U.S. patent application number 09/800865 was filed with the patent office on 2002-09-12 for integrated circuit device characterization.
Invention is credited to Gardner, Donald S..
Application Number | 20020127748 09/800865 |
Document ID | / |
Family ID | 25179576 |
Filed Date | 2002-09-12 |
United States Patent
Application |
20020127748 |
Kind Code |
A1 |
Gardner, Donald S. |
September 12, 2002 |
INTEGRATED CIRCUIT DEVICE CHARACTERIZATION
Abstract
One or more electrical characteristics of an integrated circuit
device are measured at one or more relatively lower frequencies.
One or more parameters of the integrated circuit device are
measured at one or more frequencies higher than the one or more
relatively lower frequencies. One or more parameters of the
integrated circuit device are calculated based on the measured one
or more electrical characteristics. The integrated circuit device
is characterized based on the calculated one or more parameters and
the measured one or more parameters.
Inventors: |
Gardner, Donald S.;
(Mountain View, CA) |
Correspondence
Address: |
BLAKELY SOKOLOFF TAYLOR & ZAFMAN
12400 WILSHIRE BOULEVARD, SEVENTH FLOOR
LOS ANGELES
CA
90025
US
|
Family ID: |
25179576 |
Appl. No.: |
09/800865 |
Filed: |
March 7, 2001 |
Current U.S.
Class: |
438/17 |
Current CPC
Class: |
G01R 31/2822 20130101;
G01R 31/316 20130101; G01R 27/28 20130101; G01R 31/2837 20130101;
G01R 31/2851 20130101; G01R 27/26 20130101 |
Class at
Publication: |
438/17 |
International
Class: |
H01L 021/66; G01R
031/26 |
Claims
What is claimed is:
1. A method comprising: (a) measuring one or more electrical
characteristics of an integrated circuit device at one or more
relatively lower frequencies; (b) measuring one or more parameters
of the integrated circuit device at one or more frequencies higher
than the one or more relatively lower frequencies; (c) calculating
one or more parameters of the integrated circuit device based on
the measured one or more electrical characteristics; and (d)
characterizing the integrated circuit device based on the
calculated one or more parameters and the measured one or more
parameters.
2. The method of claim 1, wherein the measuring (a) comprises
measuring one or more electrical characteristics using an impedance
analyzer.
3. The method of claim 2, wherein the measuring (a) comprises
driving a shield of each of a plurality of probe lines to
compensate for impedance of the probe lines.
4. The method of claim 3, comprising electrically isolating each
shield.
5. The method of claim 3, wherein the measuring (a) comprises
conductively coupling each shield to one another at or near the
integrated circuit device.
6. The method of claim 5, wherein the conductively coupling
comprises coupling each shield to one another at or near an end of
each shield with a foil jumper.
7. The method of claim 1, wherein the measuring (a) comprises
measuring a value for one or more circuit elements of an electrical
model of the integrated circuit device.
8. The method of claim 1, wherein the measuring (b) comprises
measuring one or more parameters using a network analyzer.
9. The method of claim 7, wherein the calculating (c) comprises
calculating one or more parameters based on the measured value for
one or more circuit elements of the electrical model.
10. The method of claim 1, wherein the measuring (b) comprises
measuring scattering parameters of the integrated circuit device;
and wherein the calculating (c) comprises calculating scattering
parameters of the integrated circuit device.
11. The method of claim 1, wherein the characterizing (d) comprises
comparing the calculated one or more parameters to the measured one
or more parameters and updating one or more values for an
electrical model of the integrated circuit device.
12. The method of claim 1, wherein the characterizing (d) comprises
iteratively comparing the calculated one or more parameters to the
measured one or more parameters, updating one or more values for an
electrical model of the integrated circuit device, and
recalculating the one or more parameters of the integrated circuit
device based on the updated one or more values of the electrical
model until the recalculated one or more parameters and the
measured one or more parameters satisfy a predetermined
condition.
13. An apparatus comprising: an impedance analyzer to measure one
or more electrical characteristics of an integrated circuit device
at one or more relatively lower frequencies; a network analyzer to
measure one or more parameters of the integrated circuit device at
one or more frequencies higher than the one or more relatively
lower frequencies; and a data processing system to calculate one or
more parameters of the integrated circuit device based on the
measured one or more electrical characteristics and to characterize
the integrated circuit device based on the calculated one or more
parameters and the measured one or more parameters.
