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Equivalent circuit model of a Ge/Si avalanche photodiode
Daoxin Dai1, Hui-Wen Chen1, John E. Bowers1, Yimin Kang2, Mike Morse2, Mario J. Paniccia2
1 University of California Santa Barbara, ECE Department, Santa Barbara, CA 93106, USA
2 Intel Corporation, 2200 Mission College Blvd, Santa Clara, CA 95054, USA
dxdai@ece.ucsb.edu, bowers@ece.ucsb.edu.
Abstract An equivalent circuit model for a separate-absorption-charge-multiplication Ge/Si avalanche photodiode
is presented. The current dependence of the resonance frequency scales with square root of current, as
expected.
Introduction
In fiber-optic communication systems, highly
sensitive photodetectors are desirable to have long
reach in ultra long-haul networks. Additionally, in access
networks (like GPON-FTTH systems), low-cost highlysensitive photodetection is essential for short distances
(several tens of kilometers) because the optical power
is split multiple times before reaching the end users.
Hence, avalanche photodetectors (APDs) with their
internal gain are a natural choice for such high
sensitivity applications.
For APDs, the gain-bandwidth product (GBP) is
one of the most important figures of merit. For
traditional InP-based APD receivers, the GBP is usually
about 100 GHz due to the large k value (~0.4-0.5) [1]. In
contrast, silicon has a low k-value (<0.1), which makes
it one of the most promising candidates for APDs that
have both high gain and high bandwidth simultaneously.
In order to make Si-APDs available in the infrared
regime, a material with a high absorption coefficient in
[2]
[3-5]
the infrared, like InGaAs
or Ge
is used for the
absorption layer along with the Si multiplication layer.
Ge is attractive since it is possible to develop an APD
based on a complementary metal-oxide-semiconductor
(CMOS)-compatible process. Although these APDs
tend to have higher dark current because of threading
dislocations due to the lattice mismatch between Ge
and Si [3], it is possible to minimize their impact with
careful processing and device design. In Ref. [3], Kang
et al. reported CMOS-compatible Ge/Si APDs with a
GBP as high as 340 GHz by using the structure of a
separate-absorption-charge-multiplication (SACM).
In this paper, we present an equivalent circuit
model for this type of SACM Ge/Si APD operated close
to breakdown. When the APD is operated close to
breakdown, it is possible to have very high GBP due to
[6]
the space charge effect . The model includes carriertransit time effects and the effect of parasitics.
Measurement of the photodetector impedance,S22, is
widely used for the characterization and modeling of
[7]
high-frequency and high-speed devices . From the
measured S22 and S21, one could extract the circuit
component values for the various elements (R, C, L) in
the equivalent circuit. We define the input light as port
1 and the photodetector current output as port 2. In this
paper, we combine the measured S22 parameters and
extract all the component values at different bias
voltages simultaneously. The component values are
estimated by fitting using a genetic algorithm, which is
suitable for obtaining the optimal solutions for the
problems that have multiple-parameters. Based on the
extracted circuit model, we calculated the device
978-1-4244-4403-8/09/$25.00 ©2009 IEEE
13
frequency response, S21, which agrees well with the
measurement results.
Device structures and modeling
Fig. 1 (a) shows the cross section of the present
normal-incident illuminated Ge/Si SACM APD, which is
the same as that in Ref. [3]. The structure consists of a
Si multiplication layer, a silicon charge layer, and a Ge
absorption layer. The thicknesses and the doping
concentrations for all layers are shown in Fig. 1 (b).
hv
Si3N4 passivation
Charge layer
Ge absorption layer
Si multiplication layer
Si n+ -contact layer
low-doped Si substrate
(a)
P-contact: p+ -Ge, 0.1µm, >1020cm-3
Absorption layer:i-Ge, 1µm, 5×1015 cm-3
Charge layer: p-Si, 0.1µm, 2×1017 cm-3
Multiplication layer: i-Si, 0.5µm, 5×1015 cm-3
N-contact: n+-Si, 1µm, >1020cm-3
(b)
Fig. 1. (a) Schematic configuration of the Ge/Si
SACM APD device; (b) the parameters for the layers.
Fig. 2 shows the equivalent circuit of a SACM APD.
In the circuit model. The RC input circuit is used to
model the transit time of the absorber [8]. The avalanche
gain is represented by the source current Iin=gIt (where
g is a constant related with the gain of the APD).
The part in the dashed rectangle in Fig. 2
represents the equivalent impedance of probe pads and
cables. The Ge/Si APD is similar to the impact
ionization avalanche transit-time (IMPATT) diode
structure. Hence, we use a LC-circuit (LA and CA) for the
[9, 11]
avalanche region
. Here the resistances (RA and Rl)
are lossy elements in the avalanche region due to the
finite reverse saturation current and field-dependent
velocity [11]. Rl is for the leakage of the diode capacitor
and RA is the series resistor of the inductor. From
modeling of the avalanche process, the inductance is
inversely proportional to the current density J0, which
will be verified below. The resistance Rd connected to
the LC circuit is for the resistance at the drift region.
