Random-Walk Models of Photoemission

Abstract

An exact solution in closed form is given for the photoyield in the isotropic random-walk model of photoemission. The proof makes use of a theorem of importance in the theory of queues and ladder-point variables. The effect of reflection of the photoelectrons at the interface is also treated. A recursion relation for the probability of emission on the $n$th step $P_n$ is derived from the expression for the photoyield. Numerical values of the photoyield and the $P_n$'s are tabulated for numerous values of the relevant parameters, and these numbers are compared with the results of approximate expressions. The exact photoyield values are in good correspondence to a slightly modified version of a formula derived by Kane. A simple approximation is also given for the values of the $P_n$'s.