A free-space measurement of complex permittivity of doped silicon wafers using transmission coefficient at microwave frequencies

Abstract

A contactless and non-destructive method is presented to characterize p-type and n-type silicon semiconductor wafers using a spot-focused free-space measurement system. In this method, the free-space reflection and transmission coefficients, S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> and S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</inf> , are measured for silicon wafer sandwiched between two teflon plates which are quarter-wavelength at mid-band. The actual reflection and transmission coefficient, S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> and S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</inf> of the silicon wafers are then calculated from the measured S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> and S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</inf> by using ABCD matrix transformation in which the complex permittivity and thickness of the teflon plates are known. Complex permittivity are computed using only the transmission coefficient, S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</inf> . From the complex permittivity, the resistivity and conductivity can be obtained. Results are reported in the frequency range of 9–12.5 GHz. The dielectric constant obtained were close to published values for silicon wafers and the resistivities agree well with that measured by other conventional method.