International Journal of High Speed Electronics and Systems

The progress of silicon technologies we have witnessed in the last twenty years has traced the path to the unprecedented revolution of information technologies, which has changed almost everybody's lifestyles. Apparently, this has happened with a little big help from TCAD tools. Big, because few major advancements have been achieved through the clever exploitation of non-conventional simulation tools, and because everyday device optimization deeply relies on TCAD tools. Little, because the qualitative feeling is that the technology would have progressed anyway, through the work of many highly-skilled technology experts, even without simulation guidelines. The purpose of this paper is to review the state-of-the-art of the field of the transport modeling of electron devices, trying to grasp the essence of the most relevant simulation models proposed so far, whence to contribute to spur the activity on the fundamental modeling of carrier transport.

A theoretical analysis of the Monte Carlo (MC) method for both semiclassical and quantum device simulation is presented. A link between physically-based MC methods for semiclassical transport calculations and the numerical MC method for solving integrals and integral equations is established. The integral representations of the transient and the stationary Boltzmann equations are presented as well as the respective conjugate equations. The structure of the terms of the Neumann series and their evaluation by MC integration is discussed. Using this formal approach the standard MC algorithms and a variety of new algorithms is derived, such as the backward and the weighted algorithms, and algorithms for linear small-signal analysis. Applying this theoretical framework to the Wigner-Boltzmann equation enables the development of particle models for quantum transport problems.

We present a thermodynamic approach to introducing quantum corrections to the classical transport picture in semiconductor device simulation. This approach leads to a modified Boltzmann equation with a quantum corrected force term and to quantum corrected fluid, or quantum hydrodynamic models. We present the quantum interaction of electrons with a gate oxide barrier potential and quantum hydrodynamic simulations of a resonant tunneling diode as application examples.

A new method for investigating quantum confinement effects in MOSFETs is presented. The method is based on the numerical solution of the Schrödinger and Boltzmann system of equations. A quantum Boltzmann equation is developed by replacing the classical potential with a quantum potential. The technique naturally accounts for highly nonequilibrium effects including velocity overshoot. The subbands are calculated and then populated using nonequilibrium statistics. Modeling results show the electron concentration and electron current density peaks shifted away from the interface. Calculations show reduced channel concentration which leads to lower drain current for the quantum case. A quantum distribution function is obtained.

A 2D hydrodynamic model based on modified Langevin forces for terminal current noise in the RF range is presented for Si and SiGe devices, where all transport and noise parameters are generated by full-band Monte Carlo simulations under bulk conditions and stored in lookup tables. Since these tables have to be built only once, the accuracy of the noise model is improved without increasing the CPU time compared to models based on analytical expressions for the parameters. The accuracy of the noise model is assessed by comparison with the Monte Carlo device model and good agreement of both models is found for diffusion and generation noise. The terminal current noise of a realistic SiGe HBT is investigated and it is found that hole diffusion noise has a strong impact on the collector current noise. The limitations of the thermodynamic model, a compact model for noise, are explored by comparison with the hydrodynamic model.

A brief review is given on electronic and transport properties of carbon nanotubes mainly from a theoretical point of view. The topics include a description of electronic states in a tight-binding model and in an effective-mass or k · p scheme. Transport properties are discussed including absence of backward scattering except for scatterers with a potential range smaller than the lattice constant, its extension to multi-bands cases, and long-wavelength phonons and electron-phonon scattering.

The distribution function of hot carriers in state-of-the-art devices is insufficiently described using just the electric field or the average carrier energy as parameters. Still, the standard models to describe carrier transport in semiconductor devices, namely the drift-diffusion model and the energy-transport model rely on these assumptions. In this article we summarize our work on six moments transport models which allow an accurate characterization of the distribution function. Within this framework it is possible to selfconsistently model the scattering integral without resorting to the relaxation time approximation. In addition, hot electron processes such as impact ionization, which are difficult to model in lower order transport models, can be described accurately.