Abstract: In this paper we investigate the basic physics of charge carriers (electrons) leaking out of the inversion layer of a metal-oxide-semiconductor capacitor with a biased gate. In particular, we treat the gate leakage current as resulting from two combined processes: (1) the time-dependent decay of electron wave packets representing the inversion-layer charge and (2) the local generation of new electrons replacing those that have leaked away. As a result, the gate current simply emerges as the ratio of the total charge in the inversion layer to the tunneling lifetime. The latter is extracted from the quantum dynamics of the decaying wave packets, while the generation rate is incorporated as a phenomenological source term in the continuity equation. Not only do the gate currents calculated with this model agree very well with experiment, the model also provides an onset to solve the paradox of the current-free bound states representing the resonances of the Schrödinger equation that governs the fully coupled metal-oxide-semiconductor system.

Abstract: A simplified quantum mechanical model is developed to investigate quantum transport features such as the electron concentration and the current flowing through a silicon nanowire metal-oxide-semiconductor field-effect transistor (MOSFET). In particular, the electron concentration is extracted from a self-consistent solution of the Schrödinger and Poisson equations as well as the ballistic Boltzmann equation which have been solved by exploiting a nonlinear variational principle within the framework of the generalized local density approximation. A suitable action functional has been minimized and details of the implementation and its numerical minimization are given. The current density and its related current-voltage characteristics are calculated from the one-dimensional ballistic steady-state Boltzmann transport equation which is solved analytically by using the method of characteristic curves. The straightforward implementation, the computational speed and the good qualitative behavior of the transport characteristics observed in our approach make it a promising simulation method for modeling quantum transport in nanowire MOSFETs.

Abstract: Recently, a renewed interest in Zener tunneling has arisen because of its increasing impact on semiconductor device performance at nanometer dimensions. In this paper we evaluate the tunnel probability under the action of a nonuniform electric field using a two-band model and arrive at significant deviations from the commonly used Kanes model, valid for weak uniform fields only. A threshold on the junction bias where Kanes model for Zener tunneling breaks down is determined. Comparison with Kanes model particularly shows that our calculation yields a higher tunnel probability for intermediate electric fields and a lower tunnel probability for high electric fields. When performing a current calculation comparing to the WKB approximation for the case of an abrupt p-n junction significant differences concerning the shape of the I-V curve are demonstrated.

Abstract: Being the working principle of a tunnel field-effect transistor, band-to-band tunneling is given a rigorous quantum mechanical treatment to incorporate confinement effects, multiple electron and hole valleys, and interactions with phonons. The model reveals that the strong band bending near the gate dielectric, required to create short tunnel paths, results in quantization of the energy bands. Comparison with semiclassical models reveals a big shift in the onset of tunneling. The effective mass difference of the distinct valleys is found to reduce the subthreshold swing steepness.

Abstract: We theoretically investigate the phonon, surface roughness and ionized impurity limited low-field mobility of ultrathin silicon n-type nanowire junctionless transistors in the long channel approximation with wire radii ranging from 2 to 5 nm, as function of gate voltage. We show that surface roughness scattering is negligible as long as the wire radius is not too small and ionized impurity scattering is the dominant scattering mechanism. We also show that there exists an optimal radius where the ionized impurity limited mobility exhibits a maximum.

Abstract: In the realm of Ehrenfests theorem, classical trajectories obeying Newtons laws have been proven useful to construct explicit solutions to the time-dependent WignerLiouville equation. Whereas previous works have particularly focused on the initial distribution function as a vehicle found to carry the signatures of quantum statistics into the time-dependent solution, the present paper shows that the LagrangeCharpit method based on classical trajectories can be successfully invoked as well to tackle quantum mechanical features with no classical counterpart, such as tunneling.

Abstract: The propagator of the Wigner function is constructed from the WignerLiouville equation as a phase space path integral over a new effective Lagrangian. In contrast to a paper by Barker and Murray (1983) [1], we show that the path integral can in general not be written as a linear superposition of classical phase space trajectories over a family of non-local forces. Instead, we adopt a saddle point expansion to show that the semiclassical Wigner function is a linear superposition of classical solutions for a different set of non-local time dependent forces. As shown by a simple example the specific form of the path integral makes the formulation ideal for Monte Carlo simulation.

Abstract: Simulation results of electrostatics in Si cylindrical junctionless nanowire transistors with a homogenous channel are presented. Junctionless transistors including strain and arbitrary crystallographic orientations are studied. Size quantization effects are simulated by self-consistent solutions of the Poisson and Schrodinger equations. The 6 x 6 k.p method is employed for the calculation of the valence subband structure in a junctionless nanowire pFET. The influence of stress/strain and crystallographic channel orientation on to the electrostatics in terms of subband structure, charge density, and C-V curve is systematically studied. (C) 2011 Elsevier Ltd. All rights reserved.

