Structural and Electronic Properties of AlN, GaN And InN, and Band Offsets at AlN/GaN (1010) and (0001) Interfaces
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for In a Koelling-Harmon scalar-relativistic equation was used [4]. Spin-orbit interaction is neglected throughout. AIN, GaN, AND InN: BULK PROPERTIES The bulk properties of the rocksalt, zincblende, and wurtzite phases of AIN, GaN, and InN are listed in Table I. For the cubic phases the structural parameters were obtained from a Murnaghan fit of the total energy vs. volume. For wurtzite, the total energy was calculated for a grid of values of a and c, assuming an ideal internal parameter u, and the theoretical values ath and Cth were extracted by polynomial interpolation. At ath and atomic positions were relaxed to obtain the internal parameter Uth. The bulk modulus was obtained changing the cell volume at Cth and Uth. Cohesive energies are referred to spin-polarized free-atom energies. k-space integrals were approximated by sums over the Chadi-Cohen 10-point and 12-point meshes for the cubic and wurtzite phases respectively. Cth,
GaN 3d
no-3d exp AIN
exp InN
exp
phase wurtzite zincblende
a (bohr) 6.04 8.54
B (Mbar) 2.13 2.00
B' 4.50 4.15
rocksalt zincblende rocksalt wurtzite
8.01 8.07 7.49 6.03
2.48 2.58 3.30 2.0
4.68 4.1 4.3
phase wurtzite zincblende rocksalt wurtzite
a (bohr) 5.814 8.20 7.59 5.88
B (Mbar) 2.071 2.04 2.55 2.079
B' 3.82 4.06 3.90 6.3
phase wurtzite zincblende
a (bohr) 6.66 9.40
B (Mbar) 1.49 1.49
B' 4.12 4.41
rocksalt
8.78
1.95
4.48
wurtzite
6.70
1.26
12.7
zincblende
9.41
c/a 1.634
u 0.375
-9.735 -14.08 -13.48 -9
1.628 c/a 1.619
Ecoh/pair (eV) -10.547 -10.536
u 0.380
Ecoh/pair (eV) -18.032 -17.990 -17.799
1.6004 c/a 1.627
Pt (KBar) 521 454
265 - 500 Pt (KBar) 132.07 104.50 140
u 0.377
Eoh/pair (eV) -8.799 -8.779
Pt (KBar) 122.9
-8.376 1.609
121
Table I: Structure, cohesive energy, and transition pressures to rocksalt for GaN, AIN, and InN. Results labeled "no-3d" for GaN were obtained without Ga 3d states in the valence. The results are in good agreement with experiment for the structural parameters as well as for the transition pressures to rocksalt. An interesting prediction is that wurtzite AIN and InN have have appreciably non-ideal structures, while GaN has an ideal u and quasi-ideal axial ratio. These deviations from the ideal wurtzite structure suggest that AIN may exhibit a large macroscopic polarization; as will be suggested below, this may influence interface properties. A calculation of the macroscopic polarization of AIN is underway. In Table II we report the gap values and deformation potentials for the principal gaps of AIN and GaN. The deformation potentials are defined as D = Oi/O InV. The valence band top is a F, singlet state (reminiscent of the p, state), with a F 6 doublet (pr - py) slightly below it. As was to be expected, the IF state is quite sensitive to variation in the axial parameters. The gaps obviously suffer from the well known DFT gap problem: however, 516
deformation potentials (which are in satisfactory agreement with previous studies [9]) are expected to be given reliably by the LDA [10].
AIN
IaN
D
E,
D
E,
4
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