Change point detection in time dependent defect spectroscopy data

Abstract

One of the most important reliability effects observed in metal-oxide-semiconductor field-effect transistors (MOSFETs) is the threshold voltage shift when the device is stressed at high gate voltages at elevated temperatures, called the bias temperature instability (BTI). In the case of p-type MOSFETs the devices are stressed with negative gate voltages and the effect is therefor called negative bias temperature instability (NBTI). Positive bias temperature instability (PBTI) goes hand in hand with a positive gate voltage stress. PBTI is observed in n-type MOSFETs but is typically weaker than NBTI in p-type devices. In order to study BTI, a new method, the time dependent defect spectroscopy (TDDS), has been recently introduced. Very fast data acquisition equipment is necessary to obtain measurement data for this method. Evaluation and visualization of measurement results is done with the help of the detection of change points in TDDS measurement data.<br />Three methods are presented and their results are discussed. First a very fast and intuitive method based on the wavelet denoising techniques is presented. The application of the discrete wavelet transform (DWT) or the redundant discrete wavelet transform (RDWT) on the measurement data gives the wavelet transform coefficients. Smoothed transform coefficients are obtained by thresholding. Then the inverse transform gives a denoised version of the observations. A final filtering process extracts steps and emission times. Several wavelet basis functions, threshold denoising methods and their impact on detection results are discussed. The second detection algorithm is based on histogram data analysis. Data is binned into histograms. After detecting peaks in the histograms, Gaussian distributions are fit to the peaks, and the denoised data is obtained by applying a maximum likelihood criterion. Histogram quality improvement by data interpolation and a histogram for not equally sampled data is presented.<br />The third and last method is a combination of cumulative sum statistic and bootstrap analysis combined with histogram supported evaluation. A threshold for change points is estimated and executed on the data set.<br />Finally, a user defined minimal-acceptable step height filter is applied.