Modeling of two-dimensional gain profiles for InP-InGaAs avalanche photodiodes with a stochastic approach

The two-dimensional (2-D) gain profiles for separate absorption, grading, charge and multiplication (SAGCM) InP-InGaAs avalanche photodiodes (APD's) have been modeled with a stochastic approach. To consider the influence of the curved diffusion edge on the electric field within the periphery region, equations are derived from the cylindrical Poisson's equation. The electric field profiles are computed at various APD radii and the electric field in the multiplication layer is reduced significantly for APD's with a partial charge sheet in the periphery. It is demonstrated by the modeled 2-D gain profiles that the premature edge breakdown can be effectively suppressed for such devices. The modeled 2-D gain profiles for APD's with a partial charge sheet incorporated in the periphery are in good agreement with the experimental results. The results and the uniformity issue of the 2-D gain profiles are discussed. The effect of using curved diffusion interfaces instead of a steep mesa step is also explored; this suggests that the fabrication of a charge sheet mesa step may complicate the gain uniformity issue. From our analyses, we find that the uncertainty and the symmetry of both patterning the charge sheet mesa structure and controlling the diffusion interface between the p/sup +/ InP top layer and the n/sup -/ InP multiplication layer are most likely to affect the uniformity and the symmetry of the 2-D gain profiles for the SAGCM InP-InGaAs APD's.