U.S. patent application number 15/148873 was filed with the patent office on 2016-09-01 for impact ionization devices under dynamic electric fields.
The applicant listed for this patent is STC.UNM, The University of Sheffield. Invention is credited to John P. David, Majeed M. Hayat, Sanjay Krishna, Luke F. Lester, David A. Ramirez, Payman Zarkesh-Ha.
Application Number | 20160254867 15/148873 |
Document ID | / |
Family ID | 56027781 |
Filed Date | 2016-09-01 |
United States Patent
Application |
20160254867 |
Kind Code |
A1 |
Hayat; Majeed M. ; et
al. |
September 1, 2016 |
IMPACT IONIZATION DEVICES UNDER DYNAMIC ELECTRIC FIELDS
Abstract
Apparatus, systems, and methods relate to use of a time-varying
bias for application to an avalanche photodiode. Embodiments
include systems and methods of determining an appropriate
time-varying bias for application to an avalanche photodiode in
linear mode. Avalanche photodiode having appropriate parameters may
also be determined. Additional apparatus, systems, and methods are
disclosed.
Inventors: |
Hayat; Majeed M.;
(Albuquerque, NM) ; David; John P.; (Sheffield,
GB) ; Krishna; Sanjay; (Albuquerque, NM) ;
Lester; Luke F.; (Albuquerque, NM) ; Ramirez; David
A.; (Albuquerque, NM) ; Zarkesh-Ha; Payman;
(Albuquerque, NM) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
STC.UNM
The University of Sheffield |
Albuquerque
Sheffield |
NM |
US
GB |
|
|
Family ID: |
56027781 |
Appl. No.: |
15/148873 |
Filed: |
May 6, 2016 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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13289645 |
Nov 4, 2011 |
9354113 |
|
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15148873 |
|
|
|
|
61456455 |
Nov 5, 2010 |
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Current U.S.
Class: |
398/212 |
Current CPC
Class: |
H01L 31/02027 20130101;
H04B 10/693 20130101; G01J 2001/4466 20130101; H01L 31/03046
20130101; H04B 10/67 20130101; H04B 10/6911 20130101; G01J 1/46
20130101; H01L 31/0304 20130101; G01J 1/44 20130101; H01L 31/0735
20130101; H01L 31/109 20130101; Y02E 10/544 20130101 |
International
Class: |
H04B 10/67 20060101
H04B010/67; H01L 31/0304 20060101 H01L031/0304; G01J 1/44 20060101
G01J001/44; H01L 31/0735 20060101 H01L031/0735 |
Claims
1. A method comprising: receiving an optical pulse at an avalanche
photodiode in linear mode or equivalent below-breakdown mode;
varying a reverse bias applied to the avalanche photodiode during
the reception of the optical pulse at the avalanche photodiode; and
outputting from the avalanche photodiode an electrical signal that
corresponds to the received optical pulse.
Description
RELATED APPLICATION
[0001] This application is a continuation application of U.S.
patent application Ser. No. 13/289,645, filed Nov. 4, 2011, which
claims priority to U.S. Provisional Application Ser. No.
61/456,455, filed Nov. 5, 2010, which applications are incorporated
herein by reference in their entirety.
FIELD OF THE INVENTION
[0002] The invention relates generally to optoelectronic devices
and methods of their operation.
BACKGROUND
[0003] To meet the demands of the exponential growth in video,
voice, data, and mobile-device traffic over the Internet, the
telecommunication industry has been moving toward 40-Gbps and
100-Gbps data rates for their core fiber-optic backbone networks
alongside the existing 10-Gbps infrastructure, which operates at
the low-loss wavelength window of 1.55 .mu.m. Many of the
modulation techniques that are effective at these high speeds (for
example, being tolerant to polarization-mode dispersion, chromatic
dispersion, and intersymbol interference (ISI), as well as having
competitive edge in price and performance combination) require
receivers that are based upon the direct detection of optical
pulses. These techniques include phase-shaped binary transmission
(PSBT) or duo-binary modulation (DM), return-to-zero on-off-keying
(RZ-OOK), and carrier-suppressed return-to-zero (CS-RZ). Typically,
such high-speed operation uses high sensitivity detectors.
[0004] Separate absorption and multiplication (SAM) InP--InGaAs
avalanche photodiodes (APDs) are normally the most preferred
photodetectors for direct-detection high-data rate systems for two
main reasons. First, they have high sensitivity, which results from
the internal gain they generate. The gain is the total number of
carriers generated through an avalanche of impact ionizations in
response to a single carrier excitation. Second, they are highly
cost effective compared to receivers that employ optical
pre-amplification. Indeed, SAM InP--InGaAs APDs have been deployed
in support of the synchronous optical networking (SONET) standards
of OC-48 and OC-192, which operate at 2.5 Gbps and 10 Gbps,
respectively. However, the long avalanche buildup time in InP,
which is the time needed for all the impact ionizations to settle,
has limited the speed of InP-based APDs and stopped them from
meeting the expectations of 40-Gbps systems. There are few or no
commercial APDs available for 40-Gbps communication, despite
numerous efforts in the past two decades or so which targeted new
APD materials and structures.
[0005] Viable options for direct detection of 40-Gbps bit streams
include InGaAs PIN photodiodes, since very high bandwidths can be
achieved with such state-of-the-art PIN photodiodes. However. PIN
photodiodes have lower sensitivity than APDs since they do not
offer any internal gain. To detect weak signals in the increased
presence of Johnson noise in high data-rate systems, where
increasing the bit rate by a factor of four causes the Jonson noise
to increase by 6 dB, erbium doped fiber amplifiers (EDFAs) are
typically used to pre-amplify the signals optically before their
detection by the PIN photodiode. The resulting EDFA-PIN receiver
can exhibit very high sensitivity (<-30 dBm), due to EDFA's high
gain and low noise, as well as high speed, which is due to the high
bandwidth of the PIN photodiode. However, these receivers can be
bulky and expensive. An EDFA uses meters of fiber, which are
generally coiled in a fairly sizeable disk, and more importantly,
it uses a pump laser, which provides the optical amplification. For
example, a 40-Gbps EDFA-InGaAs-based receiver module may cost up to
$5.000. In contrast. APD-based receivers, which run for about $500,
benefit from small form-factor packaging, since they can easily be
integrated with the electronic components of the receiver circuit,
and would offer a much more cost-effective solution than the
EDFA-PIN receiver only if their speed were to be improved. Since
ultra-low-noise APDs have already been demonstrated, the persisting
challenge is the development of 1.55 .mu.m APDs that can reliably
offer gain-bandwidth-products (GBPs) in excess of 350 GHz, for
example offering a gain of 10 at a speed of 35 GHz.
[0006] The long avalanche buildup time in InP is due to its roughly
equal electron and hole ionization rates, where the
hole-to-electron ionization coefficient ratio, k, is in the range
2.5-4 for InP. Moreover, the buildup time scales with the gain.
Specifically, the buildup time limits the bandwidth at values of
the gain (>10) that are useful in Johnson noise suppression.
FIG. 1 shows a schematic illustrating the cascade of impact
ionizations and the associated buildup time in a multiplication
region of an APD such as an InP APD. Specifically, as a parent hole
102 is generated in an absorption layer (not shown), such as an
InGaAs absorption layer, and injected in the InP multiplication
region (parent hole 102 is shown at the bottom of the structure), a
first wave of impact ionizations take place. The parent hole
injected at the bottom initiates the avalanche. While the offspring
holes drift together and reach the end of the multiplication
region, the offspring electrons, which will still be present in the
multiplication region, move in the opposite direction, as shown in
the FIG. 1, causing a second-wave of impact ionizations. After the
second wave ends, a third wave is launched, and so on, until
eventually the impact ionization process ceases when all charge
carriers exit the depletion layer, which is an intrinsic layer. The
avalanche process includes hole ionization 101 and electron
ionization 103. These ionizations provide a pulse 107 due to holes
and a pulse 109 due to electrons, where the two pulses provide a
total avalanche pulse 108. Number, locations, and times of impact
ionizations are random, and the resulting avalanche pulse, where
each drifting carrier contributes to the avalanche pulse, is
therefore stochastic, with area representing the stochastic gain.
