Investigation of Lamb waves for sensor applications in semiconductor processing

Abstract

Considering the semiconductor wafers as anisotropic plates, Lamb wave propagation characteristics are related to various parameters dynamically changing during processing. Particularly, the effect of wafer temperature and thin-film growth on phase velocity of zeroth order Lamb waves are analyzed theoretically. These modes are chosen to enable single mode operation in silicon wafers for frequency-thickness product (f*d) less than 3 MHz mm. The surface impedance approach is used in theoretical modeling of propagation in general multilayered anisotropic solid structures. Temperature, thin film, and their combined sensitivity figures are calculated for commonly used structures in semiconductor processing. The results are interpreted to obtain optimum ultrasonic sensor system parameters for certain applications. For example, in case of aluminum films on (100) silicon, antisymmetric mode in 〈100〉 direction shows negligible sensitivity to thin films around f*d=0.8 MHz mm. The same figure for silicon oxide film is 1.57 MHz mm. In a combined measurement, a temperature sensor using these system parameters to measure phase velocity will be minimally affected by thin films, enabling an isolated temperature measurement. Practical implementations of the results in rapid thermal processing environment are also discussed in the paper. [Work supported by SRC.]