Effects of Plasma Screening and Auger Recombination on the Luminescent Efficiency in GaP

A theoretical study of the concentration quenching of the luminescence in GaP is presented. The formulation takes cognizance of the effects of plasma screening on the electron- and hole-capture probability in forming bound excitons, and on various nonradiative (Auger) processes. For the system GaP(Zn,O), the luminescence is proportional to the branching ratio out of the exciton state given by $b={\{1+(\frac{{\tau }_{x\mathcal{r}}}{{\tau }_{\mathrm{xn}}})+[\frac{\mathrm{}(1-f)\mathrm{}}{f}\left]\right(\frac{{\tau }_{x\mathcal{r}}}{{\tau }_{\mathrm{en}}}\left)\right\}}^{-1\mathrm{}}$ where ${\tau }_{x\mathcal{r}}$ and ${\tau }_{\mathrm{xn}}$ are, respectively, the radiative and non-radiative (Auger) lifetimes of the bound excitons, ${\tau }_{\mathrm{en}}$ is the Auger lifetime of bare trapped electrons, and $f$ is an occupancy factor for the bound excitons. The $f$ factor depends on the Fermi level, temperature, exciton capture probability, and ${\tau }_{x\mathcal{r}}$ and ${\tau }_{\mathrm{xn}}$. The occupancy factor is found to be a sensitive function of doping. The exciton-capture probability is found to proportional to ${[1+(\frac{q_s}{\beta }\left)\right]}^{-8\mathrm{}}$, where $q_s$ is the screening parameter and $\beta$ is reciprocal of the Bohr radius of the exciton. Thus the probability falls rapidly for $q_s\ge \beta$. The two Auger lifetimes are found to have the form ${\tau }_{\mathrm{xn}}={\mathrm{}\left(\mathrm{Bp}\right)\mathrm{}}^{-1\mathrm{}}$ and ${\tau }_{\mathrm{en}}={\left(C{p}^2\right)}^{-1\mathrm{}}$, where $p$ is the hole concentration, and $B$ and $C$ are coefficients which are calculated in terms of the various binding and transition energies. The results of our calculations show that the branching ratio is close to unity in the low-doping region but falls rapidly when the acceptor concentration increases beyond ${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$. These results are in agreement with experimental data.