14. The apparatus of claim 13, comprising a plurality of probes
each coupled to a respective line coupled to the impedance
analyzer, wherein the impedance analyzer drives a shield of each
line to compensate for impedance of the line.
15. The apparatus of claim 14, wherein each shield is electrically
isolated.
16. The apparatus of claim 14, wherein each shield is conductively
coupled to one another at or near the integrated circuit
device.
17. The apparatus of claim 16, comprising one or more foil jumpers
to couple each shield to another shield at or near an end of each
shield.
18. The apparatus of claim 13, wherein the impedance analyzer
measures a value for one or more circuit elements of an electrical
model of the integrated circuit device.
19. The apparatus of claim 18, wherein the data processing system
calculates one or more parameters based on the measured value for
one or more circuit elements of the electrical model.
20. The apparatus of claim 13, wherein the network analyzer
measures scattering parameters of the integrated circuit device and
the data processing system calculates scattering parameters of the
integrated circuit device.
21. The apparatus of claim 13, wherein the data processing system
compares the calculated one or more parameters to the measured one
or more parameters and updates one or more values for an electrical
model of the integrated circuit device.
22. The apparatus of claim 13, wherein the data processing system
iteratively compares the calculated one or more parameters to the
measured one or more parameters, updates one or more values for an
electrical model of the integrated circuit device, and recalculates
the one or more parameters of the integrated circuit device based
on the updated one or more values of the electrical model until the
recalculated one or more parameters and the measured one or more
parameters satisfy a predetermined condition.
23. An apparatus comprising: (a) means for measuring one or more
electrical characteristics of an integrated circuit device at one
or more relatively lower frequencies; (b) means for measuring one
or more parameters of the integrated circuit device at one or more
frequencies higher than the one or more relatively lower
frequencies; (c) means for calculating one or more parameters of
the integrated circuit device based on the measured one or more
electrical characteristics; and (d) means for characterizing the
integrated circuit device based on the calculated one or more
parameters and the measured one or more parameters.
24. The apparatus of claim 23, wherein the measuring means (a)
measures a value for one or more circuit elements of an electrical
model of the integrated circuit device.
25. The apparatus of claim 24, wherein the calculating means (c)
calculates one or more parameters based on the measured value for
one or more circuit elements of the electrical model.
26. The apparatus of claim 23, wherein the measuring means (b)
measures scattering parameters of the integrated circuit device and
the calculating means (c) calculates scattering parameters of the
integrated circuit device.
27. The apparatus of claim 23, wherein the characterizing means (d)
compares the calculated one or more parameters to the measured one
or more parameters and updates one or more values for an electrical
model of the integrated circuit device.
28. The apparatus of claim 23, wherein the characterizing means (d)
iteratively compares the calculated one or more parameters to the
measured one or more parameters, updates one or more values for an
electrical model of the integrated circuit device, and recalculates
the one or more parameters of the integrated circuit device based
on the updated one or more values of the electrical model until the
recalculated one or more parameters and the measured one or more
parameters satisfy a predetermined condition.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates generally to the field of
circuit characterization. More particularly, the present invention
relates to the field of integrated circuit device
characterization.
[0003] 2. Description of Related Art
[0004] Integrated radio frequency (RE) circuit devices may be
measured using network analyzers that typically operate from
approximately 0.1 GigaHertz (GHz) to approximately 20 GHz. As the
sensitivity of a typical network analyzer is limited to no less
than several ohms of reactance, integrated circuit devices that are
to operate at relatively low frequencies and/or with electrical
characteristics having relatively low values may not be measured
using network analyzers.
[0005] As one example, an integrated inductor that has an
inductance below 100 nanoHenries (nH) and that is to operate at a
frequency of approximately 3 MegaHertz (MHz) could not be measured
by a typical network analyzer even if the network analyzer could be
operated at a relatively lower frequency such as approximately 1
MHz, for example. As another example, inductors comprising a
magnetic material such as a nickel iron (NiFe) permalloy, for
example, cannot be measured by a typical network analyzer because
such inductors can only be operated at relatively low frequencies
below 100 MHz, for example. The magnetic material otherwise becomes
lossy.
