MEAN GAIN OF AVALANCHE PHOTODIODES IN A DEAD SPACE MODEL

Based on a first order expansion of the recursive equations, we derive approximate analytical expressions for the mean gain of avalanche pho todiodes accounting for dead space effects. The analytical solutions a re similar to the popular formula first obtained in local approximatio n, provided that the ionization coefficients, alpha and beta, are repl aced with suitable effective ionization coefficients depending on dead space. The approximate solutions are in good agreement with the exact numerical solutions of the recursive equations for p-i-n devices as w ell as for photodiodes with nonconstant electric held profile, We also show that dead space causes non negligible differences between the va lues of the effective ionization coefficients entering in carrier cont inuity equations, the carrier ionization probability per unit length a nd the ionization coefficients derived by experimenters from multiplic ation measurements.