3336 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 11, NOVEMBER 2010

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1 3336 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 11, NOVEMBER 2010 High Power Silicon-Germanium Photodiodes for Microwave Photonic Applications Anand Ramaswamy, Student Member, IEEE, Molly Piels, Student Member, IEEE, Nobuhiro Nunoya, Member, IEEE, Tao Yin, Member, IEEE, and John E. Bowers, Fellow, IEEE Abstract We demonstrate high current operation of an evanescently coupled Ge waveguide n-i-p photodetector grown on top of a Si rib waveguide. A 7.4 m 500 m device was found to dissipate W of power ( ma at 8 V). 2-D thermal simulations of the device show that the relatively high thermal conductivities of the intrinsic Ge region and the p + doped Si layer result in efficient heat transfer and hence, lower absorber temperatures when compared to a similar InP based waveguide photodiode. Additionally, to determine the feasibility of these devices for analog photonic applications, we performed large signal and small signal radio frequency (RF) measurements as well as linearity measurements. At 1 GHz and 40 ma of photocurrent, a third order output intercept point (OIP3) of dbm is measured. The maximum RF power extracted at 1 GHz is dbm at 60 ma of photocurrent and 7 V reverse bias. Index Terms High power detectors, microwave photonics, linearity, photodiodes, silicon photonics. I. INTRODUCTION R ECENT efforts to develop photodetectors on a Si platform have centered around high data rate applications where the main focus of device structure and design hasbeento achieve wide bandwidth operation while simultaneously increasing quantum efficiencyandloweringdarkcurrent[1],[2]. However, anareathat has beenrelatively less explored isthe application of Sibased photodetectors to high performance microwave photonic systems. In general, the performance of such systems increases with received shot-noise limited optical power [3]. This necessitates the development of photodiodes that have high optical power handling capability. The majority of the work on high power microwave photodiodes has been on the InP platform where the versatility offered by complex multilayer heterojunction structures has resulted in the demonstration of photodiodes with 199 ma of compression current at a frequency of 1 GHz [4]. Such detectors Manuscript received January 07, 2010; revised June 24, 2010; accepted July 17, Date of publication October 07, 2010; date of current version November 12, This work was supported in part by the Defense Advanced Research Projects Agency (DARPA) PHOR-FRONT program under the United States Air Force Contract FA C A. Ramaswamy, M. Piels and J.E. Bowers are with the Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA USA ( anand@ece.ucsb.edu). T. Yin is with Intel Corporation, Santa Clara, CA USA ( tao. yin@intel.com). N. Nunoya was with the Department of Electrical and Computer Engineering, University of California, CA USA. He is now at NTT Photonics Laboratory, Japan ( nunoya@aecl.ntt.co.jp). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TMTT Fig. 1. Summary of recent results: Electrical power dissipated versus 3 db bandwidth of photodetector. have also shown exceptional linearity performance[5] [7]. However, thermal effects [8] in these devices pose a significant challenge to achieving higher current operation. For example, in surface illuminated InGaAs-InP devices, the thermal conductivity of the InP substrate (0.68 W/cm K) is a major factor limiting the maximum photocurrent that can be extracted from the device [8]. The problem becomes even more acute for waveguide photodiodes (WG-PD) on an InP platform [9]. This is so because the ternary absorber (usually InGaAs) sits on a quaternary (usually InGaAsP) waveguide. The thermal conductivities of these two layers are 0.05 W/cm K [10], which is a factor of 30 less than that of Silicon. Hence, heat flow out of the absorber region is further restricted (compared to a surface illuminated PD) leading to temperature build up and ultimately, thermal failure. An alternate to using an InP substrate is to use Si, because its thermal conductivity (1.5 W/cm K) is over two times that of InP [10]. Surface illuminated p-i-n detectors made from wafer bonded In- GaAs-on-Si material have been reported to dissipate over 612 mw of electrical power [11]. Recently, we demonstrated high current operation of a Ge n-i-p waveguide photodetector on silicon-on-insulator (SOI) substrate [12]. The device dissipated 1 W of electrical power prior to thermal failure [12]. Fig. 1 summarizes state of the art results for electrical power dissipation for both waveguide and surface normal detectors. The paper is organized as follows. Section II outlines the device structure. The next section presents DC characteristics of the device including data showing high electrical power dissipation. It was observed in [12] that the responsivity of the device increased with input optical power. Here, we performed /$ IEEE

