Temperature Dependent Young's Modulus of Si and Ge

Abstract

The vibrational properties of single crystal Si and Ge are studied between room and melting temperature Tm using the impulse excitation technique. From the measurements, the temperature dependent Young's moduli E<ijk> are extracted in the <100>-, <110>-and <111>-directions. For both semiconductors, the Young's moduli decrease smoothly with increasing temperature and retain high values up to Tm. Using the semi-empiric Wachtman's equation allows an excellent fit to the experimental data for the temperature dependence of E<100>, E<110> and E<111> between room temperature and 0.6Tm,. For higher temperatures, the Young's moduli decrease faster than predicted by Wachtman's equation. In the case of Ge, an apparent enhanced softening is observed starting from about 850 ºC which is due to a loss of Ge material, leading to a decrease of sample dimensions and weight.

Review: Electrostatically actuated nanobeam-based nanoelectromechanical switches – materials solutions and operational conditions

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