Predicted band-gap pressure coefficients of all diamond and zinc-blende semiconductors: Chemical trends

We have studied systematically the chemical trends of the band-gap pressure coefficients of all group IV, III-V, and II-VI semiconductors using first-principles band-structure method. We have also calculated the individual ``absolute'' deformation potentials of the valence-band maximum (VBM) and conduction-band minimum (CBM). We find that (1) the volume deformation potentials of the ${\ensuremath{\Gamma}}_{6c}$ CBM are usually large and always negative, while (2) the volume deformation potentials of the ${\ensuremath{\Gamma}}_{8v}$ VBM state are usually small and negative for compounds containing occupied valence d state but positive for compounds without occupied valence d orbitals. Regarding the chemical trends of the band-gap pressure coefficients, we find that (3) ${a}_{p}^{\ensuremath{\Gamma}\ensuremath{-}\ensuremath{\Gamma}}$ decreases as the ionicity increases (e.g., from $\mathrm{G}\stackrel{\ensuremath{\rightarrow}}{e}\mathrm{GaA}\stackrel{\ensuremath{\rightarrow}}{s}\mathrm{ZnSe}),$ (4) ${a}_{p}^{\ensuremath{\Gamma}\ensuremath{-}\ensuremath{\Gamma}}$ increases significantly as anion atomic number increases (e.g., from $\mathrm{Ga}\stackrel{\ensuremath{\rightarrow}}{N}\mathrm{Ga}\stackrel{\ensuremath{\rightarrow}}{P}\mathrm{GaA}\stackrel{\ensuremath{\rightarrow}}{s}\mathrm{GaSb}),$ (5) ${a}_{p}^{\ensuremath{\Gamma}\ensuremath{-}\ensuremath{\Gamma}}$ decreases slightly as cation atomic number increases (e.g., from $\mathrm{AlA}\stackrel{\ensuremath{\rightarrow}}{s}\mathrm{GaA}\stackrel{\ensuremath{\rightarrow}}{s}\mathrm{InAs}),$ (6) the variation of ${a}_{p}^{\ensuremath{\Gamma}\ensuremath{-}L}$ are relatively small and follow similar trends as ${a}_{p}^{\ensuremath{\Gamma}\ensuremath{-}\ensuremath{\Gamma}},$ and (7) the magnitude of ${a}_{p}^{\ensuremath{\Gamma}\ensuremath{-}X}$ are small and usually negative, but are sometimes slightly positive for compounds containing first-row elements. Our calculated chemical trends are explained in terms of the energy levels of the atomic valence orbitals and coupling between these orbital. In light of the above, we suggest that ``empirical rule'' of the pressure coefficients should be modified.