[0006] Characterizing an integrated RF circuit device such as an
inductor, for example, at relatively high frequencies with a
network analyzer is challenging. The cross-sectional area of the
conductor for the inductor becomes reduced due to skin effects,
thereby increasing the resistance of the inductor. Parasitic
capacitances and resistances in the substrate of the integrated RF
circuit device depend on the frequency at which the integrated RF
circuit device operates. Also, parasitics exist in the cables and
probes of the network analyzer.
BRIEF DESCRIPTION OF THE DRAWINGS
[0007] The present invention is illustrated by way of example and
not limitation in the Figures of the accompanying drawings, in
which like references indicate similar elements and in which:
[0008] FIG. 1 illustrates, for one embodiment, a flow diagram to
characterize an integrated circuit device;
[0009] FIG. 2 illustrates, for one embodiment, an integrated
inductor;
[0010] FIG. 3 illustrates, for one embodiment, an electrical model
for the integrated inductor of FIG. 2;
[0011] FIG. 4 illustrates, for one embodiment, a system to
characterize an integrated circuit device;
[0012] FIG. 5 illustrates, for one embodiment, a relatively lower
frequency measurement system; and
[0013] FIG. 6 illustrates, for one embodiment, a relatively higher
frequency measurement system.
DETAILED DESCRIPTION
[0014] The following detailed description sets forth an embodiment
or embodiments in accordance with the present invention for
integrated circuit device characterization. In the following
description, details are set forth such as a specific circuit
model, measurement equipment, etc. in order to provide a thorough
understanding of the present invention. It will be evident,
however, that the present invention may be practiced without these
details. In other instances, well-known algorithms, etc. have not
been described in particular detail so as not to obscure the
present invention.
[0015] FIG. 1 illustrates, for one embodiment, a flow diagram 100
to characterize an integrated circuit device, such as an integrated
inductor 200 as illustrated in FIG. 2. Although described in the
context of integrated inductor 200, any suitable integrated circuit
device including any other suitable integrated inductor may be
characterized in accordance with flow diagram 100.
[0016] As illustrated in FIG. 2, integrated inductor 200 comprises
a generally spiral-shaped conductor 210 defining a signal path
along which current may flow to generate an electromagnetic field
around conductor 210. Current may flow through conductor 210 by
applying a voltage potential across an innermost node 212 near the
beginning of the innermost turn of conductor 210 and an outermost
node 216 near the end of the outermost turn of conductor 210. Node
212 is coupled to a pad 232 by a conductive underpass 226 that
passes under each turn of conductor 210 and that is separated from
conductor 210 by a dielectric layer. Node 216 is coupled to a pad
236. Integrated inductor 200 for one embodiment also comprises pads
231, 233, 235, and 237 each coupled to a ground node. Although
described in the context of a ground node, the node coupled to each
pad 231, 233, 235, and 237 may have any suitable voltage
potential.
[0017] Integrated inductor 200 for one embodiment comprises an
optional magnetic layer 220. Conductor 210 is positioned over
magnetic layer 220 and is separated from magnetic layer 220 by at
least a dielectric layer. Magnetic layer 220 forms a reference
voltage plane for integrated inductor 200 to help contain electric
and magnetic fields around conductor 210. Magnetic layer 220 for
one embodiment is patterned to define conductive underpass 226.
[0018] Integrated inductor 200 for one embodiment is formed over a
substrate comprising a semiconductor material with at least a
dielectric layer separating magnetic layer 220 from the substrate.
As conductor 210 generates a magnetic flux toward the substrate
that would induce Eddy or mirror currents and noise in the
substrate, positioning magnetic layer 220 between the substrate and
conductor 210 helps reduce such currents and therefore helps reduce
losses in integrated inductor 200 and minimizes concern for
interference between integrated inductor 200 and neighboring
circuitry. Magnetic layer 220 also helps prevent substrate coupling
and helps reduce substrate dependency.
[0019] Integrated inductor 200 may be designed to have a suitable
quality factor Q. The quality factor Q is proportional to
.omega.L/R, where .omega. is the operating frequency for integrated
inductor 200, L is the inductance of integrated inductor 200, and R
is the resistance of integrated inductor 200. As the quality factor
Q of integrated inductor 200 is proportional to the inductance L of
integrated inductor 200 and inversely proportional to the
resistance R of integrated inductor 200, integrated inductor 200
can be designed with a relatively higher inductance L, and
therefore a relatively higher quality factor Q, for a given area or
resistance R of integrated inductor 200. Alternatively, for a given
inductance L, integrated inductor 200 can be designed with a
relatively smaller area and therefore a relatively lower resistance
R and capacitance, resulting in a relatively higher resonance
frequency .omega..sub.r and a relatively higher quality factor Q
for integrated inductor 200.
