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Evaluation of uncertainties in femtoampere current measurement for the number concentration standard of aerosol nanoparticles

We evaluated uncertainties in current measurement by the electrometer at the current level on the order of femtoamperes. The electrometer was the one used in the Faraday-cup aerosol electrometer of the Japanese national standard for number concentration of aerosol nanoparticles in which the accuracy of the absolute current is not required, but the net current which is obtained as the difference in currents under two different conditions must be measured accurately. The evaluation was done experimentally at the current level of 20 fA, which was much smaller than the intervals between the electrometer's calibration points at +1, +0.5, −0.5 and −1 pA. The slope of the response curve for the relationship between the ‘true’ and measured current, which is crucial in the above measurement, was evaluated locally at many different points within the ±1 pA range for deviation from the slope determined by a linear regression of the calibration data. The sum of the current induced by a flow of charged particles and a bias current from a current-source instrument was measured by the electrometer while the particle current was toggled on and off. The net particle current was obtained as the difference in the measured currents between the toggling, while at the same time the current was estimated from the particle concentration read by a condensation particle counter. The local slope was calculated as the ratio of the measured to estimated currents at each bias current setting. The standard deviation of the local slope values observed at varied bias currents was about 0.003, which was calculated by analysis of variance (ANOVA) for the treatment of the bias current. The combined standard uncertainty of the slope, which was calculated from the uncertainty of the slope by linear regression and the variability of the slope, was calculated to be about 0.004.