Si/Ge uni-traveling carrier photodetector
Molly Piels* and John E. Bowers
Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, USA
*
molly@ece.ucsb.edu
Abstract: We have fabricated and characterized a germanium on silicon
uni-traveling carrier photodetector for analog and coherent communications
applications. The device has a bandwidth of 20GHz, a large-signal 1dB
saturation photocurrent of 20mA at −3V, and a low thermal impedance of
520K/W.
©2012 Optical Society of America
OCIS codes: (040.5160) Photodetectors; (040.6040) Optoelectronics; (060.4510) Optical
communications.
References and links
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Received 20 Dec 2011; revised 29 Jan 2012; accepted 29 Jan 2012; published 19 Mar 2012
26 March 2012 / Vol. 20, No. 7 / OPTICS EXPRESS 7488
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1. Introduction
Coherent and analog fiber-optic links require high-power and high-speed photodetectors to
achieve good signal-to-noise ratios over wide bandwidths. As coherent modulation formats
become more common, the ability of a photodetector to handle currents above 1mA becomes
increasingly important, and receiver packaging can be simplified if the photodiode can
operate without active cooling. Power handling is even more important in radio-over-fiber
applications, where the electronics driving the antenna can be simplified by increasing the
photodiode output microwave power. In general, photodetector output power is limited by
both space-charge [1] and thermal effects. Germanium/silicon detectors are attractive for
high-power applications because the thermal conductivities of germanium and silicon are
large compared to the thermal conductivities of InGaAs and InP. Ge/Si detectors have also
gained popularity in recent years due to their compatibility with silicon photonics platforms.
Efforts thus far have mostly focused on lowering dark current [2, 3], and increasing
bandwidth [4–6]. Here, we present a germanium on silicon detector that has been designed for
high output power by using a uni-traveling carrier (UTC) structure. The device has an output
saturation photocurrent of 20mA at −3V bias, which is larger than a theoretical p-i-n detector
with the same Ge thickness. It also has a responsivity, 0.12A/W at 1550nm, larger than a
surface-normal p-i-n detector with the same transit-time limited bandwidth, while maintaining
a low thermal impedance relative to comparable InP-based detectors. Overall, it is a
promising candidate for use in analog and coherent photonic applications.
2. Device design and fabrication
The Ge/Si UTC structure consists of a highly p-doped germanium absorber and an
unintentionally doped silicon collector on an n-type silicon substrate as shown in Fig. 1. The
absorber doping is graded from 1e19cm−3, which is near the solubility of boron in germanium,
at the top of the device to 5e17cm−3 at the absorber-collector interface. This induces a small
electric field that decreases the transit time in the absorber. There are substantial differences
between the Ge/Si material system and the InP-based material system that affect the design of
a UTC photodetector. First, there are fewer appropriate materials available for use as a
diffusion-blocking layer. Without a diffusion block, carriers that are generated close to the pcontact will diffuse in the wrong direction, decreasing the collection efficiency of the device.
Because the system is not lattice-matched, growing a layer with a wider bandgap on top of the
germanium is challenging. Instead, the doping grade and the p++ contact layer are used to
modify the electric field profile such that the electrons move toward the n-side of the diode.
This may lead to some loss of internal quantum efficiency because it is still possible for
electrons to diffuse into the p-contact. However, the measured responsivity (which is
discussed in more detail in Section 3) is consistent with the trend in published literature for
comparable detectors.
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Received 20 Dec 2011; revised 29 Jan 2012; accepted 29 Jan 2012; published 19 Mar 2012
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The germanium-silicon heterojunction also differs from the InGaAs-InP heterojunction,
which affects the design near the absorber-collector interface. In InGaAs/InP detectors, the
conduction band offset is significant, and conduction band smoothing or depleted absorber [7]
layers are often used to help carriers get through the interface. In contrast, the conduction
band offset in the Ge/Si system is very small [8], so good performance should be possible
without these layers. Furthermore, the traps that form at the Ge/Si interface due to threading
defects are acceptor-like [9], so decreasing the p-doping near the heterojunction may lead to
an unwanted barrier there. The primary risk from pursuing this approach is that boron
diffusion into the undoped silicon layer during Ge growth would move the band offset into the
conduction band. However, germanium growth temperatures tend to be low enough to allow
for very abrupt junctions (<800°C).
Fig. 1. (a) Cross-section schematic (b) Optical photograph of the fabricated device.
