Shot and Johnson noises in interband cascade infrared photodetectors

Shot and Johnson noises are often incorrectly thought of as two independent noise sources. This incorrect picture has affected the evaluation of detectivities in interband cascade infrared photodetectors (ICIPs). In this work, a unified picture of shot and Johnson noises is developed for ICIPs based on a fundamental framework to understand the origin of Johnson noise and clarify the possible confusion between Johnson and shot noises. General, yet concise expressions are derived to evaluate the current noise power spectral density and detectivity for ICIPs even with complicated structures. Also, simple expressions for the signal current due to absorption of photons and the corresponding photon noise are derived, consistent with the previous results derived from alternative methods. Furthermore, a formula is derived to correctly evaluate the detectivity for conventional photodetectors under a reverse bias. The derived formulas with discussion are expected to improve the understanding of noises in ICIPs and other types of photodetectors and help us to appropriately evaluate their detectivities.