Reveil Mardochee, Sorg Victoria C, Cheng Emily R, Ezzyat Taha, Clancy Paulette, Thompson Michael O
Robert F. Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA.
Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853, USA.
Rev Sci Instrum. 2017 Sep;88(9):094704. doi: 10.1063/1.5001830.
This paper presents an extensive collection of calculated correction factors that account for the combined effects of a wide range of non-ideal conditions often encountered in realistic four-point probe and van der Pauw experiments. In this context, "non-ideal conditions" refer to conditions that deviate from the assumptions on sample and probe characteristics made in the development of these two techniques. We examine the combined effects of contact size and sample thickness on van der Pauw measurements. In the four-point probe configuration, we examine the combined effects of varying the sample's lateral dimensions, probe placement, and sample thickness. We derive an analytical expression to calculate correction factors that account, simultaneously, for finite sample size and asymmetric probe placement in four-point probe experiments. We provide experimental validation of the analytical solution via four-point probe measurements on a thin film rectangular sample with arbitrary probe placement. The finite sample size effect is very significant in four-point probe measurements (especially for a narrow sample) and asymmetric probe placement only worsens such effects. The contribution of conduction in multilayer samples is also studied and found to be substantial; hence, we provide a map of the necessary correction factors. This library of correction factors will enable the design of resistivity measurements with improved accuracy and reproducibility over a wide range of experimental conditions.
本文展示了大量计算得到的校正因子，这些因子考虑了在实际四点探针和范德堡实验中经常遇到的各种非理想条件的综合影响。在此背景下，“非理想条件”是指偏离这两种技术发展过程中对样品和探针特性所做假设的条件。我们研究了接触尺寸和样品厚度对范德堡测量的综合影响。在四点探针配置中，我们研究了改变样品横向尺寸、探针位置和样品厚度的综合影响。我们推导了一个解析表达式，用于计算在四点探针实验中同时考虑有限样品尺寸和不对称探针位置的校正因子。我们通过在具有任意探针位置的薄膜矩形样品上进行四点探针测量，对该解析解进行了实验验证。有限样品尺寸效应在四点探针测量中非常显著（特别是对于窄样品），不对称探针位置只会加剧这种效应。我们还研究了多层样品中的传导贡献，发现其贡献很大；因此，我们提供了所需校正因子的图谱。这个校正因子库将有助于在广泛的实验条件下设计出具有更高准确性和可重复性的电阻率测量。
