Accessibility of doping ranges of semiconductors by terahertz spectroscopy

While established semiconductor measurement techniques such as four-point probe or capacitance-voltage measurements require a physical contact to the material, terahertz spectroscopy is completely contact-free. Its capability to measure the doping of semiconductors is well known, yet the exact doping ranges that are accessible to terahertz spectroscopy are not obvious. Therefore, we introduce a sensitivity metric to clarify whether a semiconductor sample can be characterized in principle by reflection terahertz time-domain spectroscopy. This quantity takes into account the semiconductor material with a certain layer thickness, doping type, and doping level and is based on numerical simulations. In this work, we calculate this sensitivity value for relevant semiconductor materials (SiC, Si, GaN) in realistic layer stacks with up to three layers. It is used to create meaningful heat maps depending on the thicknesses and charge carrier densities of the sample structures of interest. The plausibility of the sensitivity is validated by mapping a variety of measurements with terahertz techniques from us and from other groups onto these heat maps. Based on these, the accessible range of charge carrier densities for terahertz spectroscopy spans roughly from 10$^{15}$ cm$^{-3}$ to 10$^{20}$ cm$^{-3}$, but with dependencies on material, doping type, and sample thickness. Furthermore, the sensitivity value allows for a substantiated assessment of the possible benefits future improvements of photoconductive antennas and terahertz systems could have, which is demonstrated by simulations based on varied bandwidths.