Electron tunnelling rates as a function of intermolecular distance, measured in a Langmuir-Blodgett assembly

Abstract

Results are presented that demonstrate an exponential dependence of the electron tunnelling rate on interlayer separation. Direct measurements of transient photocurrents with sub-nanosecond resolution have been made on a series of Langmuir-Blodgett multilayer structures assembled from two amphiphilic bis-phthalocyanine molecules. Using either homostructures of the two molecules or a heterodimer structure incorporating both molecules, three tunnelling gaps were attainable. The attempt rate, v 0, as determined by Franck-Condon factors, and the well depth in the three structures was identical for each, being determined by the phthalocyanine ring structure and electron affinity. It is thus possible to relate any change in measured tunnelling rate with the change in barrier width, b. The tunnelling rate, k ⊥, is related to the tunnelling barrier width by: k ⊥=v 0(E)exp( −2√2mA bh b) where A is the well depth (electron affinity of the conjugated rings) and m is an effective mass for the tunnelling carrier. A plot of ln( k ⊥) vs. b reveals a straight line whose gradient is −2 √2mA bh which intercepts the k ⊥ axis at k ⊥ = v 0( E). From the data a value of A = 2.4 eV and v 0 = 7 × 10 16 Hz at an electric field of 2 × 10 8 V m −1 are found. The well depth is in good agreement with expectations. The attempt rate is high but there is a large uncertainty in this value and it is in overall agreement with expectations. v 0 is expected to depend on electric field and this is the subject of a further study.