Electronic Property and Negative Thermal Expansion Behavior of Si(136-x)Ge(x) (x = 8, 32, 40, 104) Clathrate Solid Solution from First Principles

We present the electronic and vibrational studies on Si(136-x)Ge(x) (x = 8, 32, 40, 104) alloys, using the local density approximation (LDA) scheme. We find that a “nearly-direct” band gap exists in the band structure of Si(104)Ge(32) and Si(96)Ge(40), when compared with the similarly reported results obtained using a different computational code. The calculated electronic density of state (EDOS) profiles for the valence band remain nearly identical and independent of the Ge concentration (x = 32, 40, 104) even though some variation is found in the lower conduction band (tail part) as composition x is tuned from 8 (or 40) to 104. The negative thermal expansion (NTE) phenomenon is explored using quasi-harmonic approximation (QHA), which takes the volume dependence of the vibrational mode frequencies into consideration, while neglecting the temperature effect on phonon anharmonicity. Determined macroscopic Grüneisen parameter trends show negative values in the low temperature regime (1 K < T < 115 K), indicating the NTE behavior found in Si(128)Ge(8) is analogous to the experimental result for Si(136). Meanwhile, calculations for the ratio of the vibrational entropy change to the volume change at several characteristic temperatures reconfirm the existence of NTE in Si(128)Ge(8) and Si(104)Ge(32).