A Compact Model for Si-Ge Avalanche Photodiodes

Wang, Binhao; Huang, Zhihong; Zeng, Xiaoge; Sorin, Wayne V.; Liang, Di; Beausoleil, Raymond G.

Hewlett Packard Labs HPE-2018-05

Keyword(s): Avalanche photodiodes (APDs); Modeling; Optical communication

Abstract: A compact Si-Ge avalanche photodiode (APD) model, including carrier transit time and electrical parasitics, accurately captures electrical and optical dynamics in a wide range of gain. Excellent matching between simulated and measured 30 Gb/s eye diagrams is presented.

External Posting Date: May 18, 2018 [Fulltext] Internal Posting Date: May 18, 2018 [Fulltext]

Binhao Wang*, Zhihong Huang, Xiaoge Zeng, Rui Wu, Wayne V. Sorin, Di Liang, Raymond G. Beausoleil Hewlett Packard Labs, Hewlett Packard Enterprise, Palo Alto, CA, 94304, USA *[email protected]

Abstract— A compact Si-Ge avalanche photodiode (APD) each different gain-operation regime. For data communication, circuit model, including carrier transit time and electrical APDs are often operated above gain of 5 to enhance the APD parasitics, is demonstrated and accurately captures electrical and receiver sensitivity, but it also operates below the maximum optical dynamics in a wide range of multiplication gain. Excellent gain to avoid a poor signal-to-noise ratio and a large gain matching between simulated and measured 30 Gb/s eye diagrams fluctuation. Previous models for III-V or Si-Ge APDs lack is presented. accurate modeling in such a broad range of multiplication gain by considering both device electrical parasitics or carrier transit Keywords—Avalanche photodiodes (APDs); Modeling; Optical time dynamics [7, 8]. In this work, a compact model for Si-Ge communication APDs, which includes both electrical and optical dynamics in a wide range of gain, is presented. The model can be used not I. INTRODUCTION only for the low-voltage Si-Ge APD presented in paper [4], but Due to the demand of low-power and high-bandwidth in also for a broad types of Si-Ge APD as well as conventional optical interconnections for high performance computers III-V APD designs. (HPC) and data centers, advanced modulation schemes, such as PAM-4 (4-level pulse-amplitude modulation), have been II. DEVICE STRUCTURE AND MODELING motivated for investigation [1]. High sensitivity receivers are critical to achieve a PAM4 modulation with a low bit error rate A. Device Structure (BER) and consequently low latency. Avalanche photodiodes The structure of a separate-absorption-charge-multiplication (APDs) with internal multiplication gain are an attractive (SACM) with 4 m-width and 10 m-length is used in the low- choice [2]. It has been shown that silicon-germanium (Si–Ge)- voltage waveguide Si-Ge APD. The structure maintains low based APDs can have higher sensitivity compared with most electric-field in germanium and high field in silicon to achieve III–V ones due to the much lower impact ionization ratio of high gain-bandwidth-product (GBP) [2]. As shown in Fig. 1, silicon and hence lower excess noises [3]. Typical III-V or Si- the waveguide Si-Ge APD consists of a germanium absorption Ge APDs have high operation voltage (>25 V), which is much layer, a silicon charge layer, a silicon multiplication layer, and higher than the voltage supply of most pluggable transceiver a silicon n-contact layer, as shown in paper [4]. The thicknesses modules for short-distance (a few kilometer or less) and the doping concentrations for SACM layers are shown in communication. A Si-Ge based waveguide APD with a thin the inset of Fig. 1. silicon multiplication region was demonstrated and achieved <10 V operation voltage and 276 GHz gain-bandwidth product (GBP) [4]. The realization of low-voltage Si-Ge APD design B. APD Modeling can bring the low-energy and low-cost optical interconnect Fig. 2 shows the proposed SACM Si-Ge APD model, available to HPC and data centers. In order to optimize which includes effects of carrier transit time and electrical transceiver circuitry for high-efficiency and high-speed parasitics. A Gaussian filter is utilized to represent carrier operation, co-simulation environments with compact optical transit time. Due to the resonant effect in the O-E frequency device models that accurately capture the optical and electrical response, a RCL two-pole transfer function is used to describe dynamics are necessary [5, 6]. In practice, an accurate APD the Si-Ge based impact ionization dynamics. The APD model should be valid in a wide range of gain because the gain multiplication gain M and the responsivity R are multiplied to of APDs changes dramatically with the reverse-bias voltage, the two transfer functions to obtain accurate DC current. The and the gain mechanisms and the circuit models are different at device electrical parasitics consists of diode junction, as well as substrate and pad parasitics. Here, Cd is the diode capacitor, Rs is the diode series resistor, Cp is the parasitic capacitor, Rp is the parasitic resistor, and Lp is the parasitic inductor.

