U.S. patent application number 12/495532 was filed with the patent office on 2010-06-10 for electro-optic modulator on rib waveguide.
This patent application is currently assigned to Cornell Research Foundation, Inc.. Invention is credited to Carlos Angulo Barrios, Vilson Rosa de Almeida, Michal Lipson.
Application Number | 20100142877 12/495532 |
Document ID | / |
Family ID | 34526155 |
Filed Date | 2010-06-10 |
United States Patent
Application |
20100142877 |
Kind Code |
A1 |
Barrios; Carlos Angulo ; et
al. |
June 10, 2010 |
ELECTRO-OPTIC MODULATOR ON RIB WAVEGUIDE
Abstract
An electro-optic modulator is formed on a silicon-on-insulator
(SOI) rib waveguide. An optical field in the modulator is confined
by using an electrically modulated microcavity. The microcavity has
reflectors on each side. In one embodiment, a planar Fabry-Perot
microcavity is used with deep Si/SiO.sub.2 Bragg reflectors.
Carriers may be laterally confined in the microcavity region by
employing deep etched lateral trenches. The refractive index of the
microcavity is varied by using the free-carrier dispersion effect
produced by a p-i-n diode formed about the microcavity. In one
embodiment, the modulator confines both optical field and charge
carriers in a micron-size region.
Inventors: |
Barrios; Carlos Angulo;
(Toledo, ES) ; Lipson; Michal; (Ithaca, NY)
; de Almeida; Vilson Rosa; (Ithaca, NY) |
Correspondence
Address: |
SCHWEGMAN, LUNDBERG & WOESSNER, P.A.
P.O. BOX 2938
MINNEAPOLIS
MN
55402
US
|
Assignee: |
Cornell Research Foundation,
Inc.
Ithaca
NY
|
Family ID: |
34526155 |
Appl. No.: |
12/495532 |
Filed: |
June 30, 2009 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10821627 |
Apr 9, 2004 |
7555173 |
|
|
12495532 |
|
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|
60461705 |
Apr 9, 2003 |
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Current U.S.
Class: |
385/2 ;
385/14 |
Current CPC
Class: |
G02F 1/025 20130101;
G02F 2201/307 20130101 |
Class at
Publication: |
385/2 ;
385/14 |
International
Class: |
G02F 1/035 20060101
G02F001/035 |
Goverment Interests
GOVERNMENT FUNDING
[0002] The invention described herein was made with U.S. Government
support under Contract Number F49620-02-1-0396 awarded by Defense
Advanced Research Project Agency. The United States Government has
certain rights in the invention.
Claims
1. A method comprising: providing light to a silicon optical
resonator; modulating the light in the silicon optical resonator by
changing the carrier concentration in the optical resonator to vary
its refractive index.
2. The method of the claim 1 where the light is provided to the
silicon optical resonator by an optically coupled waveguide.
3. The method of claim 1 wherein the optical resonator is a ring
resonator.
4. The method of claim 1 wherein the optical resonator is a
Fabry-Perot resonator.
5. The method of claim 1 wherein the optical resonator is an
optical cavity.
6. The method of claim 1 and further comprising providing a p doped
region and an n doped region adjacent to the optical resonator.
7. The method of claim 6 wherein the doped regions are heavily
doped.
8. The method of claim 7 wherein the heavily doped regions form a
p-i-n diode about the resonator.
9. The method of claim 8 wherein the heavily doped regions are
positioned to selectively inject carriers into the optical
resonator responsive to a forward bias voltage across the diode and
to deplete carriers in the optical resonator responsive to a
reverse bias voltage across the diode.
10. A method comprising: providing light to a silicon optical
resonator; modulating the light in the silicon optical resonator by
changing its refractive index.
11. The method of claim 10 wherein the refractive index is changed
by varying the carrier concentration in the optical resonator.
12. The method of the claim 10 where the light is provided to the
silicon optical resonator by an optically coupled waveguide.
13. The method of claim 10 wherein the optical resonator is a ring
resonator.
14. The method of claim 10 wherein the optical resonator is a
Fabry-Perot resonator.
15. The method of claim 10 wherein the optical resonator is an
optical cavity.
16. The method of claim 10 and further comprising providing a p
doped region and an n doped region adjacent to the optical
resonator.
17. The method of claim 16 wherein the doped regions are heavily
doped.
18. The method of claim 17 wherein the heavily doped regions form a
p-i-n diode about the resonator.
19. The method of claim 18 wherein the heavily doped regions are
positioned to selectively inject carriers into the optical
resonator responsive to a forward bias voltage across the diode and
to deplete carriers in the optical resonator responsive to a
reverse bias voltage across the diode.
20. A method comprising: providing light to a silicon waveguide;
modulating the light in the silicon waveguide by varying the
refractive index of a silicon optical resonator coupled to the
silicon waveguide.
21. The method of claim 20 wherein the refractive index is varied
by changing the carrier concentration in the silicon optical
resonator.
22. The method of claim 21 wherein varying the refractive index
changes the coupling efficiency of the silicon optical waveguide to
the silicon waveguide.
23. A method comprising: providing light to a silicon waveguide;
and modulating the light in the silicon waveguide by varying the
coupling efficiency of a silicon optical resonator to the silicon
waveguide.
