Anomalous behavior of the optical band gap of nanocrystalline zinc oxide thin films
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Anomalous behavior of the optical band gap of nanocrystalline zinc oxide thin films V. Srikant and D. R. Clarke Materials Department, College of Engineering, University of California, Santa Barbara, California 93106 (Received 24 June 1996; accepted 2 February 1997)
The optical band gap of ZnO films on fused silica in the carrier concentration regime of 1018 –1020ycm3 is reported. Contrary to theoretical predictions there is an anomalous increase in the band gap of ZnO films at a carrier concentration of 5 3 1018ycm3 , followed by an abrupt decrease at a critical concentration of 3–4 3 1019ycm3 before the optical band gap rises again. Similar observations have been made before, but an explanation of these observations was lacking. We propose a model based on the existence of potential barriers at the grain boundaries, causing quantum confinement of the electrons in the small grains realized in these films. Quantum confinement leads to the initial rise in the optical band gap. On increasing the carrier concentration to the critical value, the potentials at the grain boundaries collapse, leading to the abrupt decrease in the optical band gap. Above this carrier concentration the films behave according to existing many-body theories.
ZnO films have been investigated extensively in the last 20 years. On the one hand insulating ZnO films are used in piezoelectric applications, while on the other hand highly conducting films are sought as transparent conducting electrodes. The interest in transparent conducting electrodes has focused attention on the optical properties of these films with very high doping levels (.2 3 1020ycm3 ). One of the primary interests has been to evaluate the optical band gap as a function of doping. Investigations on highly doped ZnO films have shown that the increase in the optical band gap with increasing carrier concentration cannot be explained solely on the basis of the Moss–Burstein shift1 In fact, the Moss–Burstein shift grossly overpredicts the optical band gap as a function of carrier concentration. This is not surprising as it is known from studies on GaAs films2 that the Moss–Burstein theory, based on the band filling, is best suited for materials having a low effective mass of electrons and holes. When the effective masses of the electrons and holes are large, as they are in ZnO, then it is important to take into account many-body effects. One of the primary effects of the many-body theory is bandgap narrowing (also referred to as bandgap renormalization or bandgap shrinkage), which arises due to the interaction of the donor levels with the conduction band and band tailing. As a consequence, the onset of the increase in the optical band gap due to band filling occurs at higher carrier concentrations. Stern and Talley3 were the first to take into account many-body effects J. Mater. Res., Vol. 12, No. 6, Jun 1997
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to understand the optical band gap as a function of carrier concentration
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