Large Signal Bias Dependent Modeling of Avalanche
Photodiode Based on Pulsed RF Measurement
A. Ghose, B. Bunz, J. Weide and G. Kompa
Dept. of High Frequency Engineering, University of Kassel, Wilhelmshöher Allee 73, D-34121, Kassel, Germany,
Tel: +49-561 804 6528, Fax: +49-561 804 6529, Email: ag@hfm.e-technik.uni-kassel.de
Abstract — This work presents a method for large signal
characterization of avalanche photodiode (APD) where
measurements were carried out using pulsed RF signal at
different DC bias points to extract dispersive parameters of
the avalanche photodiode. Pulsed optical excitation on the
photodiode were synchronized with the pulsed RF signal
using a synchronization circuit and in this way
characterization of the photodiode was possible up to 1.3
mW of peak optical power whereas using CW measurement,
device heating restricts the characterization up to 0.1 mW of
optical input power. A comparison was made between the
reflection measurements using CW RF excitation and APD
model based on pulsed RF signal to establish the present
approach for large signal characterization of the
photodiode.
Index Terms — Pulse measurement, reflection coefficient
measurement, scattering parameters, nonlinearities.
I. INTRODUCTION
High speed optoelectronic devices are of growing
interest for its use in analog to digital communication
systems and also for industrial and medical sensor
applications. Reliability of the observed high speed (pico
second) pulses are often affected by the phenomena of
jitter, time base distortion, impedance mismatches
distortion and waveform or nonlinearity distortion. An
accurate nonlinear model of the optoelectronic devices
are needed which can be implemented in commercial
CAD software to predict and correct the device behavior
in such cases. In this work we will consider the Si
avalanche photodiode (Silicon Sensor GmbH) as DUT.
For microwave characterization of photodiodes it is
necessary to regard the photodiode as two-port network
with optical port related to electrical port through a
nonlinear transfer function according to [1]. Nonlinear
dispersive electrical parameters of the large signal
photodiode model and the parasitic are extracted by RF
reflection measurement through its electrical port. Now,
using CW RF measurement together with CW optical
input, device thermal resistance increases and restricts the
measurement range up to even moderate power optical
power of 0.1 mW. Therefore pulsed RF characterization
was performed to extract the dispersive parameters of the
device at isothermal conditions and in this way
characterization was possible up to 1.3 mW of pulsed
optical power (average <0.065 mW). During pulsed RF
measurement optical input is pulsed and synchronized
with the square wave RF envelope through an external
synchronization circuit [2]. Resistive electrothermal
parameters were extracted using quasi-DC measurements
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with pulsed optical input at different DC bias conditions
[3].
To extract device parameters at isothermal conditions
pulsed RF measurements have been reported for large
signal characterization of power microwave devices
using pulsed vector network analyzers. Here in this
alternative approach, large signal model of the avalanche
photodiode was transformed to small signal linear model
and Microwave Transition Analyzer (HP 70820A) was
used in pulsed RF mode to measure small signal vector
reflection coefficients of the avalanche photodiode.
II. AVALANCHE PHOTODIODE MODEL
Nonlinear model of the photodiode was reported by
Stolze et al. [1]. The large signal model is divided into
two parts, one is optoelectronic converter and electrical
equivalent circuit part as shown in Fig. 1. Optical to
electrical conversion can be represented with the matrix
relation given below.
Where Popt is the optical power which penetrates the
surface of the photodiode and a small amount will be
reflected, denoted as Popt, refl due to complex reflection
coefficient Ropt. S characterizes the optical to electrical
conversion, which is extracted by impulse measurement
using a laser excitation of rise time 12 ps. The electrical
to optical conversion can be ignored, as the photodiode
does not radiate optical power during electrical stimulus.
The reflection of the electrical wave (a2 being incident
and b2 being reflected wave) is characterized by the
electrical complex reflection coefficient Rel.