Description
RELATED APPLICATION
[0001] This application is a continuation of U.S. patent
application Ser. No. 10/821,627, filed Apr. 9, 2004, which issued
Jun. 30, 2009 as 7,555,173, which claims priority to U.S.
Provisional Application Ser. No. 60/461,705 (entitled
Low-Power-Consumption Short-Length and High-Modulation-Depth
Silicon Electro-Optic Modulator, filed Apr. 9, 2003) which
applications are incorporated herein by reference.
FIELD OF THE INVENTION
[0003] The present invention relates to an electro-optic modulator,
and in particular to an electro-optic modulator formed on a rib
waveguide.
BACKGROUND OF THE INVENTION
[0004] Silicon-based photonic components working at 1.3 and
1.55-.mu.m fiber-optic communications-wavelengths for fiber-to-home
interconnects and local area networks (LAN) are a subject of
intensive research because of the possibility of integrating
optical elements and advanced electronics together on a silicon
substrate using bipolar or complementary metal-oxide semiconductor
(CMOS) technology. The resulting optoelectronic integrated circuit
(OEIC) should exhibit a better performance than optical and
electrical circuits when considered separately, and present a
significantly lower cost than those based on III-V semiconductor
materials.
[0005] Si passive structures, such as waveguides, couplers and
filters have been extensively studied. Less work has been reported
on Si active (or tunable) integrated devices such as modulators and
switches, despite their importance as means of manipulating light
beams for information processing (e.g., coding-decoding, routing,
multiplexing, timing, logic operations, etc) in integrated-optic
circuits. Some Si-based thermo-optic and electro-optic active
devices have been demonstrated. In thermo-optic devices, the
refractive index of Si is modulated by varying the temperature,
inducing a phase modulation which in turn is used to produce an
intensity modulation at the output of the device. For Si, the
thermal change of the real optical refractive index is large.
Nevertheless, the thermo-optic effect is rather slow and can only
be used up to 1 MHz modulation frequencies. For higher modulation
frequencies, up to few hundreds of MHz, electro-optic devices are
required.
[0006] Most of the proposed electro-optic devices exploit the free
carrier dispersion effect to change both the real refractive index
and optical absorption coefficient. This is because the unstrained
pure crystalline Si does not exhibit linear electro-optic (Pockels)
effect and the refractive index changes due to the Franz-Keldysh
effect and Kerr effect are very weak. In free-carrier absorption
modulators (FCAM), changes in the optical absorption of the
structure are directly transformed into an output intensity
modulation. Phase modulation in a specific region of optical
devices, such as Mach-Zehnder modulators, total-internal-reflection
(TIR) based structures, cross-switches, Y-switches and Fabry-Perot
(F-P) resonators, is also used to modulate the output
intensity.
[0007] Free-carrier concentration in electro-optic devices can be
varied by injection, accumulation, depletion or inversion of
carriers. Si-based electro-optic modulators based on p-i-n diodes,
metal-oxide-semiconductor field-effect-transistors (MOSFET) and
bipolar-mode-field-effect-transistor (BMFET) structures have been
proposed. Most silicon electro-optic intensity modulators and
switches present some common features: they require long
interaction distances and injection current densities higher than 1
kA/cm.sup.2 in order to obtain a significant modulation depth. Long
interaction lengths are undesirable in order to achieve high levels
of integration and miniaturization for fabricating low-cost compact
chips. High current densities may induce thermo-optic effect due to
heating of the structure, and cause an opposite effect on the
refractive index change as that produced by free-carrier
dispersion, reducing its effectiveness. There is therefore an
urgent need, from the integration point of view, for structures
that can be implemented in a micron-size region offering low
current density, low power consumption and
high-modulation-depth.
SUMMARY OF THE INVENTION
[0008] An electro-optic modulator is formed on a
silicon-on-insulator (SOI) rib waveguide. An optical field in the
modulator is confined by using an electrically modulated
microcavity. The microcavity has reflectors on each side. In one
embodiment, a planar Fabry-Perot microcavity is used with deep
Si/SiO.sub.2 Bragg reflectors. Carriers may be laterally confined
in the microcavity region by employing deep etched lateral
trenches. The refractive index of the microcavity is varied by
using the free-carrier dispersion effect produced by a p-i-n diode
formed about the microcavity. In one embodiment, the modulator
confines both optical field and charge carriers in a micron-size
region.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] FIG. 1 shows a perspective block schematic view of a
partially finished electro-optic modulator according to an
embodiment of the invention.
[0010] FIG. 2 shows a cross section view of the modulator of FIG. 1
according to an embodiment of the invention.
[0011] FIG. 3 shows a schematic perspective diagram of a cavity
region according to an embodiment of the invention.
[0012] FIG. 4 shows an example TE.sub.00 mode distribution in the
cavity region according to an embodiment of the invention.
[0013] FIG. 5 is a top view provided by a Scanning Electron
Microscope (SEM) photograph of a partially finished electro-optic
modulator according to an embodiment of the invention.
