Current transport models for nanoscale semiconductor devices

Due to the rapid decrease in device dimensions the well-established TCAD tools are pushed to the limits of their applicability. Since conventional MOSFETs are already operating in the sub-100 rim range, new physical effects and principles begin to determine the transport characteristics, and the validity of conventional current transport models is in question. The drift-diffusion model, which has enjoyed a remarkable success due to its relative simplicity, numerical robustness, and the ability to perform two- and three-dimensional simulations on large unstructured meshes, must be generalized to include hot-carrier and classical non-local effects. This motivated the development of higher order moments transport models such as the hydrodynamic, the energy-transport, and the six-moments models. After the introduction of stress for device performance enhancement the demand for accurate carrier mobility calculations based on full-band Monte Carlo algorithms has significantly increased, since they allow calibration of phenomenological mobility models and thus justify closure relations for higher order moments equations. The transport models based on the semi-classical Boltzmann transport equation already contain information which can only be obtained from quantum-mechanical consideration. These are the band structure, expressions for the scattering rates, and the Pauli exclusion principle reflecting the Fermi statistics of carriers. With scaling continuing, other quantum-mechanical effects begin to affect transport properties. Quantum confinement in the direction orthogonal to transport in inversion layers makes the energy spectrum discrete. For sufficiently long channels, however, the carrier motion in transport direction can still be treated semi-classically, and development of transport models based on a set of subband Boltzmann equations is possible. A useful approximation to mimic the quantum-mechanical carrier concentration profile is to introduce an effective potential into otherwise classical transport models. Transport calculations can then be carried out using conventional TCAD tools providing accurate and timely results. However, when modeling transport in ultra-scaled structures with only a few subbands occupied the full subband method must be applied. Parallel to the search for new technological solutions for MOSFET scaling, the development of conceptually new devices and architectures is becoming increasingly important. New nanoelectronic structures, such as carbon nanotubes, nanowires, and even molecules, are considered to be prominent candidates for the post-CMOS era. At this small device size the geometrical spread of the carrier wave packet in transport direction can no longer be ignored. When the device size becomes shorter than the phase coherence length, the complete information about carrier dynamics inside the device including the phase of the wave function is needed and one has to resort to a full quantum-mechanical description including scattering. Transport in advanced nanodevices is determined by the interplay between coherent propagation and scattering. Numerical methods for dissipative quantum transport based on the non-equilibrium Green's function formalism, the Liouville/von-Neumann equation for the density matrix, and the kinetic equation for the Wigner function are attaining relevance. (C) 2007 Elsevier B.V. All rights reserved.