The first wave refers to the carriers born in the first electron
transit time, the second wave refers to those created in the hole
transit time following the first electron transit time, and so
on.
[0007] Indeed, the GBP of InGaAs/InP APDs has been limited to 170
GHz, which corresponds to a gain value below 5 if the bandwidth is
constrained to a minimum value of 35 GHz in support of 40 Gbps bit
rates. With such low gain, the APD cannot compete with the much
faster PIN photodiodes combined with a high-gain (.about.20 dB)
EDFA.
[0008] There have been numerous efforts in the past two decades to
explore new materials or new device concepts to overcome current
limitations of InP and InAlAs APDs. For example, there have been
efforts to engineer the multiplication region to minimize
multiplication noise and maximize the GBP. Of particular importance
is the discovery in the mid-1990s that submicron scaling of the
multiplication region thickness leads to lower multiplication noise
and higher gain-bandwidth products. In fact, the highest value of a
commercial InGaAs/InP APD, 170 GHz, utilizes a very thin InP
multiplication layer of 80 nm. Other efforts involved
impact-ionization engineering of heterojunction multiplication
regions, edge-illuminated and evanescently coupled waveguide
structures, and use of In.sub.0.52Al.sub.0.48As material for
multiplication. The k factor in In.sub.0.52Al.sub.0.48As is
k=4-6.7, which gives it an edge over InP in terms of noise and GBP.
InAlAs-based APDs have showed GBPs ranging from 70 to 170 GHz with
the exception of two reported results with values of 290 GHz in
2000 and 320 GHz in 2001. It is now accepted that while both InP
and InAlAs APDs have sufficient bandwidth to support 10-Gbps
transmission, they cannot sustain gain-bandwidth tradeoff for 40
Gbps. A sensitivity of -19 dBm at 40 Gbps with a bit error rate of
10.sup.-10 has been demonstrated, providing approximately a 9 dB
improvement over conventional PIN diode. This sensitivity was
achieved by including a transimpedance amplifier with tunable
response to boost the GBP from 140 to 270 GHz and by operating the
APDs with avalanche gain values of 3 to 10. More recently, it was
reported that that a Ge absorption layer grown directly on a Si
multiplication layer provided a GBP of 340 GHz. This high GBP was
attributed to the favorable ionization properties of Si. Most
recently. Si on Ge APD with a GBP of 840 GHz operating at 1.31
.mu.m was demonstrated. Despite all these efforts and advances, to
this date there does not appear to be a commercial APD available to
detect 40 Gbps signal, and the challenge is even greater for
systems operating at 1.55 .mu.m.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] Embodiments of the invention are illustrated by way of
example and not limitation in the figures of the accompanying
drawings in which:
[0010] FIG. 1 depicts a schematic of the avalanche buildup time
showing the cascade of impact ionizations in a multiplication
region of an avalanche photodiode diode, in accordance with various
embodiments.
[0011] FIG. 2 shows an illustration of an example dynamic biasing
scheme for an avalanche photodiode diode repeated periodically over
bit-clock-synchronized intervals, in accordance with various
embodiments.
[0012] FIG. 3 shows a chart indicating the calculated time response
to a rectangular optical pulse of an example
dynamic-biased-enhanced avalanche photodiode diode and a
conventional avalanche photodiode diode, in accordance with various
embodiments.
[0013] FIG. 4 shows an electric field seen by carriers from the
first through third waves of impact ionization, in accordance with
various embodiments.
[0014] FIG. 5 shows schematics and energy band diagrams of a
single-well structure, in accordance with various embodiments.
[0015] FIG. 6 shows a modeled band structure and electric field
profile using a semi-empirical pseudopotential method, in
accordance with various embodiments.
[0016] FIG. 7 shows a reduction in the electric field in the
absorber of FIG. 6 using appropriately designed barrier layers, in
accordance with various embodiments.
[0017] FIG. 8 shows a functional block diagram of an optical
transceiver using an example dynamic-biased-enhanced avalanche
photodiode diode, in accordance with various embodiments.
[0018] FIG. 9 shows an input stage of a differential transimpedance
amplifier utilizing common mode signaling to eliminate dynamic bias
signal injection, in accordance with various embodiments.
[0019] FIG. 10 shows a schematic of an example indium phosphide
based avalanche photodiode diode with heterostructure
multiplication region, in accordance with various embodiments.
[0020] FIGS. 11A-C show a serializer/deserializer module, in
accordance with various embodiments.
[0021] FIG. 12A-B show schematic diagrams of frequency and time
domain measurement setups, in accordance with various
embodiments.
[0022] FIG. 13 shows features of an example method of operating an
optoelectronic device, in accordance with various embodiments.
[0023] FIG. 14 shows an example system including an optoelectronic
device, in accordance with various embodiments.
[0024] FIG. 15 features of an example method of determining a
time-varying bias to be applied to an optoelectronic device, in
accordance with various embodiments.
[0025] FIG. 16 an example system operable to determine a
time-varying bias to be applied to an optoelectronic device, in
accordance with various embodiments.
DETAILED DESCRIPTION
[0026] The following detailed description refers to the
accompanying drawings that show, by way of illustration and not
limitation, various example embodiments of the invention. These
embodiments are described in sufficient detail to enable those
skilled in the art to practice these and other embodiments. Other
embodiments may be utilized, and structural, logical, and
electrical changes may be made to these embodiments. The various
embodiments are not necessarily mutually exclusive, as some
embodiments can be combined with one or more other embodiments to
form new embodiments. The following detailed description is,
therefore, not to be taken in a limiting sense.
[0027] In various embodiments, an impact ionization-aware
dynamic-biasing scheme for avalanche photodiodes (APDs) can be
implemented in, but not limited to, a digital communication
mechanism. The impact ionization-aware dynamic-biasing scheme
applied to APDs is expected to result in GBPs well above 1200 GHz
and receiver sensitivities below -29 dBm for 40 Gbps digital
communication and beyond. To take the speed of APD-based digital
receivers to the next level, one can begin by exploring a mechanism
that can, in principle, eliminate the buildup-time problem in the
context of digital optical communications. If the reverse bias of
the APD is able to abruptly change near the end of the optical
pulse from its optimal value to a much lower value that permits no
impact ionizations at all, yet photons are detected, then it would
practically be quenching the APD's avalanche current in preparation
for the next incoming optical pulse. The optimal value may be
suitably selected to yield an optimal gain value while maintaining
a low excess noise factor. For such quenching effect to
materialize, the bias would need to drop in one carrier transit
time at the end of the optical bit. With this approach, the speed
of the APD-based receiver may be totally decoupled from the APD's
gain, and the speed may be limited only by the transit time of the
carriers. In fact, this is almost identical, in principle, to the
approach of active quenching in single-photon avalanche diodes
(SPADs), a very successful single-photon detection technique
pioneered in the 1980's. However. SPAD circuits run at much slower
speeds, such as pulse repetition rates in the low MHz range.
Further, such periodic, abrupt transitions in the bias are not
implementable at speeds of 40 GHz because of two main reasons: (1)
the slew-rate limit of the driver for the bias and (2) the
bandwidth limit of the electronic circuit for the bias.
Nonetheless, in various embodiments, with proper selection of
implementable time-varying biases in the bit duration, such as
sinusoids, the active-quenching phenomenon can be approximated to
elevate the APD-based receiver speed to a level comparable to that
for a PIN-based receiver. The success of such approach may be
addressed by implementing time-varying biasing schemes at high
speeds, where modeling the impact ionization process and GBP under
dynamic biasing conditions may be conducted to attain implementable
dynamic-biasing schemes that yield highest GBP possible.
[0028] FIG. 2 shows an illustration of an example embodiment of a
dynamic biasing scheme 205 for an APD repeated periodically over
bit-clock-synchronized intervals. The time unit w/v represents a
carriers' transit time across the width of the multiplication
region. Line 208 represents the traditional constant bias. The
downward change in the reverse bias from the first to the second
half of the bit period causes the gain and buildup times,
corresponding to individual avalanche triggers, to decrease, which
results in a much higher average GBP compared to the conventional
biasing scheme. Ionization-aware dynamic biasing scheme 205
introduces a non-traditional, yet practical, scheme that can enable
APDs to be suitable for digital 40-Gbps fiber-optic communication
links and beyond. Unlike the traditional biasing scheme, where a
constant dc reverse-bias is applied to the APD throughout the
detection process, dynamic biasing scheme, such as ionization-aware
dynamic biasing scheme 205, is based on varying the applied reverse
bias during each received optical pulse (optical bit) from high to
low, as schematically shown in FIG. 2.
