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

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. 7251−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.