IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 20, NO. 6, NOVEMBER/DECEMBER 2014
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Dark Count Statistics in Geiger-Mode Avalanche
Photodiode Cameras for 3-D Imaging LADAR
Mark A. Itzler, Fellow, IEEE, Uppili Krishnamachari, Mark Entwistle, Xudong Jiang, Mark Owens,
and Krystyna Slomkowski
(Invited Paper)
Abstract—We describe cameras incorporating focal plane arrays of Geiger-mode avalanche photodiodes (GmAPDs) that enable 3-D imaging in laser radar (LADAR) systems operating at
wavelengths near 1.0 and 1.5 μm. GmAPDs based on the InGaAsP
material system achieve single-photon sensitivity at every pixel of
the array and are hybridized to custom CMOS ROICs providing
0.25 ns timing resolution. We present camera-level performance
for photon detection efficiency and dark count rate, along with
a survey of the evolution of performance for a substantial number of 32 × 32 cameras. We then describe a temporal statistical
analysis of the array-level dark count behavior that distinguishes
between Poissonian intrinsic dark count rate and non-Poissonian
crosstalk counts. We also report the spatial analysis of crosstalk
events to complement the statistical temporal analysis. Differences
between cameras optimized for the two different wavelengths—
1.0 and 1.5 μm—are noted, particularly with regard to crosstalk
behavior.
Index Terms—Single-photon, avalanche photodiode (APD),
Geiger mode, laser radar (LADAR), three-dimensional (3-D) imaging, short-wave infrared (SWIR).
I. INTRODUCTION
HE ability to detect single photons is an enabling capability for numerous applications in the field of photonics. In
some cases, it is the quantum mechanical properties of single
photons that are exploited, such as in quantum communications
and quantum information processing [1], [2]. More often, detection of single photons becomes essential as classical variants of
applications such as imaging and communications are pushed
to their photon-starved limits [3]–[5]. In all of these scenarios,
Geiger-mode avalanche photodiodes (GmAPDs) have emerged
as an excellent device technology for single-photon detection.
They provide performance that meets the requirements of many
of these single-photon applications, and they do so in a robust
solid-state platform that is readily scalable to achieve a high
degree of integration at a relatively low cost. Consequently, for
the detection of single photons in the wavelength range from
T
Manuscript received February 17, 2014; revised April 13, 2014; accepted
March 30, 2014.
The authors are with Princeton Lightwave, Inc., Cranbury, NJ 08512
USA
(e-mail: mitzler@princetonlightwave.com; ukrishnamachari@
princetonlightwave.com; mentwistle@princetonlightwave.com; xjiang@
princetonlightwave.com; mowens@princetonlightwave.com; kslomkowski@
princetonlightwave.com).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JSTQE.2014.2321525
0.9 to 1.6 μm, GmAPDs based on the InGaAsP material system
have proven to be a preferred sensor technology.
Recent advances in InGaAsP-based GmAPDs have emphasized higher counting rates and integration of the devices into
large-format arrays [6], [7], and one of the most important
drivers for these advances is the deployment of GmAPD focal plane arrays (FPAs) in three-dimensional (3-D) imaging
laser radar (LADAR) systems [3], [8]. These systems—also
described as light detection and ranging (LIDAR) imaging—
exploit time-of-flight measurements at every pixel of the FPA
to create 3-D point clouds that can be processed to create 3-D
images. The ability to generate this imagery with single-photon
sensitivity is a disruptive capability. Three-dimensional LADAR
systems based on single-photon-sensitive GmAPDs, such as the
Airborne Lidar Testbed (ALIRT) system fielded by MIT Lincoln Laboratory [9] and the High Altitude Lidar Operations
Experiment (HALOE) deployed by Northrop Grumman [10],
have demonstrated the capability to collect high-resolution 3D imagery from much higher altitudes and at rates at least
an order of magnitude faster than alternative technologies. For
shorter distance applications, the single-photon sensitivity of
these FPAs allows their implementation with much more modest laser sources, greatly reducing the size, weight, and power
dissipation of the overall system.
In this paper, we describe the design and performance of
cameras incorporating InGaAsP-based GmAPD FPAs with a
32 × 32 format. Expanding on earlier work [11], [12] reported
for similar devices, we present data representing a relatively
large number of sensors. We then provide a deeper investigation of the dark count behavior of these arrays, including a
statistical temporal analysis of the dark count data that distinguishes between Poissonian intrinsic dark counts and nonPoissonian behavior arising from avalanche-mediated optical
crosstalk. A complementary spatial analysis of crosstalk is also
presented.
The remainder of the paper is organized as follows. In
Section II, we describe the design and architecture of the FPAs
and cameras as well as their operation. In Section III we describe the test set used to perform the measurements presented
in the paper. The fundamental array-level performance characteristics of photon detection efficiency (PDE) and dark count
rate (DCR) are presented in Section IV. Section V contains
a statistical temporal analysis of the dark count data, and we
supplement the temporal analysis of Section V with a detailed
spatial analysis of the crosstalk phenomenon in Section VI.
1077-260X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications standards/publications/rights/index.html for more information.
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Fig. 1. Schematic illustration of the construction of the GmAPD FPA. See
text for a description of the FPA components.
A discussion of our results and final conclusions is provided in
Section VII.
II. SENSOR ARCHITECTURE AND OPERATION
A. FPA Design
The core functionality of the GmAPD FPA is determined
by three semiconductor arrayed devices: the InGaAsP-based
GmAPD photodiode array (PDA); a 0.18 μm CMOS readout
integrated circuit (ROIC); and a GaP microlens array (MLA).
The PDA pixels are connected to their corresponding ROIC pixels by indium-bump flip-chip hybridization. The MLA is then
aligned and attached to the substrate side of the rear-illuminated
PDA to maintain a high optical fill factor of 75% for optical
coupling to the 34 μm diameter active region in each PDA pixel.
The ROIC I/O channels are wirebonded to a ceramic interposer
which facilitates routing of electrical signals to appropriate pins
of a pin grid array in the hermetic housing assembly. An integrated thermoelectric cooler maintains a temperature differential of 55 °C relative to the ambient temperature of the housing;
for a typical 25 °C ambient, the FPA operates at about −30 °C.
A schematic illustration of the FPA construction is provided in
Fig. 1.