[0020] Factors influencing the quality factor Q for integrated
inductor 200 include the amount of area covered by conductor 210,
the number of turns of conductor 210, the shape of each turn, the
conductive material used for conductor 210, the width, thickness,
and length of conductor 210, and the amount of spacing between
turns for conductor 210.
[0021] Using magnetic layer 220 also helps influence the quality
factor Q for integrated inductor 200. Magnetic layer 220 helps
increase the inductance L of integrated inductor 200, and therefore
the quality factor Q for integrated inductor 200. The magnetic
material and thickness of magnetic layer 220 help determine the
frequency at which integrated inductor 200 may be operated and the
inductance L of integrated inductor 200. Magnetic layer 220 for one
embodiment comprises a cobalt-zirconium-tantalum (CoZrTa) alloy
that can operate in the GigaHertz (GHz) range. The dielectric
material and thickness for the dielectric layer between conductor
210 and magnetic layer 220 help determine the capacitance and
therefore the resonance frequency .omega..sub.r for integrated
inductor 200. Defining optional slots in magnetic layer 220, such
as slots 222 and 224 for example, helps reduce Eddy currents in
magnetic layer 220 and helps increase the resonance frequency
.omega..sub.r for integrated inductor 200.
[0022] FIG. 3 illustrates an exemplary electrical model 300 of
integrated inductor 200. Electrical model 300 represents one or
more electrical characteristics of integrated inductor 200 with
corresponding ideal circuit elements and is used to help
characterize integrated inductor 200. Electrical model 300 for one
embodiment is an equivalent circuit model of integrated inductor
200.
[0023] Electrical model 300 for one embodiment comprises an
inductor 302 representing the inductance L of the integrated
inductor 200, a resistor 304 representing the resistance R of the
integrated inductor 200, a resistor 305 representing a resistance
R.sub.se caused by skin effect in integrated inductor 200, a
resistor 306 representing a resistance R.sub.Eddy caused by Eddy
current losses in magnetic layer 220 and the substrate, a capacitor
308 representing a capacitance C.sub.c-m between conductor 210 and
magnetic layer 220, and a capacitor 310 representing a capacitance
C.sub.c-u between conductor 210 and conductive underpass 226. Other
equivalent circuit models mathematically related to electrical
model 300 of FIG. 3 may be used for other embodiments.
[0024] The characterization of integrated inductor 200 in
accordance with flow diagram 100 of FIG. 1 may be performed using
any suitable equipment. For one embodiment, an integrated circuit
device characterization system 400 as illustrated in FIG. 4 may be
used to characterize an integrated circuit device. Integrated
circuit device characterization system 400 for one embodiment
comprises a low frequency measurement system 410, a high frequency
measurement system 420, a data processing system 430, and an output
device 440.
[0025] For block 102 of FIG. 1, one or more electrical
characteristics of integrated inductor 200 are measured at one or
more relatively lower frequencies. Any suitable electrical
characteristics may be measured at any suitable one or more
frequencies using any suitable measuring equipment. For one
embodiment, electrical characteristics may be measured in the range
from approximately 10 kiloHertz (kHz) to approximately 100
MegaHertz (MHz).
[0026] For one embodiment, low frequency measurement system 410 of
FIG. 4 is used to measure one or more electrical characteristics of
integrated inductor 200. Measurement system 410 for one embodiment,
as illustrated in FIG. 5, comprises an impedance analyzer 510, a
first probe 520, and a second probe 530. Impedance analyzer 510 for
one embodiment is manufactured by Agilent Technologies, Inc. of
Palo Alto, Calif. under model number 4294A and can measure
electrical characteristics at frequencies ranging from
approximately 40 Hertz (Hz) to approximately 110 MegaHertz (MHz).
Probes 520 and 530 may each comprise any suitable probe. Each probe
520 and 530 for one embodiment comprises a Picoprobe.RTM. dual
microwave probe manufactured by GGB Industries, Inc. of Naples,
Fla.
