Theory of Line-Shapes of the Exciton Absorption Bands

Abstract

A general theory of line-shapes of the exciton absorption bands is developed with the help of generating function method. When the exciton-lattice coupling is weak, and the exciton effective mass is small, the absorption band is of a Lorentzian shape, provided that the temperature T is not too high. The half-value width H is given by the level broadening of the optically produced K = 0 exciton due to lattice scattering, so that it is proportional to T except at low temperatures. If the coupling is strong, or the exciton effective mass is large, or the temperature is very high, the absorption band is expected to be of a Gaussian shape, and H is proportional to √T. The mutual influence of adjacent absorption bands is also discussed; it causes the asymmetry and repulsion of the components as temperature rises. If we replace T by the density of lattice imperfections, the above statements are valid, without substantial modifications, as regards the dependence on the degree of imperfections. These conclusions are in qualitative agreement with experimental data. The comparison further provides us with information on the strength of the exciton-lattice coupling and the energy band structure of the exciton.