Comment on "A single level tunneling model for molecular junctions: evaluating the simulation methods" by E. M. Opodi, X. Song, X. Yu and W. Hu, Phys. Chem. Chem. Phys., 2022, , 11958"

Gaining insight into molecular tunnel junctions with a pocket calculator without I-V data fitting. Five-thirds protocol

The protocol put forward in the present paper is an attempt to meet the experimentalists' legitimate desire of reliably and easily extracting microscopic parameters from current-voltage measurements on molecular junctions. It applies to junctions wherein charge transport dominated by a single level (molecular orbital, MO) occurs via off-resonant tunneling. The recipe is simple. The measured current-voltage curve I = I(V) should be recast as a curve of V5/3/I versus V. This curve exhibits two maxima: one at positive bias (V = Vp+), another at negative bias (V = Vp-). The values Vp+ > 0 and Vp- < 0 at the two peaks of the curve for V5/3/I at positive and negative bias and the corresponding values Ip+ = I(Vp+) > 0 and Ip- = I(Vp-) < 0 of the current is all information needed as input. The arithmetic average of Vp+ and |Vp-| in volt provides the value in electronvolt of the MO energy offset ε0 = EMO - EF relative to the electrode Fermi level (|ε0| = e(Vp+ + |Vp-|)/2). The value of the (Stark) strength of the bias-driven MO shift is obtained as γ = (4/5)(Vp+ - |Vp-|)/(Vp+ + |Vp-|) sign (ε0). Even the low-bias conductance estimate, G = (3/8)(Ip+/Vp+ + Ip-/Vp-), can be a preferable alternative to that deduced from fitting the I-V slope in situations of noisy curves at low bias. To demonstrate the reliability and the generality of this "five-thirds" protocol, I illustrate its wide applicability for molecular tunnel junctions fabricated using metallic and nonmetallic electrodes, molecular species possessing localized σ and delocalized π electrons, and various techniques (mechanically controlled break junctions, STM break junctions, conducting probe AFM junctions, and large area junctions).

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.