Exact analytic expressions are derived for the voltage distribution and current pattern for four-terminal resistance measurements on rectangular samples with corner contacts. The treatment in terms of complex functions exploits the double periodicity of the virtual mirror charge array to identify the appropriate expressions, practically without any algebra, using Jacobi elliptic functions. As shown in a worked example, the procedure can easily be extended to off-diagonal (Hall) and anisotropic resistivity tensors.
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This holds if the crystal structure is orthorhombic and the sample edges are aligned with the twofold axes (see Ref. 6). It also holds if the crystal is monoclinic and either the twofold axis is aligned with one in-plane sample edge or the mirror plane is both perpendicular to the sample plane and aligned with one sample edge; for a general discussion see
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2005
American Institute of Physics
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