2 RAMASWAMY et al.: HIGH POWER SILICON-GERMANIUM PHOTODIODES 3337 time-domain pulsed responsivity measurements of the device to ascertain whether the effect is thermal or due to carrier recombination nonlinearities. In Section IV we present results from a 3-D thermal simulation of the device. In [12] we presented results from a 2-D thermal simulation of the device that assumed a uniform absorption profile along the length of the device. However, we show here that a 3-D simulation generates more accurate results owing to the exponential absorption profile of waveguide PDs. Linearity and maximum RF power extraction are also important photodiode parameters for analog optical links. Surface illuminated PDs with OIP3s in excess of 50 dbm and output RF powers up to 29 dbm at 2 GHz have been reported [6], [13]. However, for higher frequency operation and more complex receiver functionality WG-PDs are of particular interest because 1) they can overcome bandwidth limitations by incorporating a traveling wave design and 2) they have the potential to be monolithically integrated with other optical components. In Sections V and VI we explore the potential of these devices for microwave applications by measuring their linearity and RF response under small signal and large signal modulation [14]. Further, we analyze large signal power extraction from the device and obtain the power conversion efficiency. II. DEVICE STRUCTURE The Ge waveguide detector is grown on top of a Si rib waveguide by a selective epitaxial process. The detector in this work has a width of 7.4 m and a length of 500 m. The final thickness of the Ge layer is 0.8 m. The thicknesses of the silicon and buried oxide layer are 1.5 m and 1.0 m, respectively. A cross-sectional schematic of the photodetector and is shown in Fig. 2(a). The detectors are fabricated several millimeters away from the input at the edge of the chip, which improves heat-sinking [8]. Single-mode 1.4 m-wide waveguides cover most of this distance before they taper out to the detector width over a length of 500 m. As the light propagates along the Si waveguide it evanescently couples upwards into the Ge region where it is absorbed. Details of the growth and fabrication process can be found in [1]. Fig. 2(b) shows the calculated energy-band diagram of the detector at a reverse bias of 5 V using Bandprof. As expected, the applied bias field is dropped across the intrinsic Ge layer. Additionally, at the hetero-interface between Si and i-ge, the bandgap difference ( ev) is reflected primarily in the valence band. This creates a barrier for hole transport and could lead to additional recombination at the interface. III. DC CHARACTERISTICS Fig. 3(a) shows the saturation characteristics of the device at an input wavelength of 1550 nm for different reverse bias values. The x axis takes into account a coupling loss of 4 db. It can be seen that at a lower bias the output current saturates faster because of carrier screening effects [16]. A maximum photocurrent of ma under 8 V of reverse bias was observed. This corresponds to over 1 W of electrical power dissipation in the device. As the reverse bias on the device increases, the junction temperature increases, resulting Fig. 2. (a) Cross-sectional schematic of Ge detector integrated with passive Si waveguide. (Figure adapted from [1]). (b) Band diagram when device is reverse biased to 5 V. in higher leakage currents. This increase in leakage current results in additional joule heating and in the extreme case leads to thermal runaway and consequently, device failure. In order to ensure that thermal runaway is not occurring at high bias voltages we measure the dark current of the device after high current operation. As can be seen in Fig. 3(b) the dark current is 125 A at V bias. Fig. 3(c) plots the dc responsivity of the device as a function of input optical power. Typically, at low input optical power levels, the responsivity of a photodiode remains fairly uniform. Close to saturation the photo-generated carriers in the device produce a large screening field that reduces the bias field across the depletion region leading to photocurrent compression. Consequently, the device responsivity is expected to decrease. However, from Fig. 3(c) it can be seen that the responsivity is not uniform even at lower optical powers and higher reverse biases (where space charge effects should be minimal). We performed time-domain pulsed responsivity measurements to determine whether thermal effects were responsible for the increased responsivity [17]. We measured the thermal time constant of the system using a thermoreflectance technique and found that it was 100 s [18]. We then used a 500 s optical pulse at 100 Hz (5% duty cycle) and compared the photocurrent at the beginning of the pulse to the photocurrent at the end. Fig. 4 plots the responsivity as a function of photocurrent at a reverse bias of 4 V under three input optical power conditions (1) Continuous wave (CW), (2) pulsed: cold (rising edge of the pulse) and (3) pulsed: hot (falling edge of the pulse). The hot and cold responsivities were within 1 2% of each other up to 40 ma.