Carrier Transit Time Electrical Parasitics

H  MR  H H   Gaussian dynamics Rs Rp Lp 2  0.5ln 2  1 Popt g Iin Iin Cd Cp R MR e 2 l     1Qj    RC  RC 

Diode junction Substrate and pad parasitics Fig .1. A schematic of the low-voltage waveguide Si–Ge APD with layer parameters Fig .2. The SACM Si-Ge APD compact model III. MODELED AND MEASURED RESULTS electrical amplifier. A Santec tunable laser operating at 1550 nm was connected to the modulator input and the modulator A. Parameter Extraction output was coupled to the waveguide Si-Ge APD through a In order to determine the parameters of the proposed model, grating coupler. A Keysight oscilloscope with a 63 GHz we measured the device small-signal and impulse response. electrical module was utilized to record the 30 Gb/s eye APD S-parameters were first measured by using an Agilent diagram. As shown in Fig. 4, excellent matching between the vector networking analyzer (VNA) through a bias tee for simulated and measured eye diagrams at 30 Gb/s data rates was reverse bias tuning, and the electrical parasitics were extracted achieved. by curve fitting the small-signal electrical output impedance. The carrier transit time parameters were then extracted by curve fitting the APD impulse response. A Calmar femtosecond fiber pulsed laser was coupled into the APD as the impulse light source and the response was observed on an Agilent DCA86100C sampling scope. As shown in Fig. 3(a), the impedances of the Si-Ge APD at gains of 5, 10, and 15 are on top of each other. Same parameters for the device parasitics were extracted where Cd=60.8 fF, Rs=1177.3 Ω, Cp=46.2 fF, Rp=58.7 Ω, and Lp=0 pH. The electrical parasitic bandwidth (a) (b) with a 50 Ω load is ~49 GHz. Excellent matching between the Fig. 4. (a) Simulated and (b) measured 30 Gb/s eye diagrams fitted and measured impedances of the Si-Ge APD at three different gains were achieved. Fitted and measured impulse IV. CONCLUSION responses of the Si-Ge APD at gains of 5, 10, and 15 are shown in Fig. 3(b), (c), and (d), respectively. Excellent matching Co-design of optical devices and transceiver circuitry is between the fitted and measured pulse rise and fall times was essential to achieve low-power and high-bandwidth optical achieved. The falling edge oscillations also match reasonably interconnect system, which motivates to develop accurate co- well between fitting and measurement. The extracted simulation environments. The presented compact model for Si- parameters of ω and ω at gains of 5, 10, and 15 are the same Ge APDs includes both carrier transit time and electrical g RC parasitics at a wide range of gain, allowing efficient where ωg=2π×28 Grad/s and ωRC=2π×75 Grad/s. The extracted Q parameters at gains of 5, 10, and 15 are 1.85, 1.95, and 1.65, transimpedance amplifier (TIA) design. Model parameters respectively. The APD bandwidths are achieved by doing fast were accurately extracted by curve fitting the small signal Fourier transform (FFT) of impulse responses: BW=20.3 GHz electrical output impedance and the device impulse response. at M=5, BW=22.2 GHz at M=10, and BW=18.2 GHz at M=15. Excellent matching between simulated and measured 30 Gb/s eye diagrams was obtained.

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