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

Inhomogeneous broadening of hydrogenic-donor 1s-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 ×{} 10¹³ cm^-3, characteristic of the purest GaAs samples studied to date. The self-consistency of the broadening theory for donors in strong magnetic fields is discussed.