Terahertz spectroscopy -- Algorithms, Terahertz technology, Semiconductor wafers -- Testing, Time-domain analysis
Terahertz Time Domain Spectroscopy(THz TDS) is a spectroscopic technique that can be implemented to perform non destructive material parameter extraction on a variety of materials. Accuracy of these material parameters is often limited by statistical variation between measurements and insufficient knowledge of the thickness of the slabs being measured.
The goal of this project was to develop an in house procedure that would allow us to perform THz TDS on thin wafers using an up to date signal processing algorithm that would provide accurate predictions for the thickness of the wafers, reliable estimations of the wafer’s material parameters, and demonstration of a moving average filter that considers boundaries established by the inherent noise of the measurement system.
The procedure begins with time domain measurements performed in a dry air environment. The transmitter emits a picosecond pulse of radiation in a collimated beam that is transmitted through the wafer and detected by the system’s receiving antenna, which we then define as our sample signal. The same measurement is also performed in absence of the wafer, which we define as our reference signal.
We then examine the predicted optical behavior of our experimental setup in the frequency domain to establish a mathematical model that we can then use to determine the complex index of refraction of our wafer, nsample. We use a numerical solver to find the values of nsample for an array of possible wafer thicknesses. The thickness that results in the smoothest curve for nsample indicates where our model transfer function best matches our measured results, so we proceed by assuming this value to be the correct thickness.
We then apply a spatially variable moving average filter to smooth the plots of nsample within the parameters allowed by the statistical variation between a given set of measurements.
After applying the extraction algorithm, we were able to obtain frequency dependent values for nsample that agreed well with the expected values for the silicon wafers we measured. With our values for nsample, we are able to compute additional material parameters such as complex permittivity, conductivity, and absorption coefficient. Testing wafers of differing material composition is suggested as future work to verify the algorithm’s versatility.
Jungles, Kirk R., "Material Parameter Estimation of Thin Wafers with Terahertz Time-Domain Spectroscopy" (2019). Undergraduate Research & Mentoring Program. 38.