[0027] Probes 520 and 530 for one embodiment are coupled to
impedance analyzer 510 using a four-terminal configuration. A
relatively high current terminal 511 and a relatively high voltage
potential terminal 512 are coupled to probe 520 by respective lines
541 and 542. A relatively low voltage potential terminal 513 and a
relatively low current terminal 514 are coupled to probe 530 by
respective lines 543 and 544. Probe 520 may be conductively coupled
to either pad 232 or 236, and probe 530 may be conductively coupled
to the other pad 232 or 236 to measure one or more electrical
characteristics of integrated inductor 200.
[0028] Lines 541, 542, 543, and 544 for one embodiment each
comprise a coaxial cable each having an inner wire 551, 552, 553,
and 554, respectively, surrounded by a shield 556, 557, 558, and
559, respectively. Inner wires 551 and 552 may be conductively
coupled to either pad 232 or 236 and inner wires 553 and 554 may be
conductively coupled to the other pad 232 or 236 to measure one or
more electrical characteristics of integrated inductor 200.
[0029] Each shield 556, 557, 558, and 559 for one embodiment is
driven by impedance analyzer 510 at a voltage that varies as a
function of frequency to compensate for the impedance of the
coaxial cables. Each shield 556, 557, 558, and 559 is then to
remain electrically isolated from ground and from any body of
corresponding probe 520 or 530. For one embodiment, shields 556,
557, 558, and 559 each extend to a location at or near the tip of
corresponding probe 520 or 530. Shields 556, 557, 558, and 559 may
then be conductively coupled to one another at or near integrated
inductor 200 to help obtain increased measurement sensitivity. As
one example, inductance values below one nanoHenry (nH) at
frequencies in the MegaHertz range (MHz) may be measured.
[0030] Shields 556, 557, 558, and 559 may be conductively coupled
to one another in any suitable manner. For one embodiment, shields
556 and 557 may be conductively coupled to one another at or near
the end of each shield 556 and 557 using a foil jumper 562, for
example, and shields 558 and 559 may be conductively coupled to one
another at or near the end of each shield 558 and 559 using a foil
jumper 564, for example. A foil jumper or braid 566 may be soldered
at or near the end of each shield 557 and 558, for example, to
conductively couple shields 556 and 557 to shields 558 and 559.
Foil jumper or braid 566 for one embodiment may comprise two
pieces, each soldered to a separate shield, that are then connected
together after probes 520 and 530 are positioned to measure
integrated inductor 200, for example.
[0031] Impedance analyzer 510 for one embodiment is calibrated with
an open-short-load calibration technique across the tip of each
probe 520 and 530. While impedance analyzer 510 is calibrated,
shields 556, 557, 558, and 559 are to remain electrically isolated
from any calibration substrate as impedance analyzer 510 may then
drive a contacted portion of the calibration substrate. Any
measurements made with impedance analyzer 510 may then be
inaccurate. Shields 556, 557, 558, and 559 are similarly to remain
electrically isolated from integrated inductor 200 while impedance
analyzer 510 is used to measure integrated inductor 200.
[0032] Measurement system 410 for one embodiment is used to measure
one or more circuit element values of electrical model 300 for
integrated inductor 200. Values for inductor 302 and capacitor 308,
for example, may be measured. As any increase resistance from skin
effects and Eddy currents is minimal at relatively low frequencies,
a value for resistor 304 may also be measured.
[0033] For block 104 of FIG. 1, one or more parameters of
integrated inductor 200 are measured at one or more relatively high
frequencies. Any suitable parameters may be measured at any
suitable one or more frequencies using any suitable measuring
equipment. For one embodiment, parameters may be measured in the
range from approximately 30 MegaHertz (MHz) to approximately 20
GigaHertz (GHz).
[0034] For one embodiment, high frequency measurement system 420 of
FIG. 4 is used to measure one or more parameters of integrated
inductor 200. Measurement system 420 for one embodiment, as
illustrated in FIG. 6, comprises a network analyzer 610, a first
probe 620, and a second probe 630. Network analyzer 610 for one
embodiment is manufactured by Agilent Technologies, Inc. of Palo
Alto, Calif. under model number 8720D and can measure parameters of
integrated inductor 200 at frequencies ranging from approximately
0.05 GigaHertz (GHz) to approximately 20 GHz. Probes 620 and 630
may each comprise any suitable probe. Each probe 620 and 630 for
one embodiment comprises a microwave probe manufactured by GGB
Industries, Inc. of Naples, Fla. under model number 40A.
