Absolute thermal expansion measurements of single-crystal silicon in the range 300?1300 K with an interferometric dilatometer

Abstract

The thermal expansion coefficient of single-crystal silicon has been measured in the range 300–1300 K using an interferometric dilatometer. The measurement system consists of a double-path optical heterodyne interferometer and a radiant image furnace with a quartz vacuum tube, which provides both accuracy and rapidity of measurement. The uncertainties in length and temperature determination are within 4 nm and 0.4 K, respectively. A high-purity dislocation-free FZ silicon single crystal was used in the study. Thermal expansion coefficients of silicon oriented in the [111] direction have been determined over the temperature range from 300 to 1300 K. The standard deviation of the measurement data from the best fitting for the fifth-order polynomial in temperature is 2.1×10−8 K−1. The present value for the thermal expansion coefficient agrees within 9×10−8K−1 with the interferometric measurement of polycrystalline pure silicon by Roberts (1981) between 300 and 800 K and within 1.2 × 10−7 K−1 with the single-crystal X-ray diffractometric measurement by Okada and Tokumaru (1984) between 300 and 1300 K.