Band gap bowing and electron localization of (GaxIn1-x)N Page: 2 of 12
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The semiconductors based on group-III nitrides are important for photoelectronic appli-
cations, such as ultraviolet/blue/green  light-emitting diodes and lasers. By making
alloy compounds, the frequency of the emitted light can be harnessed in a wide range. For
example, the band gap of InN and GaN is ~ 0.8 and 3.5 eV, respectively, and the alloy
compounds Ga In1_ N have band gaps spanning nearly the entire solar energy spectrum.
[4, 5] The electronic structure and the carrier distribution of disordered alloys is valuable
information for designing materials with desirable properties for various applications.
The band gap dependence of the III-nitride semiconductor alloys has been theoretical
studied primarily using empirical pseudopotential method, the local density approxima-
tion (LDA) of the density functional theory. [7, 8] While LDA is reliable in calculating the
atomic relaxation and formation energies of the semiconductor alloys, it is well known that
the band gaps calculated from these methods are underestimated due to its intrinsic errors
in describing the excited states. The LDA calculated band gap of pure III-nitrides are signif-
icantly smaller than the experiments. [9, 10] The more accurate many-body GW method, on
the other hand, has not been used for alloy calculations because of its high computational
cost. There is no clear understanding of whether the LDA band gap errors in pure bulk
crystals will cause significant errors in the band gap behavior in the alloy, especially for
quantities such as the bowing parameters.
In addition to the band gap, the carrier localization in the III-nitride alloys is also an
important issue. In Ga In1_ N alloys, for example, there is large amount of defects. These
defects of high concentration usually quench the photoluminescence and reduce the carrier
concentration. The blue laser, on the other hand, is achieved in high efficiency with small In
concentration. It has been speculated that the high efficiency of Ga In1_ N -based emitting
devices could be due to a strong hole state localization.  The first principle calculations
can shed light on this important property of the material.
Our approach in this paper is to study the electronic structures of the alloys using im-
proved density functional theory. The screened-exchange local density functional (sX-LDA)
method has been successful in many simple semiconductors, such as II-VI, III-V, and IV-IV
alloys, correcting the band gap error in the LDA method.[11, 12] The sX-LDA improves the
LDA band gap similarly to that of many-body GW calculations and also yields the ground
state structure as good as LDA. Although more expensive than LDA, sX-LDA is still cost
effective enough to be used for alloy calculations. We study Ga In1_ N alloys in zinc-blende
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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. (digital.library.unt.edu/ark:/67531/metadc888491/m1/2/: accessed December 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.