Comparing smoothing techniques for extracting MOSFET threshold voltage

Measurement noise acts as a barrier to the accurate calculation of threshold voltage by derivative-based extraction methods. We examined several smoothing techniques and their effects on measurement noise in threshold voltage extracted by the linear extrapolation method and the gm/Id method. We applied these techniques on a set of SiC power MOSFET devices before and after they had undergone accelerated thermal testing. The smoothing methods examined are least-squares polynomial fitting, low-pass filtering using Butterworth and Chebyshev fillers, and differential smoothing. These methods are compared by their shift in threshold voltage compared to unsmoothed data and their standard deviation among the measurements of each device. All methods performed poorly at smoothing when extracting via the gm/Id due to the large amounts of high-magnitude subthreshold noise, mostly tending to extract threshold voltages far below the expected value. Differential smoothing provided results closest to the expected value with an absolute shift of 1.2 V on average. The smoothing methods performed better with the LE method. On a failed device, all smoothing methods except polynomial smoothing preserved the large threshold voltage anomaly for four out of five measurements. These results show that choice of smoothing method, if used must be evaluated based on the device and extraction method.