Accuracy considerations for dielectric measurements of semiconductor wafers using free space microwave measurement system in 8-13 GHz range

An algorithm using only transmission measurements to calculate the complex permittivity of p-type and n-type silicon semiconductor wafers using a spot-focused free-space measurement system was developed. The dielectric constant obtained was close to published values for silicon wafers. The errors associated with the measurement of the complex permittivity values are discussed, and comparisons between the measured and calculated magnitude and phase of the forward reflection and transmission coefficients are presented. In this method, the free-space reflection and transmission coefficients, S₁₁ and S₂₁, are measured for a silicon wafer sandwiched between two teflon plates which are quarter-wavelength at midband. The actual reflection and transmission coefficient, S₁₁ and S₂₁ of the silicon wafers are then calculated from the measured S₁₁ and S₂₁ by using ABCD matrix transformation in which the complex permittivity and thickness of the teflon plates are known. Results are reported in the frequency range of 8-12.5 GHz.