Frequency response and bandwidth
enhancement in Ge/Si avalanche photodiodes
with over 840GHz gain-bandwidth-product
Wissem Sfar Zaoui1*, Hui-Wen Chen1, John E. Bowers1, Yimin Kang2, Mike Morse2,
Mario J. Paniccia2, Alexandre Pauchard3, Joe C. Campbell4
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
3
Chemin de Crey-Derrey 152, 1618 Châtel-St-Denis, Switzerland
4
University of Virginia, ECE Department, Charlottesville, VA 22904, USA
*wissem@ece.ucsb.edu
Abstract: In this work we report a separate-absorption-chargemultiplication Ge/Si avalanche photodiode with an enhanced gainbandwidth-product of 845GHz at a wavelength of 1310nm. The
corresponding gain value is 65 and the electrical bandwidth is 13GHz at an
optical input power of −30dBm. The unconventional high gain-bandwidthproduct is investigated using device physical simulation and optical pulse
response measurement. The analysis of the electric field distribution,
electron and hole concentration and drift velocities in the device shows that
the enhanced gain-bandwidth-product at high bias voltages is due to a
decrease of the transit time and avalanche build-up time limitation at high
fields.
© 2009 Optical Society of America
OCIS codes: (040.0040) Detectors; (040.1345) Avalanche photodiodes (APDs)
References and links
R. B. Emmons, “Avalanche photodiode frequency response,” J. Appl. Phys. 38(9), 3705–3714 (1967).
R. J. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: theory,” IEEE Trans.
Electron. Dev. 19(6), 703–713 (1972).
3. Y. Kang, H. D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y. H. Kuo, H. W.
Chen, W. Sfar Zaoui, J. E. Bowers, A. Beling, D. C. Mcintosh, and J. C. Campbell, “Monolithic
germanium/silicon avalanche photodiodes with 340GHz gain-bandwidth product,” Nat. Photonics 3(1), 59–63
(2008).
4. G. Kim, I. G. Kim, J. H. Baek, and O. K. Kwon, “Enhanced frequency response associated with negative
photoconductance in an InGaAs/InAlAs avalanche photodetector,” Appl. Phys. Lett. 83(6), 1249–1251 (2003).
5. H. S. Kang, M.J. Lee and W.Y. Choi, “Si avalanche photodetectors fabricated in standard complementary metaloxide-semiconductor process,” Appl. Phys. Lett. 90, 151118.1–151118.3 (2007).
6. J. W. Shi, Y. S. Wu, Z. R. Li, and P. S. Chen, “Impact-ionization-induced bandwidth-enhancement of a Si-SiGebased avalanche photodiode operating at a wavelength of 830 nm with a gain-bandwidth product of 428 GHz,”
IEEE Photon. Technol. Lett. 19(7), 474–476 (2007).
7. F. Capasso, Semiconductors and semimetals (Academic press, 1985), Vol. 22, part D.
8. S. Selberherr, Analysis and simulation of semiconductor devices (Springer-Verlag, 1984).
9. H. C. Bowers, “Space-charge-induced negative resistance in avalanche diodes,” IEEE Trans. Electron. Dev.
15(6), 343–350 (1968).
1.
2.
1. Introduction
A wide range of applications require photodetectors with high sensitivity to detect weak
optical signals. In addition to high data rate communication applications, new areas in
imaging, biotechnologies, sensing and quantum cryptography also have a need for such
photodetectors.
High sensitivities can be achieved by using avalanche photodetectors (APDs), which use
internal gain to reduce the noise of the first stage electrical amplifier. The APDs can be
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characterized through two functions that can be optimized separately. The first function is the
absorption of light and its conversion to an electrical signal. The second function is the
amplification of this electrical signal through the avalanche process. However, the avalanche
multiplication process that generates the internal gain, limits the speed performance of the
APD due to the avalanche buildup time, which is related to the ratio of the electron and hole
ionization coefficients [1]. Due to the large asymmetry of electron and hole ionization
coefficients in silicon (Si), this material is very attractive for APDs [2]. However, Si is not
appropriate to absorb at the telecommunication wavelengths, which require the use of smaller
bandgap materials such as germanium (Ge).