The GmAPD devices in each pixel of the PDA are based
on a buried p-n junction fabricated using a zinc dopant diffusion process that provides highly uniform and reliable pixels in
large scale arrays. PDAs optimized for operation using source
lasers with an output wavelength near 1 μm employ an InGaAsP
absorber region that results in spectral response over the wavelength range from 900 to 1150 nm. PDAs intended for use with
longer-wavelength sources near 1.5 μm make use of an InGaAs
absorber region that results in wider spectral response from 900
to 1620 nm. In previous publications, we have described the design of these GmAPD devices [6], [13] and their incorporation
into array formats [11], [14].
B. Camera-Level Integration
The GmAPD FPA has been integrated into a modular camera
head with three principal electronic boards. The FPA board supports the FPA sensor itself, and it has circuitry that controls FPA
power and temperature regulation. The FPGA board contains an
altera FPGA and a microcontroller that provide extensive onboard functionality through firmware programming. In addition
to facilitating operation of the ROIC, the FPGA also collects
and formats raw data from the ROIC for transfer off of the camera head. This data transfer is executed by the interface board
using an industry-standard CameraLink protocol, and this board
also manages external power regulation and external clock and
trigger inputs. The camera head requires only a single 15 W dc
source between 12 and 36 V, from which all required biases and
power levels are generated internally.
Through the CameraLink interface, the camera head communicates with the system computer that controls all camera
functions through comprehensive graphical user interface (GUI)
software. Beyond camera control, this software also provides
for real-time data storage to solid-state drives (SSDs) in RAID0
configuration, accommodating data rates in excess of 4 Gb/s at
the maximum camera frame rate of 182 000 Hz.
C. Sequence of Framed Operation
The framed operation of the GmAPD cameras described in
this paper proceeds according to the following sequence. Each
data frame is initiated by a trigger signal that can be provided by
the internal camera clock; by an external system clock; or by any
other synchronizing signal, such as from a “flash detector” that
generates a trigger correlated to an out-going laser pulse. Before
arming the pixels of the FPA, the camera provides for a variable
delay time ranging from 0 to 256 μs to allow for the transit time
of the ns-scale laser pulse to be reflected from distant objects.
During this delay time, the camera remains in its disarmed state,
with the reverse bias voltage across the GmAPD detectors set
to a disarm value Vd below the breakdown voltage Vb , where
Vb –Vd is generally on the order of 1 to 4 V. (All voltages in
this discussion entail reverse biasing of the GmAPD but are
expressed as positive values for convenience.) Following the
delay time, the pixels are armed by applying an additional 5 V
reverse bias using appropriate transistors in the CMOS ROIC.
This brings the reverse voltage of the GmAPDs above Vb by an
excess bias Ve and corresponds to charging up the capacitance
of each GmAPD to Ve = Vb –Vd + 5 V. This charging period
of 12 ns is the only time during which the GmAPD pixels are
connected to an external supply with the net voltage exceeding
Vb . Once the pixels are charged to the target Ve value, the external
5 V supply is disconnected, and any small leakage of charge
from the GmAPD capacitance that would cause a reduction in
voltage is compensated in the pixel-level ROIC circuitry, thereby
maintaining the target excess bias value.
Once the pixel arming sequence is complete, linear-feedback
shift register pseudorandom counters in all the pixels are enabled
to begin timing during the “range gate.” The counters have 13-bit
resolution, and a full range gate consists of the counters proceeding through 8000 counter values, ending with a final “terminal
count” value. During the counting sequence, an avalanche at
any GmAPD pixel will freeze the corresponding pixel counter
in the ROIC, indicating the arrival time of a photon or a dark
count, and the pixel is then disarmed by actively quenching the
ITZLER et al.: DARK COUNT STATISTICS IN GEIGER-MODE AVALANCHE PHOTODIODE CAMERAS
bias voltage of that pixel below Vb . A pixel records only one
time-stamp value per frame. At the end of a frame, if a pixel
returns the terminal count, then it did not detect an avalanche
event for that frame. Once the terminal count is reached, all the
remaining armed pixels are disarmed, and all counter values are
read out along shift registers in each row during a readout period
of 3.5 μs.
By adjusting the ROIC clock frequency, we can vary the time
duration associated with each counter increment from 0.25 to
1.25 ns. Given 8000 of these “time-bins” in each range gate,
the total range gate duration can be varied from 2 to 10 μs. The
sequential combination of a 2 μs range gate followed by a 3.5 μs
read-out time provides the maximum frame rate of 182 kHz.
Because the GmAPD in each pixel is disconnected from the
ROIC external 5 V bias during the range gate, an avalanche
during the range gate has a charge flow that is limited to the
charge applied in raising the bias of the device from the disarmed voltage Vd to the excess bias Ve . This total bias charge Q
is roughly equivalent to (Cd + Cp )•(5 V) where Cd 100 fF is
the APD capacitance and Cp is any parasitic capacitance. If we
assume Cp ∼ Cd , then Q 6 × 106 e− . However, during the
12 ns arming period while the pixels are connected to the external ROIC supply that charges up the APDs to Ve , the triggering
of an avalanche can result in continuous charge flow for the
remainder of the arming period. Assuming a 5 V bias across an
estimated 5 kΩ series impedance in the arming circuit, current
flow for an average duration of 6 ns (i.e., half of the 12 ns arming period) results in 108 e− , or roughly 10 times more than
a pixel avalanche during the range gate. This discharging of a
pixel during the arm cycle causes this pixel to be in the disarmed
state when the counters start, and it registers a count during the
very first time bin of the range gate. These counts are often
referred to as “early fire” events. Moreover, their comparatively
large current flow during the arming period can lead to crosstalk
events that generate additional early fires. This distinction will
be mentioned later in our discussion of the statistics of crosstalk
and the impact of segregating early fire counts at the beginning
of the range gate.
D. FPA Performance Attributes
The GmAPD FPA exhibits a number of critical performance
attributes. The probability of successfully detecting a single
photon when it arrives at one of the FPA pixels is referred to
as the PDE of that pixel. In all of the PDE data presented in
this paper, we provide camera-level PDE values which include
all optical losses associated with elements in the optical path,
including the 75% fill factor of the MLA, in which the lenses
have an acceptance angle of 6° from normal incidence.
There is also a finite probability of false counts being triggered
in the absence of photon arrivals, giving rise to an effective DCR.
