Random-Walk Models of Photoemission

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 nth step Pₙ is derived from the expression for the photoyield. Numerical values of the photoyield and the Pₙ'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 Pₙ's.