Model calculations for radiative recombination in Zn-N-doppedGaAs1−xPxin the direct and indirect composition region

Recent experiments show that the Zn acceptor causes the photoemission spectra of nitrogen-doped $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{P}}_x$ to shift to lower energy relative to the spectra obtained on $n$-type N-doped crystals. The magnitude of this spectral shift is composition dependent near and beyond the direct-indirect transition ($E_{\Gamma }=E_X$, $x\equiv x_c$), decreasing with increasing molar percent P in the crystal ($x\gtrsim x_c$). The decreased influence of the Zn acceptor in the indirect composition region ($x>\mathrm{}{x}_c$) can be understood by considering, in the Wannier representation, the localization of the wave functions of the electron and hole in the neighborhood of the N atom. The trapped electron is less confined in the immediate vicinity of the N impurity as the crystal composition is varied and $E_N$ approaches $E_{\Gamma } (x\to x_r,x_r<x_c)$. The delocalization of the trapped electron occurs too abruptly, however, to account completely for the experimental data. Accordingly, a comparison is made of the probability of the hole bound to the Zn acceptor, in the central cell of the N atom, to that of the hole portion of the bound exciton. In the direct composition region ($x<\mathrm{}{x}_c$), the wave function of the Zn-bound hole is sufficiently delocalized so that its overlap with the wave function of the trapped electron is larger than for the case of the rather weakly bound excitonic hole. As the crystal becomes more indirect ($x>\mathrm{}{x}_c$, $E_{\Gamma }-E_X$ increasing), the Zn-bound hole is confined more to the neighborhood of the acceptor, while the excitonic hole becomes more localized in the vicinity of the N trap. The calculated behavior of the Zn-bound hole relative to the excitonic hole as a function of crystal composition compares favorably with the spectral shift observed experimentally.