The measured dark counts actually include counts originating
from several mechanisms. The generation of dark carriers by
thermal excitation or trap-assisted tunneling dictates the intrinsic
DCR, and the early fire phenomenon described in the previous
sub-section can be classified as a distinct type of dark count.
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During each avalanche event, the charge flow described in
Section II-C gives rise to photon emission, likely due to intraband relaxation of hot carriers crossing the diode p-n junction
[15], and the photons emitted by this hot-carrier luminescence
effect can initiate correlated avalanches at other array pixels.
These “crosstalk” counts can be initiated by avalanches associated with photon detections or dark counts, and they therefore
are present in any array-level raw data collected for PDE or
DCR. One of the new results reported below is the unambiguous extraction of the crosstalk contribution to DCR based on a
statistical analysis of the temporal attributes of array-level DCR
data.
Another important attribute of GmAPD FPAs used for timeof-flight measurements is the uncertainty in the recorded photon
arrival times, commonly referred to as the timing jitter. We
distinguish between the uncertainty among timestamps for all
the pixels of a single frame—the “intra-frame” jitter—and the
frame-to-frame uncertainty in a given pixel—the “inter-frame”
jitter. We have reported typical values for these two types of
jitter of 175 and 380 ps, respectively [12], although more recent
results suggest that both types of jitter are inherently < 200 ps
and that previous measurements of larger inter-frame jitter were
actually dominated by system-level jitter from the pulsed laser
source [16]. Beyond this summary of previous results, we will
not address timing jitter performance further in this paper.
A final performance attribute of frequent importance for
GmAPDs is the afterpulsing effect [17] caused by the trapping of charges resulting from one avalanche and the occurrence of correlated dark counts a short time later due to the
subsequent detrapping of these charges. Afterpulsing can be
mitigated by imposing a sufficiently long “hold-off” time following an avalanche event to allow detrapping of substantially
all of the trapped charges prior to re-arming a GmAPD. Under
typical GmAPD operating conditions (e.g., 3 V excess bias and
an FPA temperature of 248 K), afterpulsing effects can be significant for hold-off times of less than 1 μs, but hold-off times
longer than this are adequate to reduce afterpulsing to inconsequential levels, as found by some of the present authors for
discrete GmAPDs [17] as well as by Frechette et al. for GmAPD
arrays operated with asynchronous ROICs [18]. For the FPAs
described in this paper, the GmAPDs are always disarmed during the 3.5 μs readout time of our framed ROIC operation, and
this readout period acts as a hold-off time that mitigates any
afterpulsing effects.
III. CHARACTERIZATION TEST SET-UP
GmAPD camera characterization is carried out using the setup illustrated schematically in Fig. 2. The camera can be powered by a 15 W supply with an input voltage at any value in
the range of 12 to 36 V. The camera provides a trigger output (trig out) to drive an Avtech pulse generator that is used
to pulse a laser diode. This trigger can be generated internally
by the camera or injected from an external trigger source (Ext
Trig). Gain-switched operation of the laser diode generates output pulses with a width of 150 ps, and output wavelengths
of either 1064 or 1550 nm are used depending on which type
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Fig. 2. Schematic layout of experimental apparatus for characterization of
GmAPD cameras. PC: personal computer; GUI: graphical user interface; SSD:
solid-state drive.
of camera is under test. The pulsed diode output is transmitted
through two attenuators before being spread by a collimator to
a beam diameter of 5 mm with a uniformity of about 5%.
The collimator attenuates the optical density by approximately
40 dB, and a mean photon number of 0.1 per 100 μm pitch
pixel per pulse is achieved with 20 dB attenuation from Atten 1 and 0–10 dB attenuation from Atten 2. To obtain single
pixel measurements, the set-up is modified by replacing the collimator with a lensed fiber that has a 5 mm working distance
and 10 μm spot size. Both the collimator and the lensed fiber
can be aligned with sub-micrometer precision using a remotely
controlled X/Y/Z translation stage.
The camera is connected to a personal computer (PC) using
the industry-standard CameraLink protocol, and the frame grabber in the PC supports CameraLink operation in base, medium,
and full configurations. Full configuration is required to establish the necessary data transfer rate to support the full frame rate
of 182 000 Hz. The GUI on the PC allows comprehensive set-up
and control of the camera, and this software supports real-time
data storage at the maximum camera frame rate to SSDs in
RAID0 configuration.
IV. FUNDAMENTAL DCR VERSUS PDE TRADEOFF
The most fundamental tradeoff in the operation of GmAPDs
is that between DCR and PDE. Higher PDE can be obtained
by operating the detector at a larger excess bias, but only at
the expense of consequently higher DCR. Both parameters are
proportional to the avalanche probability Pa , which increases
with larger excess bias, and so to first order PDE and DCR
will increase by the same proportional amount as the excess
bias is raised. To the extent that the DCR includes electric
field-mediated mechanisms—primarily trap-assisted tunneling
effects [19]—the DCR will exhibit a larger rate of increase with
excess bias than that of the PDE.
The PDE performance of a 32 × 32 format GmAPD camera
is conveniently summarized by plotting a spatial map of PDE
Fig. 3. PDE data for sensor No. 261 at an operating point with average PDE =
30.5%, average DCR = 2.2 kHz, and T = 248 K. (a) Camera-level performance
map illustrates PDE for each pixel, and (b) a histogram summarizes distribution
of PDE performance of all 1024 pixels from (a).
values obtained for all 1024 pixels, as shown in Fig. 3(a) for
an FPA sensor designated as No. 261. Pixel-level PDE values
are obtained from 10 000 frames of data. During each frame,
the array is illuminated by a short laser pulse of 150 ps duration that is collimated and calibrated to provide a mean photon number of μ = 0.1 photon per pixel area, as described in
Section III. PDE for each pixel is determined by the number of
counts observed and scaling for μ. (For other measurements in
which larger values of μ are used, correcting for the Poisson
probability of multiple photons per pixel per pulse is important
to arrive at accurate PDE values.) The measured dark counts are
subtracted from the illuminated measurements to obtain PDE
values, but these PDE values do include crosstalk counts, which
are quantified in the next section. The data presented in the figure are obtained at an excess bias corresponding to a mean DCR
of 2.2 kHz (see below) and an FPA temperature of 248 K. The
corresponding distribution of PDE values is described by the
ITZLER et al.: DARK COUNT STATISTICS IN GEIGER-MODE AVALANCHE PHOTODIODE CAMERAS
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Fig. 5. DCR data for 18 cameras corresponding to PDE = 31 ± 1% and
operating temperature 248 ± 5 K. Solid circles (•) indicate the average DCR
over the 32 × 32 array and error bars indicate the standard deviation (±σ) of
the DCR distribution.
