First-Principles Calculations of the Electron-Hole-Pair Creation Energy in Semiconductors and Dielectrics

Abstract

We present first-principles calculations of the electron-hole-pair creation energy in semiconductors and dielectrics, focusing in particular on AlN, 3C-SiC, 4H-SiC, Si, and SiO2. We have employed density functional theory (DFT) to calculate the band structure, density-functional perturbation theory to obtain the phonon dispersion, and time-dependent DFT (TDDFT) to calculate the electron energy loss function (via the dielectric function). We performed full-band Monte Carlo simulations of electron thermalization for energies up to ~100 eV and calculated the average energy required to excite an electron-hole pair. We calculated pair-creation energies of approximately 12.2, 6.5, 7.3, 3.10, and 16.7 eV/pair for AlN, 3C-SiC, 4H-SiC, Si, and SiO2, respectively. These values are in good agreement with measured data, with the largest discrepancy being that of Si (about 14.9% lower than the accepted experimental value of ~3.6 eV/pair). To improve the agreement for Si, we used the GW approach and the Bethe-Salpeter equation (BSE) to calculate the quasiparticle shifts of the electronic band structure and the dielectric function, respectively. Finally, using the GW/BSE data, we calculated a creation energy of ~3.50 eV/pair. We find that the marked improvement in the accuracy of the calculated creation energy, when using the GW/BSE approach, is primarily attributable to the slight decrease in the magnitude of the electron energy-loss function when using the GW/BSE approach for energies below ~10-15 eV. Overall, it is clear that the competition between phonon emission and ionization near the intersection of the phonon scattering and ionization rates is largely responsible for determining the value of the creation energy, with the other major factor being the location and shape of the plasmon peak in the energy-loss function.