The detectors are single mesa structures with top ring contacts to allow for illumination
from both the top side and the back side. The epitaxial structure is grown (by IQE Silicon),
then mesas of varying diameters are patterned in a chlorine-based inductively coupled plasma
etch. The mesa sidewalls are then passivated with SiO2 and vias to the Ge and Si are opened
by a combination of dry and wet etching in order to minimize the amount of Ge lost during
this step. The same contact metal stack, Ni/Ti/Au, is used on both the Ge and the Si. Before
probe metal is deposited, SU8 polymer is patterned under the probe pads in order to minimize
parasitic capacitance. Some of the devices are anti-reflection coated on the top side with Si3N4
and on others the Si substrate is thinned to 50µm to allow coupling from the back.
3. Responsivity and dark current
Figure 2(a) shows the responsivity as a function of wavelength for a top-illuminated largearea device at −1V bias and low photocurrent. The wavelength dependence is very strong due
to the proximity of the bandgap energy to the photon energy. A theoretical curve assuming
Eg,hh = 0.79eV and Eg,lh = 0.77eV [10] is also shown. The responsivity at 1310nm (not shown)
is 0.29 A/W and the responsivity at 1550nm is 0.12 A/W. The responsivity under backside
illumination is around 7dB lower due to free-carrier absorption in the substrate. Figure 2(b)
shows the responsivities of various surface-normal p-i-n photodetectors in the literature at
1550nm as a function of germanium thickness. For photodetectors without anti-reflective
coatings, the responsivity shown in Fig. 2(b) is greater than the reported value by a factor of
1.6 (1.4 in the case of detectors with top polysilicon layers) to make a fair comparison. Values
that have been thus modified are indicated by crosses in the figure. Curves for absorption
coefficients of 2000cm−1 and 5000cm−1 are also shown. The absorption coefficient of Ge at
1550nm varies with growth conditions [10, 11], but typically lies between these two values.
The top-illuminated and anti-reflection coated Ge/Si UTC responsivity is in keeping with the
trend of other reported values. Assuming an absorption coefficient of 7060cm−1 at 1310nm
and perfect antireflective coating at this wavelength, the collection efficiency is 75%. The
dark current of this large-area device at −1V is 3.8µA, and the dark current of the smaller
device discussed below is 280nA at −1V and increases to 8.9µA at −3V. In order to extract
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Received 20 Dec 2011; revised 29 Jan 2012; accepted 29 Jan 2012; published 19 Mar 2012
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the contributions of sidewall passivation and junction leakage, the dark current of diodes of
varying diameters was measured. The dark current is dominated by the area, rather than the
sidewall, component and is 35mA/cm2 at −1V bias.
Fig. 2. (a) Responsivity of a large-area topside illuminated device around 1550nm. The
theoretical curve was calculated by assuming Eg,hh = 0.79eV and Eg,lh = 0.77eV and fitting the
momentum matrix element to the data. (b) Responsivities of surface-normal Ge/Si devices
from the literature. Circles: data displayed as reported; Crosses: data modified to account for
lack of anti-reflective coating.
4. Bandwidth
The small-signal bandwidth of a backside-illuminated 14µm diameter device is shown in Fig.
3. The bandwidth of topside-illuminated detectors with the same diameter (not shown) is the
same at low photocurrents. The 3dB bandwidth at 2V and larger biases is 20GHz below 5mA
of photocurrent. The bandwidth is limited by both the resistance-capacitance (RC) charging
time and the transit time. The diode series resistance and capacitance were extracted by fitting
scattering parameter (S11) data to a small-signal model similar to that in [18]. The capacitance
of the device shown in Fig. 3 is around 80fF, which includes a parasitic capacitance around
20fF, and the series resistance is around 1Ω. The transit time can be inferred, again using the
model in [18], from the frequency response and the S11 data to be 5.5ps. The transit time
limited 3dB frequency (36GHz) is greater than the transit time limited frequency for a p-i-n
detector with the same germanium thickness, 29GHz. The frequency response as a whole is in
good agreement with the model presented in [19]. The dominant contribution to the transit
time is the response of the absorber, which implies that making the silicon collector thicker
will increase the overall bandwidth of the device by decreasing the capacitance. This would,
however, come at the expense of lower saturation output power because the saturation current
is inversely proportional to the thickness of the intrinsic region. It is worth noting that the
doping grade in the absorber significantly enhances the bandwidth. The predicted transit-time
limited bandwidth for the same structure without the grade is only 6GHz.
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Fig. 3. (a) Bandwidth as a function of bias voltage at 200µA photocurrent. (b) Bandwidth at 3V
as a function of photocurrent.
The bandwidth of the same device at −3V is shown as a function of photocurrent in Fig.
3(b) and decreases steadily to 18GHz at 15mA. The line in the curve is a fit using series
resistance and capacitance values from S11 data and assuming a constant transit time of 5.5ps.
