Mobility in GaAsN

An ab initio approach
Calculated bandstructure of GaAsN using LDA+U
Calculated bandstructure of GaAsN using LDA+U

In the dilute nitrides, the substitution of a very small proportion of nitrogen for arsenic in GaAs has a dramatic effect on the electronic structure, conveniently allowing one to vary the band gap with relatively little effect on the lattice constant and other structural parameters. Unfortunately, the strong perturbation of the conduction band states which gives rise to this band gap change also dramatically reduces the mobility of carriers [1]. Understanding at a microscopic level how the atomic structure of the alloys affects the mobility and improving the carrier mobility would be of enormous benefit for the use of these materials in laser devices and solar cell applications.

LDA-DFT approach: effective mass fails
Applying the Fermi-golden rule formalism to calculate the elastic scattering cross section, one isolates three major quantities which contribute to the electronic mobility: 1. the electronic effective mass, 2. the variation of the electronic conduction band as function of the nitrogen concentration and 3. the overlap between the scattered and unscattered electronic wave function. Besides the LDA band gap underestimation, we find a substantial discrepancy between the experimental (m*exp(GaAs)=0.067me) and LDA (m*exp(GaAs)=0.047me) effective masses in GaAs. In contradiction with the Tigh-Binding results and the experiment, the LDA effective masses reduce in the dilute case on the addition of N. As a consequence, the LDA-DFT mobility (μ=4050 cm2/Vs) is one order of magnitude larger than the experimental one (μ=300 cm2/Vs at x=3% and T=300K [2]) .Such results highlight the limitations of a direct LDA-DFT approach to the mobility. Going beyond a pure DFT approach constitutes the next challenge to solve the transport properties within the ab initio framework.

LDA+U approach: correction to the effective mass problem
Applying the LDA+U formalism, one solves the previous LDA band gap and effective mass errors. In particular, the following band structure has been obtained for the GaAs crystal. Adding nitrogen (x=3.125 %) to the crystal then increases the electronic effective mass (m* increases from 0.077 me to 0.098 me).

References
[1] "Intrinsic Limits on Electron Mobility in Dilute Nitride Semiconductors" S. Fahy and E. P. O'Reilly,Applied Physics Letters 83, 3731-3733 (2003).
[2] J. F. Geisz and D. J. Friedman, Semicond. Sci. Technol. 17 (2002) 769.

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