3 3338 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 11, NOVEMBER 2010 Fig. 4. Pulsed and CW responsivity as a function of photocurrent at a nominal reverse bias voltage of 4 V. the pulse. This can be seen on the second ordinate axis of Fig. 4 where at 20 ma the voltage swing across the device is reduced to 1.5 V. In [12] we suggested that carrier recombination nonlinearities [19] could be responsible for the nonlinear behavior of the dc optical responsivity. The 4% lattice mismatch between Si and Ge induces strain in the material. Beyond a certain thickness, strain is normally relieved by misfit dislocations. The dislocations lead to midbandgap deep level defects that contribute to leakage current and act as carrier recombination centers (traps). The mechanism for sublinear recombination events as optical power increases is not fully understood. One possibility [20] is that as the optical power in the depletion (absorber) region increases, the fraction of time that trap sites located at the Ge-Si interface are occupied increases. Consequently, proportionately lower number of minority carriers can recombine as there are fewer available recombination centers (traps). Fig. 3. (a) Photocurrent as a function of optical power at different reverse bias voltages (b) Leakage current as a function of reverse bias voltage (c) dc responsivity as a function of input c.w. optical power [12] This is within the margin of error of the experiment. The CW measurement shows a 10 20% increase in responsivity over this range. This clearly suggests that a mechanism other than thermal heating is responsible for the increased responsivity of the device. Another interesting point to note in Fig. 4 is that up to 20 ma, the responsivities measured by the pulsed and CW setups are the same. Beyond 20 ma of photocurrent, the pulsed responsivity appears to saturate sooner than the CW responsivity because of the voltage swing across the device that occurs during IV. THERMAL SIMULATIONS Fig. 5 shows the temperature profile from a 3-D thermal simulation of the device performed using COMSOL software and verified with a thermoreflectance measurement [18]. The primary mode of heat transfer is conduction through the buried oxide layer and 675 m substrate to a thermoelectrically controlled copper block below the device. While heat transfer by other mechanisms, namely convection and black body radiation, does occur, it is negligible compared to the heat transfer due to conduction. All boundaries other than the bottom of the wafer were therefore assumed to be insulating. To decrease computation time, only half of the device was simulated, and the boundary along the cut-line was treated as insulating as well. In the experiment, thermal grease was used to improve heat conduction between the controlled copper block and the device substrate. Hence, it was assumed that the bottom boundary of the Si wafer was held at the same temperature as the stage, 20 C. As the junction temperature of the diode increases, the thermal conductivity of the surrounding materials decreases and the dark current increases. Both of these effects contribute to further localized heating and, eventually, thermal runaway

4 RAMASWAMY et al.: HIGH POWER SILICON-GERMANIUM PHOTODIODES 3339 Fig. 5. Temperature profile from a 3-D thermal simulation of the device at 500 mw dissipated power. and failure. Because the device temperature is expected to be very large at the high levels of power dissipated in the device, the temperature dependence of the thermal conductivities of Ge and Si must be taken into account. The thermal conductivity of Ge, for example, decreases to 30% of its room temperature value over the 600 C temperature change our simulations show the device undergoes prior to failure at 1 W. The thermal conductivities of Si and Ge as functions of temperature were interpolated from the values given in [21]. The contact metal is Al, whose thermal conductivity is 2.37 W/cm K, and the thermal conductivity of the buried oxide is W/cm K. Heat is generated primarily in the depletion region [8] and it was assumed that the heat source was uniform in the cross section of the intrinsic Ge layer. The absorption profile of waveguide photodiodes decays exponentially in the direction of propagation. Most heat is generated by the photocurrent, which, since it is exponentially decaying, leads to localized heating near the input of the waveguide [22]. This heating in turn increases the local dark current. The