As a result, APDs with a Ge absorption layer and a Si multiplication layer can achieve
very good performance with high quantum efficiency and low noise [3]. In addition, the
multiplication gain and frequency response represent very important figures of merit to
determine the performance of APDs. The product of these is the gain-bandwidth-product
(GBP), which is usually constant at high gains [1]. Although the 4% lattice mismatch between
Ge and Si can result in a high dark current, careful processing and the right annealing
temperature can reduce the impact of threading dislocations.
Monolithically
grown
Separate-Absorption-Charge-Multiplication
(SACM)
Complementary Metal-Oxide-Semiconductor (CMOS) compatible Ge/Si APDs have recently
demonstrated 340GHz GBP. This is higher than standard III-V APDs that exhibit limited
GBPs around 120GHz [3]. The same device exhibits dramatically enhanced GBPs at elevated
bias voltage and a GBP value of 845GHz is reported here from a 30µm-diameter device.
Similar unconventional behavior in GBPs at high voltages have been observed by G. Kim
et al. in InGaAs/InAlAs APDs [4], H.S. Kang et al. in Si APDs [5] and J.W. Shi et al. in
Si/SiGe APDs [6]. We use detailed analysis of carrier transport to explain the effects observed
in our devices and associate the frequency response enhancement primarily to the decrease of
the transit time and multiplication time limitation due to space charge effects. The following
pulse response results support this explanation. The measured GBP makes such SACM Ge/Si
APDs attractive for data rates of 40Gbit/s and above.
2. Measured and simulated device structures
Figures 1(a) and 1(b) illustrate the real device structure with the corresponding layer
properties. The device consists of an intrinsic Si multiplication layer and an intrinsic Ge
absorption layer, separated by a p-doped Si charge layer, which controls the electric field
distribution in the device [3]. The structure was simulated using ATLAS assuming a uniform
doping profile without any surface and interface defects or Ge/Si interdiffusion (Fig. 1(c)).
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hν
a-Si, SiO2
p+-Ge, 0.1µm, >1020cm-3
+
and Si3N4 p -contact
i-Ge, 1µm, <5x1016cm-3
absorption
passivation layer
p-Si, 0.1µm, 1.52x1017 cm-3
charge layer
i-Si, 0.5µm, <5x1016cm-3
multiplication layer n+-Si, 1µm, >1020cm-3
n+-contact layer
SixNy ARC P-contact
N-contact
SiO2
Ge
Si
Si
Si Substrate
low-doped Si substrate
hν
(a)
(b)
anti reflection coating
anode
p+-contact
absorption
layer
charge layer
multiplication layer
cathode
Si3N4, 0.75µm
p+-Ge, 0.1µm, 5x1019cm-3
i-Ge, 1µm, 5x1015cm-3
p-Si, 0.1µm, 2x1017 cm-3
i-Si, 0.5µm, 5x1015cm-3
n+-Si, 1µm, 5x1019cm-3
n+-contact
(c)
Fig. 1. (a) Schematic drawing and (b) a scanning electron microscope (SEM) cross sectional
image of the Ge/Si SACM APD device. (c) Schematic layer view of the simulated structure.
3. Experimental and simulation results
10m
1m
100µ
10µ
1µ
100n
10n
1n
100p
10p
1p
-30
Total current
Dark current
Current [A]
Current [A]
The measured and simulated IV curves are illustrated in Fig. 2. The total current in Fig. 2(a) is
measured on a 30µm-diameter APD under an optical input power of −20dBm at 1310nm
using a Fabry-Perot laser as the light source. The same parameters are used in the simulation,
which shows similar IV characteristics in Fig. 2(b). The breakdown voltage, defined as the
voltage for a dark current of 10µA, is measured to be −24V, whereas the simulated value is
−26.4V. It can also be seen that the simulated breakdown is more abrupt than in the
measurements due to the two-dimensional ideal structure.
