Hurand Simon, Chommaux Thibault, Renault Pierre-Olivier, Girardeau Thierry, Paumier Fabien
Institut Pprime, UPR 3346 CNRS-Université de Poitiers-ENSMA, 11 Boulevard Marie et Pierre Curie, 86962 Futuroscope-Chasseneuil Cedex, France.
Rev Sci Instrum. 2022 May 1;93(5):053907. doi: 10.1063/5.0068682.
Measurements in a van der Pauw configuration often require the use of complicated mathematical expressions or implicit relations, which may be computer-time-consuming or tedious to implement in a given software. Thus, a closed-form expression is often desirable. We propose to approximate these relations by closed-form analytical functions using only basic operators that can be easily implemented. We present explicitly the functions and the numerical values of their parameters for the cases of standard van der Pauw measurement, anisotropic resistivities, and the probe position correction factor. The discrepancy with the exact values is smaller than 10, which is sufficient for practical purposes.
在范德堡配置中的测量通常需要使用复杂的数学表达式或隐式关系，这在给定软件中实现可能会耗费计算机时间或很繁琐。因此，一个封闭形式的表达式通常是很理想的。我们建议使用仅包含易于实现的基本运算符的封闭形式解析函数来近似这些关系。对于标准范德堡测量、各向异性电阻率和探针位置校正因子的情况，我们明确给出了这些函数及其参数的数值。与精确值的差异小于10，这对于实际应用来说已经足够了。
