Multiphoton exciton absorption in a semiconductor superlattice in a dc electric field

Abstract

An analytical approach to the problem of the multiphoton exciton absorption in biased narrow-well superlattices (SLs) induced by the optical transitions to the localized resonant exciton states is developed. Both the ac electric field of the intense optical wave and the dc electric field are directed parallel to the SL axis. The SL is formed by a periodic sequence of quantum wells (QWs) whose widths are taken to be much less than the exciton Bohr radius. The model of the SL potential employs a limiting form of the Kronig-Penney potential, i.e., a periodic chain of QWs separated by $\ensuremath{\delta}$-function-type barriers. A sufficiently strong dc electric field provides the localization of the carriers within one period of the SL. Analytical dependencies of the coefficient of the multiphoton exciton absorption on the characteristics of the dc and ac electric fields and on the parameters of the SL in the approximation of both isolated and interacting Wannier-Stark levels are obtained in the nearest-neighbor tight-binding approximations. Our analytical results correlate well with those obtained in numerical investigations. Estimates of the expected experimental values are performed for the parameters of a $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ SL.