-25
-20
-15
-10
Voltage [V]
(a)
-5
0
10m
1m
100µ
10µ
1µ
100n
10n
1n
100p
10p
1p
-30
Total current
Dark current
-25
-20
-15
-10
-5
0
Voltage[V]
(b)
Fig. 2. (a) Measured and (b) simulated dark current and total current on a 30µm-diameter Ge/Si
SACM APD versus bias voltage under an optical power of −20dBm at 1310nm.
The measured gain is determined by normalizing the responsivity of the APD to the primary
responsivity of a p-i-i-n device fabricated on the same wafer. The primary responsivity is
0.55A/W at 1310nm and the correspondent external quantum efficiency is 52.2%. The
simulated gain can be determined through dividing the calculated photocurrent, i.e. the
difference between total current and dark current, by the available photocurrent in the device.
The available photocurrent is defined as the current generated from the photoabsorption in the
structure, which takes into account the light reflection at the device surface and layer
interfaces, absorption coefficient and absorption layer thickness.
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The direct current (DC) gain from injected electrons can be theoretically given from [1] as
Mn =
(α − β )
e
α−β e
d (α −β )
d (α −β )
(1)
,
where d is the multiplication region width and α and β are the electron and hole ionization
coefficients, respectively, which depend strongly on the electric field. These coefficients can
be approximated by the following expressions [7]
α = An e
−
Bn
E
and β = Ap e
−
Bp
E
(2)
,
where E is the electric field and An, Ap, Bn, Bp are material dependent parameters, which can
be determined experimentally. Consequently, the gain increases exponentially with the
electric field and hence with the bias voltage.
Figure 3 shows the measured as well as the simulated gain curves at different optical
powers. The gain simulation is based on Selberherr’s impact ionization model in Si with An =
7.03x105cm−1, Ap = 1.58x106cm−1, Bn = 1.231x106cm−1 and Bp = 2.036x106cm−1 for
E<4x105Vcm−1 and An = 7.03x105cm−1, Ap = 6.71x105cm−1, Bn = 1.231x106cm−1 and Bp =
1.693x106cm−1 for E≥4x105Vcm−1 [8]. Both measurement and simulation results show akin
behavior with an exponential gain increase until a certain bias voltage. As the bias voltage
increases more, the gain decreases though, exhibiting a similar result reported by H.S. Kang et
al. and J.W. Shi et al. [4,5]. The gain reduction indicates that the electric field is reduced in
the multiplication region.
Figure 3 shows also that the optical input power has a big impact on the multiplication
gain. The gain is reduced at higher optical powers due to a change of the electric field
distribution in the multiplication region because of a change in the free carrier densities. The
highest achieved gain on a 30µm-diameter device is 90 at −30dBm and 33 at −20dBm. Two
differences are present between simulation and measurement. The simulated gain in Fig. 3(b)
attains higher values, around two times higher than measured values, and then decreases very
fast, resulting in a sharp peak. This is due to the ideal structure, which has inter alia large
electrodes in comparison to the real device. In addition the real structure exhibits higher dark
current, which originates mainly from dislocations and tunneling at the Ge/Si interface [3].
These effects are not included in the simulated structure.
250
100
90
-30dBm
-26dBm
-20dBm
80
70
Gain
60
Gain
-30dBm
-26dBm
-20dBm
200
50
150
100
40
30
50
20
10
0
-28
-27
-26
-25
Voltage [V]
(a)
-24
-23
0
-28
-27
-26
-25
-24
-23
Voltage [V]
(b)
Fig. 3. (a) Measured and (b) simulated gain curves versus bias voltage under −20dBm, −26dBm
and −30dBm at 1310nm.
