Theoretical study of characteristics of a molecular single-electron transistor V.V. Shorokhov, E.S. Soldatov * , O.V. Snigirev Department of Atomic Physics, Faculty of Physics, M.V. Lomonosov Moscow State University, 119992, Moscow, Russia Available online 11 August 2004 Abstract A technique for the calculation of current-to-voltage curves and control curves of a molecular single-electron transistor with a discrete energy spectrum has been developed. The effective recursive methods for quick computation of the Gibbs canonical distribution of electrons between energy levels, as well as techniques for the fast calculation of the distribution function for a slow relaxation process have been found. Characteristics of the single-electron transistor in the cases of different types of molecule’s energy spectrum, fast and slow energy relaxations have been compared. D 2004 Published by Elsevier B.V. Keywords: Molecular single-electron transistor; Energy spectrum; Energy relaxations 1. Introduction A rapid progress in the fabrication and study of single- electron devices based on quantum objects (small grains, dots, molecules) with the operating temperature close to 300 K calls for an adequate theoretical description of the fundamental properties of such single-electron devices. All the known approaches to consider the electron tunnel transport in the system can be conditionally divided into two classes. The first method is based on the statistical theory. This approach was previously described in Refs. [1,2] for systems based on small metallic granules and quantum dots. The second approach is to calculate the charge transport by the microscopic self-consistent [3] and quantum chemistry methods. A detailed review of these methods can be found in Ref. [4]. Both the techniques supplement each other to create a full picture of electron transport in the devices based on single molecules. The basic aim of this work is to develop a technique for the calculation of the I – V curves and control curves of a molecular single-electron transistor with a discrete energy spectrum. To provide analytical expressions for the I – V curves and control curves, we treat the molecular single- electron transistor as a system with a discrete energy spectrum containing an arbitrary number of non-degenerated energy levels. We found analytical solutions of kinetic equations in limiting cases of the fast and slow electron energy relaxation. A discreteness of the electron energy spectrum and the energy relaxation are taken in account by using the charge distribu- tion function and energy distribution functions for the elec- trons at the base of the single-electron molecular transistor. Fast relaxation processes were analyzed using the Gibbs canonical distribution, whereas for slow relaxation, we as- sumed non-interacting electrons in the system. 2. Main equations We consider a system which consists of three planar electrodes (tunneling electrodes and a gate) on the dielectric substrate with a molecule between them. This molecule can be a cluster molecule with a metallic core and an organic shell (the number of atoms is a few dozen) and is considered as a molecular part of the system. Examples of such molecules can be found in Ref. [6]. We assume that electrons in the system transfer from electrodes to molecule and back only by tunneling. We also suppose that conditions for the thermal energy, k B T , and the resonant width, hC, in comparison to Coulomb energy, e 2 / 0040-6090/$ - see front matter D 2004 Published by Elsevier B.V. doi:10.1016/j.tsf.2004.06.070 * Corresponding author. E-mail address: esold@cryop73.phys.msu.su (E.S. Soldatov). www.elsevier.com/locate/tsf Thin Solid Films 464 – 465 (2004) 445 – 451