Fig. 4. DCR data (in kHz) for sensor No. 261 at an operating point with
average PDE = 30.5%, average DCR = 2.2 kHz, and T = 248 K. (a) Cameralevel performance map illustrates DCR for each pixel, and (b) a histogram
summarizes distribution of DCR performance of all 1024 pixels from (a).
histogram in Fig. 3(b), for which the mean PDE is 30.5% and
the standard deviation σ(PDE) is 4.0%.
Under the operating conditions used to obtain the PDE performance map in Fig. 3, we demonstrate the DCR performance
for the same camera in the absence of illumination with the map
of DCR values of all pixels of the FPA in Fig. 4(a). These data
are obtained from 10 000 frames of data with the camera operating at an average PDE of 30.5% and at an FPA temperature
of 248 K. Each frame had a duration of 2 μs, and the DCR
was computed by dividing the total number of counts observed
during the 10 000 frames by the cumulative time of GmAPD
operation (i.e., 10 000 × 2 μs = 20 000 μs). (In the following
section, we discuss the probability of missed counts due to the
FPA capturing only one count per pixel per frame.) The distribution of DCR values is described by the histogram in Fig. 4(b),
for which the mean value is 2.2 kHz and the standard deviation
σ(DCR) is 0.4 kHz.
Spatial variations in pixel-level PDE and DCR across the FPA
are generally dominated by systematic variations in the breakdown voltage Vb of the GmAPDs in each pixel. Because the
same disarm voltage Vd and 5 V CMOS bias voltage swing are
applied to all pixels in the array, any variation in Vb will result
in a corresponding variation in excess bias Ve (cf. discussion in
Section II). A lower Ve will lead to lower values for both PDE
and DCR, and inspection of the performance maps in Figs. 3
and 4 indicates that there is some systematic reduction in both
of these parameters near the edges of the arrays, particularly the
lower edge. This is the result of slight differences in fabrication processes for pixels along the edges of the GmAPD PDA,
and these variations can be reduced with modest design improvements to compensate for dopant diffusion loading effects
in future iterations of device processing. We also observe systematic, fairly monotonic gradients in performance over longer
length scales encompassing full arrays, and these originate from
gradients in the properties of the epitaxial wafers used to fabricate the GmAPD PDAs. For the metal-organic chemical vapor
deposition processes used to grow these wafers, variations in
key structural attributes such as epitaxial layer thickness and
doping concentration are fairly radial, as evidenced by waferlevel characterization techniques such as Fourier transform infrared spectroscopy and photoluminescence, and these longerscale performance variations can be correlated to the underlying
wafer properties [20].
To demonstrate the maturation of the GmAPD FPA performance, in Fig. 5 we summarize the DCR characteristics of 18
cameras plotted in chronological order of fabrication and representing several fabrication lots of GmAPD PDAs. The solid
circles indicate the average DCR of each array, and the error
bars indicate the standard deviation (±σ) of the DCR distribution for each array. The average DCR has tended to decrease
appreciably, and the average ratio of the standard deviation to
the mean is σ/DCR 0.3. In addition to inherent improvements
in the DCR versus PDE tradeoff at the GmAPD device level,
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improved optical coupling of the MLA to the PDA allows a
target PDE value (e.g., 30%) to be achieved at a lower excess
bias with a consequently lower DCR.
V. STATISTICAL TEMPORAL ANALYSIS OF DCR
AND CROSSTALK EXTRACTION
In the previous section, we presented a basic description of
the DCR behavior of the GmAPD FPAs based on the number of
frames for which each pixel exhibits a dark count. In this section,
we show that we can extract a great deal more information
about the measured dark counts by considering their timing
information. In principle, dark counts possess the following
attributes of a Poisson process [21]: (i) they are memoryless—
i.e., counts from non-overlapping time intervals are mutually
independent; and (ii) for sufficiently small time intervals, the
probability of a count is proportional to the duration of the
time interval, and the probability of more than one count in this
interval is negligible. Assuming that dark count occurrences are
Poissonian in nature, we expect that the “inter-arrival” times
between successive counts will obey an exponential distribution
[21] given by
f (t) = λe−λt /C
(1)
where t is the inter-arrival time, λ is the average DCR, and
the normalization constant C is the total number of counts and
guarantees that f(t) dt = 1 where the integration is performed
over all t from 0 to . This normalization can also be generalized
to any sub-section of the measured data for T1 ≤ t ≤ T2 by
ensuring that
T2
f (t) dt = eT 1 − eT 2
(2)
T1
where C is now the number of counts in this section.
Given a group of pixels that exhibit Poisson statistics, their
collective behavior—such as the inter-arrival times for dark
counts among all of the pixels—will also obey Poisson statistics
[21]. Noting this fact, we analyze dark count inter-arrival times
from the entire array. We also consider all pixels of the array to
be an ensemble of identical devices, and this assumption is reasonable as long as the standard deviation of the pixel-level DCR
distribution is fairly small compared to the mean; for instance,
as illustrated in Fig. 4 for sensor 261, σ(DCR)/DCR 0.18.
It is important to note that the accuracy of the DCR values
obtained in the previous section—based on counting the number
of frames for which each pixel exhibits a dark count—depends
on the fact that, for each pixel, the probability of a dark count
within a single 2 μs frame is sufficiently low. Each pixel can
detect only a single avalanche event per frame, and if there
were a significant probability of multiple dark counts per frame,
all but the first dark count would be missed. However, for the
average DCR of 2.2 kHz in Fig. 4, the average time between
counts is 455 μs, and the Poisson probability of more than one
dark count [21] during a 2 μs range gate is < 0.001%. Even for
the camera with the highest average DCR of 16 kHz in Fig. 5,
the probability of a missed dark count on any frame is only
Fig. 6. Statistical analysis of the inter-arrival times between consecutive dark
counts occurring anywhere on a 32 × 32 GmAPD array with an InGaAsP
absorber for 1 μm sources. Data are from sensor No. 261 and are normalized
as described in the text. The straight-line exponential fit is from Eq. (1). The
inset shows details of data between 0 to 10 ns, particularly the peak at 1 ns.
