Energy spectrum of electrons of deep impurity centers in wide-bandgap mesoscopic semiconductors

The energy spectrum of deep impurity centers in wide-bandgap semiconductors ($E_g > 2$ eV) of mesoscopic sizes $R \gg \lambda_{\mathrm{D}}$, where $\lambda_{\mathrm{D}}$ is the de Broglie wavelength, at which the spectrum of free (uncoupled) charge carriers is not quantized, but the surface significantly affects physical processes in the bulk, has been theoretically considered. It has been shown that the binding energy of an electron on an impurity center near the surface of the crystal tends to zero. In this case, the wavefunction of the electron of the impurity center located in the surface region is delocalized; i.e., the energy of the impurity electron lies in the conduction band. The possible effect of such an energy overlap on effects observed in wide-bandgap mesoscopic semiconductors is discussed.