Inhomogeneous broadening of the Lyman-series absorption of simple hydrogenic donors

Abstract

Inhomogeneous broadening of hydrogenic-donor $1s-\mathrm{np}$ transitions due to the electric fields and field gradients of randomly distributed donor and acceptor ions is considered for the case of a simple isotropic parabolic conduction band. It is shown that for $n$ even, the transition has a nearly unshifted and relatively sharp central line, whereas for $n$ odd, the central peak is missing; what remain are peaks symmetrically split about the unperturbed transition energy and strongly broadened. Detailed calculations are made for the $1s-2p$ and $1s-3p$ line shapes. These line shapes are in qualitative but not quantitative agreement with experimental spectra for GaAs; it is pointed out, however, that the theory is self-consistent only for ionized impurity concentrations well below 4 × ${10}^{13}$ ${\mathrm{cm}}^{-3\mathrm{}}$, characteristic of the purest GaAs samples studied to date. The self-consistency of the broadening theory for donors in strong magnetic fields is discussed.