Photostimulated exoelectron emission has been conjectured to be a consequence of a slip-step-induced resonant absorption of the incident UV light by the surface plasmons. This mechanism is examined in some detail by calculating the absorption of p-polarized light by an oxidized metal with the slip steps represented by a sinusoidal interface between the metal and its oxide. Numerical results are discussed in terms of experimental results from alumin'um and found to support the model. Further experiments are suggested. PACS Codes: 68.20, 79.75, 79.60 In an earlier paper [1], referred to henceforth as I, experimental results on fatigue-enhanced photoemission from aluminum were reported. This phenomenon, also known as photostimulated exoelectron emission, was ascribed in I to an increased absorption of the incident ultraviolet light through a resonant coupling to the surface electromagnetic modes (specifically, the surface plasmon) of the metal,with that coupling due to the slip steps produced by the fatigue. This paper explores that conjecture quantitatively by calculating the absorption of (p-polarized) light incident upon an oxidized metal surface with a sinusoidalinterface between the metal and its oxide and with a flat oxidevacuum interface. This model is the simplest one containing the essential features of the observations reported in I, viz., the presence of the oxide (which drastically alters the resonance frequency, and, for s polarized light, creates a significant interference effect) and the near periodicity of the roughness. There is an experimentally significant dependence upon angle of incidence, but the model employed here (as in all other current theories of roughness-enhanced absorption) is a local theory, that is, the polarization density P(co, r) is taken to be proportional to the electric field at the same point, and such a theory [2] is unlikely to give a quantitatively correct desription of the angular dependence. Other authors have recently considered the effect of roughness on optical absorption [3-7], but not for the combination of conditions (oxide layer and periodic roughness) appropriate to this problem. Though the model is obviously idealized (the neglect of non-locality in the metal's dielectric response and of possible roughness on the oxide surface are the least justifiable features), it does contain the features known to be essential and its solution (Sec. 1) permits a quantitative test of the adequacy of the plasmon coupling interpretation (Sec. 2) and suggests further experimental tests (Sec. 3). 1. Solution of the Resonant Absorption Model The nearly periodic character of the real slip steps observed in I is represented (Fig. l) by a sinusoidal boundary between the metal and its oxide ; the boundary is given by z = q(x) = h cos (2~x/d). (1) It is easy to extend the considerations below to arbitrary periodic boundaries. Figure 1 is not drawn to scale; typical numbers for the aluminum samples studied in I are d = 4(~60 nm (2) for the period of the slip steps, a = 12 nm (3) for the thickness of the oxide layer, and it will be suggested in Sec. 2 that a value of h = 1.5 rim, (4) 368 W.J. Pardee and Otto Buck Absorbed Light I Z~ll I METAL I j~_ I4 d ~t Fig. 1. Diagram of the coordinate system defining the three characteristic lengths and illustrating the model for the slip step coupling Fig. 2. Well-annealed, commercially-pure aluminum at 10% of its fatigue life demonstrating the near periodicity and separation of the slip steps corresponding to 7-8 Burger's vectors, is reasonable for the amplitude o f the surface steps. The best quantitative procedure for defining d is to calculate the Fourier transform ~(K) of the experimental profile t/(x), determined, for example, by optical densitometry on the micrograph reproduced in Fig. 2, and defining d = 2n//s where /~ is the location of the maximum in the amplitude I~(g)l. The normal modes of interest are surface transverse magnetic modes propagating in the x direction., Whatever the detailed form of the solution, the periodicity implies that the nonvanishing field components F (representing E x, E~, and/-/y) can be chosen in the Bloch form F(co, x, z) = eiaXf(co, q, x, z), (5) where f is periodic in x with period d, and the transverse wavevector q satisfies n/d <= q < n / d . (6) For the experiments of interest here, q is related to the angle of incidence 0 by q = (co/c) sin 0. (7) Thus the fields represented by f can be expanded in Fourier series in x, f(co, q, x, z) = ~ exp(2innx/d)s q, z). (8)