The heat capacity of pure silicon and germanium and properties of their vibrational frequency spectra

Abstract

Heat capacities of pure silicon and germanium have been measured between 2.5° and 300°K. The estimated accuracies of the measurements are ±0.5% for 10° < T < 20°K and ±0.2% for T > 20°K. The results for silicon were anomalous in the region T <7°K; it is suggested that this behaviour resulted from adsorption and desorption of exchange gas in the calorimeter vessel. No anomalies were observed in the measurements on germanium; their accuracy at the lowest temperatures is estimated to be ±2%. The results for both substances are significantly different from previously published values. The temperature variation of ΘD of both silicon and germanium below about T= ΘD/3 is consistent with general harmonic theory, but at high temperatures ΘD decreases with increasing temperature. This appears to be a clearly marked anharmonic effect of a type that cannot be explained by change of volume alone. The results for T < ΘD/3 are therefore extrapolated to high temperatures to give a heat capacity consistent with harmonic theory at all temperatures. From this, propertios of an effective harmonic spectrum are derived; these include the low frequency expansion and a number of positive and negative moments. The apparent anharmonic contribution δCv =[Cv-Cv (harmonic)] is found for both elements to be approximately a linear function of the temperature in the region between ΘD/3 and room temperature. The possible significance of this result is discussed in the light of anharmonic theory. The results are compared where possible with vibrational properties determined from other experiments and the agreement is very satisfactory.