A stochastic noise model based excess noise factor expressions for staircase avalanche photodiodes

TL;DR

This paper develops generalized and simplified excess noise factor models for staircase avalanche photodiodes, accounting for impact ionization irregularities and providing accurate noise predictions across various operating regimes.

Contribution

It introduces new generalized excess noise factor expressions based on layer-wise ionization probabilities, improving noise modeling accuracy for staircase APDs.

Findings

Derived generalized excess noise factor expressions applicable across all bias regimes.

Proved that simplified expressions align with Bangera's corrections to Friis' formula.

Enhanced understanding of impact ionization irregularities in staircase APDs.

Abstract

Multistep staircase avalanche photodiodes (APDs) are the solid-state analogue of photomultiplier tubes, owing to their deterministic amplification with twofold stepwise gain via impact ionization. Yet, the stepwise impact ionization irregularities worsen with increasing step counts, which are a major source of internal noise in these APDs. Some noise models for staircase APDs have been previously reported, where the excess noise factor expressions are based on Friis' noise factor formula for cascade networks, erroneously considering the power gains as the gains. Excess noise factor being a key component in staircase APDs' noise models, we formulate generalized excess noise factor expressions for multilayer graded-bandgap APDs in terms of their layer-wise ionization probabilities, applicable for all operating biases, which include the sub-threshold, staircase, and tunnelling breakdown regimes. We further derive simplified expressions for staircase APDs and prove that these expressions match Bangera's corrections to Friis' noise factor formulas for cascade networks.