exact dependence of dark current on temperature is unknown. Below the point of failure the total dark current was observed to be small relative to the photocurrent. Because of this and because the dark current density should vary in approximately the same way as the photocurrent, it was assumed that the total heat generated in the device was distributed in the exact same way as the photocurrent. The characteristic length of the absorption profile was calculated using Beamprop, and it was assumed that heat generation decreased exponentially with the same characteristic length. The taper was included in the Beamprop simulations but not the thermal simulations. Fig. 6(a) shows the temperature along the center line of the device for total power dissipations of 100 mw, 500 mw, and 1 W. As Fig. 5 shows, there is very little heat transfer in the direction of optical propagation and most heat leaves the depletion region laterally. The heat flows downward from the absorber into the doped Si region and then spreads when it reaches the buried oxide layer. The low thermal conductivity ( Fig. 6. (a) Simulated temperature of the center of the depletion region as a function of distance from the optical input. (b) Simulated peak junction temperature versus dissipated electrical power. W/cm K) of this layer is the primary obstacle to heat extraction. Two-dimensional thermal simulations were performed on the cross-sections of both this device and that of a high linearity, high output saturation InP UTC WG-PD [9]. The bandwidths of the two devices are comparable 3 GHz for the InP UTC and 4.4 GHz for the Si-Ge detector. It was observed that the InP detector had nearly twice the transverse thermal impedance (160 C/W) of the Si-Ge device (87 C/W), thus resulting in thermal failure of the device at lower electrical power dissipation (300 mw) [23]. Fig. 6(b) shows the simulated maximum junction temperature as a function of total power dissipated in the device. At the point of failure, 1 W, the simulated peak junction temperature is 585 C. A. Small Signal V. MICROWAVE MEASUREMENTS In addition to dc response measurements, we also measured the frequency response of the device at different photocurrent levels [Fig. 7(a)]. It has been observed that the bandwidth of photodiodes decreases at high input optical power levels [24]. However, Fig. 7(b) shows that up to 50 ma of photocurrent and under 5 V reverse bias, the 3 db bandwidth of the device remains fairly constant at 4.38 GHz.

5 3340 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 11, NOVEMBER 2010 Fig. 8. Output RF power and power conversion efficiency for a 7.4 m2500 m device at 1 GHz for bias voltages values: 1 V, 3 V and 7 V (modulation depth (m) = 1). Fig. 7. (a) Measured small signal frequency response of 7.4 m2 500 m device at different photocurrent levels for a fixed reverse bias (5 V) [12] (b) 3 db bandwidth as a function of average photocurrent [12]. B. Large Signal By driving an external intensity modulator 100% we measure the maximum RF power we can extract from a 7.4 m 500 m device at 1 GHz. The maximum 1 db compression point is dbm at an average dc photocurrent of 60 ma and 7 V reverse bias (Fig. 9(b)). Fig. 8 plots output RF power as a function of average dc photocurrent. Following the analysis in [25] we calculate the power conversion efficiency where is the power dissipated in the photodetector, is the power delivered to the load, is the power supplied by the biasing circuit, and is the total optical power into the device (taking into account a coupling loss of 4 db). The power conversion efficiency is defined as (1) (2) The power delivered to the load is simply the power at the fundamental frequency. The bias power is the product of the bias voltage and the average current (both dark and photogenerated) and the total optical power is also known. The photodetector conversion efficiency as a function of photocurrent is plotted for three different bias voltage values: 1 V, 3 V, and 7 V (Fig. 8). It can be seen that prior to saturation, the conversion efficiency increases with increasing optical power. It can be inferred that is increasing faster than the combined sum of and. Also, it can be observed that the peak efficiency for any given bias voltage corresponds to the maximum value of prior to saturation. The highest conversion efficiency obtained was 6% at 4 V bias and mw. This is significantly lower than the theoretical limit of 50% for class A operation of photodiodes as output