Reproducibility of Nano- and Micro-Scale Multi-Point Probe Sheet Resistance Measurements
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Reproducibility of Nano- and Micro-Scale Multi-Point Probe Sheet Resistance Measurements Christian L. Petersen, Capres A/S, Vancouver, BC, Canada Daniel Worledge, IBM, Yorktown Heights, NY, U.S.A. Peter R. E. Petersen, Capres A/S, Lyngby, Denmark ABSTRACT We have investigated the reproducibility of micro- and nano-scale measurements of sheet resistance performed with micro-fabricated multi-point probes. The probes consisted of Au coated SiO2 cantilevers extending from a Si base. The measurements were done with a four-point probe technique on thin Au films, the probe electrode spacing ranging from 18 µm to 1.5 µm. We find that the standard deviation of repeated sheet resistance measurements ranges from 0.2% at 18 µm spacing to 2.6% at 1.5 µm spacing. It is inversely proportional to the probe electrode spacing. This behaviour is expected if the resolution of the measurements is governed by the positional errors of the probe electrode tips. The corresponding standard deviation of the probe tip positions (in both lateral directions) is calculated to be approximately 20 nm. We argue that these positional errors depend on the probe cantilever amplitude at the time of contacting the surface. The amplitude is inversely proportional to the square root of the cantilever spring constant, indicating that stiff cantilevers give the best reproducibility. We estimate the limiting reproducibility of multi-point probes with nano-scale electrode spacing. INTRODUCTION Advances in materials science lead to an increasing need for micro and sub-micron resolution metrology tools. The present paper discusses measurements performed with a new microscopic probe that enables direct measurement of lateral electrical transport in surfaces and thin films. This probe is a microscopic multi-electrode device, operated as a four-point probe [1]. Similar probes have previously been used to measure lateral transport on clean silicon surfaces [2,3]. A four point probe measurement is performed by making four electrical contacts to a sample surface, using a current source to send a set current, I, through two of the contact electrodes, while measuring the resulting voltage, V, across the other two with an electrometer [1]. This is shown schematically in figure 1. The resulting four-point resistance, R=V/I, is related to the sheet resistance, Rsq, of the sample through: Rsq=cV/I, where c is a correction factor that depends on the geometry of the probe and the sample [1]. In the case of an infinite sheet sample (sample thickness
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