Fundamental energy gap of GaN from photoluminescence excitation spectra

Abstract

In the absence of samples suitable for transmission measurements, photoluminescence excitation spectra (PLE) have been found useful in the evaluation of detailed information about the lowest direct-absorption edge of GaN. In this work the results of PLE measurements are combined with data on reflection and luminescence in the intrinsic region to determine the positions of $A\ensuremath{-}$, $B\ensuremath{-}$, and $C$-exciton ground-state transition energies and the lowest band gap. Neglecting polariton effects, the value of the $A$-exciton ground-state transition energy is determined as being ${E}_{A}^{x}=3.4751\ifmmode\pm\else\textpm\fi{}0.0005$ eV at 1.6 K from combined PLE and emission spectra. The corresponding values for $B$ and $C$ exciton transitions are found to be ${E}_{B}^{x}=3.4815\ifmmode\pm\else\textpm\fi{}0.001$ eV and ${E}_{C}^{x}=3.493\ifmmode\pm\else\textpm\fi{}0.005$ eV from PLE spectra. The lowest band gap is determined to be ${E}_{g}^{A}={3.503}_{\ensuremath{-}0.002}^{+0.005}$ eV at 1.6 K, which fixes the ground-state $A$-exciton binding energy as ${E}_{B}(A)={28}_{\ensuremath{-}3}^{+6}$ meV, in good agreement with the effective-mass value. The temperature dependence of the band gap could also be accurately measured in PLE spectra and can be described by an expression ${E}_{g}^{A}=[3.503+\frac{(5.08\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}{T}^{2})}{(T\ensuremath{-}996)}]$ eV for $T<295$ K, with an estimated relative uncertainty of \ifmmode\pm\else\textpm\fi{} 0.002 eV.