Statistical Tools for Analyzing Measurements of Charge Transport

Abstract

This paper applies statistical methods to analyze the large, noisy datasets produced in measurements of tunneling current density (J) through self-assembled monolayers (SAMs) in large-area junctions. It describes and compares the accuracy and precision of procedures for summarizing data for individual SAMs, for comparing two or more SAMs, and for determining the parameters of the Simmons model (β and J 0). For data that contain significant numbers of outliers (i.e. most measurements of charge transport), commonly used statistical techniques-e.g. summarizing data with arithmetic mean and standard deviation, and fitting data using a linear, least-squares algorithm-are prone to large errors. The paper recommends statistical methods that distinguish between real data and artifacts, subject to the assumption that real data (J) are independent and log-normally distributed. Selecting a precise and accurate (conditional on these assumptions) method yields updated values of β and J 0 for charge transport across both odd and even n-alkanethiols (with 99% confidence intervals), and explains that the socalled odd-even effect (for n-alkanethiols on Ag) is largely due to a difference in J 0 between odd and even n-alkanethiols. This conclusion is provisional, in that it depends to some extent on the statistical model assumed, and these assumptions must be tested by future experiments.

Replacing −CH2CH2– with −CONH– Does Not Significantly Change Rates of Charge Transport through AgTS-SAM//Ga2O3/EGaIn Junctions

“…To these histograms, we fitted Gaussian curves using a non-weighting algorithm to avoid biasing the data due to outliers. 69 Statistical Analysis of log(|J|) Rather than J: As noted previously by us 22,23 and others, 43,66,67,86 J is log-normally distributed, rather than normally distributed -that is, log(|J|) is (approximately) normally distributed. We chose, therefore, to plot and fit histograms of log(|J|), rather than J.…”

“…69 We collected data generated by multiple users, to avoid a singleuser bias in the results. We pooled all non-shorting (working junctions only) data from different users, and summarized the pooled data as histograms.…”

“…20,23,34,42,[57][58][59][60][61][62][63][64] We 19,21-23 and others [66][67][68] have previously reported that J through SAMs of nalkanethiols is approximately log-normally distributed (albeit often with long, asymmetrical tails and significant outliers), rather than normally distributed, and have suggested that variations from junction to junction in thickness and in the number or type of defects in the SAM and electrodes would lead to a normal distribution in the effective thickness, d, of the SAM. 19,[21][22][23]66,69 Since J is exponentially dependent on a normally distributed parameter (eq. 1), J itself should be log-normally distributed.…”

Controlling the direction of rectification in a molecular diode

“…For each junction, we recorded 24 scans (0 V-À 1.0 V-1.0 V and back to 0 V) with a 50-mV step and 0.2-s delay. We collected more than 500 traces for each type of SAM (see Supplementary Table 2), and we calculated log |J| and logR using previously reported methods 55 . Supplementary Figure 4 shows that the log-average J(V) curves and the error bars represent the one log-standard deviations.…”

Influence of Environment on the Measurement of Rates of Charge Transport across AgTS/SAM//Ga2O3/EGaIn Junctions

“…For example, measurements of current density (J(V), A/cm 2 − J at an applied bias V) are consistent and reproducible across samples and users; the distribution of data (log standard deviation, σ log ) ranges from ∼0.2 to ∼0.5 (from experiments replicated by multiple users) 18 for n-alkanethiolates on Ag TS or Au TS and ∼0.1−0.2 for n-alkanecarboxylates 3 on Ag TS (probably supported on a thin AgO X surface film) in air (a value of σ log ∼0.3 corresponds to a range from 0.5× to 2.0× of the mean).…”