Decrease in the binding energy of donors in heavily doped GaN:Si layers

The properties of Si-doped GaN layers grown by molecular-beam epitaxy from ammonia are studied by photoluminescence spectroscopy. It is shown that the low-temperature photoluminescence is due to the recombination of excitons bound to donors at Si-atom concentrations below 10$^{19}$ cm$^{-3}$. At a Si-atom concentration of 1.6 $\times$ 10$^{19}$ cm$^{-3}$, the band of free excitons is dominant in the photoluminescence spectrum; in more heavily doped layers, the interband recombination band is dominant. A reduction in the binding energy of exciton-donor complexes with increasing doping level is observed. With the use of Haynes rule, whereby the binding energy of the complex in GaN is 0.2 of the donor ionization energy $E_D$, it is shown that $E_D$ decreases with increasing Si concentration. This effect is described by the dependence $E_D=E_D^{\mathrm{opt}}-\alpha N^{1/3}_D$, where $E_D^{\mathrm{opt}}$ is the ionization energy of an individual Si atom in GaN. The coefficient that describes a decrease in the depth of the impurity-band edge with increasing Si concentration is found to be $\alpha$ = 8.4 $\times$ 10$^{-6}$ meV/cm$^{-1}$.