chapter  8

Quantum Transport Simulations of Nano-systems

An Introduction to the Green’s Function Approach
WithAndrea Droghetti, Ivan Rungger

Charge transport properties of materials (in particular metals) at the macro- and microscale are well described according to the Drude model (see, e.g., Chapter 1 in Ref. [2]). The model assumes that electrons in a solid can be treated much like classical particles in a pinball machine instantaneously bouncing off each other, the crystal ions and other degrees of freedom such as the lattice vibrations. In modern days, the Drude model is recovered from the semi-classical Boltzmann equation which treats electrons as particles having an effective mass m* determined by the material band structure (as well as interactions) and undergoing random quantum scattering (see, e.g., Chapter 17 in Ref. [28]). The most significant result of the Drude model is that it explains the empirical Ohm’s law and it relates the conductivity to the mean-free path between scattering events l. The success of the semi-classical picture relies on the fact that the scattering events associated with l are inelastic, which means that they do not conserve the energy and therefore the quantum mechanical phase of the electron wave-function. In metals at low temperatures, l can be of the order of 100 Å.