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We present a hierarchical approach to the "atomistic" simulation of aggressively scaled sub-0.1-/spl mu/m MOSFETs. These devices are so small that their characteristics depend on the precise location of dopant atoms within them, not just on their average density. A full-scale three-dimensional drift-diffusion atomistic simulation approach is first described and used to verify more economical, but restricted, options. To reduce processor time and memory requirements at high drain voltage, we have developed a self-consistent option based on a solution of the current continuity equation restricted to a thin slab of the channel. This is coupled to the solution of the Poisson equation in the whole simulation domain in the Gummel iteration cycles. The accuracy of this approach is investigated in comparison to the full self-consistent solution. At low drain voltage, a single solution of the nonlinear Poisson equation is sufficient to extract the current with satisfactory accuracy. In this case, the current is calculated by solving the current continuity equation in a drift approximation only, also in a thin slab containing the MOSFET channel. The regions of applicability for the different components of this hierarchical approach are illustrated in example simulations covering the random dopant-induced threshold voltage fluctuations, threshold voltage lowering, threshold voltage asymmetry, and drain current fluctuations.

One of the biggest challenges in nanotechnology is the need to simulate entire molecular assemblies of up to 100 million atoms or more. This requires about one million to one billion fold more computing power than is available today. For nanotechnology to be successful, it will be essential to develop Petaflops computing systems and associated software. We will survey the various enabling technologies, such as semiconductors, superconducting, photonic, and exotic (quantum integrated circuits, molecular computers, DNA computers) that are expected to be available in the next 20 to 25 years for making Petaflops computing and nanotechnology feasible. It will be shown that progress in nanotechnology and progress in future high-performance computer systems are mutually interdependent.

In this paper we use 3D simulations to study the amplitudes of random telegraph signals (RTS) associated with the trapping of a single carrier in interface states in the channel of sub 100 nm (decanano) MOSFETs. Both simulations using continuous doping charge and random discrete dopants in the active region of the MOSFETs are presented. We have studied the dependence of the RTS amplitudes on the position of the trapped charge in the channel and on the device design parameters. We have observed a significant increase in the maximum RTS amplitude when discrete random dopants are employed in the simulations.

A detailed study of the influence of quantum effects in the inversion layer on the random dopant induced threshold voltage fluctuations and lowering in sub 0.1 micron MOSFETs has been performed. This has been achieved using a full 3D implementation of the density gradient (DG) formalism incorporated in our previously published 3D 'atomistic' simulation approach. This results in a consistent, fully 3D, quantum mechanical picture which implies not only the vertical inversion layer quantisation but also the lateral confinement effects manifested by current filamentation in the 'valleys' of the random potential fluctuations. We have shown that the net result of including quantum mechanical effect, while considering statistical fluctuations, is an increase in both threshold voltage fluctuations and lowering.

The first Born approximation with boundary conditions which take the asymptotic Coulomb phases into full account is used to calculate the muon charge-transfer cross sections from \ensuremath{\alpha}\ensuremath{\mu} to protons at intermediate and high collision energies. Our computed cross sections are in good agreement with the experimental data on the equivalent electronic system in the energy range 50 to 180 keV.

The method of adiabatic switching (AS) is applied to the problem of a hydrogen atom in a strong magnetic field, i.e., the quadratic Zeeman effect (QZE). The QZE is one of the simplest realistic physical problems exhibiting classical chaos which presents conceptual and computational obstacles to the implementation of many semiclassical quantization methods, while the highly nonseparable nature of the problem makes exact quantum treatments problematic. The AS method is straightforward, mainly involving integration of Hamilton's equations of motion, and in addition, unlike most other trajectory-based semiclassical methods, works even in mildly chaotic volumes of classical phase space. In AS, a zeroth-order classical torus is quantized and then the perturbation is switched on adiabatically using a time-dependent or time-independent switching function which is incorporated into the Hamiltonian. A central problem in AS is the choice of the most appropriate zeroth-order tori. Based on a comprehensive study of the classical dynamics of the QZE it is shown that the best zeroth-order tori for AS are those obtained by quantizing the zeroth-order Hamiltonian (i.e., the hydrogen atom) and simultaneously an adiabatic invariant found by Solov'ev. AS is performed for a wide variety of magnetic fields and energies including states lying in mildly chaotic regions of phase space where Solov'ev's invariant is no longer conserved. Results are generally in excellent agreement with exact quantum results, and additionally the method is self-diagnostic, yielding large standard deviations in energies should it begin to fail. However, AS is seen to break down in the strongly chaotic regions of phase space where the quantum levels display multiple avoided crossings (strongly n-mixing regime). Application of AS to the QZE leads to a number of new developments in the theory of AS, including AS in extended phase space where the Hamiltonian is explicitly independent of time.

