
multilayer in order to detect a change in another part of the thin
film, such as a presence of a chemical reaction, intermixing, or
alloying at one or more interfaces within the sample.
[0289] Relatedly, the teaching of this invention also encompasses
the characterization of interfacial chemical reactions between two
or more layers, or between a layer and interface, and the
correlation of the acoustical and optical measurements with
reactant species. This includes the characterization of the
structural phase, and one or more of the thickness and sound
velocity of the layers in the sample, including any new layers
formed by the chemical reaction.
[0290] The teachings of this invention also pertain to the
characterization of ion implant dose, energy, species, or any other
ion implant parameters for an ion implant made through a film for
the purpose of, by example, altering its adhesion to a substrate or
an underlying layer. This characterization is carried out in
accordance with any of the above-described techniques, in which the
adhesion may be deduced from the temporal characteristics of the
observed probe response, or by a simple comparison with a reference
response for a sample prepared under like conditions.
[0291] Finally, this invention teaches a method for deducing the
derivative of the index of refraction n or extinction coefficient
.kappa. of a material with respect to stress or strain by making
measurements of the reflectivity change in the material caused by a
stress pulse, of which a computable fraction has also been detected
in a second material whose derivatives of index of refraction and
extinction coefficient with respect to stress or strain are known
or may be determined separately.
[0292] It should thus be apparent that while the invention has been
particularly shown and described with respect to a number of
embodiments thereof, the teachings of this invention are not to be
construed to be limited to only these disclosed embodiments. That
is, changes in form and details may be made to these disclosed
embodiments without departing from the scope and spirit of the
invention. The teaching of this invention should thus be afforded a
scope that is commensurate with the scope of the claims which
follow.
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