Can room temperature data for tunneling molecular junctions be analyzed within a theoretical framework assuming zero temperature?

TL;DR

This work assesses whether zero-temperature theoretical models can accurately describe room-temperature tunneling molecular junctions by analyzing thermal effects on conductance and current across various parameters.

Contribution

It quantifies the impact of temperature on transport properties within the single level Lorentzian model, providing criteria for applying zero-temperature formulas to real experimental data.

Findings

Thermal effects are most significant at biases below resonance.

The temperature influence extends over an energy range about nine times thermal energy.

Mathematical inequalities are derived to determine the applicability of zero-temperature approximations.

Abstract

Routinely, experiments on tunneling molecular junctions report values of conductances ($G_{RT}$) and currents ($I_{RT}$) measured at room temperature. On the other side, theoretical approaches based on simplified models provide analytic formulas for the conductance ($G_{0K}$) and current ($I_{0K}$) valid at zero temperature. Therefore, interrogating the applicability of the theoretical results deduced in the zero temperature limit to real experimental situations at room temperature i.e., $G_{RT} \approx G_{0K}$ and $I_{RT} \approx I_{0K}$) is a relevant aspect. Quantifying the pertaining temperature impact on the transport properties computed within the ubiquitous single level model with Lorentzian transmission is the specific aim of the present work. Comprehensive results are presented for broad ranges of the relevant parameters (level's energy offset $\varepsilon_0$ and width $\Gamma_a $, and applied bias $V$) that safely cover values characterizing currently fabricated junctions. They demonstrate that the strongest thermal effects occur at biases below resonance ($2 \left\vert \varepsilon_0 \right\vert - \delta\varepsilon_0 \alt \vert e V\vert \alt 2 \left\vert \varepsilon_0 \right\vert$). At fixed $V$, they affect an $\varepsilon_0$-range whose largest width $\delta\varepsilon_0 $ is about nine times larger than the thermal energy ($\delta\varepsilon_0 \approx 3 \pi k_B T$) at $\Gamma_a \to 0$. The numerous figures included aim at conveying a quick overview on the applicability of the zero temperature limit to a specific real junction. In quantitative terms, the conditions of applicability are expressed as mathematical inequalities involving elementary functions. They constitute the basis of an interactive data fitting procedure proposed, which aims at guiding experimentalists interested in data processing in a specific case.