Carrier concentration dependence of band gap shift in n-type ZnO:Al films

Al-doped ZnO (AZO) thin films have been prepared by mist chemical vapor deposition and magnetron sputtering. The band gap shift as a function of carrier concentration in n-type zinc oxide (ZnO) was systematically studied considering the available theoretical models. The shift in energy gap, evaluated from optical absorption spectra, did not depend on sample preparations; it was mainly related to the carrier concentrations and so intrinsic to AZO. The optical gap increased with the electron concentration approximately as ne2∕3 for ne≤4.2×1019 cm−3, which could be fully interpreted by a modified Burstein–Moss (BM) shift with the nonparabolicity of the conduction band. A sudden decrease in energy gap occurred at 5.4−8.4×1019 cm−3, consistent with the Mott criterion for a semiconductor-metal transition. Above the critical values, the band gap increased again at a different rate, which was presumably due to the competing BM band-filling and band gap renormalization effects, the former inducing a band gap widening and the latter an offsetting narrowing. The band gap narrowing (ΔEBGN) derived from the band gap renormalization effect did not show a good ne1∕3 dependence predicated by a weakly interacting electron-gas model, but it was in excellent agreement with a perturbation theory considering different many-body effects. Based on this theory a simple expression, ΔEBGN=Ane1∕3+Bne1∕4+Cne1∕2, was deduced for n-type ZnO, as well as p-type ZnO, with detailed values of A, B, and C coefficients. An empirical relation once proposed for heavily doped Si could also be used to describe well this gap narrowing in AZO.