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

Abstract

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 V^5/3/I versus V. This curve exhibits two maxima: one at positive bias (V = V_p+), another at negative bias (V = V_p−). The values V_p+ > 0 and V_p− < 0 at the two peaks of the curve for V^5/3/I at positive and negative bias and the corresponding values I_p+ = I(V_p+) > 0 and I_p− = I(V_p−) < 0 of the current is all information needed as input. The arithmetic average of V_p+ and |V_p−| in volt provides the value in electronvolt of the MO energy offset ε₀ = E_MO − E_F relative to the electrode Fermi level (|ε₀| = e(V_p+ + |V_p−|)/2). The value of the (Stark) strength of the bias-driven MO shift is obtained as γ = (4/5)(V_p+ − |V_p−|)/(V_p+ + |V_p−|) sign (ε₀). Even the low-bias conductance estimate, G = (3/8)(I_p+/V_p+ + I_p−/V_p−), 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).