Theory of the Surface Photoelectric Effect for One and Two Photons

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Abstract
The theory of the surface photoelectric effect for the absorption of one and two photons is discussed systematically using Green's functions. The asymptotic form of Green's function leads naturally to the incoming wave solution used previously by Makinson. By exploiting a commutation relation between the operators of momentum and Green's function, one can express the amplitude of the electron outgoing wave in a series which involves explicitly the force and the potential acting on the electron. In the Wentzel, Kramers, Brillouin, and Jeffreys (WKBJ) approximation, valid for a slowly varying potential, the leading term of the series gives the major contribution. In the other extreme, where the potential varies rapidly in an electron wavelength all terms can be approximately evaluated. In particular, for the square-well potential the results are immediate. Other simple examples are given to illustrate the method. A discussion of the second-order photocurrent is given and our results are compared with earlier work. Finally, the equivalence of two models used in surface problems is discussed. It is shown that the finite plate model reduces to the semi-infinite model if one takes the average of the wave function, and not its square, as the plate thickness becomes infinitely large.

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