[0029] A dynamic biasing scheme that varies an applied reverse bias
during each received optical pulse includes two features. First,
photons that arrive early in the optical bit result in avalanche
pulses that are very strong as long as the bias is high, after
which they are quenched by the low bias in the latter part of the
bit period. This process may result in a very high gain for
avalanches that are triggered by "early" photons, yet they may have
a limited buildup time due to the quenching mechanism. Second,
photons that arrive late in the received optical bit are still
detected as the photodetector remains reverse biased, albeit the
resulting gain is low and the buildup time is naturally very short.
Through such dynamic and periodic biasing, photons arriving in each
bit can collectively generate a high gain while their buildup times
are dynamically controlled. As a result, a very high
photon-arrival-time-averaged (PATA) GBP can be generated. In
effect, the behavior of a detector structured for such dynamic
biasing, which detector is termed herein dynamic-biased-enhanced
APD (DBE-APD), is akin to a hypothetical bi-mode detector whereby
the detector behaves like a high-gain, short-build up time APD in
the first half of the bit, while it switches to a simple PIN diode
in the later part of the bit. The detector in its mode as a
high-gain, short-build up time APD may be considered to be similar
to silicon or mercury-cadmium-telluride APDs.
[0030] It is to be noted that, while the optoelectronic gain
present in the DBE-APD's photocurrent is time varying, since the
APD's responsivity is time varying due to the changing reverse
bias, the total charge accumulated in each bit in an
integrate-and-dump receiver is not affected by the time-variant
behavior of the DBE-APD. More precisely, since the photocurrent is
integrated over each bit in the receiver, the total charge is
simply proportional to the product of the PATA gain and the total
number of photons in the optical pulse in each bit. In other words,
the charge produced in each bit remains proportional, with a
proportionality constant that is constant from bit to bit, to the
energy in the optical pulse in each bit. Thus, while the DBE-APD
may not be directly applicable to simple analog detection (unless
gain equalization is employed), it is a perfect fit to digital
communications. It is also to be noted that a sinusoidal-gating
approach has been proposed for Geiger-mode APDs in the context of
gated photon counting. However, the purpose there is to force
quenching of the avalanche pulse after each detection-gate (high
cycle of the sinusoidal bias) and therefore minimize the total
number of multiplications, which, in turn, would reduce
afterpulsing. As such, it is totally different from the linear-mode
dynamic biasing approach as taught in various embodiments herein.
Specifically, photon counting with the sinusoidal-gating approach
is a binary detection: the APD is responsive to only one photon
each gate. In contrast, in embodiments of a linear-mode dynamic
biasing approach, essentially each and every photon in the optical
pulse that is absorbed by the photodetector contributes to the
analog photocurrent.
[0031] Preliminary results from rigorous analytical modeling shows
that even without any device optimization, a DBE-APD approach can
increase the gain-bandwidth product of an APD by a factor of 5
compared to the same APD operated under the conventional static
biasing scheme. FIG. 3 shows a chart indicating the calculated time
response to an 8.3-ps rectangular optical pulse 302 of an example
DBE APD and a conventional APD. As an example, an InP APD was
considered for both dynamic biasing 305 and constant bias 308. A
sinusoidal-dynamic bias function can be used for dynamic biasing
305. As noted, a 5.times. enhancement in the GBP is predicted. FIG.
3 also shows a simulated PATA mean impulse-response function 311 of
a 200-nm InP APD with the sinusoidal dynamic-field profile 305 and
a simulated PATA mean impulse-response function 314 of the 200-nm
InP APD with the traditional constant reverse bias 308. To
reiterate, the PATA response can be thought as the response of the
APD to an NRZ optical pulse. The width of the optical pulse is 8.3
ps in this example, consistent with 60-Gbps NRZ bit stream. The
amplitude, de-bias, and phase shift of the sinusoidal periodic
function has been selected to maximize the GBP. Calculations
predict an enhancement in the buildup-time limited GBP from 238
GHz, corresponding to a mean gain of 28 and bandwidth of 8.5 GHz,
in the traditional constant-bias scheme to 1169 GHz, corresponding
to a PATA mean gain of 27 and PATA bandwidth of 43.3 GHz. Note that
the GBP for the constant-bias scheme is larger than that normally
reported for a 200-nm InP APD since only buildup-time limitations
are considered here (for example, RC effects are ignored).
Nonetheless, the results show an enhancement factor of 5. Even
greater improvement is anticipated when the dynamic bias
characteristics (for example, other implementable shapes and
voltage swings) are optimized for a maximal GBP and when the
multiplication region is also optimized via doping and
heterostructure engineering.
[0032] The design of the dynamic biasing may be coupled with
material and doping engineering of the multiplication region of the
APD with the aim of simultaneously maximizing the GBP and
minimizing the avalanche multiplication noise. Through judicious
doping and heterostructure engineering of the multiplication
region, the ionization-coefficient profile in the multiplication
region can be modulated spatially so that the impact ionizations
are tuned to the dynamic bias so as to maximize the GBP. Coupled
bias and device design can be structured to promote the first-wave
of impact ionizations while discouraging second-wave
ionizations.
[0033] FIG. 4 illustrates an electric field seen by carriers from
the first through third waves of impact ionization. As shown in
FIG. 4, appropriate doping of the multiplication region can yield
an ascending electric field gradient. A constant doping is assumed
in the multiplication region, which results in an ascending field
gradient in the x-direction. When combined with the proposed
decreasing bias, the electric field seen by odd-wave carriers
becomes almost constant over their transit time while that seen by
even-wave carriers are sharply decreasing. In an InP multiplication
layer, this hybrid dynamic-spatial field modulation reduces the
probability of impact ionization by electrons in the second-wave
phase, which, in turn, helps quenching the avalanche pulse.
[0034] In the first wave of multiplications within the first hole
transit time, the high dynamic bias offsets the low field in the
beginning of the multiplication region, which yields an overall
robust field that promotes ionizations in the first wave. As the
second wave of ionizations begins, defined as the electron transit
time directly following the first wave, the dynamic bias continues
to drop, and, as the electrons traverse a descending field, their
capability to impact ionize will deteriorate as they march toward
the edge of the multiplication region. This combination discourages
second-wave electrons to impact ionize and tends to break the
symmetry in the hole and electron ionization coefficients that InP
notoriously suffers from.
[0035] It is also possible to bandgap engineer the multiplication
region to further discourage ionizations in the second and
subsequent waves. FIG. 5 shows the schematics and energy band
diagrams of a single-well structure. Use of an InAlAs--InAlGaAs
heterostructure multiplication region for materials 1 and 2 has
been proposed, where the parent hole first experiences the lower
bandgap InAlGaAs material, creating a large number of impact
ionizations due to the high field during this phase, and then
enters the higher bandgap InAlAs material. In the second-wave
phase, the electrons encounter a lower field than the electrons
experience in the first-wave phase. However, these electrons also
have less probability of impact ionizing due to the higher bandgap,
which together with the lower field impede second-wave impact
ionizations.
[0036] In various embodiments, a dynamic-biasing approach can be
implemented for elevating and optimizing the performance of APDs in
high-speed optical communication. This new paradigm for APD design
adds a new dimension to the traditional material- and
structure-based design. Much greater GBP may be achieved compared
to earlier efforts, which only focused on device materials and
structures. Another feature of this approach is that it is
essentially APD-agnostic; that is, it can be used to improve the
GBP of any APD device. As compared to conventional schemes, dynamic
biasing scheme of the DBE-APD approach can provide for the
relaxation of stringent requirements of the width of the
multiplication region. Such relaxation may be provided in a manner
as normally done to enhance the APD speed. This, in turn, reduces
the electric field in the multiplication region, which reduces
tunneling current, the principal component of the notorious dark
current in high-speed APDs. With such performance enhancement and
cost effectiveness, it is anticipated that the DBE-APD approach for
digital receivers may have a huge impact on next-generation long
haul and metro networks.