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-10
-12
-14
-16
0.1
3
peaking
0
-3
-6
-9
0.1
1
Frequency [GHz]
10
1
10
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
0.1
-26.5V
-27V
-26V
-25V
-28V
-24V
3
Relative frequency response [dB]
-6
-8
Frequency response [dBe]
-24V
-24.8V
-26V
-26.8V
-28V
4
2
0
-2
-4
Relative frequency response [dB]
Frequency response [dBe]
To characterize the frequency response of the APD, a lightwave component analyzer with
an internal laser and optical modulator operating at 1310nm is used. The set of the frequency
response curves depicted in Fig. 4(a) are measured under −20dBm input power at bias voltage
values between −24V and −28V. We can clearly see that the response at low frequencies
follows a similar behavior as the DC-gain curve from Fig. 3(a). However, the response at high
frequencies keeps increasing. Consequently, the origin of the reported electrical 3dBbandwidth (BW) enhancement, which is illustrated in Fig. 5(a), is not only due to the
enhancement at high frequencies, but also due to the decrease of the response at low
frequencies.
Figure 4(b) shows the simulated frequency response. It can be clearly seen from the figure
that the low frequency response increases by increasing the bias voltage until −26.5V and then
decreases again, whereas the high frequency part above around 9GHz keeps increasing. This
behavior agrees well with the measurements. The insets of Fig. 4 represent the normalized
frequency response. The observed peaking in the insets, noted as radio-frequency (RF)
resonance or RF-peaking [5,6], in both experiment and simulation is due to two-dimensional
effects and contributes fractionally and not principally in the BW enhancement. More
simplified simulated structures that have stacked layers with the same area dimensions and
electrodes arranged oppositely to each other exhibit also BW enhancement without the
existence of any peaking in the frequency response.
peaking
0
-3
-6
-9
0.1
1
10
Frequency [GHz]
1
10
Frequency [GHz]
Frequency [GHz]
(a)
(b)
Fig. 4. (a) Measured and (b) simulated frequency response at different bias voltages under
−20dBm at 1310nm. The inset shows the normalized frequency response.
Figure 5 shows the voltage dependence of the BW. It can be seen that the BW decreases
between −23V and −26V and then increases again due to the frequency response
enhancement, exceeding 10GHz. At around −23V, the APD is RC and transit time limited,
since the multiplication gain is low. As the voltage increases to −26V and the gain reaches its
maximum, the avalanche buildup time, also called multiplication time, increases and hence the
BW drops. As the voltage increases above −26V, the gain drops and thus the multiplication
time, giving a raise to the BW. However, the BW in this enhanced mode is higher than the
transit time limited BW at lower voltages. This is explained below by investigating the
internal properties such as the electron and hole drift velocities across the Ge absorption layer.
Figure 5 shows also the impact of optical power on the BW. Around −23V, there is no
considerable influence, and the BW value is almost constant. As the bias voltage increases,
any perturbation of the electric field through excess of charge carriers has a big influence on
the gain and on the speed performance of the APD. This behavior is in general due to the
trade-off between the gain and the BW. High optical powers produce low gains and high
BWs, and vice versa.
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20
20
-20dBm
-26dBm
-30dBm
18
16
18
14
BW [GHz]
BW [GHz]
14
12
10
8
12
10
8
6
6
4
4
2
0
-20dBm
-26dBm
-30dBm
16
2
-28
-27
-26
-25
-24
0
-23
-28
-27
-26
-25
Voltage [V]
Voltage [V]
(a)
(b)
-24
-23
Fig. 5. (a) Measured and (b) simulated electrical 3dB-BW versus bias voltage under −20dBm,
−26dBm and −30dBm at 1310nm.