Abstract: The tunneling current has been computed for a cylindrical nanowire tunneling field-effect transistor (TFET) with an all-round gate that covers the source region. Being the underlying mechanism, band-to-band tunneling, mediated by electron-phonon interaction, is pronouncedly affected by carrier confinement in the radial direction and, therefore, involves the self-consistent solution of the Schrodinger and Poisson equations. The latter has been accomplished by exploiting a non-linear variational principle within the framework of the modified local density approximation taking into account the nonparabolicity of both the valence band and conduction band in relatively thick wires. Moreover, while the effective-mass approximation might still provide a reasonable description of the conduction band in relatively thick wires, we have found that the nonparabolicity of the valence band needs to be included. As a major conclusion, it is observed that confinement effects in nanowire tunneling field-effect transistors have a stronger impact on the onset voltage of the tunneling current in comparison with planar TFETs. On the other hand, the value of the onset voltage is found to be overestimated when the valence band nonparabolicity is ignored. (C) 2013 AIP Publishing LLC.

Abstract: Starting from Feynmans Lagrangian description of quantum mechanics, we propose a method to construct explicitly the propagator for the Wigner distribution function of a single system. For general quadratic Lagrangians, only the classical phase space trajectory is found to contribute to the propagator. Inspired by Feynmans and Vernons influence functional theory we extend the method to calculate the propagator for the reduced Wigner function of a system of interest coupled to an external system. Explicit expressions are obtained when the external system consists of a set of independent harmonic oscillators. As an example we calculate the propagator for the reduced Wigner function associated with the CaldeiraLegett model.

Abstract: We study the resistivity scaling in nanometer-sized metallic wires due to surface roughness and grain-boundaries, currently the main cause of electron scattering in nanoscaled interconnects. The resistivity has been obtained with the Boltzmann transport equation, adopting the relaxation time approximation of the distribution function and the effective mass approximation for the conducting electrons. The relaxation times are calculated exactly, using Fermi's golden rule, resulting in a correct relaxation time for every sub-band state contributing to the transport. In general, the relaxation time strongly depends on the sub-band state, something that remained unclear with the methods of previous work. The resistivity scaling is obtained for different roughness and grain-boundary properties, showing large differences in scaling behavior and relaxation times. Our model clearly indicates that the resistivity is dominated by grain-boundary scattering, easily surpassing the surface roughness contribution by a factor of 10. (C) 2014 AIP Publishing LLC.

Abstract: Group IV based tunnel field-effect transistors generally show lower on-current than III-V based devices because of the weaker phonon-assisted tunneling transitions in the group IV indirect bandgap materials. Direct tunneling in Ge, however, can be enhanced by strain engineering. In this work, we use a 30-band k.p method to calculate the band structure of biaxial tensile strained Ge and then extract the bandgaps and effective masses at Gamma and L symmetry points in k-space, from which the parameters for the direct and indirect band-to-band tunneling (BTBT) models are determined. While transitions from the heavy and light hole valence bands to the conduction band edge at the L point are always bridged by phonon scattering, we highlight a new finding that only the light-holelike valence band is strongly coupling to the conduction band at the Gamma point even in the presence of strain based on the 30-band k.p analysis. By utilizing a Technology Computer Aided Design simulator equipped with the calculated band-to-band tunneling BTBT models, the electrical characteristics of tensile strained Ge point and line tunneling devices are self-consistently computed considering multiple dynamic nonlocal tunnel paths. The influence of field-induced quantum confinement on the tunneling onset is included. Our simulation predicts that an on-current up to 160 (260) mu A/mu m can be achieved along with on/off ratio > 10(6) for V-DD = 0.5V by the n-type (p-type) line tunneling device made of 2.5% biaxial tensile strained Ge. (C) 2014 AIP Publishing LLC.

Abstract: We propose a simple quantum mechanical model describing the time dependent diffusion current between two fermion reservoirs that were initially disconnected and characterized by different densities or chemical potentials. The exact, analytical solution of the model yields the transient behavior of the coupled fermion systems evolving to a final steady state, whereas the long-time behavior is determined by a power law rather than by exponential decay. Similar results are obtained for the entropy production which is proportional to the diffusion current. (C) 2014 Elsevier B.V. All rights reserved.

Abstract: Ando's surface roughness model is applied to metallic nanowires and extended beyond small roughness size and infinite barrier limit approximations for the wavefunction overlaps, such as the Prange-Nee approximation. Accurate and fast simulations can still be performed without invoking these overlap approximations by averaging over roughness profiles using finite domain distribution functions to obtain an analytic solution for the scattering rates. The simulations indicate that overlap approximations, while predicting a resistivity that agrees more or less with our novel approach, poorly estimate the underlying scattering rates. All methods show that a momentum gap between left- and right-moving electrons at the Fermi level, surpassing a critical momentum gap, gives rise to a substantial decrease in resistivity.