Time and frequency response of the conventional avalanche photodiode

An analytical expression for the time course of the average impulse response function for a conventional avalanche photodiode is derived. Delta-function absorption of a single photocarrier and single-carrier-initiated/single-carrier multiplication conditions are assumed. The result is obtained as a limiting case of a previously derived equation for the staircase avalanche photodiode. The initial exponential growth of the curves is shown to represent electron and hole contributions arising from multiplication in the avalanche region whereas the subsequent exponential decay arises from residual holes transiting backward across the multiplication region. The associated frequency response function is obtained by Fourier transformation. The analytical results are shown to be in good accord with average impulse response functions obtained by Riad and Hayes by means of simulation from the transport equations. The results should also apply to the channeling avalanche photodiode and to related structures in which the carriers are spatially separated and the multiplication is essentially single-carrier like.