Comparison of Multiple Methods for Obtaining P$\Omega$ Resistances With Low Uncertainties

Abstract

Capabilities for high resistance determinations are essential for calibration of currents below 1 pA, as typically requested in several applications, including semiconductor device characterization, single electron transport, and ion beam technologies. This need to calibrate low currents warrants the expansion of accessible values of high resistance. We present several methods for measuring resistances on the PΩ scale, namely potentiometry, dual source bridge measurements, and teraohmmeter usage, all of which are subsequently compared to theoretical calculations. These methods were used to measure four 1 PΩ resistances, one 10 PΩ resistance, and one 100 PΩ resistance, all generated by wye-delta networks containing three resistance elements. The differences between the experimentally obtained values and the theoretical values typically agree within 1 % for 1 PΩ, 10 PΩ and 100 PΩ resistances and the measurement uncertainties for the three techniques were estimated to be between 0.4 % to 4.8 % for 1 PΩ, 2.8 % to 5.6 % for 10 PΩ, and 4.4 % to 10.2 % for 100 PΩ.