Two-layer Hall-effect model with arbitrary surface-donor profiles: Application to ZnO

Abstract

A complete two-layer Hall-effect model, allowing arbitrary donor and acceptor profiles, is presented and applied to the problem of conductive surface layers in ZnO. Temperature-dependent mobility and carrier concentration data in the temperature range of 20-320 K are fitted with an efficient algorithm easily implemented in commercial mathematics programs such as MATHCAD. The model is applied to two ZnO samples, grown by the melt (MLT) and hydrothermal (HYD) processes, respectively. Under the assumption of a "square" surface-donor profile, the fitted surface-layer thicknesses are 48 and 2.5 nm, respectively, for the MLT and HYD samples. The surface-donor concentrations are 7.6× 1017 and 8.3× 1018 cm-3, and the integrated surface-donor concentrations are 2.1× 1012 and 3.6× 1012 cm-2. For an assumed Gaussian [NDs (0) exp (- z2 / ds2)] donor profile, the fitted values of ds are nearly the same as those for the square profile. The values of ND,s (0) are about 50% larger and the integrated donor-concentration values are about 15% larger, for both samples. As a surface-analysis tool, the Hall effect is extremely sensitive and applicable over a wide range of surface-layer conditions. © 2008 American Institute of Physics.