DETAILED DESCRIPTION OF THE INVENTION
[0014] In the following description, reference is made to the
accompanying drawings that form a part hereof, and in which is
shown by way of illustration specific embodiments in which the
invention may be practiced. These embodiments are described in
sufficient detail to enable those skilled in the art to practice
the invention, and it is to be understood that other embodiments
may be utilized and that structural, logical and electrical changes
may be made without departing from the scope of the present
invention. The following description is, therefore, not to be taken
in a limited sense, and the scope of the present invention is
defined by the appended claims.
[0015] An electro-optic modulator may be formed on a
silicon-on-insulator (SOI) rib waveguide. An optical field in the
modulator is confined by using an electrically modulated
microcavity. The microcavity has reflectors on each side. In one
embodiment, a planar Fabry-Perot microcavity is used with deep
Si/SiO.sub.2 Bragg reflectors. Carriers may be laterally confined
in the microcavity region by employing deep etched lateral
trenches. The refractive index of the microcavity is varied by
using the free-carrier dispersion effect produced by a p-i-n diode
formed about the microcavity. In one embodiment, the modulator
confines both optical field and charge carriers in a micron-size
region.
[0016] FIG. 1 shows a perspective block schematic view of a
partially finished electro-optic modulator 100. The structure will
be described first, followed by a fabrication description and a
description of potential operating principles and characteristics
of various embodiments. For ease of illustration, an SiO.sub.2
layer covering the modulator 100 is not shown in FIG. 1. The
modulator 100 is formed on a buried oxide (BOX) layer 110 supported
by a silicon substrate 115. The modulator 100 consists of a
Fabry-Perot (F-P) 120 cavity formed by two distributed Bragg
reflectors (DBRs) 125, 130 in a SOI rib waveguide 135. Other types
of reflectors may be used in further embodiments.
[0017] Some typical dimensions and doping for the modulator 100 are
shown in FIG. 2, in which an SiO.sub.2 layer 210 covering the
modulator 100 is shown. A top silicon layer 140 (device layer) is
approximately 1.5-.mu.m-high (h.sub.d) with a n-type background
doping concentration of 10.sup.15 cm.sup.-3. Both DBRs 125, 130
consist of the same number of Si/SiO.sub.2 periods down to the BOX
layer 110. The DBRs are formed of alternating Si and SiO.sub.2
regions as indicated at 215 and 220 respectively. The length of the
Si and SiO.sub.2 regions is denoted as L.sub.Si and L.sub.ox,
respectively.
[0018] FIG. 3 shows a schematic perspective diagram of the cavity
120 region. As in FIG. 1, the covering layer of SiO.sub.2 is not
shown for better visualization. The rib 135 width and height are
chosen to be approximately w.sub.rib=1.5 .mu.m and h.sub.rib=0.45
.mu.M, respectively. Two lateral trenches 310, 315 down to the BOX
layer 110 are formed on sides of the rib with a width of
approximately w.sub.tr=150 nm. The lateral trenches are
substantially transverse to the Si and SiO.sub.2 regions of the
DBRs in one embodiment, and substantially parallel to the rib
waveguide 135. The width of the cavity region 120 delimited by the
lateral trenches 310, 315 is W.sub.pin. Heavily doped p.sup.+ and
n.sup.+ regions 320 and 325 are defined in the cavity region, at
both sides of the rib 135, separated the rib by regions 330, 335
w.sub.sep=0.5 .mu.m from the corresponding rib edge and extended to
the corresponding lateral trenches. These highly-doped regions form
p and n portions of a p-i-n diode above the cavity under the rib
waveguide 135. Conductors and a voltage source 150 are coupled to
the heavily doped regions. The voltage is then used to modulate
light passing through the modulator 100.
[0019] A Gaussian doping profile is assumed for both highly-doped
regions with a maximum peak concentration of approximately
10.sup.20 cm.sup.-3 at y=[(h.sub.d-h.sub.rib)-0.01 .mu.m]=1.04
.mu.m, located along a line from x=(W.sub.pin/2) to
x=[(w.sub.rib/2)+w.sub.sep] for one doped region and from
x=-(W.sub.pin/2) to x=-[(w.sub.rib/2)+w.sub.sep] for the other one,
and a standard deviation along the y-axis of 0.05 .mu.m. At
x>-[(w.sub.rib/2)+w.sub.sep] for one doped region and
x<[(w.sub.rib/2)+w.sub.sep] for the other one, the doping drops
off laterally (along the x-axis) with a standard deviation of 0.035
.mu.m. The length of the highly-doped regions is equal to that of
the cavity (L.sub.cav). Metal electrodes contact both the p.sup.+
(anode) and n.sup.+ (cathode) regions of the p-i-n diode with the
same width and length as those. A planar silicon dioxide layer 210
covering the whole structure has been assumed.
[0020] The microcavity provides for the confinement and enhancement
of the optical field in a very small region. The transmission of
these structures is highly sensitive to small index changes in the
cavity, making microcavities adequate for intensity modulation
applications in a short length. In addition, since the refractive
index modulation can be confined to the cavity region, the
electrical power to produce the desired phase change can be made
very small.
