Effects of Substrate Orientation on the Valence Band Splittings and Valence Band Offsets in GaN and AlN Films
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917 Mat. Res. Soc. Symp. Proc. Vol. 482 ©1998 Materials Research Society
POLARITY OF INTERFACE AND FORMATION ENTHALPIES Substrate orientation and interface polarity In the following, we consider cubic or wurtzite AIN as substrate and study heterostructures of strained GaN that are pseudomorphically grown on AIN. For the cubic heterostructures, we consider [001], [110], and [111], and for the wurtzite heterostructures [0001], [0110], and [1210] growth directions, respectively. Since we consider GaN/AIN heterostructures where substrate and epilayers have the same crystallographic phase, the growth direction determines the type of heterostructure uniquely (e.g. [001] GaN/AIN denotes cubic GaN grown on cubic AIN with [001] growth direction). In the case of stacking fault interfaces, we we assume the growth axis to be the hexagonal c-axis ([0001] in wurtzite, [111] in zincblende). The space group P6 3 mc (CQv) of wurtzite is compatible with a spontaneous polarization along the hexagonal c-axis. Therefore, the polarization can be of both pyroelectric and piezoelectric origin in wurtzite AIN and GaN, but only piezoelectric in the cubic phases. Since the polarization is always directed along the hexagonal direction, its change across the interface is equivalent to an interface charge. This occurs whenever the polarization lies parallel to the growth direction. Among the studied interfaces between GaN and AIN, [111] GaN/AIN and [0001] GaN/AIN are of this polar type. Another example are stacking fault interfaces between wurtzite and zincblende GaN. On the other hand, the polarization lies parallel to the interface and therefore does not give rise to a charge accumulation in cases such as [1210] GaN/AIN and [0110] GaN/AIN. In the [1101 GaN/AIN heterostructure, only strained GaN is polarized, but the polarization lies also parallel to the interface which is nonpolar, consequently. Finally, both materials are unpolarized in the cubic [001] GaN/AIN interface; thus, this interface is obviously nonpolar. Computationally, we have modeled these interfaces by supercells containing up to 40 atoms (for [0110] and [121-0] wurtzite structures). All atomic positions in the unit cell have been optimized by calculating the Hellmann-Feynman forces since the valence band offsets and formation enthalpies depend sensitively on them. If we were to assume, for example, the interface lattice constant of the [001] GaN/AIN heterostructure to be equal to the arithmetic average of the bulk lattice constants (giving an interface spacing of 1.126 A), we would obtain a VBO of 1.11 eV. The relaxed interface height, on the other hand, is 1.174 A and yields a VBO of 0.76 eV. Similiarily, the VBO for the relaxed [0001] GaN/AIN interface is 0.4 eV smaller than for the unrelaxed one. The length of the supercell was determined by minimizing the stress tensor component in growth direction. Our first-principles calculations reveal that lattice relaxation near the interface reduces the monopole contribution of the interface charge approximately by a factor of tw
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