Absorption coefficient, energy gap, exciton binding energy, and recombination lifetime of GaN obtained from transmission measurements

The absorption coefficient for a 0.4-μm-thick GaN layer grown on a polished sapphire substrate was determined from transmission measurements at room temperature. A strong, well defined exciton peak for the $A$ and $B$ excitons was obtained. The $A$ , $B$ , and $C$ excitonic features are clearly defined at 77 K. At room temperature, an energy gap $E_g\text{=3.452±0.001\hspace{0.17em}}\mathrm{eV}$ and an exciton binding energy $E_x^{\mathrm{A,B}}\text{=20.4±0.5\hspace{0.17em}}\mathrm{meV}$ for the $A$ and $B$ excitons and $E_x^C\text{=23.5±0.5\hspace{0.17em}}\mathrm{meV}$ for the $C$ exciton were determined by analysis of the absorption coefficient. From this measured absorption coefficient, together with the detailed balance approach of van Roosbroek and Shockley, the radiative constant ${\text{B=1.1×10}}^{\text{−8}}\hspace{0.17em}{\mathrm{cm}}^{\mathrm{3}}\mathrm{/s}$ was obtained.