The semiclassical method based on the Einstein-Brillouin-Keller quantization of invariant phase-space tori and the hypothesis of adiabatic invariance of classical action variables is applied in the calculation of highly excited energy levels of two-dimensional coupled oscillator systems. The results obtained are in good agreement with quantum-mechanical calculations even in the regions where the corresponding classical dynamics becomes apparently irregular. General limitations of the method are discussed.

The classical Born-Oppenheimer method is applied to the two-degrees-of-freedom Henon-Heiles potential. The resulting one-dimensional potentials are then treated semi-classically to give the eigenvalues for the regular states. No trajectories are needed and the results are in good agreement with the exact results.

A general theoretical base and a general strategy for implementing semiclassical quantization using the adiabatic-switching method are presented for two-dimensional systems. The method proposed does not depend on specialized coordinates, trajectory, or surfaces-of-section studies and is generalizable to multidimensional systems. The choice of the initial tori for the switching procedure is accomplished by simple diagonalizations of small-dimensional matrix representations of invariant operators obtained from perturbation theory. The method gives quantum energies at a useful level of accuracy for the vast majority of states in many of the well-known nonresonant and resonant Hamiltonian cases. Many eigenvalues previously thought unobtainable when the adiabatic-switching method is used are obtained in a quite simple manner.

A semiclassical perturbation method based on the Lie transform is used to calculate vibrational energy levels for multidimensional systems. No trajectories, initial searches, iterative procedures, Fourier analyses, or reference Hamiltonian searches are needed and the results are in good agreement with Einstein-Brillouin-Keller based methods.

The method of adiabatic switching of perturbation is applied in semiclassical calculations of the eigenvalues of classically near‐integrable Hamiltonian describing a two‐dimensional coupled oscillator whose dynamics is dominated by an intrinsic 2:1 resonance. At low‐to‐intermediate excitations the semiclassical eigenvalues are generally in good agreement with quantum‐variational results. Even at high excitations, close to the classical escape energy, useful information on the location of quantal levels can be obtained. Limitations of the method are discussed.

A variational method particularly suitable for the pulsedneutron problem was suggested by Ahmed et al.; in this method, one needed the exact solution of the eigenvalue equation for two values of the buckling. In the modification suggested no solution of the eigenvalue equation is required; however, compared to the earlier method the results are a little less accurate. A similar variational method was also developed for the case of neutron diffusion. As examples, the decay of a neutron pulse and neutron diffusion in beryllium and beryllinm oxide blocks were studied. (auth)

We have thoroughly investigated electron capture from a hydrogen atom by bare nuclei at intermediate and high energies. The first Born approximation with and without correct boundary conditions is used to compute total cross sections. Both methods possess the same perturbation potential for the reaction under study. The only difference is in the logarithmic phase distortion of the exit channel state due to the long-range Coulomb interaction between the two aggregates. Evidence is presented which substantiates that these Coulomb phases for the relative motion of heavy particles are of paramount importance for an adequate description of charge exchange. The standard Jackson-Schiff approximation which does not consider the boundary condition problem fails completely in comparison with the measurement. In contrast, the first Born approximation with the correct boundary conditions, which takes the asymptotic Coulomb effect into full account, is found to be systematically in excellent agreement with the experimental data for values of the projectile charge ranging from 1 to 6.

A quantum theory of the magnetized hydrogen atom based on partitioning the space into physically important regions is given. Using known formalism, this partitioning supplies a fully quantal explanation of the effect of periodic orbits on the Fourier transforms of the spectra, scars in the wavefunctions, and level clustering. The formalism also leads to a simple non-periodic trajectory guided method to calculate quantum mechanically the Fourier peaks. The motion of the system is shown to be consistently that of a chaotic trajectory with segments of near periodic orbit-type motion.