[0035] Network analyzer 610 for one embodiment measures integrated
inductor 200 at a first port between pad 232 and pads 231 and/or
233 and at a second port between pad 236 and pads 235 and/or
237.
[0036] Probes 620 and 630 for one embodiment are coupled to network
analyzer 610 using a two-terminal configuration. A terminal 611 is
coupled to probe 620 by a line 641. A terminal 612 is coupled to
probe 630 by a line 642. Probe 620 may be conductively coupled to
either the first or second port of integrated inductor 200, and
probe 630 may be conductively coupled to the other port of
integrated inductor 200 to measure one or more parameters of
integrated inductor 200. Probes 620 and 630 for one embodiment each
has a ground-signal-ground (GSG) footprint to couple to pads
231-233 and pads 235-237. For another embodiment, each probe 620
and 630 may have a ground-signal (GS) footprint and use only one
pad 231 or 233 with pad 232 and only one pad 235 or 237 with pad
236.
[0037] Lines 641 and 642 for one embodiment each comprise a coaxial
cable each having an inner wire 651 and 652, respectively,
surrounded by a shield 656 and 657, respectively. Inner wire 651
may be conductively coupled to either pad 232 or 236 and inner wire
652 may be conductively coupled to the other pad 232 or 236 to
measure one or more parameters of integrated inductor 200. Shield
656 may be conductively coupled to pads 231 and/or 233 when inner
wire 651 is to be conductively coupled to pad 232. Shield 656 may
be conductively coupled to pads 235 and/or 237 when inner wire 651
is to be conductively coupled to pad 236. Shield 657 may be
conductively coupled to pads 231 and/or 233 when inner wire 652 is
to be conductively coupled to pad 232. Shield 657 may be
conductively coupled to pads 235 and/or 237 when inner wire 652 is
to be conductively coupled to pad 236.
[0038] Network analyzer 610 for one embodiment is calibrated with
an open-short-load calibration technique between the signal tip and
ground node for each probe 620 and 630 and with a through
calibration technique across the signal tips and ground nodes for
each probe 620 and 630.
[0039] For one embodiment, scattering parameters (s-parameters) of
integrated inductor 200 may be measured. S-parameters are power
wave descriptors that allow the input-output relations of a network
to be defined in terms of incident, transmitted, and reflected
power waves. S-parameters may therefore be used to describe how a
circuit behaves.
[0040] Power waves can be fed into and taken from each port of
integrated inductor 200. An incident power wave applied to one port
can be partially reflected by integrated inductor 200 to form a
reflected power wave at that port and partially transmitted through
integrated inductor 200 to form a transmitted power wave at the
other port.
[0041] The incident normalized power waves for the first and second
ports may be represented by complex quantities a.sub.1 and a.sub.2,
respectively, and the transmitted or reflected normalized power
waves for the first and second ports may be represented by complex
quantities b.sub.1 and b.sub.2, respectively. The transmitted or
reflected waves may be expressed in terms of the incident waves by
the matrix equation B=S.times.A, where B is a vector containing
b.sub.1 and b.sub.2, A is a vector containing a.sub.1 and a.sub.2,
and S is a 2.times.2 square matrix of s parameters s.sub.11,
s.sub.12, s.sub.21, and s.sub.22.
[0042] The s-parameters s.sub.11, s.sub.12, s.sub.21, and s.sub.22
for integrated inductor 200 therefore satisfy the following
equations:
b.sub.1=s.sub.11.times.a.sub.1+s.sub.12.times.a.sub.2
b.sub.2=s.sub.21.times.a.sub.1+s.sub.22.times.a.sub.2
a.sub.1=(V.sub.1+Z.sub.0.times.I.sub.1)/(2.times.Z.sub.0.sup.1/2)
a.sub.2=(V.sub.2+Z.sub.0.times.I.sub.2)/(2.times.Z.sub.0.sup.1/2)
b.sub.1=(V.sub.1-Z.sub.0.times.I.sub.1)/(2.times.Z.sub.0.sup.1/2)
b.sub.2=(V.sub.2
-Z.sub.0.times.I.sub.2)/(2.times.Z.sub.0.sup.1/2)
[0043] where V.sub.1 represents a voltage at the first port of
integrated inductor 200, I.sub.1 represents a current at the first
port of integrated inductor 200, V.sub.2 represents a voltage at
the second port of integrated inductor 200, I.sub.2 represents a
current at the second port of integrated inductor 200, and Z.sub.0
represents the characteristic impedance of the connecting lines at
the first and second ports of integrated inductor 200.