0.05%. The probability of more than one dark count per 2 μs
range gate exceeds 1% only for DCR > 75 kHz.
A. Temporal Analysis of 1.0 μm FPAs
We proceed with a statistical analysis of the DCR data from
10 000 frames as follows. From each frame, we order the dark
counts collected from all of the pixels according to their time
stamp values, and the elapsed time between each pair of successive dark counts provides us with a set of inter-arrival times for
that frame. The distribution of all inter-arrival times obtained
from all frames is then plotted on a semi-log scale as in Fig. 6.
The timing resolution of the plot is 0.25 ns—i.e., each plotted
point corresponds to a 0.25 ns interval—as dictated by the time
bin resolution of the time stamp counters in the array. Except for
very short inter-arrival times, the distribution exhibits the exponential behavior expected of a Poisson process. An exponential
fit according to (1) was obtained for the inter-arrival time data
between 25 and 450 ns, with appropriate normalization provided
by (2). Ideally, this fit should yield identical values for the prefactor and exponent, and the values found—2.64 × 10−3 and
2.77 × 10−3 , respectively—agree to within 5%. Taking their
average as a best estimate for λ, and noting that this is the DCR
per nanosecond, we rescale to dark counts per second to obtain
an array-level DCR of 2.7 × 106 Hz. Considering that this rate
is for all 1024 pixels of the array, the DCR per pixel of λ/1024
is 2.6 kHz. Based on the assumption of Poissonian behavior for
this analysis, this value is the intrinsic pixel-level DCR of the
FPA. We note that the value of 2.2 kHz obtained from Fig. 4
agrees to within 15%.
We now consider the deviation of the distribution in Fig. 6
from exponential behavior at very short inter-arrival times; this
behavior is shown more clearly in the inset of the figure. All discernible deviation from the Poisson exponential behavior occurs
for inter-arrival times < 2 ns, with a clear peak seen at 1 ns. If
ITZLER et al.: DARK COUNT STATISTICS IN GEIGER-MODE AVALANCHE PHOTODIODE CAMERAS
we ascribe this non-Poissonian contribution to crosstalk events,
this analysis gives us significant insight into crosstalk behavior.
For instance, these data suggest that the most frequent delay
between a primary avalanche and its correlated crosstalk event
is 0.75–1 ns. Much short delays of <0.25 ns—i.e., a crosstalk
count occurring within the same time bin as the primary count—
are much less likely, as are longer delays of >2 ns. Moreover,
we can integrate over the non-Poissonian counts to find a worstcase estimate (assuming all deviation from Poisson behavior are
crosstalk counts) of the fraction of total dark counts that should
be attributed to crosstalk events. Again referring to the Fig. 6
inset, the cumulative crosstalk is 12.6% of the intrinsic DCR of
2.6 kHz at 30% PDE. Note that this includes all non-Poisson
temporally correlated events, without regard for their spatial
separation, which will be treated in the next section.
For the statistical analysis in this section, we have eliminated
dark count data that occurred within the first 2.5 ns of the range
gate to avoid possible inaccuracies in the analysis that might
be introduced by early fire counts and their associated crosstalk
events, as described in Section II-C. In principle, this statistical
analysis should work for any shorter-time subset of the full range
gate data, and we have confirmed that we obtain very similar
quantitative results when eliminate the first 50 or 250 ns of the
range gate from the dark count data set. (The only expected
change would be in the probability of very long inter-arrival
times.) For a typical operating condition with 30% PDE, we
find that the probability of an early fire is <0.5%.
B. Temporal Analysis of 1.5 μm FPAs
The operation of GmAPDs at longer wavelengths near 1.5 μm
requires a detector structure with an InGaAs absorber. The narrower bandgap of this material, relative to InGaAsP used for
detection of wavelengths near 1.0 μm, dictates that higher thermal dark carrier generation rates will lead to higher DCR under
comparable operating conditions for temperature and bias. Additionally, other device design considerations tend to favor the
use of thinner absorption regions for 1.5 μm, resulting in lower
PDE at a given excess bias. We have reported reasonably extensive results for the DCR versus PDE behavior of GmAPDs at
1.5 μm for discrete devices [6] as well as arrays [11].
However, the much wider spectral response of the 1.5 μm
GmAPD FPAs has implications regarding their crosstalk behavior. In a study of crosstalk effects in 1.06 μm GmAPD FPAs,
Younger et al. [22] reported measurements of the breakdown
spectrum due to avalanches in the InP multiplication region,
with a peak in the spectrum centered near the InP band edge
and a broad blackbody component extending to at least 1.7 μm.
Because an InGaAs absorber detects photons over this entire
spectral band, one finds substantially higher crosstalk effects
for these longer wavelength FPAs.
In Fig. 7 we present results for a 1.5 μm FPA obtained from
the same statistical analysis described in the previous section.
Once again, the inter-arrival time histogram is accurately fit by
the expected Poisson exponential behavior in (1), and there is
close agreement between the values of the prefactor and the
exponent in this fit. From these fit values, we compute an in-
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Fig. 7. Statistical analysis of the inter-arrival times between consecutive dark
counts occurring anywhere on a 32 × 32 GmAPD array with an InGaAs absorber
for 1.5 μm sources. Data are normalized as described in the text, and the
straight-line exponential fit is from Eq. (1). The inset shows details of data
between 0 to 30 ns, particularly the peak at 1 ns.
trinsic (Poisson) DCR of 9.2 kHz. This value is less than half
of the 22 kHz DCR found by simply counting all dark counts
(as described in Section IV) for the corresponding operating
conditions of 20% PDE and 253 K.
This discrepancy in DCR determination can be understood
upon closer examination of the non-Poisson behavior at short
inter-arrival times exhibited in the inset to Fig. 7. Just as found
for the 1.0 μm FPA in the Fig. 6 inset, the inter-arrival time
distribution for the 1.5 μm FPA peaks sharply at 0.75–1.0 ns.