It is necessary to transform the large signal model to
small signal linear model, which can be readily modeled
by commercial circuit simulators (e.g. Advanced Design
System, Agilent Technologies) and based on small signal
scattering parameter measurement. Optoelectronic
converter is the transfer function matrix defined by three
measurable time constants (t1, t2, t3). I0 represents the
internal current source of the diode, Q represents the
charge source for photodiode conductance and Q1 is the
charge source, which accounts for delay in the avalanche
multiplication. Gr is the conductance for diode dark
current. Cm and Cp are parasitic capacitance of the diode
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bond pad. Rm and Lm are bond wire resistance and
inductance respectively. The large signal model describes
the nonlinear dependence of internal photocurrent I2 to
the diode current I1 by the current source I0 and charge
source Q. Rs being the internal series resistance of the
photodiode is a nonlinear element dependent on I2 and
V2.
In Fig. 2 linearized photodiode model is shown with
charge sources replaced by diode conductance G0 and
diode capacitance C0. Delay charge source is represented
by time constant of the series R1 and C1. Control current
I1 is delayed by the delay coefficient tp1. Electrothermal
parameters were measured by quasi-DC I-V
characteristic of the diode and dispersive parameters were
extracted by pulsed RF measurements.
Fig. 1. Large signal model of the avalanche photodiode
Fig. 2. Derived small signal model of the avalanche photodiode
[2]
The set up was built around Microwave Transition
Analyzer (HP70820A) with synthesized signal generator
(HP 8360B) as shown in Fig. 4. RF pulses were provided
by synthesized source through bias decouple circuit
followed by a directional coupler and 23 dB attenuator to
the DUT (avalanche photodiode). Reflected pulses were
coupled from the forward RF signal by the directional
coupler (3 dB). Low frequency components of the
electrical pulse from the photodiode (5 micro second
pulse width, 5 kHz PRF) were filtered by the bias
decoupling circuit. Pulsed RF measurement was carried
out from 1 GHz to 30 GHz. Synthesized sweeper was
controlled by Microwave Transition Analyzer in the
pulsed RF mode. Optical stimulus on the photodiode was
synchronized with a synchronization circuit having
adjustable amplitude, pulse width and delay. TTL pulses
from the Microwave Transition Analyzer trigger the input
of the synchronization circuit and output pulses from the
synchronization circuit drives a low noise voltage to
current converter (LDX3620) for the laser diode (LQ6780-4a/OECA). Optical power was measured at the
output of the optical fiber. Establishment of the
measurement point over the pulse is done by placing the
microwave transition analyzer in time sweep mode and
then a time delay is set between the trigger point (leading
edge of the pulse) and measurement point. Measurement
point was set near the end of the pulse to avoid overshoot
of the pulse [5]. The vector reflection measurement of the
device at a specific input pulsed RF power yields a set of
raw measurement vectors. S parameters of the directional
coupler were measured separately using a HP8510 vector
network analyzer and vector error correction was done of
the measured reflection coefficients.
10 MHz Ref.
III. MEASUREMENT TECHNIQUE
Input
MOD
Output
HP IB
In Fig. 3 Schematic of the principle of the used
pulsed RF measurement is shown. Optical pulses are
synchronized with the pulse envelope of the RF
excitation. A safe limit of about 1 micro second was left
to perform the measurement at relatively ripple free
region of the pulse.
CH1
Out
RF Source
Power
Splitter
CH2
Microwave
Transition
Analyser
(+/- 2 V or 16 dBm Tol.)
RF Out
11 dBm
(0 V or 0.5 Watt Tol.)
20 dB
6 dB
Bias supply
3 dB
23 dB
2 mV peak
(measured)
DUT
(APD)
Bias
decouple
Directional
Coupler Blocking Cap.
3 dB
0.15 V peak
+5 V
Sync.
Circuit
Current
source
Laser
diode
Fig. 4. Set up for pulsed RF characterization
Fig. 3. Pulsed (RF and opt.) measurement principle
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OP.
Fibre
IV. EXTRACTED PARAMETERS
Intrinsic parameters of the photodiode were extracted
after de-embedding the extrinsic parameters Lm and Cp
from the measured Y parameters. Extrinsic parameters
are bias independent and also independent of optical
power.
