International Journal of High Speed Electronics and Systems

It is clear that continued scaling of semiconductor devices will bring us to a regime in which device gate lengths are less than 50 nm within another decade. Pushing to dimensional sizes such as this will probe the transition from classical to quantum transport, and there is no present approach to the quantum regime that has proved effective. Contrary to the classical case in which electrons are negligibly small, the finite extent of the momentum space available to the electron sets size limitations on the minimum wave packet—this is of the order of a few nanometers. While quantum transport formalism has been applied to a variety of problems, in most cases it has not been overly successful. In this paper, we discuss the problems and some of the approximate approaches which will ease the above-mentioned transition.

In this paper a review of the research performed in recent years by the group of the authors is presented. The definition and basic properties of the Wigner function are first given. Several forms of its dynamical equation are then derived with the inclusion of potential and phonon scattering. For the case of a potential V(r) the effect of the classical force, for any form of V(r), is separated from quantum effects due to rapidly varying potentials. An elaboration of the dynamical equation is introduced that leads to Wigner paths formed by free flights and scattering events. These are especially suitable for a Monte Carlo solution of the transport equation for the Wigner function very similar to the semiclassical traditional Monte carlo simulation. The Monte Carlo simulation can be extended also to the momentum and frequency dependent Wigner function based on a two-time Green function. Several numerical results are presented throuhout the paper.

The influence of local inhomogeneities on the electric field dependent properties of Bloch electrons is studied. The homogeneous electric field is described through the use of the vector potential, and the instantaneous Wannier functions of the homogeneous field dependent Hamiltonian are used as bases states to depict Bloch dynamics and properties. Model examples are treated using Slater-Koster inhomogeneities and nearest-neighbor tight-binding band structure in a one dimensional, single-band analysis. Detailed analysis is presented for the special case of a constant electric field; here the influence of localization due to the presence of the electric field is shown to clearly affect the energy spectrum of the Bloch electron for a single and double impurity configuration.

Recent developments in the understanding of the theory and consequences of collision broadening through sequences of scattering events are reviewed and expanded upon, particularly in regard to semiclassical Monte Carlo simulation. Using basic theory backed up by quantum transport simulations, it is demonstrated that the requirement for energy conservation in the coupled carrier-phonon system prohibits the accumulation of the uncertainty in the carrier energy associated with collision broadening through a sequence of scattering events. This accumulation, however, had been possible with the conventional treatment of collision broadening in semiclassical Monte Carlo. Accordingly, an improved, more physically accurate algorithm for connecting sequences of collision broadened scattering events within semiclassical Monte is described. The potential consequences of collision broadening are then reassessed using both the quantum transport simulations and semiclassical Monte Carlo simulations incorporating the new algorithm, including full-band Monte Carlo simulations for the first time. The broadening assisted runaway of the high-energy tail of the carrier distribution possible with the conventional algorithm is shown to be an artifact of that algorithm, not of the form of the collision broadening used (Lorentzian, etc.) as often assumed. Simulation results obtained with the new algorithm also demonstrate that for important cases, Golden-Rule-based Monte Carlo simulations can remain accurate despite the presence of significant collision broadening. A notable class of exceptions, however, is when collision broadening allows for a threshold or scattering bottle-neck to be overcome, although the ultimate requirement for energy conservation remains critical. Specifically, it is shown that collision broadening lowers but does not eliminate the impact ionization threshold energy, producing simulated impact ionization coefficients for holes in silicon that accurately track experimental results as a function of field. Similarly, the quantum transport simulations illustrate how collision broadening can significantly affect optical absorption, but that simply subjecting low energy carriers to scattering induced collision broadening does not allow them to overcome large potential barriers.

AlGaN/GaN structures constitute a new class of 2D systems in that a large population of electrons can be produced without doping as a result of spontaneous and strain-induced polarization. Electron transport can, in principle, be mediated solely by phonon scattering and, for the first time, it is possible to realistically envisage the formation of a drifted Maxwellian or Fermi-Dirac distribution in hot-electron transport. We first describe a simple model that relates electron density in a heterostructure to barrier width and then explore electron-electron (e-e) energy and momentum exchange in some depth. We then illustrate the novel hot-electron transport properties that can arise when only phonon and e-e scattering are present. These include S-type NDR, electron cooling and squeezed electrons.

Impact ionization plays a crucial role for electron transport in wide-bandgap semiconductors at high electric fields. Therefore, a realistic band structure has to be used in calculations of the microscopic scattering rate, as well as high field quantum corrections such as the intercollisional field effect. Here we consider both, and evaluate the impact ionization rate for wide-bandgap materials such as ZnS. A pronounced softening of the impact ionization threshold is obtained, as found earlier for materials like Si and GaAs. This field dependent impact ionization rate is included within a full-band ensemble Monte Carlo simulation of high field transport in ZnS. Although the impact ionization rate itself is strongly affected, little effect is observed on measurable quantities such as the impact ionization coefficient or the electron distribution function itself.

Organic semiconductors have processing and performance advantages for low cost and/or large area applications that have led to their rapid commercialization. Organic semiconductors are π conjugated materials, either small molecules or polymers. Their electrical transport properties are fundamentally distinct from those of inorganic semiconductors. Organic semiconductor thin films are amorphous or polycrystalline and their electronic structures consist of a distribution of localized electronic states with different energies. The localized sites are either individual molecules or isolated conjugated segments of a polymer chain. Electrical transport results from carrier hopping between neighboring sites. At room temperature, equilibration between neighboring sites of different energy is fast enough that carrier transport can be described using a mobility picture. Hopping transport in these disordered systems leads to a mobility that can depend strongly on both the electric field and carrier density. This article presents experimental measurements and theoretical analysis of the electrical transport properties of representative organic semiconductors.