Simple Matrix-Method Modeling for Avalanche Photodetectors With Arbitrary Layer Structures and Absorption/Multiplication Coefficients

A simple matrix-method model is presented for calculating the impedance and the short-circuit frequency response of an avalanche photodiode (APD) with arbitrary layer structures and absorption/multiplication coefficients. In our matrix method model, the depletion region of the APD is divided into many thin layers. In each thin layer the absorption and the multiplication coefficients are assumed to be uniform. As an example, we use this matrix-method model to analyze in detail a resonant Ge/Si SACM (separated absorption charge multiplication) APD. The impedance analysis shows that the avalanche region is equivalent to an LCR-circuit including a negative resistance, an inductance with a series resistance, and a capacitance in parallel connection. At higher bias voltages, the negative resistance and series resistance become very small and consequently the LCR circuit shows a strong resonance. Furthermore, the inductance also becomes smaller at higher bias voltages, which introduces a higher resonance frequency. This increases the 3 dB-bandwidth, in agreement with experiment.