Cepstral Strain Mapping for Small Pixel-Count Detectors

With the decreasing sizes of integrated-circuit components, the semiconductor industry is in growing need of high-throughput strain mapping techniques that offer high precision and spatial resolution, with desired industry goals of 0.01-0.1% and 1 nm respectively. As the fundamental limitation on the measurement precision is set by the Poisson noise, pixel array detectors with high saturation current, high dynamic range and fast readout are ideally suited for this purpose. However, due to the limited pixel count on these detectors, they do not work well with traditional strain mapping algorithms that were optimized to work on datasets with a large pixel count. Here, we evaluate the cepstral transform that was designed to address this problem, with the precision determined by the convergence, collection angles and dose while remaining insensitive to the pixel count. We test the performance of our method on silicon wedges and Si-SiGe multilayers, and using datasets collected at different conditions, we show how the measured strain precision scales as a function of dose, aperture size and sample thickness. Using precession gives a further improvement in precision by about 1.5-2x, whereas energy filtering does not have a significant impact on the cepstral method for device-relevant sample thickness ranges.