Often, UTC PDs exhibit an increase in bandwidth at moderate photocurrents that is not
evident in Fig. 3(b). This is generally attributed to a decrease in transit time due to electron
velocity overshoot in the collector [20] and the space-charge induced field in the absorber
[21]. Since there is no velocity overshoot in silicon and the absorber transit time is much
longer than the collector transit time, it is not expected that the first effect would occur in
these detectors. The second effect, where a favorable potential drop is created by the
photocurrent and the resistivity of the absorber, on the other hand, could occur. It most likely
does, but is not noticeable because the resistivity of p-type Ge is very low (compared to most
semiconductors), which results in a low induced potential: approximately 2mV at 15mA,
which is much smaller than the 80mV potential induced by the doping grade. Instead, the
decrease in bandwidth is due to increasing series resistance and capacitance caused by the
space-charge effect in the collector. Both the resistance and the capacitance increase by about
10% as the current is increased from 200µA to 15mA.
5. 1dB compression measurements
The large-signal compression characteristics of the backside-illuminated device are shown in
Fig. 4(a) and 4(b) along with theoretical curves in 4(b). An 80% modulation depth tone fixed
at 20GHz was generated using the standard heterodyne technique with two free-running lasers
at 1537nm. The saturation of the response is caused by both the voltage drop across the load
resistance and the space-charge effect in the collector. The voltage across the photodetector,
VPD, can be written as:
VPD = Vbias − I dc Rs − I ac ( RL + Rs )
1 + ( 2π fRC )
2
(1)
where Iac is the time-varying photocurrent, Idc is the time-average photocurrent, and RL and Rs
are the load and series resistances, respectively. The time-varying and time-average
photocurrents are related to each other, the 1dB compression current, and the maximum
current (Imax) by the modulation depth as discussed below. At the 1dB compression point and
for 80% modulation depth, Idc = 0.65Imax and Iac = 0.35Imax. The space-charge effect is the
reduction in electric field in the collector due to the presence of unscreened negative charges.
Once the current density reaches a high enough value, the electric field at the collector input
collapses. This maximum current density can be found by solving Poisson’s equation in the
collector and is written as:
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J max =
2ε Si vn
wc2


qwc2
V
+
V
−
E
w
+
N DC 
 bi
PD
crit c
2ε Si


(2)
where εSi is the dielectric constant of silicon, vn is the saturated electron drift velocity
(1e7cm/s in Si at room temperature), wc is the collector width, Vbi is the built-in voltage, Ecrit
is the electric field below which the electron velocity is not saturated (35kV/cm in Si), and
NDC is the donor concentration in the collector. Slightly above the maximum current density,
the electric field goes to zero at the collector input and no more current can be collected from
the device. Solving Eq. (1) and Eq. (2) simultaneously assuming uniform illumination and
current density yields the maximum current as a function of bias voltage.
Fig. 4. (a) Output RF power at 20GHz as a function of photocurrent. (b) 1dB compression
current as a function of bias voltage. Circles: Measured data; Upper line: 1dB compression
current predicted by model without thermal effects; Lower line: model with thermal effects.
The maximum current calculated by solving Eqs. (1) and (2) simultaneously is used to
calculate the 1dB compression current, which is shown as the upper theoretical line in Fig.
4(b). The 1dB compression current is defined as the time-average photocurrent at which the
RF output power is lower than the output power predicted by the time-average photocurrent
by 1dB. In order to relate the maximum current to the 1dB compression current, some
assumptions have to be made about the shape of the waveform. When the photodiode is
operating in compression, the output is approximately a clipped sinusoid with the maximum
output limited to the maximum current that can be sustained by the device. As the portion of
the sinusoid’s period (T) during which time the output is clipped (Tc) increases, both the timeaverage and the RF photocurrent decrease. The DC photocurrent decreases by
I DC
m
 T
= 1 − sin  π c
ℜPave
π
 T
Tc

 Tc 
 + m T cos  π T 



(3)
where ℜPave is the product of the responsivity and the average optical power and m is the
modulation depth. The RF photocurrent decreases by
T
I RF
1
 T 
sin  2π c  .
= 1− c +
(4)
T 2π
T 
ℜPRF

It should be noted that although Eq. (4) can be used to accurately predict the RF power of
the waveform, the Fourier series converges very slowly, so this equation should not be used to
calculate the current in the time domain. The 1dB compression current can be found by
comparing the RF power predicted by Eq. (3) to the power given by Eq. (4). The result is that
the 1dB compression current (Idc in Eq. (1)) is the maximum photocurrent multiplied by 0.60
for the case of 100% modulation depth and 0.65 for 80% modulation depth. Since Eq. (1)
assumes that the maximum current through the device is the sum of Idc and Iac, the appropriate
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value for Iac in that equation is the maximum photocurrent multiplied by 0.40 for 100%
modulation depth and 0.35 for 80% modulation depth. The theoretical line (for 80%
modulation depth) is also plotted in black in Fig. 4(b).