[0021] Carrier confinement in the active region of the
electro-optic device helps to optimize the device performance. The
confinement is illustrated in FIG. 4, which shows an example
TE.sub.00 mode distribution in the cavity for W.sub.pin=8 .mu.m,
h.sub.rib=0.45 .mu.m, w.sub.rib=1.5 .mu.m and h.sub.d=1.5 .mu.m. In
one embodiment, the use of lateral trench isolation 310, 315 in a
silicon p-i-n phase modulator may improve both the dc and transient
device performances. This is because the lateral carrier diffusion
that does not contribute to alter the refractive index in the
central active region of the modulator is reduced, allowing a
better use of the injected carriers. In addition, carrier
confinement permits high scale integration due to electrical
isolation between neighbor devices.
[0022] Formation of the electro-optic modulation device 100 may
utilize different processes. In one embodiment, a pattern for the
trenches of the distributed Bragg reflectors 125 and 130, and the
cavity isolation trenches 310 and 315 is defined by e-beam
lithography in an oxide file grown on silicon layer 140. The
trenches are etched down to the buried oxide layer 110 by reactive
ion etching (RIE) using the top oxide layer as a mask. The trench
sidewalls are then passivated by thermal oxide, and the trenches
are filled with SiO2 by low pressure chemical vapor deposition
(LPCVD).
[0023] The trenches of the distributed Bragg reflectors 125 and 130
should be fairly smooth and vertical for optimal optical
performance of the DBRs. Conventional CMOS Si processing tools may
be used to obtain small roughness and high verticality.
[0024] The rib waveguide 135 is then defined with photoresist,
using UV photolithography. The rib is then etched into the surface
using RIE that has low selectivity between Si and SiO2. The
photoresist is then removed and the etched surfaces are passivated
by thermal oxide growth. FIG. 5 is a top view provided by a
Scanning Electron Microscope (SEM) photograph of the device at this
point in the example fabrication process. It illustrates at least
the DBRs 125, 130, the isolation trenches 310 and 315, and the rib
waveguide 135.
[0025] The entire surface of the device is then covered in oxide,
such as by PECVD, chemical vapor deposition (CVD) or spin-on-glass
(SOG) techniques. Windows are defined and etched for ion
implantation. The windows may be defined using common lithographic
processes, such as e-beam or UV lithography, and the etching in one
embodiment comprises RTE. The doped areas 315 and 320 are formed,
and ohmic contacts are produced on them. Metal pads on the ohmic
contacts may be defined for final bounding.
[0026] In one embodiment, an undoped silicon layer with a
background doping of n=10.sup.15 cm.sup.-3 is used for the diode
layer between the highly doped p and n portions of the p-i-n diode.
Low doping in the waveguide helps avoid free carrier absorption
losses. Other possibilities, besides the p-i-n, diode for
modulation, are MOS and MOSFET devices. The former produces little
effect on the refractive index although it has no dc power
consumption. The latter may be implemented by placing a gate
electrode on top of the rib waveguide, and keeping the highly doped
n and p regions (cathode and anode). The MOSFET may improve the
speed operation with respect to the p-i-n case with the use of high
gate voltages. Less variation of the refractive index implies a
longer device (along the z-axis) in order to produce the same
effect as that produced by a high refractive index change in a
short device.
[0027] The DBR trenches in one embodiment, are substantially
transverse or perpendicular to the rib waveguide (that is, the
trenches that formed the two DBRs). The DBR trenches also define
the cavity (length). Light goes back and forth between the two DBRs
(each DBR acts as a mirror perpendicular to the waveguide). The
lateral trenches (one at each side of the rib waveguide) parallel
to the waveguide are not necessary for the cavity to work, and by
placing them at a correct distance from the waveguide, they should
not affect the optical (passive) performance of the cavity. The
role of the lateral trenches is essentially for electrical
isolation and carrier confinement, that is, keep carriers injected
from the high doped n and p regions from spreading out laterally.
In this way, by using the lateral trenches, the drive current (or
injected carriers) are efficiently used only in the
cavity/waveguide region where they should change the refractive
index. Thus, the device will operate without the trenches. If
desired, other means of carrier confinement may be used.
[0028] An electrical model may utilize a commercially available
two- and three-dimensional simulation package, ATLAS from SILVACO
employed to achieve the electrical calculations. The program
simulates internal physics and device characteristics of
semiconductor devices by solving Poisson's equation and the charge
continuity equations for electrons and holes numerically. The
software allows a complete statistical approach (Fermi-Dirac
statistics) when, for example, heavily doped regions are
considered. Carrier recombination models include Shockley-Read-Hall
(SRH) recombination, Auger recombination and surface recombination.
A concentration and temperature dependent model has been used to
model the carrier mobility. The simulation package also includes
thermal modeling, which accounts for Joule heating, heating and
cooling due to carrier generation and recombination, and the
Peltier and Thomson effects. The heat flow equation is solved for
specific combination of heat sink structures, thermal impedances
and ambient temperatures.
[0029] In simulations, a carrier concentration dependent SRH
recombination model may be employed, with an estimated carrier
lifetime in the Si device layer (intrinsic region) of electrons and
holes of .tau..sub.p=700 ns and .tau..sub.p300 ns, respectively,
for a n-type doping concentration of 10.sup.15 cm.sup.-3. Ohmic
contacts without additional contact resistance or capacitance may
be assumed. In addition, the electrical contacts (electrodes) may
be considered to act as thermal contacts (heat sinks) at a fixed
temperature of 300 K.
