Thermal expansion coefficient of single-crystal silicon from 7 K to 293 K

Abstract

We measured the absolute lengths of three single-crystal silicon samples by means of an imaging Twyman-Green interferometer in the temperature range from 7 K to 293 K with uncertainties of about 1 nm. From these measurements we extracted the coefficient of thermal expansion with uncertainties on the order of $1\times {10}^{-9}/\mathrm{K}$. To access the functional dependence of the length on the temperature, usually polynomials are fitted to the data. Instead we used a physically motivated model equation with seven fit parameters for the whole temperature range. The coefficient of thermal expansion is obtained from the derivative of the best fit. The measurements conducted in 2012 and 2014 demonstrate a high reproducibility, and the agreement of two independently produced samples supports single-crystal silicon as a reference material for thermal expansion. Although the results for all three samples agree with each other and with measurements performed at other institutes, they significantly differ from the currently recommended values for the thermal expansion of crystalline silicon.