Band Offsets in GaN/AlN and AlN/SiC Heterojunctions
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there has been considerable progress in understanding and controlling the bulk properties of these wide-gap materials, the situation is less satisfactory as far as their interface properties are concerned. In particular, few experimental or theoretical data are available on the band offsets that control carrier injection and confinement in nitride heterojunctions, and little is known on their trends as compared to other semiconductor heterojunctions. Here we examine from first principles the structural trends of the band offsets in nitride heterojunctions, including the offset dependence on interface orientation, strain, and polytype. As prototype systems we selected the isovalent GaN/A1N and the heterovalent AlN/SiC heterojunctions in the zincblende (3C) and wurtzite (2H) crystalline forms. METHOD The ab initio calculations were performed within the local-density approximation to density-functional theory, using Troullier-Martins pseudopotentials and a plane-wave basis set [1]. The Ga-3d orbitals were treated as valence states. We also carried out, however, some calculations with the Ga-3d states in the core in order to assess their influence on the band offsets. To evaluate the valence-band offset (VBO), we used the technique described in Ref. [2]. The interfaces were modeled with supercells containing 12 atomic layers for the (110) junctions and 24 atomic layers for the (100), (111) and (0001) junctions. The supercell 911 Mat. Res. Soc. Symp. Proc. Vol. 482 ©1998 Materials Research Society
computations were performed with kinetic energy cutoffs of 60 and 100 Ry for AIN/SiC and GaN/AIN, respectively. The bulk band-structure calculations were performed using a 70 Ry cutoff for AIN and SiC, and a 120 Ry cutoff for GaN [3]. Other computational details will be reported elsewhere [4]. Most of the calculations were performed for heterojunctions pseudomorphically grown on a SiC substrate. For the in-plane lattice parameters, we used the theoretical equilibrium lattice constants of SiC: a3c = 4.32 A and a2H = 3.05 A. The experimental values are a3C = 4.36 A and a2H = 3.08 A. We neglected the small difference between the theoretical equilibrium lattice constants of AIN and SiC ('-- 0.2 %), and treated these materials as lattice matched. For the coherently strained GaN/AIN junctions, we evaluated the tetragonal deformation of GaN and AIN following macroscopic elasticity theory, and using the calculated elastic constants of GaN and AIN given in Ref. [5]. The theoretical equilibrium lattice parameters of GaN, a 3 c = 4.46 A and a2H = 3.15 A, were used, which yield a - 3 % lattice mismatch between AIN and GaN. The experimental values are a 3c = 4.5 A, a2H = 3.19 A and the lattice mismatch is also - 3 %. ORIENTATION AND STRAIN EFFECTS In Table 1, we present the calculated VBO's for the isovalent zincblende GaN/AJN (100), (110) and (111) heterojunctions, for GaN pseudomorphically strained to AIN. Using the experimental bandgap value of 3.2 eV and the estimated value of 4.9 eV for cubic GaN
and AIN [6], respectively, a band a
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