However, unlike the shorter wavelength FPA, the non-Poisson
peak associated with crosstalk counts possesses a fairly long
tail the does not merge with the Poisson background until interarrival times as long as 15–20 ns. (Given this much longer tail,
we extended our mitigation of early fire counts by eliminating
the first 50 ns of range data.) Integrating over the total number of crosstalk events indicated by the non-Poisson peak, we
find a much larger cumulative crosstalk probability of 90%. The
combination of these crosstalk counts with the 9.2 kHz intrinsic
DCR would yield an apparent DCR of 17.5 kHz, in reasonable
agreement with the 22 kHz found from simply counting all dark
events. We believe the remaining discrepancy may be related
to early fire effects, but these effects will require further investigation. With these relatively high crosstalk probabilities (i.e.,
compared with the 1.0 μm array), it seems likely that the long
tail in the inset of Fig. 7 is due to cascades of crosstalk events,
and the length of the tail suggests a non-negligible probability
for cascades with at least ten successive events.
VI. SPATIAL DISTRIBUTION OF CROSSTALK
The analysis of the GmAPD FPA dark count data in the
previous section provides valuable information concerning the
intrinsic DCR and crosstalk characteristics, and the exploitation
of their different temporal statistical properties (Poisson and
non-Poisson, respectively) has not been presented previously.
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However, this analysis does not yield any information pertaining to the spatial distribution of crosstalk events. Therefore, in
this section, we describe the complementary analysis of spatial
correlations of dark counts occurring within short temporal separations to infer the spatial characteristics of crosstalk behavior.
We have employed two approaches to measuring the spatial
dependence of crosstalk. One technique involves illumination
focused to a single pixel, with a short pulse incident on this
single pixel at a specific time within each successive frame. For
those frames in which the illuminated pixel fires at the time of
the pulse arrival, we then analyze the timing data for all other
pixels to see if any of them fired a short time thereafter. The
second technique for extracting crosstalk behavior is based on
just the consideration of dark count data: instead of creating
primary avalanches initiated by illumination, one can consider
dark counts to be primary avalanches and then look for correlated counts at short time intervals later, just as in the illuminated
case. In both techniques, the analysis of the resulting data depends on the choice of time frame considered to be temporally
correlated, as well as the choice of distance considered to be
spatially correlated. In previous preliminary work on crosstalk
behavior, we have confirmed that both techniques yield comparable results [14].
It is instructive to review the dark count statistical analysis in
Fig. 6 to guide our choice of a relevant time duration over which
dark counts can be considered to be temporally correlated. In
particular, the inset to this figure for 1.0 μm FPAs suggests that
non-Poissonian behavior associated with crosstalk is dominant
for only 2 ns. Given the possibility of subtle correlations that
persist for longer inter-arrival times, we have used Tc = 10 ns as
a conservative choice of correlation timeframe Tc during which
counts are considered to be temporally correlated and are associated with crosstalk events. According to this reasoning, we then
generate a spatial map of crosstalk probabilities in the following
fashion. We consider each dark count as a primary avalanche
and then search for temporally correlated counts within correlation time Tc . If a temporally correlated count is found, it is
assumed to be a crosstalk event, and its position relative to the
primary avalanche pixel is noted. Every primary event is considered to be at the origin of our spatial map, and the number
of crosstalk counts found at every pixel location relative to this
origin is summed. Any crosstalk event can then be considered
to take the role of a primary avalanche, and in this way cascades of crosstalk events may be identified. We note that any
procedure for assigning spatial correlations such as the one just
described may have an inherent ambiguity in certain cases in
which a crosstalk event has more than one earlier avalanche as
a candidate for its primary avalanche (i.e., there was more than
one avalanche that occurred with a temporal separation less than
Tc ). In these cases, the key is to avoid double-counting in which
a single avalanche is identified as a crosstalk count more than
once.
For a given number of non-illuminated frames (e.g., 10 000),
we find every dark count in each frame and use the correlations just described to create a spatial map of how many times
a crosstalk event occurred at a given pixel location relative to
the primary avalanche. This procedure can be used for arbi-
Fig. 8. Spatial map of crosstalk events from 10 000 frames of data for 1.0 μm
FPA sensor 261 operated at 30% PDE. Values represent number of crosstalk
counts at each location within a 21 × 21 pixel area. The primary avalanche
pixel is represented by the white square at the center. Structure in the map is
discussed in the text.
Fig. 9. Illustration of crosstalk photon propagation in the GmAPD PDA from
primary avalanche pixel “1.” Line-of-sight coupling from “1” to “2” is reduced
by etched isolation trenches. Reflective coupling from “1” to “4” is reduced by
an absorptive metallic coating at “A.” The requirement for a dielectric aperture
at “B” to allow signal photons (incident from top of figure) to reach pixel “3”
promotes relatively high reflection from “1” to “5.”
trarily large distances bounded only by the size of the array.
We exhibit such a map in Fig. 8 for the 1.06 μm FPA sensor
261 used to generate the data in previous sections while operated at an average PDE of 30%. Although we have reduced
line-of-sight coupling of photons to adjacent pixels by etching
optical isolation trenches between them, the crosstalk between
these near-neighbor pixels is still dominant. Trenches are etched
through the entire epitaxially grown structure (i.e., through the
absorber), and the anisotropy in this near-neighbor coupling is
related to the crystallographic dependence of the InP wet-etch
chemistry used, resulting in a V-groove geometry in one direction and a nearly vertical dove-tail geometry in the orthogonal
direction, as described previously [14]. Beyond the eight lineof-sight near-neighbors, crosstalk coupling to further neighbors
occurs by reflection from the back surface of the PDA substrate,
as shown schematically in Fig. 9. Such reflections have been
reduced by depositing an absorptive metallic film over as much
of the PDA back surface as possible. However, it is necessary to
ITZLER et al.: DARK COUNT STATISTICS IN GEIGER-MODE AVALANCHE PHOTODIODE CAMERAS
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found in Section V-B using the temporal analysis presented in
Fig. 7.
VII. DISCUSSION AND CONCLUSION
Fig. 10. Cumulative crosstalk probability as a function of the number of
pixels considered to be spatially correlated with the primary avalanche pixel.
The abscissa represents the dimension N of an N × N pixel area with the primary
avalanche at the center (cf. Fig. 8).
have dielectric anti-reflection coatings (ARCs) within apertures
placed directly above each pixel to facilitate coupling of light
collected from each microlens in the MLA to its corresponding
PDA pixel active region. For large angles of incidence, these
ARCs give rise to high reflectance and define symmetry points
for significant reflections to further neighbor pixels. These reflection characteristics are illustrated schematically in Fig. 9 and
explain the high-level symmetry seen in the spatial crosstalk map
in Fig. 8.
