Impact ionization under dynamic fields

Abstract

Due to the stochastic nature of the impact-ionization process, the buildup time of an avalanche photodiode (APD) is also stochastic and can degrade its performance. In particular, when an APD is operated in an optical receiver, the APD's finite and stochastic buildup time gives rise to intersymbol interference (ISI) and limits the bandwidth of the communication system [1]. While the buildup time of an APD is dependent on the material (e.g., on k, the hole-to-electron ionization coefficient ratio) it also has a dependence on the applied electric field and its profile in time and space [2] as it governs the cascade of impact ionizations. Several approaches have been explored to model the buildup time in order to increase the gain-bandwidth product (GBP) of APDs, including GBPs for heterojunction multiplication regions [2,3]. However, all existing models focused, mainly, on optimizing the APD's structure. In particular, the effect of modulating the electric field on the impact ionization characteristics of APDs remains unexplored, and to the best of our knowledge, no analytical model for avalanche multiplication exists for APDs that are driven by a time-varying bias voltages. The modulation of the applied electric field to control the impact ionization process could be beneficial in communication systems since it opens up the possibility of increasing the GBP in a simple and efficient way. The optimization problem becomes that of finding the optimal electric-field profile, for a fixed mean gain, that maximizes the GBP. In this paper we outline the potential benefits of modulating the applied electric field on the performance of APDs. Our approach enables the calculation of the impulse response, gain and and excess noise factor, breakdown probability, as well as pulse duration time all under conditions of a dynamic field in the multiplication region.