By Edward Winter
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According to Vegard’s law, CABC = 0 for the lattice constant. Bowing is also not pronounced for the effective mass of most alloys. However, strong bowing is often observed for the energy gap. 8. It should be noted that the smallest band gap may change from direct to indirect as composition is varied. 42 (Fig. 16). 2). Based on empirical interpolation formulas for ternary compounds, properties of quaternary alloys Ax B1−x Cy D1−y can be interpolated as Q(x, y) = [x(1 − x)[yTABC (x) + (1 − y)TABD (x)] + y(1 − y)[xTACD (y) + (1 − x)TBCD (y)]]/[x(1 − x) + y(1 − y)].
18). 9, and they are obtained by calculating the average electrostatic potential for model-solids of neutral atoms. The position of the conduction band edge is calculated by 0 + Ec0 = Ev0 + Eg = Ev,av 0 3 + Eg . 5. 16: Direct ( ) and indirect (L, X) band gaps of Alx Ga1−x As as a function of composition x at room temperature . 17: Direct band gap Eg bowing for quaternary III–V compounds latticematched to InP. 46 CHAPTER 2. 18: Illustration of band offset parameters. constants aAC and aBC . This deformation of the binary model-solid is accounted for by the bowing parameter (see Eq.
R. Enderlein and N. J. M. Horing, Fundamentals of Semiconductor Physics and Devices, World Scientific, Singapore, 1997. N. W. Ashcroft and N. D. Mermin, Solid State Physics, Saunders, Forth Worth, 1976.
A Chessplaying Astronomer by Edward Winter