Theory of second-harmonic generation from quantum well states in ultrathin metal films on semiconductors

Second-harmonic generation from quantum well states in metal films deposited on a semiconducting substrate is discussed theoretically within a microscopic approach. The thickness dependence of electronic eigenstates as well as band-structure effects related to motion in the plane of the film an taken into account and semianalytical quantum well states are obtained at the perturbation level. Based on a general treatment of the second-harmonic response of inhomogenous systems an effective second-order response tensor is obtained. Agreement between theory and experiment is demonstrated from a comparison of calculated and measured thickness dependence of the nonlinear response. In the case of p to p curves the agreement is over the entire range of film thicknesses, whereas the agreement in the p to s case is restricted to relatively thin films due to the applied perturbation approximation. The transitions that are responsible for experimentally observed resonances are identified.