[0037] In various embodiments, DBE APDs and receivers can be
modeled, designed, and optimized based on theoretical and
simulation approaches. The result of the theoretical and simulation
approaches can be applied to fabricate, characterize, and deploy
DBE APDs in the form of a 40 Gbps receiver module. In the modeling
and optimization of a DBE APD, a generalization of a recursive
technique can be applied to include a time-varying bias of the APD.
This can provide an analytical model for the mean gain, the excess
noise factor, the mean impulse-response function, as well as the
probability distribution function of the buildup time, under the
assumption of a heterostructure multiplication region with an
arbitrary electric field profile. The model can, for example, be
applied to impact-ionization engineered (I.sup.2E) APDs. The model
captures the dead space and the initial energy effects, both of
which have been shown to play a critical role in the noise and
bandwidth properties of high-speed APDs with thin (<500 nm)
multiplication regions. The dead space is the minimum distance a
newly born (generated) carrier must travel before acquiring
sufficient kinetic energy, equal to the ionization threshold
energy, which enables it to effect impact ionization
stochastically.
[0038] The analytical model can be used to assess the GBP
performance of the DBE-APD and optimize the performance over the
choice of the biasing function and the material and structure of
the APD. The analytical model may also be used to generate data
and/or relationships to calculate the receiver sensitivity
associated with DBE-APDs such as InP DBE-APDs. The analytical
receiver-sensitivity model may include the effects of ISI,
avalanche noise, avalanche duration, tunneling current, and
amplifier noise.
[0039] Suppose that a time-varying bias. V.sub.BD(t), is applied to
an APD, as shown in FIG. 2, with the implicit assumption that the
time reference is t=0. Consider the multiplication region of the
APD, which extends from x=0 to x=w, as shown in FIG. 1, with the
convention that the electric field is pointing in the positive x
direction. Suppose that a parent hole (electron) is created at an
arbitrary location x in the charge-depleted multiplication region,
and assume that the field is sufficiently high such that
conduction-band electrons and valence-band holes travel at their
material-specific saturation velocities in the material. The
stochastic multiplication factor is defined as the total number of
electron-hole pairs generated as a result of a parent carrier. The
buildup time is the time from the creation of the parent carrier to
when all carriers have exited the multiplication region. Clearly,
the buildup time is simply the duration of the impulse-response
function. The multiplication factor, impulse-response function, and
the buildup time are all stochastic, and are also dependent on the
position of the birthplace of the parent carrier, and can be either
finite or infinite. While Monte-Carlo and analytical models exist
that describe the statistics of the impulse-response function,
multiplication factor, and the buildup time in the case when the
bias V.sub.BD(t) is a constant, there appears to be no conventional
model for the case when the bias is time varying.
[0040] In a dynamic-field scenario, it turns out that the age of
the carrier measured from the point in time when the dynamic bias
is launched (namely, the age is measured from t-=0) plays a key
role in the impact ionization characteristics, based on the
observation that the carriers' ionization coefficients are
dependent on time as the field varies dynamically. As such,
carriers born at different times will experience a dynamical
electric field as they generate their own chains of offspring
carriers through series of impact ionizations. Specifically, if it
is assumed that a causal and spatially nonuniform electric field,
E(x,t), is launched at time t=0, then a hole born at location x and
at time 0 will experience this progressive field as it generates
its chains of impact ionizations. On the other hand, if a hole is
born at location .xi. and at time s (relative to t=0), it will
experience the s-delayed progressive field E(.xi.,t-s)u(t-s), where
u(.) is the unit-step function. For example, at any time .delta.s
after time s, the electron will have an ionization coefficient,
.alpha.(.xi.,s+.delta.s), signifying the position of the carrier
.xi. and the time s+.delta.s elapsed since the launch of the
dynamic field at t=0; namely, the electric field value governing
the ionization coefficient .alpha.(.xi.,s+.delta.s) is
E(.xi.,s+.delta.s).
[0041] To take the "age" factor into account in modeling of the
avalanche multiplication process, a model can be used in which the
ionization probability is parameterized by the time at which the
parent carrier is injected in the multiplication region. The model
assumes that a parent carrier initiates the multiplication process
at an arbitrary location in the multiplication region and at an
arbitrary instant (age) after the launch of the dynamic bias. A set
of novel recurrence equations discussed herein can be used to
calculate the mean impulse-response function, the mean
multiplication factor, and the excess noise factor, as a result of
the parent carrier initiating the multiplication process.
[0042] In various embodiments, an appropriate APD design can be
structured based on choices of doping profile and material. A
Poisson solver can be used to accurately model the electric field
profile in heterostructures with different doping profiles. For
example, a poison solver based on a commercial T-CAD Sentaurus
platform can be used. It is suggested to implement constant and
variable doping to affect the field gradients in the multiplication
region of APDs, such as InAlAs--InAlGaAs APDs, and examine the best
doping profile that yields the highest GBP according to the
analytical recursive model. In the analysis as described earlier,
an ascending field gradient from x=0 to x=w in FIG. 1 can be used.
Schrodinger solvers can be used, where such Schrodinger solvers
have been previously used by researchers to model the quantum
effects from thin semiconductor layers and integrate these effects
with various barrier and absorber regions to accurately predict the
field profile in heterostructures. For example to model the
electric field and band structure in thin semiconductor
superlattices, band offsets and bandgaps can be obtained from a
semi-empirical pseudopotential method (SEPM) with the output of
this calculation provided to the Sentaurus T-CAD for further
simulations. FIG. 6 shows a modeled band structure and electric
field profile using the semi-empirical pseudopotential method. In
the representative modeled band structure and the electric field
shown in FIG. 6, unipolar barriers were used to reduce the electric
field drop in the absorber region. FIG. 7 shows a reduction in the
electric field in the absorber of FIG. 6 using appropriately
designed barrier layers.
[0043] In various embodiments, a processing system can be
structured to implement a generalized theory of avalanche
multiplication under time-varying electric fields for application
to optoelectronic devices arranged to be subjected to a
dynamic-biasing scheme. A recurrence theory for the
impulse-response function under nonuniform, static electric fields
was originally formulated by one of the inventors and later
extended to accommodate stochastic carrier velocity by another
researcher. Such generalized recurrence theories for the mean
impulse response can be adjusted to include dynamic fields. This
adjusted generalization can be termed the age-dependent recursive
theory for avalanche multiplication. An outline of the formulation
of the age-dependent recursive theory for avalanche multiplication
is provided in the following discussion. Assume that at time t=0, a
spatially nonuniform, dynamic-field profile E(x,t) is launched in
the multiplication region of an APD. Assume that a parent carrier
is created in the multiplication region at location x with an age
s, measured from the time origin at t=0. Begin by defining,
I.sub.e(t,x,s), the stochastic impulse-response function at t,
initiated by an electron injected at location x with age s.
Similarly, I.sub.h(t, x, s) is the stochastic impulse-response
function at t, initiated by a hole injected at location x with age
s. The age variable s can also be associated with the absorption
time of a photon, which results in a photo-generated parent
carrier.
[0044] The rationale for the age-dependent recurrence theory is
also based on stochastic renewal. To implement the stochastic
renewal, the appropriately time-dependent field evolution, namely
E(.xi.,t-s)u(t-s), associates to every time of birth s and birth
location .xi.. A renewal argument is raised that will allow
recursive characterization of the means of I.sub.e(t,x,s) and
I.sub.h(t,x,s). Suppose that a parent electron at x impact ionizes
for the first time at location .xi.>x. A key observation is that
at the time just after this first ionization, there will be two
freshly born electrons at .xi. (the re-born parent electron and its
offspring) and a freshly born hole also at .xi. (parent electron's
hole offspring). Each of these two electrons at .xi. will
independently instigate a statistically equivalent multiplication
process similar to the one originated by the parent electron at
location x, with v.sub.e being electron velocity, albeit their age
is not s but instead it is s+(.xi.-x)/v.sub.e, which is the age of
the original electron plus the time it took it to undergo its first
ionization at. A similar argument can be made for the offspring
hole.
