Band gap bowing and electron localization of (GaxIn1-x)N Page: 4 of 12
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eV both in experiments and sX-LDA. For InN the correction of sX-LDA is more pronounced.
The recently experimentally measured band gap for WZ structure is 0.8 eV.  The sX-LDA
result for WZ InN is 0.89 eV, which is in the same quality as in the many-body GW method.
The LDA band gap, on the other hand, is negative and predicts a qualitatively incorrect
metallic state. Another effect of sX-LDA on the band structures of both GaN and AlN is
the increase of the valence band width by ~i 2 eV, which has been observed in other bulk
To model the disordered zinc-blende Ga In1_ N alloy with Ga molar fraction 0 < x < 1,
we employed the special quasi-random structures (SQSs).  SQSs are finite model systems
constructed to mimic the radial correlation functions of an infinite random structure. They
have been extensively used to study the electronic structures of alloys. We considered two
classes of model systems of SQS8 and SQS16. In SQS8 the cell consists of n In, n Ga, and
8 N atoms with n + n = 8. In SQS16 the cell contains twice the number of atoms in SQS8.
For each model system, the lattice constant was inferred from experimental lattice constant
using Vegard's law. The equilibrium atom positions were obtained by minimizing the
total energy within LDA. A total of 16 k-point were used to integrate over SQS Brillouin
zone for SQS8. Table II shows that the band gap difference between SQS8 and SQS16 is
less than 0.1 eV for all alloy compounds. Further increase of SQS cell size does not change
TABLE I: Band gap of GaN and InN in zinc-blende and wurtzite crystal structures. Energy is in
LDA sX-LDA Experiment
GaN (ZB) 1.97 3.04 3.3a
GaN (WZ) 2.11 3.20 3.39b, 3.5
InN (ZB) -0.22 0.76
InN (WZ) -0.014 0.89 0.8d
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Lee, Byounghak & Wang, Lin-Wang. Band gap bowing and electron localization of (GaxIn1-x)N, article, May 9, 2006; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc888491/m1/4/: accessed March 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.