Band Structure and Effective Masses of Zn 1-x Mg x O
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Band Structure and Effective Masses of Zn1-xMgxO Christian Franz, Marcel Giar, Markus Heinemann, Michael Czerner, and Christian Heiliger I. Physikalisches Institut, Justus Liebig University, 35392 Giessen, Germany ABSTRACT We analyze the influence of the Mg concentration on several important properties of the band structure of Zn1-xMgxO alloys in wurtzite structure using ab initio calculations. For this purpose, the band structure for finite concentrations is defined in terms of the Bloch spectral density, which can be calculated within the coherent potential approximation. We investigate the concentration dependence of the band gap and the crystal-field splitting of the valence bands. The effective electron and hole masses are determined by extending the effective mass model to finite concentrations. We compare our results with experimental results and other calculations. INTRODUCTION Zinc oxide is a promising, sustainable material with many prospective applications, especially in opto-electronics. It is well known that the band gap and other properties can be tuned by adding magnesium. For Mg concentrations up to ca. 30%, the resulting Zn1-xMgxO alloy has wurtzite structure and a direct band gap [1]. This can be used in multilayer structures to form e.g. light-emitting diodes [2]. Recently, a two-dimensional electron gas with high charge carrier mobility was created in a ZnMgO-ZnO multilayer structure [3]. This paves the way to new fields of applications like high-frequency and high-power devices. Tsukazaki et al. were able to measure the integer [4] as well as the fractional quantum Hall effect [5] in ZnMgO-ZnO heterostructures. While both require a high degree of control of the material properties, the latter is of particular interest from a fundamental research point of view, since it arises from a strongly correlated state with extraordinary properties. In order to advance these and other applications reliable numerical tools are of great value. Some of the necessary physical parameters like the valence band effective masses are still unknown for finite concentrations. Thus, recent calculations have to resort to linear interpolation between the pure components, or even use the ZnO value for all concentrations [6]. The most important part of the ZnO band structure, which is the bottom of the conduction band and the top of the valence bands in the vicinity of the ī-point, can be well described within the effective mass approximation. We extend this approach to finite Mg concentrations using a Bloch spectral density [7] defined within the coherent potential approximation (CPA) [8]. Thereby, we provide the bang gap, the valence band splittings, and the electron and hole effective masses for concentrations up to 30%. For pure ZnO the band gap and the valence band splittings are well established from experiments [9,10]. While the band gap is well described by modern ab initio methods, there are still open questions on how to compare the calculated masses to experimental results [11]. Ohtomo et al. were among the fir
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