Mathematical proof of errors in Capasso's excess noise factor formula for an n-step staircase multiplier

TL;DR

This paper identifies and mathematically proves errors in Capasso's excess noise factor formula for staircase avalanche photodiodes, showing it incorrectly treats power gains as gains in the noise calculation.

Contribution

It provides a rigorous mathematical proof that Capasso's formula misapplies Friis' total noise factor formula to staircase APDs.

Findings

Capasso's formula incorrectly considers power gains as gains.

The proof clarifies the proper calculation of excess noise factors.

Results impact the theoretical modeling of avalanche photodiodes.

Abstract

Solid-state devices such as multistep staircase avalanche photodiodes (APDs) are analogues to the photomultiplier tubes and are considered as a cascade-amplifier. The major source of internal noise in these APDs is due to the randomness in their stepwise impact ionization. Recent literature on staircase APDs by research groups such as Campbell and co-workers have reported the theoretical estimates of total excess noise factors using Capasso's excess noise factor formula. This formula is based on Friis' total noise factor formula for cascade networks. This article proves that Capasso's formula for a staircase APD, erroneously considers the power gains in Friis' total noise factor formula as the gains.