Thin film effects in ultrasonic wafer thermometry

We use an ultrasonic technique where the temperature dependence of lowest order anti-symmetric Lamb wave velocity in the silicon wafer is utilized for in-situ temperature measurement in the 20-1000°C range. In almost all wafer processing steps, one or more layers of thin films are present on the wafers. The effects of these films on temperature sensitivity is investigated. A theoretical model for Lamb wave propagation in general multilayered plates is developed using the surface impedance approach. This model is utilized to calculate the effects of anisotropy and thin films on temperature coefficients in semiconductor wafers. Calculations predict 2.38E-5 (1/°C) sensitivity for a 10 cm (100) silicon wafer with 238b anisotropy. The same figures for gallium arsenide are 2.2B-5 (1/°C) and 8.7%. Thin film effects are considered for various materials commonly used in semiconductor processing. The density and shear elastic constants of film materials are found to be effective parameters in determining sensitivity figures. The frequency dependent sensitivity calculations show that it is possible to minimize effects of aluminum and silicon dioxide on silicon wafers by choosing the frequency-thickness products around 1.6 MHz-mm and 3.3 MHz-mm in temperature measurements, respectively. Using a simple propagation model, the time of flight sensitivity is calculated and compared with experimental data obtained from a Rapid Thermal Processor