Accessibility of doping ranges of semiconductors by terahertz spectroscopy

Abstract

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.

Figures (5)

• Figure 1: Schematic of the simulation steps to calculate the sensitivity. First, an IR fs-laser pulse (red) is calculated, triggering a THz-pulse to be emitted from a photoconductive antenna (purple). After calculation of the propagation in the frequency domain (green), the material interaction is simulated (blue); here, $N$ of one layer of the sample is varied systematically leading to a series of spectra (green). Between the spectra of neighboring $N$ the sensitivity is calculated. The same is repeated for various thicknesses leading to a $d$-$N$-heat map with the colorbar representing the sensitivity of terahertz measurements.
• Figure 2: Sensitivity heat map (center) for 3-layer SiC samples simulated with the methods described in Fig. \ref{['fig:1_Schematic_Simulation']}. Further explanatory graphs show the attenuation coefficient (a) and the reflectance (b) for SiC as a function of the charge carrier density for the relevant terahertz frequencies. The ranges of $N$, which they each influence the sensitivity dominantly in, are marked above the heat map. In (c) - (f) corresponding spectra and waveforms for the respectively marked $d$- and $N$-values in the heat map are plotted, exemplarily showing the impact of an increasing attenuation and reflectance.
• Figure 3: Sensitivity heat map for 3-layer n-type SiC samples with logarithmic $d$-axis and colorbar. Further, the lines of noise devided by the sensitivity value equaling 1, 5, and 10 are sketched and samples measured in peer-reviewed papers as well as ones, which a model-based characterization failed for, are plotted.
• Figure 4: Sensitivity heat maps for (a) 1-layer n-type Si and (b) 2-layer n-type GaN on top of sapphire, both with samples plotted, which were measured in peer-reviewed publications with terahertz spectroscopy techniques.
• Figure 5: Sensitivity heat maps based on simulations of terahertz pulses with varied bandwidths, roughly (a) 2 THz, (b) 4 THz, and (c) 7 THz. The insets show the respectively used terahertz spectra of the incoming terahertz pulse used for each simulation.