In the processing of 3-D point cloud data from the GmAPD
camera, strongly correlated crosstalk events can degrade resulting imagery. However, even for crosstalk events that are temporally correlated (i.e., occur within Tc ), if they occur at large
distances from the primary avalanche, then spatial correlation
will be weak. For this reason, it has been customary to consider
the total crosstalk counts occurring within an N × N pixel region
centered on the primary avalanche, with N being dictated by the
distance over which spatial correlations are considered to be of
concern. In Fig. 10, we show the dependence of the cumulative
crosstalk summed over all pixels within an N × N region as a
function of N. At a PDE of 30%, we see that the cumulative
crosstalk saturates at a value of 12.2%, in good agreement with
the cumulative crosstalk of 12.6% extracted from the temporal
statistical analysis presented in Section V. This spatial analysis shows that a considerable fraction of the total cumulative
crosstalk counts occur at reasonably large distances from the
primary avalanche. The impact of these crosstalk events with
weaker spatial correlation on overall image quality will depend
on the details of the image processing algorithms.
We also performed a similar analysis of cumulative crosstalk
probability as a function of N × N area size for the 1.5 μm
FPAs. For these longer wavelength arrays, the saturation of
the cumulative crosstalk is qualitatively similar to the behavior
exhibited in Fig. 10 for the 1.0 μm FPA, but the saturation value
is much higher, at 95% for a 1.55 μm PDE of 20%. This
value is quite consistent with the cumulative crosstalk of 90%
The temporal statistical analysis presented in Section V gives
us an extremely useful method for distinguishing between
intrinsic DCR and crosstalk events. In the 1.0 μm FPAs, for
which the crosstalk is relatively low, the non-Poissonian interarrival time behavior that we have ascribed to crosstalk events is
limited to very short inter-arrival times of less than 2 ns, with a
strong peak at 0.75–1 ns. It is likely that this timescale simply reflects the avalanche build-up and quench decay, and this explanation is supported by previous modeling of avalanche timescales
[6], [22]. It is not surprising that the 1.5 μm FPA results exhibit
that same exact peak behavior since both GmAPD device structures employ the same InP multiplication region. However, the
much longer tail found for the longer wavelength detector array
is almost certainly due to the wider spectral response leading
to elevated crosstalk probabilities and consequent cascades of
crosstalk events. In future work, we intend to develop a model
for crosstalk cascades with the goal of providing a quantitative
explanation for the non-Poissonian interarrival time behavior
observed experimentally.
This leads to the question of how much crosstalk can be tolerated. As mentioned earlier, this will depend on the algorithms
used for data analysis. Certainly, impressive imagery has been
obtained using 1.0 μm FPAs with performance comparable to
those described here [9], [10]. Moreover, notwithstanding the
much higher crosstalk observed for the 1.5 μm FPAs, these
sensors have already proven to yield excellent field-trial results
[23].
Nevertheless, it is unquestionably desirable to reduce
crosstalk effects; even when it can be tolerated, there is overhead
associated with crosstalk compensation in the image processing
algorithms. One relevant design improvement is the inclusion of
an epitaxially grown “filter” layer beneath the avalanche layer
of the GmAPD structure to promote broadband absorption of
crosstalk photons emitted towards the back surface of the substrate [22]. Appropriate choice of the cut-off wavelength of this
layer can provide absorption of the majority of the crosstalk
photons while allowing the LADAR return photons to transmit
unattenuated. We have already implemented such a crosstalk
reduction strategy for newer 1.0 μm FPAs, and its application
to 1.5 μm sensors is in progress. (It is worth noting, though,
that the resulting reduction in the detector’s overall spectral
response width may pose a performance tradeoff in situations
where the camera is also intended to perform broadband passive
single-photon imaging.)
Reducing the size of the GmAPD active region within each
pixel can also provide significant reduction in crosstalk and will
simultaneously improve numerous other GmAPD performance
metrics such as DCR, afterpulsing, and radiation tolerance [24].
Additionally, the migration to smaller pitch and larger format
arrays will demand smaller active area sizes based on simple
geometric considerations as well as the fact that crosstalk effects
will be exacerbated considerably as GmAPD pixels are scaled to
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smaller pitch. While active size reduction provides substantial
benefits, these come at the expense of more challenging optical
coupling.
The Poisson statistics of GmAPD dark counts and the associated exponentially distributed interarrival times have been
described previously [25], [26]. In this study, we have made use
of these statistics to perform a temporal statistical analysis for
dark counts from the entire array that is useful for distinguishing
between intrinsic dark counts and crosstalk counts. The application of this analysis to other situations in which both Poisson
and non-Poisson processes co-exist has been equally fruitful, as
in the extraction of afterpulsing counts—which will have nonPoissonian statistics—from intrinsic dark counts using the same
statistical analysis of inter-arrival times [27].
Finally, to the extent that background photons entering the
sensor can be described by Poissonian statistics, a similar statistical analysis can be carried out for the response of the sensor
to illumination by background photons.
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Mark A. Itzler (M’96–SM’07–F’11) received the B.S. degree in physics from
Brown University, Providence, RI, USA, in 1986, the Ph.D. degree in physics
from the University of Pennsylvania, Philadelphia, PA, USA, in 1992, and pursued postdoctoral research at Harvard University, Cambridge, MA, USA, from
1992 to 1995.
He joined Epitaxx Optoelectronics, Inc., in 1996, was promoted to the Director of R&D in 1999, and following the acquisition of Epitaxx by JDS Uniphase
in November, 1999, he became Chief Technical Officer and the Vice-President
of Device Engineering for the Epitaxx Division of JDSU in 2000. He joined
Princeton Lightwave, Inc., as CTO in 2003, where he has led the development
of high-performance photodetector technology and provided oversight for the
company’s other device technology programs. He assumed the position of CEO
at Princeton Lightwave, Inc., Cranbury, NJ, USA, in 2012 where he is currently
the CEO and the CTO. His technical focus is in the field of semiconductor photodetectors, particularly in the areas of single photon counting and avalanche
photodiodes. He is the author of about 90 technical papers and conference presentations and has had 17 patents awarded to date.
