Temperature Dependent Young's Modulus of Si and Ge

摘要

The vibrational properties of single crystal Si and Ge are studied between room and melting temperature T_m using the impulse excitation technique. From the measurements, the temperature dependent Young's moduli E_(ηk) 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 T_m. Using the semi-empiric Wachtman's equation allows an excellent fit to the experimental data for the temperature dependence of E_(100), E_(100), and E_(111) between room temperature and 0.6T_m. 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 ℃ which is due to a loss of Ge material, leading to a decrease of sample dimensions and weight.