Avalanche-Photodiode Frequency Response

Abstract

The short-circuit photocurrent from an avalanche photodiode is calculated using an exact solution of the differential transport equations for the multiplication region. The dc electric field and the hole and electron velocities are assumed constant in the avalanche region into which photoelectrons are injected. It is shown that the electron- and hole-ionization coefficients α and β remain constant over a practical range of multiplied photocurrents. Computer studies of the solution show that avalanche multiplication does not reduce the device bandwidth as long as the dc multiplication M0 is less than the ratio of α and β, i.e., as long as M0<α/β. The previously obtained frequency dependence of the multiplication, M(ω) = M0[1 + ω2M02τ12]−1/2, which indicates a constant-multiplication bandwidth product, is now shown to be valid only if M0>α/β. The previously unspecified ``effective'' transit time, τ1, in this equation is approximately τ1 = N(β/α)τ, where N is a number varying slowly from ⅓ to 2 as β/α varies from 1 to 10−3, and τ is the multiplication-region transit time. The complete solution of this problem thus shows that the widely different results previously obtained for β/α = 0 and β/α = 1 are continuously joined, and provides a simple criterion for judging the ranges of validity of the two limiting cases. The results emphasize the practical importance of obtaining the required multiplication at fields such that M0<α/β where the multiplication does not affect the bandwidth. This also leads to minimum excess avalanche-region noise, and hence to the closest possible solid-state analog to the vacuum-tube photomultiplier.