Full-band Monte Carlo simulation of single photon avalanche diodes

Abstract

Single photon avalanche diodes (SPADs) enable a variety of innovative applications in the fields of biology, medicine, and physics. The propagation of single photons with optical fibers requires the usage of telecommunication wavelengths in the near infrared (NIR) spectral range. NIR SPADs, which can be employed for this application, consist of an absorber layer (In 0.53 Ga 0.47 As) and a multiplication layer (InP or In 0.52 Al 0.48 As). The product of the quantum efficiency η q , the probability that the photoexcited carrier survives into the multiplier P c , and the breakdown probability P b that the carrier activates a self-sustaining avalanche designate the photon detection efficiency [1] PDE = η q P c P b . The breakdown probability contributes primarily to the electric field dependence of the PDE and increases with the electric field. Therefore, a higher electric field enhances the photon detection efficiency. However, band-to-band or trap-assisted tunneling in the multiplication layer initiate dark counts and degrade the performance of SPAD devices at higher electric fields. Hence, to obtain a higher photon detection efficiency for a given increase of the electric field and tunneling rate, a steep rise of the breakdown probability with applied bias is favorable. The SPAD's timing jitter arises from various sources. The avalanche build-up time is the main contribution to the timing jitter [1].The full-band Monte Carlo (FBMC) method is considered to be the most accurate device simulation method within the physics of semiclassical charge transport. The FBMC approach for the solution of the Boltzmann transport equation serves as benchmark for approximate methods. FBMC simulations are computationally heavy. This burden forced previous numerical investigations on the SPAD * denis.dolgos@synopsys.com breakdown characteristics to use simplified charge transport models [2-6]. However, nowadays standard computer clusters together with computationally efficient approaches [7] enable the gathering of sufficient statistics with FBMC simulations. The computation of breakdown probabilities and timing jitter has become feasible. The details of our ensemble full-band Monte Carlo simulator CarloS and the approximations of the scattering model have been presented in Refs. [8,9].We simulate PIN diode structures with intrinsic region widths between 55 nm and 500 nm (made of InP, In 0.52 Al 0.48 As, and GaAs) operated in the Geigermode with a temperature of T = 300 K [6]. Single carriers are injected with an energy of 10 meV at time t = 0 ps into the PIN diode. Breakdown occurs when the total number of carriers exceeds 30 within the simulation domain. The simulation stops when a breakdown has not taken place within 500 ps. We have repeated the simulations 2500 times per reverse bias point. Figure 1 presents the breakdown probability versus the excess bias V ex = V r − V b for the different gain materials and multiplication layer widths. We define the breakdown voltage V b as P b (V b ) = 10 −3 . Three regions characterize the d...

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