How to Extract the Sheet Resistance and Hall Mobility From Arbitrarily Shaped Planar Four-Terminal Devices With Extended Contacts

摘要

Van der Pauw's method enables the sheet resistance $R_{rm sq}$ and the Hall mobility $mu_{rm H}$ to be extracted from arbitrarily shaped simply connected planar samples with four peripheral pointlike contacts. This paper generalizes the method for devices with extended contacts. It is found that $R_{ rm sq}$ and $mu_{rm H}$ can be extracted using only six resistance measurements in the absence of a magnetic field and a single magnetic sensitivity measurement. Conversely, if the $mu_{rm H}$ of a simply connected planar conducting device with peripheral contacts is known, the magnetic sensitivity of the device can be predicted based on six resistance measurements in the absence of a magnetic field, without any further knowledge of the device geometry. The new method is applied to a variety of differently shaped diffused silicon $n$-wells with peripheral contacts. The extracted sheet resistance and Hall mobility values show excellent consistency and are in agreement with the fabrication specifications.