[0030] A finite-difference time-domain (FDTD) method and transfer
matrix method (TMM) may be used for optical analysis of the DBRs
and F-P cavity. From the values of the electron and hole
concentrations at any point of the p-i-n/cavity region, the induced
real refractive index and optical absorption coefficient variations
(.DELTA.n and .DELTA.a, respectively) at a wavelength of 1.55 .mu.m
produced by free-carrier dispersion (highly-doped regions and
carrier injection in the cavity) are calculated by using:
.DELTA.n=.DELTA.n.sub.e+.DELTA.n.sub.h=-[8.8.times.10.sup.-22.DELTA.N+8.-
5.times.10.sup.-18(.DELTA.P).sup.0.8] [1]
.DELTA.a=.DELTA.a.sub.e+.DELTA.a.sub.h=8.5.times.10.sup.-18.DELTA.N+6.0.-
times.10.sup.-18.DELTA.P [2]
where [0031] .DELTA.n.sub.e is the refractive index change due to
electron concentration change; [0032] .DELTA.n.sub.h is the
refractive index change due to hole concentration change; [0033]
.DELTA.N is the electron concentration change in cm.sup.-3; [0034]
.DELTA.P is the hole concentration change in cm.sup.-3; [0035]
.DELTA.a.sub.e(in cm.sup.-1) is the absorption coefficient
variations due to .DELTA.N; [0036] .DELTA.a.sub.h (in cm.sup.-1) is
the absorption coefficient variation due to .DELTA.P.
[0037] Diffraction losses and material optical absorption may be
calculated with the FDTD method. The fundamental mode of the
waveguide is launched at the input and the reflected (R) and
transmitted (T) powers are recorded by virtual detectors. Losses
(A) are obtained by using the relation R+T+A=1. Scattering losses,
due to surface roughness, are neglected. A one-dimensional (1-D)
(along the propagation direction) model may be used based on the
TMM to calculate the transmission and reflection spectra of the
structure. The effect of the transverse and lateral geometry of the
structure, the diffraction and the absorption are considered in the
1-D model by using an equivalent complex effective refractive index
obtained from the three-dimensional FDTD calculations of the entire
structure for a short cavity length (.lamda..sub.p/2n.sub.Si, where
.lamda..sub.p=1.55 .mu.m and n.sub.Si is the effective refractive
index of the Si region). The purpose of using this technique is to
simplify the calculations by employing a flexible model that allows
predicting the optical performance of the device for different
design parameters in a shorter time.
[0038] Both electron (N) and hole (P) concentrations in the cavity
region are nearly equal for forward bias voltages between 0.8 V and
1.1 V, assuming a surface recombination velocity of 10.sup.2 cm/s
at the interface between the Si cavity and the surrounding
SiO.sub.2. This surface recombination velocity may correspond to Si
surfaces passivated with thermally grown SiO.sub.2. The p-i-n diode
operates under high injection condition within the considered
forward bias voltage range. The injected carrier distribution is
highly uniform throughout the central region of the cavity. This
result simplifies the optical calculations since the spatial
distribution of the refractive index and absorption coefficient in
the cavity when carriers are injected in the guiding region can be
considered uniform.
[0039] A carrier concentration of N=P=3.times.10.sup.17 cm.sup.-3
is predicted for a forward bias of 0.87 V which induces a real
refractive index change of .DELTA.n=-10.sup.-3 [Eq. 1] and an
absorption coefficient variation of .DELTA..alpha.=4.35 cm.sup.-1
[Eq. 2].
[0040] Simulations show that some of the injected free carriers
into the low-doped n-type Si layer spread laterally away from the
central guiding region as the distance between the lateral trenches
(W.sub.pin) is increased. This leads to a leakage current component
that increases the necessary dc power in order to obtain the
targeted carrier concentration (refractive index change) in the
central guiding region. Particularly, the dc power consumption for
W.sub.pin equal to 4.5, 8 and 12 .mu.m was calculated to be 0.81,
1.51 and 2.27 .mu.W per .mu.m length, respectively, for a free
carrier concentration in the cavity of 3.times.10.sup.17 cm.sup.-3.
That is, the dc power increases 180% when W.sub.pin is varied from
4.5 .mu.m to 12 .mu.m, indicating the need to confine carriers in
the guiding region in order to reduce the drive dc power.
[0041] Hereafter, a W.sub.pin value of 8 .mu.m is assumed as a
compromise between low power consumption and good optical
properties. In the same way as occurs in the lateral direction
(x-axis), carriers may diffuse along the longitudinal direction
(z-axis) if no carrier confinement means are accounted. By using
lateral and longitudinal trenches down to the BOX layer, electrical
isolation of the cavity is achieved along all directions leading to
injection carrier confinement in the central guiding region,
suppressing the leakage current due to carrier spreading.
[0042] Table I shows the drive current density (J), percentage of
the current component due to surface recombination (J.sub.s) to the
total current (J), dc power (P.sub.dc) and free-carrier
concentration (N, P) in the central region of the cavity for the
aforementioned surface recombination velocities. The current
density is defined as the total injection current divided by the
longitudinal cross-section area of the cavity at the middle (x=0).