Fig. 7. Extracted Q from pulsed RF measurement
Fig. 5. Measured photodiode capacitance using pulsed RF
signal and its variation with optical power and bias voltage
Lm is found to be 276 nH and Cp, the pad capacitance
is 0.020 pF. Fig. 5 shows the extracted nonlinear diode
capacitance with change in bias voltage and optical
conditions using above method of pulsed RF
measurement. From Fig. 5, it is evident that the diode
capacitance is nearly 2 pF over the bias region of 50 Volt
to 148 Volt and a slight decrease to 1 pF is noticed at
optical power higher than 1 mW. This is because of
increased diode conductance at the reverse bias in the
breakdown region (measured breakdown voltage 148.5
V) and optical power of more than 1 mW.
In Fig. 7, charge stored at the depletion region of the
photodiode is plotted with photodiode bias and optical
power input. Charge stored in the depletion region
increases steadily with increase in optical power and bias
voltage. Slight variation is noticed at break down region
of more than 100 volt due to variation of capacitance at
that region (Fig. 5).
Fig. 8a. Magnitude of measured (triangle) reflection coefficient
using Vector Network Analyzer (HP 8510) and modeled (solid)
based on pulsed RF measurement
Fig. 6. Measured (pulsed RF) diode conductance
Fig. 6, [1/g0]RF (diode conductance: g0) shows slight
monotonous variation at the bias region of 50 Volt to 100
Volt and rapid decrease is noticed with optical power
input of more than 1 mW. This indicates a decreased gain
and simultaneously increased thermal resistance of the
device [3].
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Fig. 8b. Measured phase response of reflection coefficients
using Vector Network Analyzer (HP 8510) (triangle) and
modeled (solid) based on pulsed RF measurement
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Fig. 8a and Fig. 8b shows the comparison of
measured reflection coefficient using Vector Network
Analyzer (HP 8510) [4] and modeled photodiode based
on pulsed RF measurement at the similar optical
conditions. Slight deviation (Fig. 8a) is observed after 28
GHz due to increased loss at the bias network.
V. CONCLUSION
It was confirmed that the pulsed RF measurement,
which is generally used for power microwave devices to
measure low frequency dispersion etc. can also be used
for optoelectronic devices like avalanche photodiode to
characterize optical power dependent nonlinearities of the
photodiode. Avalanche gain is very sensitive to device
temperature, therefore present approach allows near
isothermal characterization of the device. It was possible
to characterize the device up to 1.3 mW of peak optical
power, which covers the dynamics of the signal at which
it is exposed in practical use e.g. pulsed laser radar
system. Photodiode model was implemented by a
harmonic balance simulator and modeled reflection
coefficients were compared with standard reflection
measurement using CW RF signal by Vector Network
Analyzer for confirmation at the low optical power level.
ACKNOWLEDGEMENT
This work was performed within the European
research project (INTAS 51615009). Financial support is
greatly acknowledged.
REFERENCES
[1]
Stolze, A., and Kompa, G., “Nonlinear modeling of
dispersive photodiodes based on frequency and timedomain measurements”, 26th European microwave
conference. Proc., Prague, Czech Republ., pp. 379382, September 9-12, 1996.
[2]
Ghose, A., Bunz, B., Weide, J., and Kompa, G.,
“Measurement of nonlinear dispersive parameters of
avalanche photodiode using pulsed RF signal and
quasi-DC optical stimulus,” 34th European
Microwave
Conf.,
Proc.,
Amsterdam,
The
Netherlands, pp. 925-928, November 11-15, 2004.
[3]
Ghose, A., and Kompa, G., “Electrothermal parameter
extraction of avalanche photodiode using quasi-DC
optical pulses,” 10th IEEE International Symposium
on Electron Devices for Microwave and
Optoelectronic Applications, Proc., Manchester, UK,
pp. 69-74, November 18-19, 2002.
[4]
Ghose, A., Ring, M, and Kompa, G., “Simultaneous
gain and noise matching of a wideband optical
receiver front end,” 2003 Asia Pacific Microwave
Conference, Proc., Seoul Korea, pp. 431-434,
November 4-7, 2003.
[5]
Baylis, C. P., and Dunleavy, L. P., “Performing and
analyzing pulsed current-voltage measurements,”
High Frequency Electronics, pp. 64-69, May 2004.
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