Multilayer Thickness Measurements below the Rayleigh Limit Using FMCW Millimeter and Terahertz Waves

We present thickness measurements with millimeter and terahertz waves using frequency-modulated continuous-wave (FMCW) sensors. In contrast to terahertz time-domain spectroscopy (TDS), our FMCW systems provide a higher penetration depth and measurement rates of several kilohertz at frequency modulation bandwidths of up to 175 GHz. In order to resolve thicknesses below the Rayleigh resolution limit given by the modulation bandwidth, we employed a model-based signal processing technique. Within this contribution, we analyzed the influence of multiple reflections adapting a modified transfer matrix method. Based on a brute force optimization, we processed the models and compared them with the measured signal in parallel on a graphics processing unit, which allows fast calculations in less than 1 s. TDS measurements were used for the validation of our results on industrial samples. Finally, we present results obtained with reduced frequency modulation bandwidths, opening the window to future miniaturization based on monolithic microwave integrated circuit (MMIC) radar units.