[0045] If i.sub.e(t,x,s) and i.sub.h(t,x,s) are defined as the mean
quantities of I.sub.e(t,x,s) and I.sub.h(t,x,s), respectively, then
the recursion can be obtained (omitting the mathematical
derivation)
i.sub.e(t,x,s)=[1-(qv.sub.e/w)u(t-(w-x)/v.sub.e)].intg..sub.w.sup..infin-
.h.sub.e(.xi.;x,s)d.xi.+.intg..sub.x.sup.min(w,x+v.sup.h.sup.e+t)[2i.sub.e-
(t-(.xi.-x)/v.sub.e,.xi.,s+(.xi.-x)/v.sub.e+i.sub.h(t-(.xi.-x)/v.sub.e,.xi-
.,s+(.xi.-x)/v.sub.e)]h.sub.e(.xi.;x,s)d.xi.
A similar equation can be obtained for i.sub.h(t,x,s) with vi,
being hole velocity:
i.sub.h(t,x,s)=[1-(qv.sub.h/w)u(t-x/v.sub.h)].intg..sub.x.sup..infin.h.s-
ub.h(.xi.;x,s)d.xi.+.intg..sub.0.sup.min(x,x-v.sup.h.sup.t)[2i.sub.h(t-(x--
.xi.)/v.sub.h,.xi.,s+(x-.xi.)/v.sub.h)+i.sub.h(t-(x-.xi.)/v.sub.h,.xi.,s+(-
x-.xi.)/v.sub.h)]h.sub.h(.xi.;x,s)d.xi.
In the above recursive equations, h.sub.e(.xi.;x,s) and
h.sub.h(.xi.;x,s) are the age-dependent probability density
functions of the free-path-distance, d.sub.fp, of the first
ionization position due to an electron and hole, respectively,
positioned at x and of age s. These density functions are new as
they capture the dependence on the dynamic field. Specifically,
they are given by
h e ( .xi. ; x , s ) = { .alpha. ( .xi. , s + ( .xi. - x ) / v e )
exp { - .intg. x + d e ( x ) .xi. .alpha. ( .sigma. , s + ( .sigma.
- x ) / v e ) .sigma. } , .xi. .gtoreq. x + d e ( x ) 0 , otherwise
and h h ( .xi. ; x , s ) = { .beta. ( .xi. , s + ( x - .xi. ) / v h
) exp { - .intg. .xi. x - d e ( x ) .beta. ( .sigma. , s + (
.sigma. - x ) / v h ) .sigma. } , .xi. .ltoreq. x - d h ( x ) 0 ,
otherwise ##EQU00001##
where, .alpha.(x,s) (.beta.(x,s)) is the electron (hole)
time-varying non-localized ionization coefficient associated with
location x in the multiplication region and at time s since the
launch of the electric field for an electron (hole) that has
already traveled the dead space. It is given by .alpha.(x,s)=A
exp(-[E.sub.c/E(x;s)].sup.m). The material-specific constants A,
E.sub.c, and m, are known for various III-V materials. The two
coupled equations can then be solved numerically using an iterative
approach. An example iterative approach is provided in M. M. Hayat,
and B. E. A. Saleh, "Statistical properties of the impulse response
function of double carrier multiplication avalanche photodiodes
including the effect of dead space," IEEE J. Lightwave Technol.,
vol. 10, pp. 1415-1425, 1992. The mean impulse-response function,
i(t,s), (in the case of a hole injection to the multiplication
region at x=0) is then obtained using i(t,s)=i.sub.h(t,0,s).
[0046] In digital communications, photons arrive randomly with the
duration of a bit. As a result in digital communications, the
appropriate quantity would be the photon-arrival-time averaged
(PATA) impulse-response function (previously introduced), which can
be obtained through
i.sub.PATA(t)=.intg..sub.0.sup.Ti(t,s)p.sub.ph(s)ds, where
p.sub.ph(s) is the probability density of photons within a bit of
duration T, which is governed by the intensity profile of the
received optical pulse within the optical bit. This is the relevant
impulse-response function in the context of an integrate-and-dump
receiver with a periodically modulated electric field. By
calculating the 3 dB bandwidth of the Fourier transform of
i.sub.PATA(t), the bandwidth of the DBE-APD device can be obtained.
Proof-of-concept time-response results shown with respect to FIG.
3, for example, were derived based on the techniques described
here.
[0047] In various embodiments, a generalization of a modified
dead-space multiplication model (MDSMT) modified to include
time-varying fields can be implemented with respect to dynamic
biasing schemes for optoelectronic devices. MDSMT is an analytical
model, which enables the correct prediction of the gain and the
excess noise factor for arbitrary heterostructure APDs under static
electric fields. See, for example, M. M. Hayat, O-H. Kwon, S. Wang,
J. C. Campbell, B. E. A. Saleh, and M. C. Teich, "Boundary effects
on multiplication noise in thin heterostructure avalanche
photodiodes," IEEE Trans. Electron Devices, vol. 49, pp. 2114-2123,
December 2002.
[0048] The generalized MDSMT recurrence theory including
time-varying fields can be applied for the mean gain and the excess
noise factor, which is outlined in the following. As before, it is
assumed that at time t=0 a dynamic and spatially nonuniform
electric field E(t,x) is launched in the multiplication region of
an APD. Assume that a parent carrier is created in the
multiplication region at location x with an age s. Z(x,s) is
defined as the totality of all offspring electrons and holes
initiated by an electron injected at location x with age s.
Similarly, Y(x,s) is the same as Z but with the initialing parent
electron replaced by a parent hole. A renewal argument is invoked
to obtain the following pair of recursive equations for the mean of
the quantities Z(x,s) and Y(x,s), denoted by z(x,s) and y(x,s),
respectively:
z(x,s)=.intg..sub.w.sup..infin.h.sub.e(.xi.;x,s)d.xi.+.intg..sub.x.sup.w-
[2z(.xi.,s+(.xi.-x)/v.sub.e)+y(.xi.,s+(.xi.-x)/v.sub.e)]h.sub.e(.xi.;x,s)d-
.xi. and
y(x,s)=.intg..sub.x.sup..infin.h.sub.h(.xi.;x,s)d.xi.+.intg..sub.0.sup.x-
[2y(.xi.,s+(.xi.-x)/v.sub.h)+z(.xi.,s+(.xi.-x)/v.sub.h)]h.sub.h(.xi.;x,s)d-
.xi.
The age-dependent multiplication factor, m(x,s), can be calculated
using m(x,s)=0.5[z(x,s)+y(x,s)], and the PATA mean is
m.sub.PATA(x)=.intg..sub.0.sup.Tm(x,s)p.sub.ph(s)ds. Note that in
the case of edge injection of a hole at x=0, the PATA gain is
simply m.sub.PATA(0).
[0049] A recursive equation for the second moments of Z(x,s) and
Y(x,s) may be derived. Following the renewal-theory approach and
the age-dependent formulation described herein, and the PATA excess
noise factor may be obtained using the second moments of Z(x,s) and
Y(x,s). In addition, to facilitate the calculation of receiver
sensitivity in a communications apparatus using the analytical
model for receiver sensitivity, the PATA joint probability
distribution function of the gain and the buildup time may be
computed as a generalization of the formulation to time-varying
electric fields.
[0050] Modeling and optimization of components for dynamic biasing
may be implemented in various computational formats. For example,
algorithms may be generated using high performance FORTRAN. The
modeling may include solving multidimensional recursive equations,
which can be both memory and CPU intensive. In order to optimize
the memory usage for high accuracy calculations, a serial code can
be used that allows the multidimensional recursive equations to be
solved sequentially (in blocks of time t) in multiple separate
parts, one part for each block of time. The accuracy of the
calculations may be increased by increasing the total size of
three-dimensional (3D) arrays generated by solving the
multidimensional recursive equations. In this effort, the desired
total size of the 3D arrays can be determined beforehand. Then, the
execution of the code can be divided in several parts in which each
part will calculate a section of the 3D arrays. Therefore, the
memory required for the execution of an individual part of the code
will be the memory to store the calculated section. Consequently,
the numbers of parts in which the executable code is divided can
depend on the size of the larger section of the 3D arrays that can
be stored in memory. Every part of the code execution can use data
calculated in the previous part and it can save data for the
calculation of the next part.
