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 $\text{P}\Omega $ scale, namely potentiometry, dual-source bridge measurements, and teraohmmeter (TM) usage, all of which are subsequently compared to theoretical calculations. These methods were used to measure four 1- $\text{P}\Omega $ resistances, one 10- $\text{P}\Omega $ resistance, and one 100- $\text{P}\Omega $ resistance, all generated by wye-delta (Y- $\Delta $ ) networks containing three resistance elements. The differences between the experimentally obtained values and the theoretical values typically agree within 1% for 1-, 10-, and 100- $\text{P}\Omega $ resistances and the measurement uncertainties for the three techniques were estimated to be between 0.4%–4.8% for 1 $\text{P}\Omega $ , 2.8%–5.6% for 10 $\text{P}\Omega $ , and 4.4%–10.2% for 100 $\text{P}\Omega $ .

中文翻译：

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获得低不确定度Ω电阻的多种方法的比较

高电阻测定能力对于校准低于 1 pA 的电流至关重要，这在多种应用中通常需要，包括半导体器件表征、单电子传输和离子束技术。这种校准低电流的需要保证了可访问的高电阻值的扩展。我们提出了几种测量电阻的方法 $\text{P}\Omega $ 标度，即电位计、双源电桥测量和太欧姆计 (TM) 使用，所有这些随后都会与理论计算进行比较。这些方法用于测量四个 1- $\text{P}\Omega $ 电阻，一个 10- $\text{P}\Omega $ 阻力，和一个 100- $\text{P}\Omega $ 电阻，全部由星形-三角形（Y- $\Delta $ ) 包含三个电阻元件的网络。对于 1-、10- 和 100-，实验获得的值与理论值之间的差异通常在 1% 以内 $\text{P}\Omega $ 三种技术的电阻和测量不确定度估计在 0.4%–4.8% 之间，对于 1 $\text{P}\Omega $ , 2.8%–5.6% 为 10 $\text{P}\Omega $ , 4.4%–10.2% 为 100 $\text{P}\Omega $ .