Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500 K

Abstract

The lattice parameter of high-purity silicon is measured as a function of temperature between 300 and 1500 K, and the linear thermal expansion coefficient is accurately determined. Precise measurements are made by the high-temperature attachment for Bond’s x-ray method to a few parts per million. It is found that the temperature dependence of the linear thermal expansion coefficient α(t) is empirically given by α(t)=(3.725{1−exp[−5.88×10−3{(t−124)} +5.548×10−4t)×10−6 (K−1), where t is the absolute temperature ranging from 120 to 1500 K. It is shown that the lattice parameter in the above temperature range can be calculated using α(t) and the lattice parameter at 273.2 K (0.5430741 nm). Measured values of the lattice parameter and the thermal expansion coefficient for high-purity float-zoned (100 kΩ cm) and Czochralski-grown (30 Ω cm) single crystals are uniformly distributed within ±1×10−5 nm and ±2×10−7 K−1 with respect to the values obtained from the above empirical formula.