Temperature-Composition Dependence of the Bandgap and Possible Non-complanar Structures in GaN-AlN, GaN-InN and InN-AlN
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Internet Journal o f
Nitride S emiconductor Research
Volume 2, Article 3
Temperature-Composition Dependence of the Bandgap and Possible Non-complanar Structures in GaN-AlN, GaN-InN and InN-AlN Mixed Crystals E. V. Kalashnikov Institute of Mechanical Engineering, RAN V. I. Nikolaev Ioffe Physical-Technical Institute This article was received on May 31, 1996 and accepted on January 24, 1997.
Abstract The virtual crystal approximation has been used to determine the temperature-composition dependence of the GaN-AlN, GaN-InN, and InN-AlN band gap energies. Also, the thermodynamic instability states in the mixed crystals were studied. The expression for the band gap of mixed A-B crystals has been derived: EgAB = (1-x)EgA + xEgB - bSx x , where EgA and EgB are the direct gaps for compounds A and B, respectively, and x is the alloy concentration. The term Sx x ~ T0/(∂2G/∂x2) where G is the thermodynamic potential of the mixed crystal, b is a bowing parameter, and T0 has the meaning of a growth temperature.
1. Introduction Recent progress in the nitride semiconductors is connected with the realization of high-quality AlGaN and InGaN crystal layers and their application to high brightness light-emitting diodes (LEDs) operating from the near ultraviolet (~3.4 eV) to yellow (~2.1 eV) [1] [2]. The bright emission of the LEDs is associated with direct band-to-band transitions in unstrained InGaN quantum wells [2] in which the InN mole fraction is varied from 0 - 70%. It is obvious that the band gap (Eg) of semiconductor alloys (mixed crystals) is strongly composition dependent. However, theoretically the alloy bandgap can only be solved at small deviations from the pure components. Experimental Eg values have been measured in nitride alloys throughout the entire compositional range [1] [2] [3] [4] [5] [6] [7] by optical absorption spectroscopy and edge luminescence measurements. The compositional dependence of the band gap is generally described by a parabolic function of the molar fraction x: (1) where EgA and EgB are the band gaps of the pure components, and b is the bowing parameter. To be more precise we have to note that the term containing x(1-x) is reasonable based on the assumption that the mixed crystal is an ideal solid solution. This approximation is well suited to mixed crystals at small concentrations of one component or at very high temperature where the interactions between the A and B components can be neglected. Larger concentrations of both components usually lead to additional ordering, and in some respects these alloys can be likened to the order in a liquid where Brillouin zones have no conventional meaning. Derivation of the compositional dependence of Eg under these conditions requires special theoretical analysis and calculations.
2. Correction of the Compositional Dependence of the Band Gap Experiments [8] show that the group III nitride alloys are substituted solid solutions in the cation sublattice of A1 xB
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