Figure 6(a) shows the extracted GBP of the APD under different input powers. The GBP is
proportional to the gain increase at low gain values due to the constant BW. As the gain
increases, the BW drops due to the multiplication time, and the GBP saturates [1]. Beyond the
gain peak, the GBP starts to increase again dramatically because of the BW enhancement and
the slow decrease of the gain. The highest measured GBP is 845GHz at −30dBm,
corresponding to a gain of 65 and a BW of 13GHz. The simulated GBP in Fig. 6(b) exhibits
some differences to the measurement results. One difference appears in the lower GBP values
in the simulation, especially after the gain peak. This is expected since the simulated gain falls
off much faster than is measured.
500
900
800
-20dBm
-26dBm
-30dBm
400
GBP [GHz]
700
GBP [GHz]
845GHz
-20dBm
-26dBm
-30dBm
600
500
400
300
200
300
200
100
100
0
0
10 20 30 40 50 60 70 80 90 100
0
0
50
100
150
Gain
Gain
(a)
(b)
200
Fig. 6. Calculated GBP versus gain under −20dBm, −26dBm and −30dBm at 1310nm from (a)
experiment and (b) simulation results.
To investigate the very high GBP of the Ge/Si APDs, a pulse response measurement is
realized using a Digital Communication Analyzer with 28GHz optical BW and a 1.55µm
femtosecond fiber-laser with 20MHz repetition rate and 600fs pulse-width. Figure 7 depicts
the pulse responses taken at −20V to −30V under average optical input powers of −20dBm
and −26dBm.
The pulse response exhibits a similar behavior to the frequency response, where a slow,
low frequency part increases with increased bias voltage until around −26V and then
decreases, whereas a fast, high frequency part continues to increase. We believe that the slow
pulse part results from low carrier drift velocities in the absorption region, as described below.
It can be seen that the pulse width becomes very narrow at higher bias voltages than −26V,
which means that the APD becomes faster. The full width at half maximum (FWHF) at −30V
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is 37ps at −20dBm and 30ps at −26dBm, which is in agreement with the enhanced GBP
behavior that rises at lower optical powers.
300
120
-20V
-22V
-24V
-26V
-28V
-30V
200
150
100
50
0
100
150
200
250
-20V
-22V
-24V
-26V
-28V
-30V
100
Pulse response [mV]
Pulse response [mV]
250
80
60
40
20
0
100
300
150
200
Time [ps]
Time [ps]
(a)
(b)
250
300
Fig. 7. Measured pulse responses at different bias voltages under an optical power of (a)
−20dBm and (b) −26dBm at 1550nm.
Electric field magnitude [kV/cm]
At high bias voltages, the space charge effect from the large amplified photo and dark
currents cannot be ignored [9], and we can understand the trends by examining the spatial
dependence of the electric field. The behavior of the electric field in the multiplication layer
illustrated in Fig. 8 explains clearly the decrease of the gain after −26.5V. Since the gain
depends exponentially on the ionization coefficients, which depend exponentially on the
electric field, any small change in the electric field influences strongly the gain behavior.
The zoom-in in Fig. 8 indicates an increase of the electric field in the middle of the
multiplication layer as the bias voltage is increased to −26.5V and then a drop at higher
values, which agrees well with the DC gain measurements. The electric field part at the edge
between the charge layer and the multiplication layer increases, however, continuously and
therefore can be the reason for the high frequency gain, which was also observed to increase
continuously. The electric field in the absorption region is relatively small, resulting in low
electron and hole velocities, which result in the relatively slow tail in the impulse response.
Since the voltage across the device is constant, the reduction of the field in the multiplication
region at voltages above −26.5V causes the field in the absorber to rise, reducing the electron
and hole transit times, resulting in shorter impulse responses.
500
400
300
200
100
-25V
-26.5V
-27V
-28V
-29V
charge
layer
0
0.0
mult.
layer
abs.
layer
0.5
1.0
1.5
2.0
2.5
Position [µm]
Fig. 8. Simulated electric field distribution in the APD at different bias voltages. The inset
shows the zoom-in electric field in the Si multiplication layer.