power amplifier stages [25]. Theminimumbiasvoltagefromthesourcerequiredtomaintain class A operation is dependent on two metrics of the photodiode ( and ) as follows [25]: where is defined as the slope of the 1 db small signal compression current db as a function of applied bias voltage and is the x-intercept of the same plot. is a factor that depends on the incident waveform and compression characteristics of a particular PD, while is the modulation depth ( corresponds to a modulation depth of 100%). By inserting (2) into (3), where can be written as follows [25]: The above expression however, makes use of two parameters ( and ) obtained from a small signal measurement db and as such is valid only as long as db. Instead of using a small signal measurement to predict large signal behaviorwe directly usethe large signal 1 db compressioncurrent (3) (4)

6 RAMASWAMY et al.: HIGH POWER SILICON-GERMANIUM PHOTODIODES 3341 Fig. 9. (a) P db as a function of bias voltage (b) Large signal compression data as a function of bias voltage extracted from the data in Fig. 8. Fig. 10. Two-tone and three-tone OIP3 at 1 GHz as a function of (a) bias voltage (photocurrent = 40 ma) (b) photocurrent (reverse bias = 8 V). data to obtain and. Fig. 9(b) plots 1 db large signal compression current as a function of applied bias voltage and the slope is equal to ma/v, while the x-intercept V. Inserting these values into (4) and for and, the maximum efficiency that can be obtainedwith15dbmofoutputrfpoweris10%.itcanbeseenfrom (4) that for higher and lower, the conversion efficiency is higher. Additionally, for power detectors the efficiency increases as the output RF power from the detector increases [25]. From Fig. 9(b) we see that the maximum RF power we can obtain is 15 dbm. is a significant limitation to the efficiency of our device. Currently, it is a factor of 10 lower than state of the art high power PDs [25]. Hence, future designs of high-power Si-Ge photodiodes need to focus on improving and increasing the RF power out of the device. VI. LINEARITY High performance analog optical links require photodiodes that have high power handling capability as well as high linearity. Typically, for suboctave links, we are interested in the third order intermodulation distortion (IMD3) components generated in the device because they fall very close to the carrier frequencies and are difficult to filter out. There are several mechanisms that contribute to nonlinearities in photodiodes [15]. For instance, space charge effects leading to carrier velocity modulation is one of the primary sources of microwave nonlinearities at low bias voltage values and moderately high optical power levels. Additional sources of nonlinearities include voltage dependent responsivity as well as voltage and current dependent capacitance of the device [26], [27]. We measured the linearity of the device both as a function of bias voltage and average dc photocurrent at a frequency of 1 GHz. We used a standard two-tone and more complicated three-tone technique for this measurement [28]. Fig. 10 shows the OIP3 results from both measurement techniques, wherein theoretically, the three-tone OIP3 should be 3 db less than the two-tone OIP3 [29]. It can be seen that with increasing bias the OIP3 increases and reaches a maximum of dbm at 8 V and 40 ma of photocurrent [Fig. 10(a)]. Additionally, it was observed that at lower photocurrents the OIP3 is actually lower, even at higher biases [Fig. 10(b)]. If we assume space charge effects are negligible at relatively low photocurrents and high bias, one possibility for the lower linearity is the voltage dependent responsivity of the device. From Fig. 4 we see that even at low

7 3342 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 11, NOVEMBER 2010 optical power levels the device has a strong voltage dependent responsivity. In the same figure we also observe that the device has a strong photocurrent dependent responsivity. Currently we are investigating whether the photocurrent dependent responsivity of the device contributes to the measured microwave nonlinearity trends. By determining the sources of nonlinearities in these devices it may be possible to minimize them by using compensatory effects [30]. VII. CONCLUSION In summary, we have demonstrated high power operation of a Ge n-i-p waveguide photodetector on silicon-on-insulator (SOI) substrate. A 7.4 m 500 m device was able to dissipate 1 W of electrical power. Thermal simulations indicate heat