[0051] In various embodiments, an optimal design of dynamic bias
for an application can be generated using a machine analysis. A
parametric approach can be arranged to perform a systematic study
to identify the bias schemes that are most amenable to GBP
enhancement. A systematic study can include analyzing bias signals
of various formats such as sinusoidal, sawtooth, triangular, and
other non-constant formats. For each candidate realizable shape,
such as but not limited to sinusoidal, sawtooth, triangular, and
other non-constant formats, parameters can be assigned that govern
the amount of swing in the reverse bias, the dc value, as well as
phase shift with respect to a recovery clock. The analytical model
for the GBP can then be used to optimize over this parameter space
for each bias shape.
[0052] The accuracy of the implementation of a dynamic bias scheme
depends upon the shape of the dynamic bias. For example, periodic
functions that possess abrupt changes, such as the rectangular bias
scheme, are difficult to implement accurately. It is therefore
important to understand the sensitivity of the GBP enhancement to
errors and perturbations resulting from the implementation of the
bias function. To this end, the effects of rounding and
accentuating edges can be systematically analyzed, as well as other
non-ideal effects such as fluctuations in the amplitude of the
bias, bias phase misalignment and skew, bias jitter and phase noise
and clock-synchronization errors, as well as bias waveform
distortion. Bias waveforms can be identified that are most robust
in the presence of non-idealities and implementation uncertainties.
An appropriate bias waveform can be selected from the bias
waveforms analyzed.
[0053] In various embodiments, a machine analysis applying models
as discussed herein can be conducted to perform a device-structure
optimization for enhanced GBP performance. Models as discussed
herein can be used to optimize the field-gradient (in space) in the
multiplication region of an APD to maximize the GBP. To facilitate
this optimization, a parametric model for field gradient can be
used in which linear, quadratic and higher order models for the
gradient can be considered. Once the best field spatial profile is
identified, doping, using appropriate doping techniques, can be
used to implement the field gradient. To verify that the desired
field gradient has been achieved, the T-CAD Sentaurus simulation
platform can be used in conjunction with profilometer and SEM
measurements to calculate the field profile.
[0054] As an example, for InGaAs APDs with heterostructure
multiplication region consisting of two InAlGaAs and InAlAs layers,
the theoretical model can be employed to optimize the widths of the
InAlAs and InAlGaAs layers to maximize the GBP. The predicted
excess noise factor may also be calculated as a function of the
heterostructure geometry. Receiver sensitivity can be calculated at
various bit rates (10 GHz-60 GHz) using a receiver sensitivity
model, as is known to those skilled in the art. For example, a
receiver sensitivity model can be employed in a manner as discussed
in D. S. G. Ong, J. S. Ng, M. M. Hayat. P. Sun, and J. P. R. David,
"Optimization of InP APDs for High Speed Lightwave Systems," IEEE
J. Lightwave Technol., vol. 27, pp. 3294-3302, 2009. To benchmark
the performance, the excess noise factor and receiver sensitivity
can be calculated in the constant bias scheme and, in comparison,
enhancement provided by the dynamic biasing approach characterized.
Optimization of elements of a dynamic biasing scheme can be
conducted on an individual basis. A joint optimization can be
performed over the entire parameter spaces encompassing the field
gradient, the heterostructure geometry, and the dynamic biasing
characteristics.
[0055] In various embodiments, a DBE-APD implementation can be
directed to an APD specifically designed for the implementation.
Alternatively, an example DBE-APD implementation can be directed to
an off-the-shelf APD, for example a DBE-APD implementation with
off-the-shelf InGaAs--InP APD. FIG. 8 shows a functional block
diagram of an optical transceiver 800 using an example
dynamic-biased-enhanced avalanche photodiode diode. Optical
transceiver 800 can use an off-the-shelf telecom InP APD or a
custom-designed APD. FIG. 9 shows an input stage of a differential
transimpedance amplifier utilizing common mode signaling to
eliminate dynamic bias signal injection that can be used in optical
transceiver 800 of FIG. 8. Optical transceiver 800 using either the
off-the-shelf telecom InP APD or the custom-designed APD
demonstrates the impact of DBE-APD in optical communication
systems. The transceivers of FIGS. 8 and 9 can be based on a
full-duplex serial electrical and serial optical link at the
standard rate of 40 Gbps.
[0056] Optical transceiver 800 can include an equalizer 821, a
laser modulator 822, a transmitter optical subassembly (TOSA) 823,
an optical fiber 824, a receiver optical subassembly (ROSA) 825, a
transimpedance amplifier 826, a post amplifier 827, a receiver
clock/data recovery (CDR) circuit 828, and a dynamic bias generator
805. The transmitter path can convert serial NRZ electrical data to
a standard compliant optical signal. The differential input signal
(TX+ and TX-) pass through a signal conditioner 821 with
equalization that compensates for losses and deterministic noise on
the input data stream. The conditioned and clean data is then sent
to the modulator driver 822, which transforms the small-swing
digital voltage to an output modulation that drives the laser
through the TOSA 823. The laser is coupled to a single-mode optical
fiber 824 through an industry standard LC optical connector.
Optical fiber 824 is representative of an optical medium for
coupling to an optical network for transmission from optical
transceiver 800.
[0057] The receiver path can convert the incoming DC-balanced,
serial NRZ optical data into a serial electrical data utilizing an
embodiment of a dynamic bias enhanced technique. Optical fiber 824
is also representative of an optical medium for coupling to an
optical network for reception of light in optical transceiver 800.
The incoming light is coupled to an APD from the single-mode
optical fiber 824 through ROSA 825. The photocurrent from the APD
photodetector of ROSA 825 can be converted into a voltage by
transimpedance amplifier 826 and then amplified by a post-amplifier
circuit 826. However, unlike conventional receivers, the bias of
the APD is dynamically changed. Dynamic bias generator 820 uses an
extracted clock from the CDR circuit 828 to synchronize the bias
with incoming data stream. The CDR circuit 828 generates a clock
that is at the same frequency as the incoming data bit rate. This
clock can be phase aligned by a phase-locked loop (PLL) that
samples the data in the center of a data eye pattern. Dynamic bias
generator circuit 805 uses the main clock to synchronously vary the
APD bias for performance enhancement. Care should be taken in
designing the transimpedance amplifier, since the dynamic bias
signal may get injected into the amplification path and wipeout the
weak photo current signal. To eliminate the bias signal injection
into transimpedance amplifier 826, a fully differential
transimpedance amplifier can be implemented (FIG. 9), where the
dynamic bias in applied equally on the DBE-APD 824 and a dummy APD
834. As a result, the dynamic bias, which is a common-mode signal,
can be eliminated via the differential output voltage, V.sub.o, as
shown in FIG. 9.
[0058] FIG. 10 shows an APD with separate, absorption, charge, and
multiplication regions (SACM) structure. Multiplication regions
1005 can include typical structures having one or more of an InAlAs
region and an InAlAs/InAlGaAs heterostructure. The heterostructure
can be structured, through the thickness of the individual layers,
to benefit the GBP enhancement caused by the dynamic biasing. The
widths of the InAlAs and InAlGaAs layers of the multiplication
region can be chosen according to guidelines provided by the
theoretical optimizations implemented according to processes
discussed herein.
[0059] A process to select appropriate structures for
optoelectronic devices and dynamic biasing of these devices can
include simulating different heterostructures to optimize the
electric field profile; growing a series of APDs using different
doping profiles to effect the field-gradient properties as
determined from analysis using theoretical optimizations as
discussed herein; fabricating a family of APDs parameterized by the
width of the multiplication region over a selected range of widths;
perform device characterization of each of the APDs developed
including I-V characteristics (under a constant bias), dark
current, gain, quantum efficiency, breakdown voltage and excess
noise factor; and benchmarking performance against commercial APDs.