Figure 9 illustrates both simulated hole and electron concentration profiles at different
biases. At high bias voltages when the density of electrons and holes become comparable to
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the density of donors in the multiplication region (≈5x1015cm−3), the electric field profile can
be affected through the space charge of these electrons and holes. Because of the net excess in
holes at the edge between the charge and the multiplication region, the magnitude of the
electric field increases there. The net excess in electrons in the multiplication region and at the
edge to the n+-contact layer causes the decrease of the electric field magnitude, and therefore
of the multiplication gain due to the exponential dependence of the gain on the electric field
[9].
20
10
19
Concentration [cm ]
10
-3
18
10
Electron(-24V)
Hole(-24V)
Electron(-26.5V)
Hole(-26.5V)
Electron(-28V)
Hole(-28V)
17
10
16
10
15
10
14
10
13
10
12
10
0.0
0.5
1.0
1.5
2.0
2.5
Position [µm]
Fig. 9. Simulated electron and hole concentration in the APD at different bias voltages.
To understand in detail the BW enhancement in SACM Ge/Si APDs, the electron and hole
drift velocities are now studied and are illustrated in Fig. 10. It can be seen that the electron
and hole velocities have reached their saturation values in the Si multiplication layer even at
low bias voltages through the high electric field in that region, whereas in the Ge layer the
drift velocities reach the saturation values only at around −26.5V. At lower voltages, the
velocities are very small in Ge due to the low electric field, so that the transit time is relatively
high and reaches its minimum only at voltages higher than −26.5V, where the drift velocities
reach their maximum. This explains well the BW enhancement above −26.5V, which uses the
fact of the decrease of both multiplication and transit times.
8
Hole drift velocity [10 cm/s]
10
6
-28V
8
6
-26.5V
-24V
4
-22V
2
0
0.0
0.5
1.0
1.5
Position [µm]
2.0
2.5
-28V
7
6
6
Electron drift velocity [10 cm/s]
12
-26.5V
-24V
5
4
-22V
3
2
1
0
0.0
0.5
1.0
1.5
2.0
2.5
Position [µm]
Fig. 10. Simulated electron and hole drift velocity in the APD at different bias voltages.
The increase in GBP at higher voltages can be explained by the rise of hole velocity in the
absorber layer and space charge effects. The experimental observation of shorter impulse
response at higher voltages strongly supports this explanation. One should note in addition
that the band discontinuities at the Ge/Si interface of the APDs have no impact on the GBP
behavior at high bias voltages, since the discontinuities get flatten out through the high electric
field in the device and smoothed out by the Ge/Si interdiffusion.
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4. Conclusion
We have experimentally and theoretically investigated the frequency response enhancement in
Ge/Si SACM APDs and demonstrated a GBP of 845GHz on a 30µm-diameter device. Both
measurement and simulation show similarities in gain and BW behaviors. The enhancement
behavior appears to be the result of decrease of the multiplication time limitation due to the
gain drop through the space charge effect, and to reduction of the transit time because of the
electric field increase in the Ge layer at high bias voltages.
Since the enhanced GBP depends strongly on the incoming optical power, the studied
device, when operated in enhanced mode, has more advantages in some specific applications
where the optical power is fixed, such as quantum cryptography. Future structures with
smaller multiplication and absorption regions can exhibit GBPs over 400GHz in the normal
mode, and perhaps over 1THz in the enhanced mode, especially at optical input powers lower
than −30dBm.
Acknowledgments
This work was sponsored by the Defense Advanced Research Projects Agency (DARPA)
under contract number HR0011-06-3-0009. We thank Herbert Kroemer and Daoxin Dai for
useful discussions.
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20 July 2009 / Vol. 17, No. 15 / OPTICS EXPRESS 12649