trapped in the absorber contributes to device failure. Since Ge has nearly 12x higher thermal conductivity than an InGaAs absorber, we predict and experimentally verify the thermal performance of these Si-Ge waveguide devices to be significantly better than comparable InP devices. The devices presented here were not optimized for power conversion efficiency or high linearity. Improvements in device design by implementing partially depleted absorbers or charge compensated UTCs can result in improved performance [31], [15]. Further, all the microwave measurements presented in this paper were made at 1 GHz. The advantage of waveguide detectors increases at higher frequencies, beyond the bandwidth of surface normal photodetectors. ACKNOWLEDGMENT The authors would like to thank K. J. Williams, R. Esman and L.A. Johansson for useful discussions and M. N. Sysak for help with simulations. REFERENCES [1] T. Yin et al., 31 GHz Ge n-i-p waveguide photodetectors on silicon-on-insulator substrate, Opt. Exp., vol. 15, no. 21, pp , Oct [2] D. Ahn et al., High performance, waveguide integrated Ge photodetectors, Opt. Exp., vol. 15, no. 7, pp , Apr [3] V. J. Urick et al., Photodiode linearity requirements for radio-frequency photonics and demonstration of increased performance using photodiode arrays, presented at the Microwave Photonics Conf (MWP), Canada, Oct [4] D. A. Tulchinsky et al., High saturation current wide-bandwidth photodetectors, IEEE J. Sel. Topics in Quantum Electron., vol. 10, no. 4, pp , Aug [5] J. Klamkin, A. Ramaswamy, N. Nunoya, L. A. Johansson, J. E. Bowers, S. P. DenBaars, and L. A. Coldren, Uni-traveling-carrier waveguide photodiodes with > 40 dbm OIP3 for up to 80 ma of photocurrent, presented at the Device Research Conference (DRC), Santa Barbara, Jun [6] A. Beling et al., Measurement and modeling of a high-linearity modified uni-traveling carrier photodiode, IEEE Photon. Technol. Lett., vol. 20, no. 14, pp , Jul [7] A. Joshi, S. Datta, and D. Becker, GRIN lens coupled top illuminated highly linear InGaAs photodiodes, IEEE Photon. Technol. Lett., vol. 20, no. 17, pp , Sep [8] K. J. Williams and R. D. Esman, Design considerations for high-current photodetectors, J. Lightw. Technol., vol. 17, no. 8, pp , Aug [9] J. Klamkin et al., High output saturation and high-lineaity uni-traveling-carrier waveguide photodiodes, IEEE Photon. Technol. Lett., vol. 19, no. 3, pp , Feb [10] S. Adachi, Lattice thermal conductivity of group-iv and III-V semiconductor alloys, J. Appl. Phys., vol. 102, no. 6, Sep [11] A. Pauchard et al., Infrared-sensitive InGaAs-on-Si p-i-n photodetectors exhibiting high-power linearity, IEEE Photon. Technol. Lett., vol. 16, no. 11, pp , Nov [12] A. Ramaswamy et al., A high power Ge n-i-p waveguide photodetector on silicon-on-insulator substrate, presented at the Group IV Photonics 2009, San Fransisco, Sep [13] N. Duan et al., Thermal analysis of high power InGaAs-InP photodiodes, IEEE J. Quantum Electron., vol. 42, no. 12, pp , Dec [14] A. Ramaswamy et al., Microwave characteristics of Ge n-i-p waveguide photodetector on silicon-on-insulator substrate, presented at the Photonics Society Annual Meeting 2009, Turkey, Oct [15] N. Li et al., High saturation current charge compensated InGaAs-InP unitraveling-carrier photodiode, IEEE Photon. Technol. Lett., vol. 16, no. 3, pp , Mar [16] K. J. Williams, R. D. Esman, and M. Dagenais, Non-linearities in p-i-n microwave photodetectors, J. Lightw. Technol., vol. 14, no. 1, pp , Jan [17] T. H. Stievater and K. J. Williams, Thermally induced nonlinearities in high-speed p-i-n photodetectors, IEEE Photon. Technol. Lett., vol. 16, no. 1, pp , Jan [18] M. Piels et al., Three-dimensional thermal analysis of a waveguide Ge/Si photodiode, in Integr. Photon. Res., Monterey, California, Jul , [19] K. J. Williams and R. D. Esman, Photodiode DC and microwave nonlinearity at high currents due to carrier recombination nonlinearities, IEEE Photon. Technol. Lett., vol. 10, no. 7, pp , Jul [20] A. R. Schaefer, E. F. Zalewski, and J. Geist, Silicon detector nonlinearity and related effects, Appl. Opt., vol. 22, no. 8, pp , Apr [21] C. J. Glassbrenner and G. A. Slack, Thermal conductivity of silicon and germanium from 3 K to the melting point, Phys. Rev., vol. 134, no. 4A, pp. A1058 A1069, May [22] K. S. Giboney, M. J. W. Rodwell, and J. E. Bowers, Traveling wave photodetector design and measurements, IEEE J. Sel. Topics Quantum Electron., vol. 2, no. 9, pp , Sep [23] J. Klamkin, Coherent