[0044] Each s-parameter s.sub.11, s.sub.12, s.sub.21, and s.sub.22
is frequency-dependent and has a real and imaginary part. They can
also be converted to a magnitude and phase angle.
[0045] Where no power waves are applied to the second port, that is
when a.sub.2=0, the power wave incident to the first port, that is
a.sub.1, may be partially reflected from the first port as
reflected power wave b.sub.1=s.sub.11.times.a.sub.1 and partially
transmitted out of the second port as transmitted power wave
b.sub.2=s.sub.21.times.a.sub.1. S-parameter s.sub.11 then
represents the ratio of the reflected power wave at the first port
to the incident power wave at the first port when a.sub.2=0, and
s-parameter s.sub.21 then represents the ratio of the transmitted
power wave at the second port to the incident power wave at the
first port when a.sub.2=0.
[0046] Where no power waves are applied to the first port, that is
when a.sub.1=0, the power wave incident to the second port, that is
a.sub.2, may be partially transmitted out of the first port as
transmitted power wave b.sub.1=s.sub.12.times.a.sub.2 and partially
reflected from the second port as reflected power wave
b.sub.2=s.sub.22.times.a.sub.2. S-parameter s.sub.12 then
represents the ratio of the transmitted power wave at the first
port to the incident power wave at the second port when a.sub.1=0,
and s-parameter s.sub.22 then represents the ratio of the reflected
power wave at the second port to the incident power wave at the
second port when a.sub.1=0.
[0047] The conditions a.sub.1=0 and a.sub.2=0 imply that no power
waves are applied at the first port and the second port,
respectively, of integrated inductor 200. For one embodiment, the
connecting transmission lines for the first and second ports are
terminated into their characteristic impedances to ensure the
conditions a.sub.1=0 and a.sub.2=0, respectively, are
satisfied.
[0048] S-parameters s.sub.11 and s.sub.21 may be measured, for
example, by measuring voltage and current values at the first and
second ports of integrated inductor 200 while a power wave is
applied to the first port, no power waves are applied to the second
port, and the second port is terminated into the lines'
characteristic impedance. S-parameters s.sub.12 and s.sub.22 may be
measured, for example, by measuring voltage and current values at
the first and second ports of integrated inductor 200 while a power
wave is applied to the second port, no power waves are applied to
the first port, and the first port is terminated into the lines'
characteristic impedance.
[0049] Although described as measuring one or more parameters at
two ports of integrated inductor 200, one or more parameters may be
measured at another suitable number of one or more ports of the
integrated circuit device to be characterized. As one example, each
probe 620 and 630 for another embodiment may have only a signal
footprint to measure scattering parameters of integrated inductor
200 at pads 232 and 236.
[0050] For block 106 of FIG. 1, one or more parameters of
integrated inductor 200 are calculated based on the one or more
electrical characteristic measurements. Any suitable parameters may
be calculated based on the one or more electrical characteristic
measurements using any suitable data processing system.
[0051] For one embodiment, data processing system 430 of FIG. 4 is
used to calculate one or more parameters of integrated inductor 200
based on the one or more electrical characteristic measurements.
Data processing system 430 may comprise any suitable circuitry
and/or devices including, for example, one or more processors to
execute instructions to process data, main memory to store
instructions and data that may be readily accessed by a processor,
and a non-volatile memory to store software and data.
[0052] For one embodiment, low frequency measurement system 410
transmits the one or more electrical characteristic measurements to
data processing system 430 over a suitable communication medium.
The one or more electrical characteristic measurements for other
embodiments may be manually entered into data processing system 430
or read by data processing system 430 from a suitable memory
device, for example.
