The derivation of the multiplication factor for an avalanche photodiode

Anyone with information on the derivation of the multiplication factor for an avalanche photodiode? Thanks

hi
dear navina,
the multiplication factor M is defined by
M=Im/Ip
where Im is the average valu of total multiplied output current and Ip is the primary un multiplied photocurrent defined by
Ip=q*po*(1-exp(-alfa*w))*(1-Rf)/h*freq
where
po is the optical power incident on the photo detector
q is the electron charge
and h*feq is electon energy
alfa is absorpition cofficent at wavelength landa
w is the wideth of the depletion reigon
finaly ihope i helped
note there is atext book witch used which called optical fiber comunications chapter 6 will help u
by keiser
yours ,mohamed assad