The pad and interconnection line
Rs
It
Ct
Rl
RA
Cp
0.5
Rp
RL
0.5
-0.5
-0.5
-1
-1
0
1
-1
-1
0
1
1
(c) Vbias=–26.2V
(b) Vbias=–26.0V
0.5
0.5
0
0
-0.5
-0.5
0
1
-1
-1
0
1
Fig. 3. The measured and fitted reflection coefficients
of GeSi APD under -14dBm optical illumination (a)
Vbias= –26.6V; (b) Vbias= –26.4V; (c) Vbias= –26.2V; (d)
Vbias= –26.0V.
The avalanche region
Fig. 2. The equivalent circuit of the present SCAM
APD.
Table I Fitted device parameters.
Vbias (V)
Rd (Ω)
R l (Ω)
RA(Ω)
CA (pF)
LA (nH)
In order to determine the parameters of the
equivalent circuit, first we measured the microwave
reflection parameter S22 by using an Agilent E8364A
network analyzer. Then all the parameters for the
elements included in the equivalent circuit were
extracted by fitting the measured S22 with the geneticalgorithm (GA) optimization. In order to obtain more
reasonable fitting parameters, here we combine the
measured the S22 parameters at a series of inverse
bias voltages (e.g., Vbias= –26.6, –26.4, –26.2 and –
26.0V) and extract all the parameters at each bias
voltage. At different bias voltages, all the parasitic
impedance (Rs ,Cp, Lp, Rp) should be the same while
the other parameters will change as the gain changes.
Fig. 3 (a)-(d) shows the measured (dotted
curves) and fitted (solid curves) S22 parameters with
an optical power of –14 dBm at different bias voltages
Vbias= –26.6, -26.4, -26.2, and –26V, respectively. The
corresponding currents are I=9.66, 8.06, 6.65, 5.36
mA. The diameter of the APD is D=80µm. The fitted
results for the Rs, Cp, Lp, and Rp are: Rs =16.76Ω,
Cp=0.193Ω, Lp=0.082 Ω, and Rp=6.65 Ω, independent
of the bias voltage. The fitted parameters for all other
bias-dependent elements are shown in Table I. For
the avalanche region, the capacitance C changes
very slightly while the inductance decreases as the
bias voltage increases (which is due to the variation
of current density as theoretically predicted).
The products of LA×I are 29.74, 29.78, 29.33,
and 29.18 for the case of Vbias= –26.6, -26.4, -26.2,
and –26V, respectively. This product is almost
constant as the bias voltage varies. This indicates
that the inductance LA is almost inversely proportional
to the current density, which is similar to the
theoretical predicted relationship for an IMPATT diode
in Ref. [9].
978-1-4244-4403-8/09/$25.00 ©2009 IEEE
(b) Vbias=–26.4V
measured
fitted
0
-1
-1
CA L
A
1
(a) Vbias=–26.6V
0
1
Rd
Iin=gIt
Rt
Lp
1
–26.6
32.27
557.8
21.06
0.21
3.08
–26.4
34.60
578.9
25.27
0.21
3.69
–26.2
37.33
584.4
30.33
0.21
4.41
–26.0
38.35
650.3
42.68
0.21
5.44
Having the equivalent circuit extracted, we
calculate device frequency response. Here we show
the results for Vbias= –26.6 and –26.0V as examples in
Fig. 4(a) and (b), respectively. Here the parameters
for the part of transit-time circuit are: g=150, Rt·Ct
=26.0 Ω·pF and the quantum efficiency η is about
0.55 A/W. From this figure, one sees that the
simulated curve (dashed) and measured data (circled)
agree well with each other. And there is a peakenhancement at a certain frequency, which is similar
to that reported in Ref. [10, 12, 13]. Such a peak
enhancement is beneficial to increase the bandwidth,
but a rise of 3 dB or less doesn’t cause too much eye
closure in a digital system. For the present case, the
3dB bandwidth is about 11 GHz, and 9 GHz for
Vbias=–26.6 and –26.0V, respectively.
Conclusions
We have presented the equivalent circuit for a
SACM Ge/Si avalanche photodiode. A genetic
algorithm has been used to extract the equivalent
circuit model based on the measured S22 parameters.
In this equivalent circuit, one of the most key
elements is the inductance due to the finite buildup
time of the avalanche current. It has been shown that
this inductance is inversely proportional to the inject
current, which is in agreement with the theoretical
prediction. With these fitted parameters, we have also
calculated the frequency response, which agrees well
with the experimental one.
14
15
Response (dB)
10
measured
fitted
2.
5
3.
0
-5
4.
g=150; Rt·Ct =26.0Ω·pF;
-10
-15 -1
10
5.
0
10
f (GHz)
1
10
6.
(a)
15
Response (dB)
10
measured
fitted
7.
5
8.
0
-5
g=150; Rt·Ct =26.0Ω·pF;
9.
-10
-15 -1
10
10.
0
10
f (GHz)
1
10
(b)
Fig. 4. The measured and fitted frequency responses
when the illuminated optical power P=–14dBm for (a)
Vbias= –26.6V; (b) Vbias= –26.0V.
11.
12.
Acknowledgement
This work was sponsored by the Defense Advanced
Research Projects Agency (DARPA) under contract
number HR0011-06-3-0009. We thank J. C. Campbell,
A. Ramaswamy, H. Kroemer, A. Pauchard and M.
Rodwell for useful discussions.
13.
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