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

TL;DR

This study precisely measures the thermal expansion coefficient of single crystal silicon from 7 K to 293 K using interferometry, proposing a physically motivated model that challenges existing reference values.

Contribution

It introduces a new measurement approach with high accuracy and a physically based model for silicon's thermal expansion over a wide temperature range.

Findings

High reproducibility of measurements across samples

Agreement with other measurements but deviation from standard references

Supports silicon as a reliable reference material

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 extract the coefficient of thermal expansion with uncertainties in the order of $1\times 10^{-9} {\rm /K}$. To access the functional dependence of the length on the temperature usually polynomials are fitted to the data. Instead we use a physically motivated model equation with 7 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 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 recommended values for thermal expansion of crystalline silicon.