Daniel C. Cole

Quantum mechanical ground state of hydrogen obtained from classical electrodynamics

The behavior of a classical charged point particle under the influence of only a Coulombic binding potential and classical electromagnetic zero-point radiation, is shown to agree closely with the probability density distribution of Schrodingers wave equation for the ground state of hydrogen. These results again raise the possibility that the main tenets of stochastic electrodynamics (SED) are correct.

Using advanced simulation to aid microlithography development

An early historical overview is first presented here on the use of simulation in optical microlithography, along with a description of the general physical models. This paper then turns to more recent development work in microlithography simulation, which has followed several very different tracts. Three of the most important areas are discussed here. The first involves improvements in the underlying physical models, such as advances beyond the Kirchhoff boundary condition in optical diffraction theory, as well as a deeper understanding into the chemistry and physical behavior of photoresist materials. Such work guides basic understanding both in the optics and photoresist areas. At the other extreme, phenomenological models are being advanced to enable simulation results on large scales to be placed in the hands of device and circuit designers. Finally, optimization of the large number of allowable parameters is a pervasive problem that has received much attention and interest by the engineering community.

The use of simulation in semiconductor technology development

Abstract An overview is presented on the types of problems encountered in semiconductor technology development that are actively studied today via simulation methods. Most of the simulation examples presented here are ones that have been explicitly used in actual industrial semiconductor device design cycles to aid in the optimization of device structures. The examples described here include process simulations, such as the diffusion of dopant atoms, oxidation, etching, deposition, and epitaxial growth, as well as device simulations, which predict the flow of charge carriers and field distribution within a semiconductor device, given its material structure and operating conditions. The main aim here is to illustrate, by example, some of the capabilities of state-of-the-art simulators used in characterizing and predicting semiconductor process and device-related phenomena. We will attempt to outline the degree of sophistication of the physics incorporated in such simulation programs, and provide some contrast to the fundamental physics required for a complete physical description. As will be indicated, simulation development necessarily involves molding the appropriate physical models and numerical algorithms into a package that can be handled in a reasonable length of time by modern computing systems. We briefly outline some of the advances that have been made, and some concerns that remain, in such simulation development.

Derivation and Simulation of Higher Numerical Aperture Scalar Aerial Images

The application of scalar diffraction theory to a projection optics system is examined here for somewhat higher numerical aperture conditions upon removing the paraxial, or small angle, approximation that is typically made. A detailed derivation is given that notes the key physical assumptions originally contained in work by others on vector imaging theory. The asymptotic limit of large lenses and focal length sizes to object and image sizes is explicitly carried out, while keeping numerical apertures and magnification fixed. Numerical results of the resulting equations are presented for a variety of imaging conditions, including phase shift masks and modified illumination.

Extending scalar aerial image calculations to higher numerical apertures

The usual formula for the scalar aerial image of an isolated object due to a projection lens system has been generalized beyond the paraxial approximation in an attempt to extend scalar diffraction theory to include numerical aperture (NA) values up to about 0.6. Beyond this regime, or certainly beyond NA=0.7, polarization effects need to be included, thereby demanding a full vector treatment and invalidating the present scalar formulation. A key point to the present scalar result without the paraxial approximation is the predicted functional dependence of the aerial image on magnification as NA increases. A second key point is that the usual scaling of λ/NA for the object dimensions and λ/NA2 for defocus become invalid for high NA systems. Numerical results of illustrative test cases are shown.

Review of Experimental Concepts for Studying the Quantum Vacuum Field

We review concepts that provide an experimental framework for exploring the possibility and limitations of accessing energy from the space vacuum environment. Quantum electrodynamics (QED) and stochastic electrodynamics (SED) are the theoretical approaches guiding this experimental investigation. This investigation explores the question of whether the quantum vacuum field contains useful energy that can be exploited for applications under the action of a catalyst, or cavity structure, so that energy conservation is not violated. This is similar to the same technical problem at about the same level of technology as that faced by early nuclear energy pioneers who searched for, and successfully discovered, the unique material structure that caused the release of nuclear energy via the neutron chain reaction.

Simulation Study of Aspects of the Classical Hydrogen Atom Interacting with Electromagnetic Radiation: Elliptical Orbits

The present study examines the behavior of a classical charged point particle in near-elliptic orbits about an infinitely massive and oppositely charged nucleus, while acted upon by applied electromagnetic radiation. As recently shown for near-circular orbits, and now extended here to the elliptical case, rather surprising nonlinear dynamical effects are readily produced for this simple system. A broad range of stability-like conditions can be achieved by applying radiation to this classical atom. A perfect balance condition is examined, which requires an infinite number of plane waves representing harmonics of the orbital motion. By applying a scale factor to this radiation, stability-like conditions are produced where periodic variations in semimajor and semiminor axes occur for extended periods of time, before orbital decay eventually takes over due to the effects of radiation reaction. This work is expected to lead to both practical suggestions on experimental ideas involving controlling ionization and stabilization conditions, as well as hopefully aiding in theoretical explorations of stochastic electrodynamics.

Vector aerial image with off-axis illumination

As the numerical aperture (NA) in optical projection systems increases, the vector nature of the projected electric and magnetic fields becomes more important. Recent advances in off- axis illumination, tilting condenser lenses, and applying spatial filters, as well as phase-shift masks, hold the potential of increased depth of focus. To simulate these techniques in the high- NA regime, we have developed new fast algorithms. The development reported here builds on our recent work (1) extending scalar aerial imaging. The systematic treatment of (1) has now been applied to account for the vector nature of light.

Perturbation Analysis and Simulation Study of the Effects of Phase on the Classical Hydrogen Atom Interacting with Circularly PolarizedElectromagnetic Radiation

The classical hydrogen atom is examined for the situation where a circularly polarized electromagnetic plane wave acts on a classical charged point particle in a near-circular orbit about an infinitely massive nucleus, with the plane wave normally incident to the plane of the orbit. The effect of the phase α of the polarized wave in relation to the velocity vector of the classical electron is examined in detail by carrying out a perturbation analysis and then comparing results using simulation methods. By expanding the variational parts of the radius and angular velocity about their average values, simpler nonlinear differential equations of motion are obtained that still retain the key features of the oscillating amplitude, namely, the gradual increase of the envelope of the oscillating amplitude and the point of rapid orbital decay. Also, as shown here, these key features carry over nicely to conventional quantities of interest such as energy and angular momentum. The phase α is shown here to have both subtle yet very significant effects on the quasistability of the orbital motion. A far wider range of phase conditions are found to provide stability than might intuitively be expected, with the time to orbital decay, td, varying by orders of magnitude for any plane wave with an amplitude A above a critical value, Ac.

Classical electrodynamic systems interacting with classical electromagnetic random radiation

In the past, a few researchers have presented arguments indicating that a statistical equilibrium state of classical charged particles necessarily demands the existence of a temperature-independent, incident classical electromagnetic random radiation. Indeed, when classical electromagnetic zero-point radiation is included in the analysis of problems with macroscopic boundaries, or in the analysis of charged particles in linear force fields, then good agreement with nature is obtained. In general, however, this agreement has not been found to hold for charged particles bound in nonlinear force fields. The point is raised here that this disagreement arising for nonlinear force fields may be a premature conclusion on this classical theory for describing atomic systems, because past calculations have not directed strict attention to electromagnetic interactions between charges. This point is illustrated here by examining the classical hydrogen atom and showing that this problem has still not been adequately solved.