Derivation of the Small Signal Response and Equivalent Circuit Model for a Separate Absorption and Multiplication Layer Avalanche Photodetector

A small signal analysis for a separate-absorption-charge-multiplication (SACM) avalanche photodetector (APD) is presented for the general case when the electrons and the holes have different ionization coefficients and different velocities. The analytic expressions for the impedance and frequency response are given and a simplified equivalent circuit (including an inductance with a series resistance in parallel with a capacitance) for the APD is obtained. The calculation and experimental results show that the impedance of the APD operated at high bias voltages has a maximal value at a certain frequency due to the resonance of the LC-circuit, and this is the origin for a peak-enhancement of the frequency response.