For the purpose of comparison, the same model can be used to estimate the 1dB
compression current of a p-i-n detector with the same germanium thickness and total device
area by modifying Eq. (2). The calculated compression current for such a device at −3V is
8mA, which is smaller than the compression current of the Ge/Si UTC at the same voltage,
20mA. At high levels of photocurrent, the measured 1dB compression current drops below the
value predicted by the model. This is due to heating in the device, which decreases the
saturated electron velocity and thus decreases the maximum current. The lower theoretical
line in Fig. 4(b) includes this effect, using the empirical fit from [22] for the electron
saturation velocity in Si, measured thermal impedance of 520°C/W for electrical power
dissipation, and an estimated thermal impedance of 550°C/W for incident optical power. As
will be discussed below, most of the heating in the backside-illuminated device is due to freecarrier absorption in the doped substrate, which implies that better output RF power could be
obtained by using a semi-insulating substrate.
6. Thermal impedance
The thermal impedance of the Ge/Si UTC is low due to the high thermal conductivities of Ge
and Si relative to InGaAs and InP, respectively. Figure 5(a) shows the simulated peak
junction temperature as a function of dissipated power for the Ge/Si UTC and a comparable
InGaAs/InP device. The simulation is performed using Comsol software. It is a 2D finiteelement model with radial symmetry. The heat source is assumed to be uniformly distributed
in the collector, and the bottom of the chip is assumed to be held at a constant temperature by
the heat sink. The thermal conductivity of silicon (at room temperature) is 1.5 W/cm·K, 2.2
times higher than the thermal conductivity of InP, 0.68 W/cm·K. The thermal conductivity of
Ge, 0.56W/cm·K is similarly 11 times higher than the thermal conductivity of InGaAs
(0.05W/cm·K), and the net effect is that the device thermal impedance is 1.7 times lower than
the thermal impedance of the comparable III-V based device. Thermal conductivities tend to
decrease with temperature, and this is taken into account in the model using the data from [23]
for Si and Ge [24], for InGaAs, and [25] for InP.
To verify the simulation result, thermoreflectance imaging [26] was used to measure the
temperature of the device under operation. A thermal image of the device when it is
dissipating 40mW of electrical power is shown in Fig. 5(b). This technique measures surface
temperature by comparing images of the device when it is dissipating a large amount of power
to images taken when it is dissipating a very small (typically 10µW) amount of power. The
change in temperature, ∆T, is linearly proportional to the change in surface reflectivity, ∆R:
∆T =
∆R
Cth R
(5)
where R is the reflectivity when the device is off and Cth is the thermoreflectance coefficient.
At 530nm, the wavelength of the illumination source used in this experiment, the
thermoreflectance coefficient is −2.5e-4 for gold and −1.6e-4 for germanium. These values
were measured by changing the entire die temperature by a known amount using a Peltier
cooler and a microthermocouple and comparing the hot and cold images. To change the
amount of power dissipated by the device during the thermal impedance measurement, the
optical input was held constant while the bias voltage was pulsed. The measured detector
surface temperature is shown along with the theoretical line in Fig. 5(a). Though the
simulation result shown is for maximum temperature rather than surface temperature, these
were always within 0.2K in the simulation. The temperatures predicted by the model are well
within the margin of error of the experiment.
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Because the laser was on for both the high-power and low-power images, heating due to
optical absorption in the substrate does not appear in the images. This heating was measured
by moving the fiber far from the device and pulsing the optical input rather than the voltage,
and is typically larger than the heating due to normal device operation. For example, when the
device is dissipating 5mW of power (1.5mA photocurrent and 3.3V bias), the total
temperature rise is 16K, but 13.5K can be attributed to heat generation in the substrate. The
effect of substrate heating is also evident in Fig. 4(b), as the 1dB compression current falls
below the predicted value at higher powers.
Fig. 5. (a) Measured and simulated photodiode temperatures as a function of dissipated power.
A simulated line for an InP/InGaAs device with the same dimensions is also shown. (b)
Thermal image of the photodetector mesa while it is dissipating 40mW of electrical power.
7. Conclusions
We have presented a Si/Ge uni-traveling carrier photodetector designed for high-power
operation. The UTC design increases the saturation current at a given voltage by allowing for
a thin intrinsic region without compromising on responsivity (germanium thickness). Despite
being thicker in total than a p-i-n detector with the same germanium thickness, the transit-time
limited bandwidth is faster because of the graded doping profile in the absorber. The thermal
impedance of the device is low, and it shows promise for use in high-power applications.
Acknowledgements
This work was supported by the DARPA CIPhER program under contract HR0011-10-10079. The authors thank Anand Ramaswamy, Jin-Wei Shi, Keith Williams, and Joe Campbell
for useful discussions.
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