HARMONIC AND ANHARMONIC PROPERTIES OF DIAMOND STRUCTURE CRYSTALS WITH APPLICATION TO THE CALCULATION OF THE THERMAL EXPANSION OF SILICON

Silicon has interesting harmonic and anharmonic properties such as the low-lying transverse acoustic modes at the X and L points of the Brillouin zone, negative Gruneisen parameters, negative thermal expansion and anomalous acoustic attentuation. In an attempt to understand these properties, a lattice dynamical model employing long-range, nonlocal, dipole-dipole interactions has been developed. Several interesting features of this interaction are found and discussed. Analytic expressions for the Gruneisen parameters of several modes are presented. These expressions explain how the negative Gruneisen parameters arise. It is found that short-range anharmonicity is inadequate to explain the experimental data for the Gruneisen parameters. Application of this model to the calculation of the thermal expansion of silicon from 5K to 1700K is made. Good agreement with experiment is obtained from 17K to the melting point. The thermoelastic contribution to the acoustic attenuation of silicon is computed from 1-300K. Strong attenuation anomalies associated with negative thermal expansion are found in the vicinity of 17K and 125K. Electrostatic multipole interaction energies in a nonlocal dielectric medium and the Ewald method and its application to dipole sums are discussed in detail in the appendices.