Description of the Geiger Mode in Avalanche p-i-n Photodiodes by Elementary Functions

We consider the possibility of using elementary functions to describe transient processes in p-i-n avalanche photodiodes (APDs), particularly those operating at an initial voltage V-0 greater than the avalanche breakdown voltage V-BD. This task is related to the need for determining the initial conditions for APD operation in the Geiger mode. A simple expression is obtained that described the dynamics of the Geiger avalanche process, a formula for the total time of this process is derived, and an explicit analytical relation for the Geiger mode realization in APDs is presented. Conditions of the validity of the proposed analytical description are determined.