Single‐Molecule Dynamic Triangulation

Abstract

A proposal for using single molecules as nanoprobes capable of detecting the trajectory of an elementary charge is discussed in detail. Presented numerical simulations prove that this single-molecule technique allows determination of a three-dimensional single-electron displacement within a few seconds with an accuracy better than 0.006 nm. Surprisingly, this significantly exceeds the accuracy with which the probe molecule itself can be localized (given the same measuring time) by means of single-molecule microscopy. It is also shown that the optimal concentration of probe molecules in the vicinity of the electron (i.e. the concentration which provides the best accuracy of the inferred electron displacement) is of the order of 10(-5) m.

Sensing single electrons with single molecules

“…[8] it is estimated that the values of s dn ¼ 0:05 MHz, s d ¼ 0:5 nm, s m =m ¼ 1% are optimistic but achievable within several seconds of data accumulation. Given a % À3 Â 10 6 MHz nm 2 D À1 , m ¼ 1D, and s ¼ 0:1 nm, a prediction of s s =s % 2% follows from Eq.…”

“…1. For this case a set equations (1) can be solved analytically [8]. The accuracy of triangulation will be characterized by a standard deviation s s of the electron location and will depend on the data inaccuracies s d , s m , s dn according to the error propagation formulae [8] …”

Optical tracing of multiple charges in single-electron devices

“…Considering this gigantic sensitivity and the small size of these molecules, Caruge and Orrit have suggested to detect electronic currents in semiconductors using organic molecules as nanoprobes [17]. Later, Plakhotnik has shown that subnanometer displacement of a single electron in a dielectric medium can be detected by simultaneously looking at the line shifts of multiple molecular probes [18,19]. Here, we will use a typical electron-in-a-box model and the Fermi golden rule for spontaneous emission to identify the origin of this sensitivity and routes to its optimization.…”

“…This triangulation method and its accuracy have been previously discussed in the context of studying charge transfer in a chemical bond [18]. In that work, an optimal localization precision of about 10 pm has been suggested based on Monte Carlo simulations.…”

Anthracene-Based Organic Field-Effect Transistor: Temperature Dependence of the Current-Voltage Characteristics

“…In a former publication [11], we proposed to study charge transport by means of single-molecule spectroscopy and microscopy at cryogenic temperatures as this technique could ultimately allow us to optically probe displacements of individual charges with a very high accuracy [12]. High-resolution single-molecule spectroscopy in crystalline matrixes requires a ''good'' fluorescent guest (with both a large absorption cross section and a high fluorescence yield) and a good insertion of the guest into the host lattice, giving rise to a strong and narrow zerophonon line.…”