Determination of dislocation density of a class of n-GaN based on the variable temperature Hall-effect method

Abstract

An analytical model for electron mobility in a class of wurtzite n-GaN, whose carrier concentration is over 1018 cm-3 (Mott's critical limit), is developed. With the dislocation density and two donor levels serving as the important parameters, the proposed model can accurately predict the electron mobility as a function of temperature. The edge and screw dislocation densities in two samples, which are respectively grown on sapphire (001) by metal organic chemical vapor deposition and hydride vapor phase epitaxy, are determined by using this model which is discussed in detail. It is shown that the data-fitting of H-T characteristic curve is a highly suitable technique for accurately determining the edge and screw dislocation densities in n-GaN films. Quantitative analyses of donor concentration and donor activation energy indicate that the impurity band occurs when the carrier concentration is under 1017 cm-3, much lower than the critical carrier concentration of Mott transition (1018 cm-3). Such a behavior can also be confirmed by the results from solving the Boltzmann transport equation by using the Rode iterative method. Another anomaly is that the dislocation density in Mott transition material perhaps is lower than that of material with carrier concentration under 1018 cm-3. This fact indicates that the cause of Mott transition should not be the shallow donor impurities around dislocation lines, but perhaps the deeper donor impurities or other defects. In the theoretical model calculation, two transition characteristics together with the donor distribution and its energy equilibrium are taken into account. Based both on the Mott transition and the H-like electron state model, the relaxation energies for the shallow-donor defects along the screw and edge dislocation lines are calculated by using an electrical ensemble average method. Besides, an assumption that should be made is that there are 6 shallow-donor defect lines around one dislocation line. The research results show that the Hall mobility should be taken as the live degree of the ionizing energy for the shallow-donor defects along the dislocation line. The experimental results indicate that our calculation function can be best fit by the experimental curve, with the values of dislocation density being between our model and others determined by X-ray diffraction or by chemical etching method, which are all in good agreement with each other. The method reported can be applied to the wurtzite n-GaN films grown by various preparation technologies under any condition, with the peak-mobility temperature about or over 300 K, whose Hall mobility near 0 K perhaps is over 10 cm2/(Vs) and even 100 cm2/(Vs).