The accuracy of any measurement with terahertz time-domain spectroscopy (THz-TDS) depends strongly on knowing and supplying the precise sample thickness when processing the raw terahertz data. Sample thickness usually is estimated using other (non-THz) metrology and invariably involves some degree of uncertainty. It turns out that the terahertz data itself typically also contains information regarding sample thickness. However, there is limited systematic work addressing the following questions: What is the best method for extracting sample thickness from THz-TDS data? And, what is the thickness resolution obtainable with THz-TDS? In this study we demonstrate how these questions can be answered in general by answering them for a specific example: undoped silicon wafers. We determine the accuracy with which the exact thickness of nominally 500 μm silicon wafers can be measured using transmission mode THz-TDS. We analyze and compare the resolution of 5 different approaches for determining sample thickness using THz-TDS data, including two new methods and three methods proposed in the literature. The quantitative results and analyses of methods we present will be useful in developing far-infrared optical metrology. Conversely the quantitative results presented can be used to relate uncertainty in sample thickness to uncertainty in the measured terahertz data both in the time domain and frequency domain (phase and amplitude). Finally, a precise understanding of the relationship between sample thickness and THz-TDS data can be used to formulate superior THz-TDS data work-up methodologies.
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