Determination of the Si Young's modulus between room and melt temperature using the impulse excitation technique

Stress induced by the thermal gradients near the meltsolid interface affects the intrinsic point defect properties and the quality of single crystal Si grown from a melt. Also during device processing, stress in the Si substrate influences point defect behavior during thermal treatments. To be able to simulate and control the stress distribution one needs to know the elastic constants of single crystal Si at high temperatures. In the present study, the vibrational properties of single crystal Si samples are studied between room and melt temperature using the impulse excitation technique. From the measurements, the temperature dependent Young’s moduli Eijk of moderately doped Czochralski-grown Si samples are extracted in the 100, 110 and 111 crystallographic directions. Close to the melt temperature, very high Young’s moduli values between 110 and 160 GPa are obtained, depending on the crystallographic direction. Empiric expressions are derived for the temperature dependence of E100, E110 and E111 and of the elastic compliances s11 and s12 +s44/2, useful for application in process simulation.status: publishe