Sheet Resistance Determination Using Symmetric Structures With Contacts of Finite Size

Abstract

This paper proposes an extension of van der Pauw's celebrated method for the extraction of the sheet resistance R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sq</sub> of planar homogeneously conducting samples with four point-like contacts to symmetric samples with contacts of finite length. Using the method, R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sq</sub> can be extracted, e.g., from symmetric integrated Hall plates and stress sensors, without having to resort to dedicated van der Pauw structures. First, the analog of van der Pauw's formula for arbitrarily shaped samples with four extended contacts separated by point-like insulations is derived. Based on this and van der Pauw's original result, an interpolation formula applicable to symmetric samples with contacts of arbitrary length is constructed. The new formalism was successfully put to the test using ten widely differing CMOS sensor structures, with contacts covering between 10.1% and 91.3% of the device periphery. The extracted R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sq</sub> values lie within the range specified by the CMOS foundry used for the fabrication of the samples and show a relative standard deviation of 1.04%.