Integrated Receiver for Highly Linear Microwave Photonic Links, Ph.D. dissertation, Univ. California, Santa Barbara, Sep [24] K. J. Williams and R. D. Esman, Observation of photodiode nonlinearities, Electron. Lett., vol. 28, no. 8, pp , [25] D. A. Tulchinsky et al., High-current photodetectors as efficient, linear, and high-power RF output stages, J. Lightw. Technol., vol. 26, no. 4, pp , Feb [26] A. Beling et al., Impact of voltage-dependent responsivity on photodiode nonlinearity, presented at the LEOS Annual Meeting 2008, Newport Beach, CA, Nov [27] H. Pan et al., The frequency behaviour of the intermodulation distortions pf modified uni-traveling carrier photodiodes based on modulated voltage measurements, IEEE J. Quantum. Electron., vol. 45, no. 3, pp , Mar [28] A. Ramaswamy et al., Experimental analysis of two measurement techniques to characterize photodiode linearity, presented at the Int. Topical Meeting Microw. Photon., Valencia, Spain, Oct , [29] T. Ohno et al., Measurement of intermodulation distortion in a unitraveling-carrier refracting-facet photodiode and a p-i-n refracting-facet photodiode, IEEE Photon. Technol. Lett., vol. 14, no. 3, pp , Mar [30] A. Hastings et al., Minimizing photodiode nonlinearities by compensating voltage-dependent responsivity effects, presented at the Proc. Int. Topical Meeting Microw. Photon., Valencia, Spain, Oct , [31] X. Li et al., High saturation current InP-InGaAs photodiode with partially depleted absorber, IEEE Photon. Technol. Lett., vol. 15, pp , Sep Anand Ramaswamy (S 06) received the B.S. degree in electrical engineering with a minor in physics and the M.S. degree in electrical engineering from the University of Southern California and the University of California, Santa Barbara, in 2005 and 2007, respectively. He is currently working towards the Ph.D. degree under Professor John E. Bowers at the University of California, Santa Barbara. His research interests lie in Coherent Communication Systems and nonlinear mechanisms in high power photodetectors.

8 RAMASWAMY et al.: HIGH POWER SILICON-GERMANIUM PHOTODIODES 3343 Molly Piels (S 08) received the B.S. degree in engineering and the B.A. degree in history from Swarthmore College, Swarthmore, PA, in 2008 and the M.S. degree in electrical engineering from University of California, Santa Barbara, in 2010, where she is currently working toward a Ph.D. under Professor John E. Bowers. Tao Yin received the Ph.D. degree in electrical engineering from Beijing University of Technology, Beijing, China in She is currently a Senior Optical Researcher at Photonics Technology Lab at Intel Labs, Intel, Santa Clara, CA. Her primary areas of research include high speed Ge photodetectors, Ge epitaxy, monolithic de-multiplexers, low power receivers, and high microwave power photodetectors. Nobuhiro Nunoya received the B.E., M.E. and Ph.D. degrees in physical electronics from Tokyo Institute of Technology, Japan, in 1997, 1999 and 2001, respectively. In 2002, he joined Nippon Telegraph and Telephone (NTT) Photonics Laboratories, NTT Corporation, Atsugi-shi, Japan. From 2008 to 2009, he worked in the University of California, Santa Barbara, CA, where he was a visiting researcher. He is currently with NTT Photonics Laboratories. His current research interests include semiconductor lasers and integrated devices for optical communications. Dr. Nunoya is a member of the Japan Society of Applied Physics (JSAP), the Institute of Electronics, Information and Communication Engineers (IEICE), and the IEEE/Photonics Society. John Bowers (S 78 M 81 SM 85 F 93) received the M.S. and Ph.D. degrees from Stanford University, Stanford, CA. He worked for AT&T Bell Laboratories and Honeywell before joining the University of California, Santa Barbara (UCSB). He holds the Fred Kavli Chair in Nanotechnology, and is the Director of the Institute for Energy Efficiency and a Professor in the Department of Electrical and Computer Engineering at UCSB. He has published eight book chapters, 450 journal papers, 700 conference papers and has received 52 patents. Dr. Bowers is a member of the National Academy of Engineering, a fellow of OSA and the American Physical Society, and a recipient of the OSA Holonyak Prize, the IEEE LEOS William Streifer Award and the South Coast Business and Technology Entrepreneur of the Year Award. He and coworkers received the EE Times Annual Creativity in Electronics (ACE) Award for Most Promising Technology for the hybrid silicon laser in 2007.