For example, such a procedure can begin with simulating different
heterostructures with InGaAs absorbers and InAlAs/InAlGaAs
absorbers using a T-CAD Sentaurus platform to optimize the electric
field profile. A series of APDs can be grown using different doping
profiles to affect the field-gradient properties as directed from
analysis implementing example theoretical optimization as discussed
herein. A family of InGaAs/InAlAs and InGaAs/InAlAs/InAlGaAs APDs
parameterized by the width of the multiplication region ranging
from 150 nm to 200 nm can then be fabricated. After forming theses
APDs, the procedure can include performing device characterization
of each of the APDs developed including I-V characteristics (under
a constant bias), dark current, gain, quantum efficiency, breakdown
voltage and excess noise factor. The performance of these
fabricated APDS can be benchmarked against commercial APDs such as
commercial InP APDs tested and characterized in a similar fashion
as the fabricated custom APDs.
[0060] FIGS. 11A-C show a serializer/deserializer (SERDES) module.
An example SERDES testchip was fabricated using 0.5 um ON
semiconductor manufacturing process through a fabrication service
provider. FIG. 11A shows the testchip layout. FIG. 11B shows the
die of the SERDES with couplings for external connection. FIG. 11C
shows a test board for the SERDES. This custom designed SERDES can
be utilized to interface an optical transceiver to a desktop
computer for overall data transmission test, bit error rate, and
maximum data rate measurements.
[0061] FIGS. 12A-B show schematic diagrams of frequency and time
domain measurement setups. FIG. 12A shows a schematic diagram of
frequency domain measurement setup that includes APD 1205, network
analyzer 1231 having a first port 1233 and a second port 1234, and
an electro-absorption modulated DFB laser 1232. The frequency
response of APD 1205 can be measured on a 40 GHz network analyzer
1231 using an electro-absorption modulated DFB laser 1232 as a
calibrated light source on first port 1233. This particular emitter
operates at a wavelength of 1550 nm, has a very flat small-signal
response across the desired frequency range, and up to 10 mW
optical output power. On the receiver end. APD 1205 itself can be
fabricated in a low parasitic package that permits on-wafer
microwave probing up to 40 GHz and connection to second port 1234
of GHz network analyzer 1231.
[0062] FIG. 12B shows a schematic diagram of a time domain
measurement setup that includes APD 1205, a 1550 nm erbium-doped
fiber mode-locked laser 1242, and a digital serial analyzer 1241.
For time domain measurements, 1550 nm erbium-doped fiber
mode-locked laser 1242 can be used to generate 1.5 ps pulses and
connect the on-wafer probed APD 1205 to digital serial analyzer
1241 with a 70 GHz bandwidth electrical sampling module. These
measurements are particularly useful for elucidating the fast/slow
time responses in the APDs and for crosschecking the frequency
response behavior with its time domain transform.
[0063] FIG. 13 shows features of an example embodiment of a method
1300 of operating an optoelectronic device. System 1300 may include
one or more features of methods with respect to other figures and
methods as discussed herein. At 1310, an optical pulse is received
at an avalanche photodiode. An optical pulse can be received at an
avalanche photodiode in linear mode or equivalent below-breakdown
mode. Receiving the optical pulse at the avalanche photodiode can
include receiving an optical pulse at an InP avalanche photodiode.
Receiving the optical pulse at the avalanche photodiode can include
receiving an optical pulse at an avalanche photodiode having a
multiplication region containing an InAlAs--InAlGaAs
heterostructure. Other materials may be used for the construction
of the avalanche photodiode. At 1320, a reverse bias applied to the
avalanche photodiode is varied during the reception of the optical
pulse at the avalanche photodiode. Varying the reverse bias can
include varying voltage applied to the avalanche photodiode from a
high voltage to a low voltage. Varying the reverse bias may include
applying a sinusoidal waveform. Varying the reverse bias may
include applying a sawtooth waveform. Varying the reverse bias may
include applying a triangular waveform. Varying the reverse bias
may include applying other non-constant waveforms. At 1330, an
electrical signal that corresponds to the received optical pulse is
output from the avalanche photodiode.
[0064] FIG. 14 shows an example embodiment of a system 1400
including an optoelectronic device. System 1400 may include one or
more features of components with respect to other figures and
methods as discussed herein. System 1400 can include an avalanche
photodiode 1410 and a bias generator 1405 coupled to avalanche
photodiode 1410. Avalanche photodiode 1410 can be arranged to
receive an optical pulse from an optical medium and to output an
electrical signal that corresponds to the received optical pulse.
Avalanche photodiode 1410 can be arranged in linear mode or
equivalent below-breakdown mode to receive an optical pulse from an
optical medium and to output an electrical signal that corresponds
to the received optical pulse. Avalanche photodiode 1410 can
include an InP avalanche photodiode. Avalanche photodiode 1410 can
include an avalanche photodiode having a multiplication region
containing an InAlAs--InAlGaAs heterostructure.
[0065] Bias generator 1405 can be arranged to apply a time-varying
bias to avalanche photodiode 1410 such that a reverse bias applied
to avalanche photodiode 1410 varies during the reception of the
optical pulse at avalanche photodiode 1410. The applied
time-varying bias can be a bit-synchronized time-varying bias. Bias
generator 1405 can be structured to apply a reverse bias to
avalanche photodiode 1410 by varying voltage applied to avalanche
photodiode 1410 from a high voltage to a low voltage. Bias
generator 1405 may include a sinusoidal waveform circuit 1406
structured to apply a sinusoidal waveform. Bias generator 1405 may
include a sawtooth waveform circuit 1408 structured to apply a
sawtooth waveform. Bias generator 1405 may include a triangular
waveform circuit 1407 structured to apply a triangular waveform.
Bias generator 1405 may include a non-constant waveform circuit
1409 structured to apply a non-constant waveform.
[0066] System 1400 may include a transimpedance amplifier coupled
to bias generator 1405 and avalanche photodiode 1410. The
transimpedance amplifier can be structured as a differential
transimpedance amplifier using a dummy avalanche photodiode
arranged to receive the time-varying bias as a reverse bias. For
system 1400, the optical medium can include a single mode fiber
such that avalanche photodiode 1410 is arranged to receive the
optical pulse from the single mode fiber. The single mode fiber may
be coupled to a digital communications network.
[0067] FIG. 15 shows features of an example embodiment of a method
1500 of determining a time-varying bias to be applied to an
optoelectronic device. Method 1500 may include one or more features
of methods with respect to other figures and methods as discussed
herein. At 1510, a processor in conjunction with a memory system is
operated to perform a recursive characterization of means of
electron and hole stochastic impulse-response functions with
respect to an avalanche photodiode under dynamic bias conditions,
each respective mean based on an age-dependent probability density
function for the respective electrons or holes, each age-dependent
probability density function dependent on a time-varying applied
electric field, each time-varying applied electric field
corresponding to a time-varying reverse bias to apply to the
avalanche photodiode. The time-varying applied electric field can
be selected from a set of time-varying applied electric fields,
where each time-varying applied electric field corresponds to a
different time-varying reverse bias to apply to the avalanche
photodiode. The set may include only one time-varying electric
field. At 1520, material-specific constants are applied to the
age-dependent probability density functions in the operating of the
processor to perform the recursive characterization with respect to
the avalanche photodiode such that a mean impulse function for
holes or for electrons is generated.
[0068] At 1530, a product of the mean impulse function for holes or
for electrons and a probability density function of photons
received at the avalanche photodiode within a bit of a time
duration is processed such that a photon-arrival-time averaged
impulse-response function is generated. At 1540, the
photon-arrival-time averaged impulse-response function is
processed, forming a bandwidth of the avalanche photodiode.
Processing the photon-arrival-time averaged impulse-response
function, forming the bandwidth of the avalanche photodiode, can
include calculating a 3 dB bandwidth of a Fourier transform of the
photon-arrival-time averaged impulse-response function. At 1550, a
gain of the avalanche photodiode is determined based on recursive
processing using the age-dependent probability density function for
the electrons or holes. At 1560, the avalanche photodiode is
evaluated based on a product of the gain and the bandwidth.
[0069] Method 1500 can include, for the set having more than one
time-varying applied electric field and for each time-varying
applied electric field in the set, performing the operations such
that a product of a gain and a bandwidth is determined for each
time-varying applied electric field of the set. Method 1500 can
include selecting one of the different time-varying reverse biases
from the set, based on evaluation of the products of the gain and
bandwidth corresponding to each reverse bias, to operatively apply
to the avalanche photodiode.
