Theory of electronic transport in semiconductor nanostructures
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Theory of electronic transport in semiconductor nanostructures. Y.M. Niquet, C. Delerue, G. Allan, and M. Lannoo1, Institut d’Electronique et de Microélectronique du Nord, Département ISEN, Boîte Postale 69, F-59652 Villeneuve d’Ascq Cedex, France. 1 L2MP, Marseille, France. ABSTRACT We review the orthodox theory of single charge tunneling in a semiconductor quantum dot and we extend it to treat both single electron and hole charging effects. We analyze recent tunneling spectroscopy experiments. We show that for sufficiently large bias voltages V, both electrons and holes can tunnel into the quantum dot, leading to specific features in the I(V) curve. We present detailed simulations of the I(V) curves based a tight binding method for the electronic structure. A very good agreement is obtained with available experiments on InAs nanocrystals, allowing a complete interpretation of the spectra. Finally, we make some predictions concerning Si nanocrystals. INTRODUCTION Progress made in the growth of semiconductor quantum dots (QD) opens the door to exciting studies of artificial atoms where the electrons are confined in the three directions of space. These studies reveal rich optical and transport properties. If optical spectroscopy probes transitions between valence states and conduction states, transport measurements, on the other hand, can probe separately the discrete states in the bands. Moreover, the charging energy of semiconductor nanocrystals may be large due to the dielectric mismatch with the surrounding medium. Single charge effects can be observed in tunneling spectroscopy experiments and can be used in single-electron devices such as single electron transistors and memories. Recent experiments based on tunneling spectroscopy have been made on semiconductor nanocrystals [1,2] and on submicron quantum dots obtained by semiconductor heterostructures engineering [3,4]. In these systems, both the effects of quantum confinement and Coulomb interaction become strong. The analysis of tunneling spectroscopy experiments usually relies on the so-called Orthodox theory of single charge tunneling [5], which was first applied to metallic tunnel junctions, then to semiconductor quantum dots [6]. In this paper, we extend this theory to include simultaneously the transport of electrons and holes. A tightbinding calculation of the electronic structure is presented, applicable to quantum dots of realistic size (up to 8 nm diameter). We show in the case of InAs that it allows a complete interpretation of the experimental spectra. We obtain that simultaneous electron and hole tunneling occurs in some parts of the I(V) characteristics. Finally, we present results on Si quantum dots. DESCRIPTION OF THE MODEL In this section, we extend the theory of single charge tunneling of D. V. Averin et al. [6] to the transport of both electrons and holes in a semiconductor quantum dot. We consider the double barrier tunnel junction schematically shown in Fig. 1. It consists of two metallic electrodes E1 and E2 (STM tip, substrate, breaking j
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