Optical study of interacting donors in semiconductors

Detailed measurements and theoretical analysis are presented of the far-infrared absorption coefficient of phosphorous donors in uncompensated silicon at low temperatures. The study covers over 3 orders of magnitude in doping density, i.e., from the regime of isolated donors to near the insulator-metal transition at 3.7×${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The photon energy was varied from 5% of the isolated donor ionization energy (45.5 meV) to about 25% above it. The spectra are described quantitatively by including pair states (donor excitons), charge-transfer excitations at low densities and energy, and excitation processes in larger random clusters at higher densities. The results indicate that the donors form a nearly ideal, random, three-dimensional system in which there are large-scale potential fluctuations which dominate the approach to the delocalization transition.