Are Asymmetric SAM‐Induced Work Function Modifications Relevant for Real Molecular Rectifiers?

Can tunneling current in molecular junctions be so strongly temperature dependent to challenge a hopping mechanism? Analytical formulas answer this question and provide important insight into large area junctions

Analytical equations like Richardson-Dushman's or Shockley's provided a general, if simplified conceptual background, which was widely accepted in conventional electronics and made a fundamental contribution to advances in the field. In the attempt to develop a (highly desirable, but so far missing) counterpart for molecular electronics, in this work, we deduce a general analytical formula for the tunneling current through molecular junctions mediated by a single level that is valid for any bias voltage and temperature. Starting from this expression, which is exact and obviates cumbersome numerical integration, in the low and high temperature limits we also provide analytical formulas expressing the current in terms of elementary functions. They are accurate for broad model parameter ranges relevant for real molecular junctions. Within this theoretical framework we show that: (i) by varying the temperature, the tunneling current can vary by several orders of magnitude, thus debunking the myth that a strong temperature dependence of the current is evidence for a hopping mechanism, (ii) real molecular junctions can undergo a gradual (Sommerfeld-Arrhenius) transition from a weakly temperature dependent to a strongly ("exponential") temperature dependent current that can be tuned by the applied bias, and (iii) important insight into large area molecular junctions with eutectic gallium indium alloy (EGaIn) top electrodes can be gained. E.g., merely based on transport data, we estimate that the current carrying molecules represent only a fraction of f ≈ 4 × 10-4 out of the total number of molecules in a large area Au-S-(CH2)13-CH3/EGaIn junction.

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

Routinely, experiments on tunneling molecular junctions report values of conductances (G_RT) and currents (I_RT) measured at room temperature. On the other hand, 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 ≈ G_0K and I_RT ≈ 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 ε₀ and width Γ_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|ε₀| - δε₀ - 0.3 ≲ |eV| - 0.3 ≲ 2|ε₀|). At fixed V, they affect an ε₀-range whose largest width δε₀ is about nine times larger than the thermal energy (δε₀ ≈ 3πk_BT) at Γ_a → 0. The numerous figures included aim to convey 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 a proposed interactive data-fitting procedure, which aims to guide experimentalists interested in data processing in a specific case.

Nanoscale molecular rectifiers

The use of molecules bridged between two electrodes as a stable rectifier is an important goal in molecular electronics. Until recently, however, and despite extensive experimental and theoretical work, many aspects of our fundamental understanding and practical challenges have remained unresolved and prevented the realization of such devices. Recent advances in custom-designed molecular systems with rectification ratios exceeding 10⁵ have now made these systems potentially competitive with existing silicon-based devices. Here, we provide an overview and critical analysis of recent progress in molecular rectification within single molecules, self-assembled monolayers, molecular multilayers, heterostructures, and metal-organic frameworks and coordination polymers. Examples of conceptually important and best-performing systems are discussed, alongside their rectification mechanisms. We present an outlook for the field, as well as prospects for the commercialization of molecular rectifiers.