Electronic Structure of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Hg</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Cd</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mi mathvariant="normal">Te</mml:mi></mml:math>Alloys and Charge-Density Calculations Using Representative<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi></mml:math>Points

Abstract

We have calculated the electronic band structures and charge densities near $\ensuremath{\Gamma}$ for the ${\mathrm{Hg}}_{1\ensuremath{-}x}{\mathrm{Cd}}_{x}\mathrm{Te}$ alloy system using the empirical-pseudopotential method. We find that the energy gap varies linearly with $x$, with the semimetal-semiconductor transition occurring at $x=0.165$. We have calculated the total electronic charge densities of HgTe and CdTe by using a weighted sum of the charge densities at a few symmetry points in the Brillouin zone and for the nonsymmetry point used by Baldereschi. We show that for a large class of semiconducting compounds the total electronic charge density can be obtained to a very high degree of accuracy using these representative $k$ points.