If you have undoped GaAs it might be possible to estimate the permittivity from Cole models using knowledge of conductivity from the carrier transport phenomena and real part of the permittivity from crystal polarisability of the unit cell of the lattice. It might also be worth speaking with those who model the complex transport phenomena in the semiconductors. Good luck, Neil

James:

I am not expert in this field but I am providing you the following paper. See Figure 7 of this paper. If you are wanting pure semi-insulating Ga As substrate permittivity, it is hard to locate corresponding research findings. This paper has films grown on semi-insulating GaAs and extraction of Figure 7 might not be the 100% permittivity values of semi-insulating GaAs substrate beneath the thin film but at least it is in THz and the profile shape of the permittivity should be familiar to you.

I generally request the questioner to recommend my answer if it helps his work. Your question is really difficult to fit with relevant research material but if you feel the paper is still useful, please recommend my answer.

Sincerely,

Dr. Nabil Shovon Ashraf.

In the 0.1 to 4 THz range, semi-insulating GaAs is slightly dispersive. It has a refractive index of approximately n = 3.6 to 3.7 as measured using a THz-TDS. So, permittivity calculated as epsilon_r = n^2 would be approximately 13.

Please see the following paper for more details:

Article Far-infrared time-domain spectroscopy with terahertz beams o...

The permitivity can be calculated from transmission. The transmission for SI-GaAs is about 60% for frequency ranging from 0-3 THz. It goes to small values for 3-30 THz and is again about 60% for 30-300 THz. http://www.tydexoptics.com/materials1/for_transmission_optics/gaas/

There is a region of strong absorption between 7.5 THz to 10 THz.

Article Infrared dielectric constant of gallium arsenide

Model prediction for few semiconductors can be found here.

https://refractiveindex.info/?shelf=main&book=InAs&page=Aspnes