[0070] Method 1500 can include replacing the material-specific
constants with one or more sets of material-specific constants and
repeating the operations for each set of material-specific
constants forming a gain bandwidth product for each item in a
combination of the set of material-specific constants and the set
of time-varying reverse biases. Method 1500 can include selecting a
structure of an avalanche photodiode applicable to a selected
apparatus and a selecting a time-varying reverse bias applicable to
the selected apparatus, the structure and time-varying reverse bias
selected from the combination. Method 1500 can include selecting a
structure by selecting material of a multiplication region of the
avalanche photodiode. Method 1500 can include selecting a structure
by selecting a thickness of a multiplication region of the
avalanche photodiode.
[0071] Method 1500 can include replacing the material-specific
constants with one or more sets of material-specific constants and
repeating the operations for each set of material-specific
constants forming a gain bandwidth product for each set of
material-specific constants. Method 1500 can include selecting an
avalanche photodiode for an apparatus based on a comparison of the
gain bandwidth products for each set of material-specific
constants.
[0072] Method 1500 can include recursive processing sequentially in
blocks of time in multiple separate parts, one part for each block
of time. Method 1500 can include processing using data calculated
in a previous part and saving data in a current part for use in a
next part.
[0073] Various components of a system can include implementations
using a processor operable to determine a time-varying bias to be
applied to an optoelectronic device. These implementations may
include a machine-readable storage device having machine-executable
instructions, such as a computer-readable storage device having
computer-executable instructions, to: operate a processor in
conjunction with a memory system to perform a recursive
characterization of means of electron and hole stochastic
impulse-response functions with respect to an avalanche photodiode,
each respective mean based on an age-dependent probability density
function for the respective electrons or holes, each age-dependent
probability density function dependent on a time-varying applied
electric field from a set of time-varying applied electric fields,
each time-varying applied electric field corresponding to a
different time-varying reverse bias to apply to the avalanche
photodiode; to apply material-specific constants to the
age-dependent probability density functions in the operating of the
processor to perform the recursive characterization with respect to
the avalanche photodiode such that a mean impulse function for
holes or for electrons is generated; to process a product of the
mean impulse function for holes or for electrons and a probability
density function of photons received at the avalanche photodiode
within a bit of a time duration such that a photon-arrival-time
averaged impulse-response function is generated; to process the
photon-arrival-time averaged impulse-response function, forming a
bandwidth of the avalanche photodiode; to determine a gain of the
avalanche photodiode based on recursive processing using the
age-dependent probability density function for the electrons or
holes; and to evaluate the avalanche photodiode based on a product
of the gain and the bandwidth. The instructions can include
instructions to select a time-varying bias from a number of
time-varying biases to apply to an avalanche photodiode. The
instructions can include instructions to select the structural
properties of an avalanche photodiode, The instructions can include
instructions to select the structural properties of an avalanche
photodiode and to select a time-varying bias from a number of
time-varying biases to apply to the avalanche photodiode. The
instructions can include instructions to operate a system to
analyze parameters for an avalanche photodiode and time-varying
bias schemes for the avalanche photodiode such that the avalanche
photodiode has an enhanced gain bandwidth product relative to
conventional avalanche photodiodes biased by a constant signal in
accordance with the teachings herein. For example, instructions can
include instructions to perform the operations of the example
method associated with FIG. 15. Further, a machine-readable storage
device, herein, is a physical device that stores data represented
by physical structure within the device. Examples of
machine-readable storage devices include, but are not limited to,
read only memory (ROM), random access memory (RAM), a magnetic disk
storage device, an optical storage device, a flash memory, and
other electronic, magnetic, and/or optical memory devices.
[0074] FIG. 16 shows an example embodiment of a system 1600
operable to determine a time-varying bias to be applied to an
optoelectronic device. System 1600 may include one or more features
of components with respect to other figures and methods as
discussed herein. System 1600 can include a processor 1625, a
memory unit 1630, a bus 1627, an electronic apparatus 1665,
peripheral devices 1645, display unit(s) 1655, and communication
unit 1635. In an embodiment, processor 1625 can be realized as a
processor or a group of processors that may operate independently
depending on an assigned function. Memory unit 1630 can include one
or more memory devices.
[0075] Memory unit 1630 can include instructions stored thereon to
operate according to algorithms and techniques discussed herein
including, but not limited to, the methods associated with FIG. 15.
Memory unit 1630 can have instructions stored thereon, which when
executed by processor 1625, cause the system 1600 to perform
operations to operate a processor in conjunction with a memory
system to perform a recursive characterization of means of electron
and hole stochastic impulse-response functions with respect to an
avalanche photodiode, each respective mean based on an
age-dependent probability density function for the respective
electrons or holes, each age-dependent probability density function
dependent on a time-varying applied electric field from a set of
time-varying applied electric fields, each time-varying applied
electric field corresponding to a different time-varying reverse
bias to apply to the avalanche photodiode; to apply
material-specific constants to the age-dependent probability
density functions in the operating of the processor to perform the
recursive characterization with respect to the avalanche photodiode
such that a mean impulse function for holes or for electrons is
generated; to process a product of the mean impulse function for
holes or for electrons and a probability density function of
photons received at the avalanche photodiode within a bit of a time
duration such that a photon-arrival-time averaged impulse-response
function is generated; to process the photon-arrival-time averaged
impulse-response function, forming a bandwidth of the avalanche
photodiode; to determine a gain of the avalanche photodiode based
on recursive processing using the age-dependent probability density
function for the electrons or holes; and to evaluate the avalanche
photodiode based on a product of the gain and the bandwidth. The
instructions can include instructions to select a time-varying bias
from a number of time-varying biases to apply to the avalanche
photodiode. The instructions can include instructions to select the
structural properties of an avalanche photodiode, The instructions
can include instructions to select the structural properties of an
avalanche photodiode and to select a time-varying bias from a
number of time-varying biases to apply to an avalanche photodiode.
The instructions can include instructions to operate a system to
analysis parameters for an avalanche photodiode and time-varying
bias schemes for the avalanche such that the avalanche photodiode
has an enhance gain bandwidth product relative to conventional
avalanche photodiodes biased by a constant signal in accordance
with the teachings herein. For example, instructions can include
instructions to perform the operations of the example method
associated with FIG. 15. Further, a machine-readable storage
device, herein, is a physical device that stores data represented
by physical structure within the device. Examples of
machine-readable storage devices include, but are not limited to,
read only memory (ROM), random access memory (RAM), a magnetic disk
storage device, an optical storage device, a flash memory, and
other electronic, magnetic, and/or optical memory devices. Memory
unit 1630 can be realized as any type of storage device. Memory
unit 1630 provides a machine-readable storage medium, which can
have instructions stored thereon such that when the instructions
are executed by processor 1625, system 1600 can perform operations
such as determining a time-varying bias for an avalanche photodiode
and determining an appropriate avalanche photodiode for enhanced
operation according to the teachings herein.
[0076] Bus 1607 can provide electrical conductivity among the
components of system 1600. Bus 1607 can include an address bus, a
data bus, and a control bus, each independently configured. Bus
1607 can be realized using a number of different communication
mediums that allows for the distribution of components of system
1600. Use of bus 1607 can be regulated by processor 1625.
[0077] Display units 1645 can be arranged to provide a user
interface to input parameters for the processing performed by
system 1600 using various algorithms and techniques as taught
herein. In various embodiments, electronic apparatus 1635 can
include additional display units, additional storage memory, and/or
other control devices that may operate in conjunction with
processor 1625 and/or memory 1630.
[0078] Although specific embodiments have been illustrated and
described herein, it will be appreciated by those of ordinary skill
in the art that any arrangement that is calculated to achieve the
same purpose may be substituted for the specific embodiments shown.
Upon studying the disclosure, it will be apparent to those skilled
in the art that various modifications and variations can be made in
the devices and methods of various embodiments of the invention.
Various embodiments can use permutations and/or combinations of
embodiments described herein. Other embodiments will be apparent to
those skilled in the art from consideration of the specification
and practice of the embodiments disclosed herein. It is to be
understood that the above description is intended to be
illustrative, and not restrictive, and that the phraseology or
terminology employed herein is for the purpose of description.
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