Theory for spatial distribution of impact-ionization events in avalanche photodiodes

Avalanche photodiodes (APDs) are widely deployed in direct-detection, high-data rate optical-fiber communication systems as well as modern LIDAR systems. Various approaches have been explored to reduce the excess noise of APDs, which is a measure of the uncertainty in the stochastic avalanche gain that the APD offers. They include the use of thin multiplication regions and impact-ionization engineered (I²E) multiplication regions; both of these structures exploit the dead-space effect to reduce the excess noise [1-2]. Another approach is to suppress the impact ionization of holes, β → 0, (or electrons, α → 0) to make the hole-to-electron ionization ratio, k=β/α, as disparate as possible, which would too serve to reduce the excess noise factor. As a result, there has been a growing interest in APD structures that suppress the impact ionization of one species of carrier by impact-ionization-engineering the multiplication region [3-4]. In these structures the suppression of the impact ionizations of one species of carrier is achieved by judiciously engineering the different layers of the heterojunction multiplication region and the electric field profile therein. A key challenge in understanding the operation of such multi-layer multiplication regions and optimizing their design is the ability to analytically determine the locations at which electrons and holes trigger impact-ionization events.