In all the cases, a forward voltage of 0.87 V and a cavity length
of 1 .mu.m are assumed. As expected, it is seen that the injection
current and electrical power increase as the surface recombination
velocity is increased. For case (b) the injection current component
due to surface recombination (leakage current) represents 28.1% of
the total current, whereas this leakage component reaches a
significant 98.5% of the total injected current for case (c). The
dissipated power for case (b) increases by 32.4% as compared to
case (a), as a consequence of leakage current via surface
recombination; nevertheless, the total drive power is kept to a low
value.
TABLE-US-00001 TABLE I S.sub.p, S.sub.n (cm/s) J (A/cm.sup.2)
J.sub.s/J (%) P.sub.dc (.mu.W) N, P (cm.sup.-3) 0 83.33 0 1.14 3
.times. 10.sup.17 10.sup.2 115.86 28.1 1.51 3 .times. 10.sup.17
10.sup.5 5514.6 98.5 71.9 5 .times. 10.sup.16
[0043] These results indicate that of electrical passivation of the
surfaces of the p-i-n/cavity region may be used to reduce the
component of the total current due to surface recombination and,
therefore, the dc power consumption. In addition, surface
passivation by thermal SiO.sub.2 is also advantageous from the
optical point of view since it reduces the scattering losses from
the surface. Hereafter, a surface recombination velocity of
S.sub.p=S.sub.n=10.sup.2 cm/s will be assumed. For this case, the
calculated increase of the device temperature was less than
10.sup.-2 K.
[0044] The effect of the contact resistance of the electrodes on
the total power is not significant for a forward injection current
of 1.74 .mu.A/.mu.m (V=0.87 V) if proper contact metallization is
achieved. For example, if Co/Si contacts are assumed on both
electrodes, the corresponding contact resistance values, after a
rapid thermal annealing (RTA) process, on the highly doped n.sup.+
and p.sup.+ regions should be around 1.6.times.10.sup.-7
.OMEGA.cm.sup.2 and 8.9.times.10.sup.-7 .OMEGA.cm.sup.2,
respectively. This means a total series resistance due to the
contacts of 38.2 .OMEGA..mu.m, which leads to a negligible increase
of 1.1.times.10.sup.-10 W/.mu.m in dc power consumption.
[0045] An excitation voltage pulse with V.sub.OFF=0 V (OFF-state)
and V.sub.ON=0.87 V (ON-state) may be used for the transient
analysis. The duration of both OFF and ON states is 300 ns, whereas
both the rise time and fall time for the voltage bias step are 0.1
ns. For the refractive index modulation, the turn-on time
(t.sub.ON) is defined as the time required for the refractive index
change (.DELTA.n) to change from 10% to 90% of its maximum absolute
value (|.DELTA.n|). Likewise, the turn-off time (t.sub.OFF) is
defined as the time needed for the refractive index change to vary
from 90% to 10% of its maximum absolute value. The turn-on time
(15.27 ns) is longer than the turn-off time (5.72 ns) in one
embodiment.
[0046] The decrease of refractive index occurs because of carrier
injection (forward bias) by diffusion from the highly doped regions
into the intrinsic (low doped) material. This is because the
characteristic length for diffusive transport in the intrinsic
region, 1-(D.sub.a.tau..sub.eff).sup.1/2=5.2 .mu.m [D.sub.a=18
cm.sup.2/s is the ambipolar diffusion coefficient and .tau..sub.eff
(=t.sub.ON=15.27 ns) is the effective carrier lifetime in the
intrinsic region], is comparable to the lateral dimension of the
device.
[0047] On the other hand, the increase of refractive index results
from depletion of carriers in the central guiding region. Carrier
removal is achieved by both carrier recombination and the increased
electric field across the intrinsic region. A higher reverse
V.sub.OFF would result in a shorter turn-off time since the
depletion electric field is increased.
[0048] The simulations reveal that both voltage rise and fall
processes lead to the appearance of current peaks for a short time
interval. In particular, a remarkable reverse current peak occurs
during the transition from V.sub.ON to V.sub.OFF. the transient
current and maximum device temperature In both cases, it is
observed that the transient reverse current peak during the
stepping down of the applied voltage from V.sub.ON=0.87 V to
V.sub.OFF=0 V and -5V, (2.times.10.sup.-3 and 1.times.10.sup.-3
A/.mu.m for V.sub.OFF=-5V and V.sub.OFF=0V, respectively) is around
three orders of magnitude higher than the corresponding
steady-state current (1.74 .mu.A/.mu.m), and the maximum current
for V.sub.OFF=-5V is twice higher than that reached for
V.sub.OFF=0V. The higher the reverse V.sub.OFF, the shorter becomes
the rise time and the larger the transient current peak.
[0049] This leads to an appreciable increase of the device
temperature, around 1K for V.sub.OFF=-5V. For .lamda.=1.55 .mu.n
the thermal change of refractive index of silicon is
.differential.n/.differential.T=+1.86.times.10.sup.-4K.sup.-1. That
is, a maximum temperature increase of 1 K corresponds to an
increase of the refractive index of +1.86.times.10.sup.-4, which is
one order of magnitude smaller than that induced by the
free-carrier dispersion (.DELTA.n=-10.sup.-3). Therefore, the
thermo-optic effect for both V.sub.OFF=0V and V.sub.OFF=-5V is
predicted to be not significant.
