Various quantum mechanical formulations have been used for the modeling of the carrier transport in semiconductor devices. During the 1980s advances in the semiconductor technology made it possible to fabricate conductors so small that the quantum nature of electrons could be directly observed in transport experiments. The typical systems used for these studies include quantum dots  and quantum point contacts , which are formed by manipulating the electrostatic potential in a two-dimensional electron gas by means of gate electrodes. The size of these semiconductor structures is of the order of 1ìm, which characterizes them as mesoscopic systems intermediate between the microscopic and macroscopic scale. Several important discoveries such as the quantum Hall effect and the quantization of conductance are all results of the intense study of electron transport in the mesoscopic regime [3, 4]. In this chapter a general method for describing quantum electron transport will be introduced. These formulations are based either on the Schrödinger equation [5-8], the Pauli master equation [9, 10], the density matrix , the Wigner function [12-14], or the Green function [15, 16]. Among these approaches, the NEGF formalism was first introduced by Keldysh , Kadanoff and Baym  to solve the nonequilibrium problems in statistical physics, which is based on the contour-ordered Green function formalism first introduced by Martin and Schwinger . The method is based on the non-equilibrium Green’s function was originally used to study transport in mesoscopic systems. In this chapter, we describe the microscopic quantum theory of electron transport in silicon devices based on the NEGF formalism. We review the NEGF formalism and derive its key equations. We use the effective mass approximation, and consider the steady-state condition, neglecting the transient effects. Also, we include the electron-phonon interactions and other scattering mechanisms such as the impurity scattering and the surface roughness scattering. For the electron-electron interactions, we used the assumption that each electron moves independently and sees only the average field generated by all the other electrons, where the average field is obtained from the self-consistent solution of the Poisson equation. This paper is organized as follows. In section 2.2, we start with an introduction of three important length scales which are used characterize electron ransport in the quantum regime. In section 2.3, we describe the Hamiltonian of the system and introduction to green function. Section 2.4, includes green function and study of properties of kinetic equations. The electron-phonon nteractions, other scattering mechanisms (including surface roughness scattering) will be included in section 2.5. A simple silicon nano film and 2D double gate MOSFET example will be discussed in section 2.6. In section 2.7, we conclude this chapter. A brief introduction to single-particle Green’s functions is given in Appendix A.
Journal: TechConnect Briefs
Volume: 1, Nanotechnology 2008: Materials, Fabrication, Particles, and Characterization – Technical Proceedings of the 2008 NSTI Nanotechnology Conference and Trade Show, Volume 1
Published: June 1, 2008
Pages: 292 - 296
Industry sector: Advanced Materials & Manufacturing
Topics: Composite Materials