Dr. Itzler was the past Chair of the IEEE Photonics Society (formerly LEOS)
Technical Committee on Photodetectors and Imaging, and he is presently the
Chair of the Advanced Photon Counting Techniques conference held as part of
the SPIE Defense, Security + Sensing Symposium. He has been an Associate
Editor of the IEEE PHOTONICS TECHNOLOGY LETTERS.
ITZLER et al.: DARK COUNT STATISTICS IN GEIGER-MODE AVALANCHE PHOTODIODE CAMERAS
Uppili Krishnamachari received the B.S. degree in electrical engineering from
the University of Illinois-Urbana Champaign, Champaign, IL, USA, in 2005
and the Ph.D. degree in electrical engineering from the University of California,
Santa Barbara, CA, USA.
His graduate work involved design and fabrication of InP-based feedback
coherent receivers, consisting of balanced UTC-photodetectors, phase modulators, and an ultracompact etched trench optical beam splitter. He also carried
out flip chip hybrid integration of the coherent receiver photonic integrated circuit with an electronic integrated circuit designed and fabricated at Northrop
Grumman Space Technologies under the funding of the DARPA Phorfront program. In 2011, he joined Binoptics Corporation and led a project that resulted
in a dramatic increase in laser to fiber coupling over the industry standard.
His work made the transition from proof of concept simulations to fabrication
process development and further led to high volume production in a short six
months. His past work in semiconductors includes InP-based MOCVD growth
of quantum nanowires in Lund University, Sweden, design of quantum cascade
lasers at Texas A&M University, and design and fabrication of vertical cavity
lasers at the University of Illinois. He has published 15 technical papers. His
work in coherent receivers received the Best Student Paper Award at the 2010
Microwave Photonics Conference in Montreal.
Mark Entwistle received the B.S. degree in electrical engineering from the
DeVry Institute of Technology, Woodbridge, NJ, USA, in 1986.
During graduation, he joined Tram Electronics, Inc., as an Electronic Engineer and was later promoted to the Manager of Engineering where his main
responsibilities were high reliability design and test engineering of military
electronic assemblies. In 1996, he joined Epitaxx Optoelectronics, Inc. (which
became a division of JDS Uniphase, after its acquisition of Epitaxx in 1999)
as a Senior Manufacturing Engineer and was promoted to the Manager of Test
Engineering. His main responsibilities were in the development of high-speed
optoelectronic test platforms in support of 10 Gb/s receiver and laser production.
He was also involved in the development of 40 Gb/s receiver technologies. He
joined Princeton Lightwave, Inc., in 2003 as the Manager of Software and Test
Engineering, where he is responsible for the development of test platforms in
support of new product development as well as support of existing platforms
on established product lines. Additionally, he is responsible for electronic hardware and firmware development on PLI’s module-level product lines, He has
substantial experience in camera electronics design and sensor testing, including
board design and layout, FPGA and microcontroller programming, and module
testing.
Xudong Jiang received the B.S., M.S., and Ph.D. degrees in physics from
Peking University, Beijing, China, in 1989, 1992, and 1995, respectively.
He has a background in semiconductor physics and has done extensive work
in the area of optoelectronic devices. He did Postdoctoral work at Harvard
University (1995–1996) and Princeton University (1996–1997) on the electrical
and optical properties of superlattices and thin film transistors. He joined the
University of Florida as Coprincipal Investigator on a project funded by the
U.S. Army Research Office and focused on MWIR and LWIR quantum well
infrared photodetector design, processing, and characterization from 1997 to
2000. From 2000 to 2006, he worked at Multiplex, Inc., as a Distinguished
Member of the Technical Staff and Manager of laser engineering and operation.
At Multiplex, Inc., he led the effort in the development and manufacturing of
980-nm pump laser and electroabsorption modulated laser devices and modules.
In 2006, he joined Princeton Lightwave Inc., Cranbury, NJ, USA, where he
is currently a Principal Scientist and leads programs focused on the design
and characterization of high-performance photodetectors and detector-based
products. Dr. Jiang is the author/coauthor of more than 40 technical publications
on solid state physics and optoelectronic devices.
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Mark Owens received the B.S. degree in physics from the State University of
New York, Stony Brook, NY, USA, in 1992.
He joined Gage Lab Corporation in 1992 as a Metrology Engineer with responsibility for practical thermodynamic standards. He joined Epitaxx (which
later was acquired by JDS Uniphase) in 1999 as a Senior Engineer. There,
he worked on the development, qualification, and production of high reliability undersea receivers, and he fulfilled similar roles for high bit rate receiver
and source laser product lines. He joined Princeton Lightwave in 2005 as the
Product Engineer to support quality, process, and reliability engineering for the
company’s aerospace-qualified 820-nm SLD module. Since joining PLI, he has
functioned in multiple roles such as Process Engineer and Program Manager for
space-qualified chip development and packaging efforts. He has considerable
experience in package assembly processes and failure analysis pertaining to
photodiode sensors in both discrete and array-based formats. He is currently a
Principal Engineer at Princeton Lightwave Inc., Cranbury, NJ, USA.
Mr. Owens is a U.S. Air Force Veteran and a Member of the International
Microelectronics and Packaging Society and American Society for Quality.
Krystyna Slomkowski received the B.A. degree in microbiology from Rutgers
University, Douglass College, New Brunswick, NJ, USA, in 1976.
In 1978, she joined Laser Diode Laboratories as a Senior Process Technician
and was responsible for all processing of GaAs Burrus LEDs. In 1985, she joined
Epitaxx Optoelectronics, Inc., as a Senior Process Engineer. At Epitaxx, she was
responsible for the process development of planar InGaAs-InP p-i-n photodiodes
and establishing a manufacturing line for this product. In 1989, she joined the
R&D development group at Epitaxx. During this time, she was responsible
for developing new processes and product platforms for fiber-optic detectors
and receiver packages, and supporting and improving existing wafer fabrication
processes. In 1999, she was promoted to Technical Manager leading the Process
Development Group at the Epitaxx Division of JDS Uniphase. She managed
the R&D Process Development Staff in the development of new processes and
platforms for photodiodes with successful programs for 10 Gb/s APDs and 40
Gb/s PIN detectors. In January, 2004, she joined Princeton Lightwave, where
she is responsible for all photodetector and laser diode process development
and execution, including photomask design and process flow definition. She is
currently a Senior Staff Engineer at Princeton Lightwave Inc., Cranbury, NJ,
USA.