[0050] Another factor that could limit the switching time of the
device is the photon lifetime in the F-P cavity. The photon
lifetime (.tau..sub.ph) corresponds to the time for the stored
energy in the cavity to vanish after the external supply is shut
off. However, the photon lifetime values for the considered device
configurations are calculated to be on the order of tens to
hundreds of ps, that is, much shorter than the switching times
obtained in the electrical transient analysis. Therefore carrier
diffusion, for the turn-on time, and carrier depletion, for the
turn-off time, should be pointed out as the switching speed
limiting factors in the device under study.
[0051] It must be noted that a larger value of W.sub.pin, would
increase the switching time (t.sub.s) since the refractive index
must be changed (carrier injection and depletion) in a larger
volume. For example, the calculated t.sub.s for W.sub.pin=12 .mu.m,
V.sub.ON=0.87 V and V.sub.OFF=-5 V is predicted to be 18.56 ns,
that is, 17.7% larger than that calculated for W.sub.pin=8
.mu.m.
[0052] Simulations show single-mode operation in the SOI rib
waveguide for both TE and TM polarization modes, for h.sub.rib=0.45
.mu.m, w.sub.rib=1.5 .mu.m and h.sub.d=1.5 .mu.m. The distance
between the lateral trenches, W.sub.pin=8 .mu.m, was chosen in
order to minimize the optical mode mismatch between the DBR and the
cavity region, as well as the power consumption and switching time.
FIG. 4 shows the intensity profile of the propagating fundamental
TE mode (TE.sub.00) for W.sub.pin=8 .mu.m. The overlap integral
between the TE.sub.00 mode in the cavity region and TE.sub.00 mode
in the DBR region was calculated to be 99.99%. Lower W.sub.pin
values may lead to unstable single mode operation. The free-carrier
absorption losses of the propagating mode due to the highly-doped
p.sup.+ and n.sup.+ regions were found to be negligible because of
the small overlap between these regions and the optical mode.
Free-carrier absorption losses due to carrier injection [ON state
(N=P=3.times.10.sup.17 cm.sup.-3)] were calculated to be 20.6
dB/cm.
[0053] The lengths of the Si and SiO.sub.2 regions of the DBRs were
chosen according to the condition
n.sub.SiL.sub.Si+n.sub.oxL.sub.ox=.lamda..sub.p/2, where n.sub.Si
and n.sub.ox are the effective refractive indeces of the Si and
SiO.sub.2 regions, respectively, and .lamda..sub.p=1.55 .mu.m.
Particularly, we chose L.sub.Si=160 nm and L.sub.ox=150 nm, which
lead to an optical path n.sub.oxL.sub.ox smaller than
n.sub.SiL.sub.Si in order to minimize diffraction losses. The
calculated reflectivity spectrum for the TE.sub.00 mode of a 6
Si/SiO.sub.2-period DBR indicated a stop-band of .about.800 nm and
a maximum reflectivity of 98.7% (transmittivity=0.57% and
diffraction losses=0.73%).
[0054] The modulation depth (M) is defined as:
M = 1 - T MIN T MAX = P OFF - P ON P OFF ( 3 ) ##EQU00001##
where T.sub.MAX(MIN) is the maximum(minimum) transmittivity, i.e.,
the ratio between the output in the OFF(ON)-state and the input
power, P.sub.OFF is the output optical power from the device when
there is no free-carrier injection (OFF-condition), and P.sub.ON is
the output optical power from the modulator when plasma injection
occurs into the cavity (ON-condition). Hereafter, the maximum
transmittivity will be called just transmittivity (T). The output
optical power is calculated at .lamda..sub.p=1.55 .mu.m (probe
wavelength), which corresponds to a cavity resonance wavelength in
the OFF-condition.
[0055] Table II shows the full width at half maximum (FWHM) of the
spectral intensity (.DELTA..lamda.) of the resonance peak at 1.55
.mu.m, modulation depth (M), transmittivity (T) and dc dissipated
power (P.sub.dc) for different cavity lengths and number of DBR
periods.
TABLE-US-00002 TABLE III L.sub.cav (.mu.m) periods .DELTA..lamda.
(nm) M (%) T (%) P.sub.dc (.mu.W) 5.684 3 1.275 27.6 86.3 7.8
(25.lamda..sub.p/2n.sub.Si) 4 0.396 82.3 59.3 5 0.170 93.8 21.4
9.074 3 0.807 50.3 86.3 12.3 (40.lamda..sub.p/2n.sub.Si) 4 0.251
89.8 59.3 5 0.108 98.4 21.4 18.117 3 0.408 80.8 86.3 24.5
(80.lamda..sub.p/2n.sub.Si) 4 0.127 97.7 59.3 5 0.055 99.6 21.4
22.638 3 0.327 86.8 86.3 30.6 (100.lamda..sub.p/2n.sub.Si) 4 0.102
98.5 59.3 5 0.044 99.7 21.4
[0056] A refractive index change in the cavity of
.DELTA.n=-10.sup.-3 is assumed. It is seen that (i) the modulation
depth increases and (ii) the transmittivity decreases as the number
of periods is increased for a given cavity length. (i) is due to
the increase of the resonance peak sharpness (decrease of
.DELTA..lamda.) as a consequence of the increase of the DBRs
reflectivity. (ii) is originated by the increase of the diffraction
losses.
