Modeling of silicon thermal expansion using strained phonon spectra

Based on lattice dynamics theories, a model has been developed to examine the thermal expansion of crystalline silicon. The thermal expansion coefficient α of crystalline silicon has been extracted by using the strained phonon spectra. It is found to be 2.49 × 10⁻⁶ K⁻¹ at room temperature. Based on the temperature dependence of second-order elastic constants and Raman scattering, a semiempirical model for the thermal expansion coefficient of crystalline silicon as a function of temperature has been presented. The obtained results are in good agreement with available experimental data, and the average deviation of thermal expansion coefficient from experiments is less than 2.4%. (paper)