Piezoresistive Theory For 4h Silicon Carbide Stress Sensors On Four-Degree Off-Axis Wafers

Piezoresistive stress sensors have been shown to be a powerful tool for experimental evaluation of die stress distributions. Silicon Carbide (SiC) wide bandgap semiconductors are promising materials for development of high temperature power electronics. In the past, the analysis and design of stress sensors on silicon carbide have assumed that the wafer surface is aligned with the crystallographic axes. However, 4H silicon carbide wafers are produced with a four-degree off-axis cut to ensure high -quality homoepitaxial growth, so that the tilted wafer surface does not perfectly coincide with the fundamental crystallographic axis. Thus, the prior "on-axis" theory is an approximation, and errors in piezoresistive theory caused by such tilted wafer plane need to be discussed. These errors can affect both the results from calibration experiments as well as the stresses extracted during application of sensor rosettes. This paper discusses the theory and extraction of piezoresistive coefficients for 4H-SiC silicon carbide materials in the presence of off-axis starting wafers. Coordinate transformations for the piezoresistive coefficients are reviewed, the required direction cosines between the new rotated axes and the ideal axes are discussed, and the 6 x 6 matrix of piezoresistive coefficients (it -matrix) for the on-axis and off-axis cases are calculated. Many of the elements of the ideal on-axis it -matrixes are zero. In contrast, the off-axis is completely filled with non-zero values indicating additional coupling, particularly among the shear coefficients. Examples of the overall impact of these new terms on calibration and stress measurement are discussed.