[0057] Intensity attenuation transmission characteristics of the
device in the ON- and OFF-state for a
80(.lamda..sub.p/2n.sub.Si)-long cavity with 3-period and 4-period
DBRs due to the injected carriers in the ON-state may be observed.
Although the use of a specific configuration may depend on the
specific application, a good trade-off between modulation depth
(80%) and transmittivity (86%) is obtained for a
.about.18-.mu.m-long cavity with 3-period DBRs, which represents a
total device length of .about.20 .mu.m. It must be noted the low
values of the electrical power shown in Table III as well as the
small refractive index change in the cavity (0.1%) required to
achieve high modulation depths.
[0058] Producing high aspect ratio trenches on SOI with high
verticality may be performed using current semiconductor
fabrication techniques. Nevertheless, deviations from the
considered dimensions of the optical structure (length of the DBRs
and cavity) due to fabrication tolerances may affect the predicted
device performance. The effect of fabrication errors on the
spectral transmittance may be estimated by calculating the
transmittivity spectra for different length deviations of the
structure using the effective index method together with the TMM,
and calculating their average. Spectral transmittivity for a
3-period DBR with a maximum length deviation of 20 nm (that is,
L.sub.Si=160.+-.10 nm, L.sub.ox=150.+-.10 nm and
L.sub.cav=18.097.+-.0.010 .mu.m), 10 nm and 5 nm may result in
degraded resonance peak shape. The length deviation of the DBR and
cavity was assumed to be the same and the period of the DBR
constant. The resonance peak shape becomes degraded as the length
deviation increases. This is mainly due to the variations of the
cavity length, which shift the resonance wavelength for each length
component, broadening the averaged resonance peak. As a
consequence, the transmittivity is considerably reduced as compared
to the ideal case. It is also observed that high modulation depths
can still be achieved (.about.72% at 1.5508 .mu.m wavelength for a
20 nm length deviation). Simulations show that if the considered
length variations occur only in the DBR regions, the transmission
spectrum is not significantly affected with respect to the ideal
case.
[0059] The performance of a new planar silicon electro-optic
modulator based on a F-P microcavity by deep high-index-contrast
Si/SiO.sub.2 Bragg reflectors and confinement of free carrier
plasma dispersion in a SOI rib waveguide has been analyzed. Free
carrier concentration change in the cavity region produced by an
integrated lateral p-i-n diode induces a refractive index change
that modulates the output power at 1.55 .mu.m wavelength. Deep
lateral trenches in the p-i-n/cavity region laterally confine the
injected carriers into the cavity. Deep Si/SiO.sub.2 DBRs confine
longitudinally (i) the free carriers and (ii) the optical field
into the cavity region. The device has been analyzed by using
electrical and optical models. Analysis shows that a distance of
W.sub.pin=8 .mu.m between the cavity lateral trenches permits to
minimize (j) the dc electrical power and switching time of the
device, and (jj) the mode mismatch between the cavity and the DBRs.
Electrical passivation of the cavity surfaces with thermal
SiO.sub.2 (S.sub.p=S.sub.n=10.sup.2 cm/s) is predicted to reduce
the leakage current due to surface recombination by 70% as compared
to a non-passivated surface cavity (S.sub.p=S.sub.n=10.sup.5 cm/s),
without significantly affecting the injection carrier concentration
as compared to the case of no surface recombination
(S.sub.p=S.sub.n=0 cm/s). Diffraction is found to be the main cause
of optical power losses in our device for .DELTA.n=-10.sup.-3 in
the cavity. Calculations show that a trade-off between modulation
depth and transmittivity of the device must be considered.
[0060] A 20-.mu.m long device with S.sub.p=S.sub.n=10.sup.2 cm/s,
W.sub.pin=8 .mu.m and electrical contacts acting as heat sinks is
predicted to exhibit .about.80% of modulation depth with a
transmittivity of .about.86% at 1.55-1 .mu.m operation wavelength
by using .about.25 .mu.W of electrical power and a drive current
density of 116 A/cm.sup.2 under dc operation, leading to an
increase of the device temperature <10.sup.-2 K. The switching
speed of this device is calculated to be .about.16 ns for
V.sub.ON=0.87 V and V.sub.OFF=-5 V, with no significant
thermo-optic effect. The estimated dc power consumption for this
device may be at least one order of magnitude smaller than the
smallest currently reported (theoretical) value. These
characteristics reveal the benefits of confining both the optical
field and the injection carriers in the cavity region in order to
improve the electro-optic modulator performance in terms of power
consumption, current density, device length and modulation depth.
Si CMOS process compatibility makes this device very promising for
low-cost and low-power silicon-based integrated photonic
systems-on-a-chip (PSOC) for low frequency applications such as
local area networks, fiber-to-home return links, interconnects, and
sensor systems for chemical and biochemical applications.
* * * * *