[0053] For one embodiment, scattering parameters (s-parameters) of
integrated inductor 200 may be calculated. For one embodiment, the
s-parameters s.sub.11, s.sub.12, s.sub.21, and s.sub.22 for
integrated inductor 200 may be calculated based on the one or more
measured circuit element values for electrical model 300. Values
for resistor 304 and capacitor 308, for example, have been measured
for block 102. An initial value for inductor 302, for example, has
also been measured for block 102. An initial value for capacitor
310 may be theoretically calculated, for example, based on the
amount of area conductive underpass 226 overlaps conductor 210, the
dielectric material between conductor 210 and conductive underpass
226, and the thickness of the dielectric material between conductor
210 and conductive underpass 226. Initial values for resistor 305
and 306 may be estimated. With initial values determined for each
circuit element of electrical model 300, s-parameters s.sub.11,
s.sub.12, s.sub.21, and s.sub.22 for integrated inductor 200 may be
calculated based on the predictable behavior of electrical model
300.
[0054] For block 108 of FIG. 1, integrated inductor 200 is
characterized based on the calculated one or more parameters and
the measured one or more parameters. Integrated inductor 200 may be
characterized in any suitable manner using any suitable data
processing system.
[0055] For one embodiment, data processing system 430 of FIG. 4 is
used to characterize integrated inductor 200 based on the
calculated one or more parameters and the measured one or more
parameters.
[0056] For one embodiment, high frequency measurement system 420
transmits the measured one or more parameters to data processing
system 430 over a suitable communication medium. The one or more
measured parameters for other embodiments may be manually entered
into data processing system 430 or read by data processing system
430 from a suitable memory device, for example.
[0057] For one embodiment, the calculated one or more parameters
are compared to the measured one or more parameters and one or more
values for electrical model 300 are adjusted to help better fit the
calculated one or more parameters to the measured one or more
parameters. The one or more parameters are then recalculated based
on the updated electrical model 300 and again compared to the
measured one or more parameters. One or more values for electrical
model 300 are iteratively adjusted in this manner until the
calculated one or more parameters and the measured one or more
parameters satisfy a predetermined condition. For one embodiment,
one or more values for electrical model 300 are iteratively
adjusted in this manner until a best fit is obtained.
[0058] For one embodiment, the values for resistor 304 and
capacitor 308 remain fixed through the iterative updating of
electrical model 300 as these values are substantially independent
of frequency. The values of inductor 302, resistor 305, and
resistor 306 are frequency dependent. The values of inductor 302,
resistor 305, resistor 306, and/or capacitor 310 may each be
iteratively adjusted within an estimated predetermined range of
values.
[0059] For one embodiment where the calculated and measured
parameters are s-parameters, one or more values for electrical
model 300 are iteratively adjusted such that the magnitude and
phase angles of the ratios of each calculated s-parameter match
those of the corresponding measured s-parameter. For another
embodiment, one or more values for electrical model 300 are
adjusted such that the magnitude of the normalized differences
between the calculated s-parameters and the measured s-parameters
are minimized.
[0060] The values for electrical model 300 obtained by fitting the
calculated one or more parameters to the measured one or more
parameters may be used to determine the quality factor Q, parasitic
resistances and capacitances, and the inductance L of integrated
inductor 200 as a function of frequency. The resonance frequency
.omega..sub.r for integrated inductor 200 may also be
determined.
[0061] Integrated inductor 200 may therefore be characterized for
block 108 by the updated electrical model 300, by any one or more
determined electrical characteristics for integrated inductor 200,
and/or by the calculated one or more parameters based on the
updated electrical model 300.
[0062] Although described in the context of scattering parameters,
other suitable parameters such as open circuit impedance parameters
(z-parameters) or short circuit admittance parameters
(y-parameters) for example, may also be used. Any parameters
measured for block 104 and/or calculated for blocks 106 and 108 may
be converted into any other suitable parameters in iteratively
analyzing and updating electrical model 300.
[0063] Data processing system 430 for one embodiment outputs a
characterization of integrated inductor 200 to output device 440
for analysis by a user. Output device 440 may comprise a display or
printer, for example. Any suitable characterization of integrated
inductor 200 as determined by data processing system 430 may be
output to output device 440 for display or presentation in any
suitable manner.
[0064] In the foregoing description, the invention has been
described with reference to specific exemplary embodiments thereof.
It will, however, be evident that various modifications and changes
may be made thereto without departing from the broader spirit or
scope of the present invention as defined in the appended claims.
The specification and drawings are, accordingly, to be regarded in
an illustrative rather than a restrictive sense.
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