A simple model to determine multiplication and noise in avalanche photodiodes

Avalanche multiplication and noise in 1.0, 0.5, 0.1, and 0.05 μm GaAs $p^{+}{\mathrm{-i-n}}^{+}$ diodes have been calculated for both electron and hole initiated multiplication using a simple model which incorporates a randomly-generated ionization path length (RPL) and a hard-threshold dead space. We find that the mean multiplication obtained using this RPL model is in excellent agreement, even for the shortest structure, with that obtained from an analytical-band structure Monte Carlo (MC) model, which incorporates soft-threshold effects. However, it predicts slightly lower avalanche noise in the shorter devices. This difference results from the narrower ionization path length probability distribution and larger dead space of the hard-threshold RPL model at high electric fields as compared to the more realistic distribution function associated with the relatively sophisticated MC model.