Analytical Formulas for Mean Gain and Excess Noise Factor in InAs Avalanche Photodiodes

It has been known that McIntyre's local multiplication theory for avalanche photodiodes (APDs) does not fully explain the experimental results for single-carrier InAs APDs, which exhibit excess noise factor values below 2. While it has been established that the inclusion of the dead-space effect in the nonlocal multiplication theory resolves this discrepancy, no closed-form formulas for the mean gain and excess noise factor have been specialized to InAs APDs in a nonlocal setting. Upon utilizing prior analytical formulation of single-carrier avalanche multiplication based on age-dependent branching theory in conjunction with nonlocal ionization coefficients and thresholds for InAs, closed-form solutions of the mean gain and the excess noise factor for InAs APDs are provided here for the first time. The formulas are validated against published experimental data from InAs APDs across a variety of multiplication region widths and are shown to be applicable for devices with multiplication widths of 500 nm and larger.