ELASTO-VISCOPLASTIC WAVE THERMOMETRY FOR SINGLE CRYSTALLINE SILICON PROCESSING

Abstract

Laser-induced stress wave thermometry (LISWT) is a non-contact thermal diagnostic technique for the rapid thermal processing (RTP) of silicon wafers using laser-generated, ultrasonic, dispersive stress waves. The required knowledge base for establishing LISWT as a viable alternative to current pyrometric technology for temperature measurement up to 1000°C with ±1°C resolution is presented. A 3D elasto-viscoplastic wave model is developed for describing wave behaviors from being elastic to viscoplastic subject to the RTP annealing temperature ranging from room temperature to exceeding 1000°C. The model is a system of nine coupled first-order hyperbolic equations formulated based on the kinematics of elasto-plastic deformation, conversion of linear momentum and a temperature-dependent viscoplastic constitutive law for single crystalline silicon derived from the material models developed by Hassen–Sumino and Tsai. The group velocity of the wave propagating in silicon wafer is a nonlinear function of temperature. As nonlinearity becomes prominent at high temperature for high frequency components, low frequency components are preferably exploited to achieve the desired thermal resolution at high temperature.