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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1976

Quantum principles and free particles

The quantum principles that establish the energy levels and degeneracies needed to evaluate the partition functions are explored. The uncertainty principle is associated with the dual wave-particle nature of the model used to describe quantized gas particles. The Schroedinger wave equation is presented as a generalization of Maxwell's wave equation; the former applies to all particles while the Maxwell equation applies to the special case of photon particles. The size of the quantum cell in phase space and the representation of momentum as a space derivative operator follow from the uncertainty principle. A consequence of this is that steady-state problems that are space-time dependent for the classical model become only space dependent for the quantum model and are often easier to solve. The partition function is derived for quantized free particles and, at normal conditions, the result is the same as that given by the classical phase integral. The quantum corrections that occur at very low temperatures or high densities are derived. These corrections for the Einstein-Bose gas qualitatively describe the condensation effects that occur in liquid helium, but are unimportant for most practical purposes otherwise. However, the corrections for the Fermi-Dirac gas are important because they quantitatively describe the behavior of high-density conduction electron gases in metals and explain the zero point energy and low specific heat exhibited in this case.

Source record↗
NASA NTRS2005

N-Type delta Doping of High-Purity Silicon Imaging Arrays

A process for n-type (electron-donor) delta doping has shown promise as a means of modifying back-illuminated image detectors made from n-doped high-purity silicon to enable them to detect high-energy photons (ultraviolet and x-rays) and low-energy charged particles (electrons and ions). This process is applicable to imaging detectors of several types, including charge-coupled devices, hybrid devices, and complementary metal oxide/semiconductor detector arrays. Delta doping is so named because its density-vs.-depth characteristic is reminiscent of the Dirac delta function (impulse function): the dopant is highly concentrated in a very thin layer. Preferably, the dopant is concentrated in one or at most two atomic layers in a crystal plane and, therefore, delta doping is also known as atomic-plane doping. The use of doping to enable detection of high-energy photons and low-energy particles was reported in several prior NASA Tech Briefs articles. As described in more detail in those articles, the main benefit afforded by delta doping of a back-illuminated silicon detector is to eliminate a "dead" layer at the back surface of the silicon wherein high-energy photons and low-energy particles are absorbed without detection. An additional benefit is that the delta-doped layer can serve as a back-side electrical contact. Delta doping of p-type silicon detectors is well established. The development of the present process addresses concerns specific to the delta doping of high-purity silicon detectors, which are typically n-type. The present process involves relatively low temperatures, is fully compatible with other processes used to fabricate the detectors, and does not entail interruption of those processes. Indeed, this process can be the last stage in the fabrication of an imaging detector that has, in all other respects, already been fully processed, including metallized. This process includes molecular-beam epitaxy (MBE) for deposition of three layers, including metallization. The success of the process depends on accurate temperature control, surface treatment, growth of high-quality crystalline silicon, and precise control of thicknesses of layers. MBE affords the necessary nanometer- scale control of the placement of atoms for delta doping. More specifically, the process consists of MBE deposition of a thin silicon buffer layer, the n-type delta doping layer, and a thin silicon cap layer. The n dopant selected for initial experiments was antimony, but other n dopants as (phosphorus or arsenic) could be used. All n-type dopants in silicon tend to surface-segregate during growth, leading to a broadened dopant-concentration- versus-depth profile. In order to keep the profile as narrow as possible, the substrate temperature is held below 300 C during deposition of the silicon cap layer onto the antimony delta layer. The deposition of silicon includes a silicon- surface-preparation step, involving H-termination, that enables the growth of high-quality crystalline silicon at the relatively low temperature with close to full electrical activation of donors in the surface layer.

Blacksberg, Jordana↗
NASA NTRS1985

Statistical mechanics of light elements at high pressure. VII - A perturbative free energy for arbitrary mixtures of H and He

A model free energy is presented which accurately represents results from 45 high-precision Monte Carlo calculations of the thermodynamics of hydrogen-helium mixtures at pressures of astrophysical and planetophysical interest. The free energy is calculated using free-electron perturbation theory (dielectric function theory), and is an extension of the expression given in an earlier paper in this series. However, it fits the Monte Carlo results more accurately, and is valid for the full range of compositions from pure hydrogen to pure helium. Using the new free energy, the phase diagram of mixtures of liquid metallic hydrogen and helium is calculated and compared with earlier results. Sample results for mixing volumes are also presented, and the new free energy expression is used to compute a theoretical Jovian adiabat and compare the adiabat with results from three-dimensional Thomas-Fermi-Dirac theory. The present theory gives slightly higher densities at pressures of about 10 megabars.

Hubbard, W. B.↗
NASA NTRS1999

Integrating Partial Polarization into a Metal-Ferroelectric-Semiconductor Field Effect Transistor Model

The ferroelectric channel in a Metal-Ferroelectric-Semiconductor Field Effect Transistor (MFSFET) can partially change its polarization when the gate voltage near the polarization threshold voltage. This causes the MFSFET Drain current to change with repeated pulses of the same gate voltage near the polarization threshold voltage. A previously developed model [11, based on the Fermi-Dirac function, assumed that for a given gate voltage and channel polarization, a sin-le Drain current value would be generated. A study has been done to characterize the effects of partial polarization on the Drain current of a MFSFET. These effects have been described mathematically and these equations have been incorporated into a more comprehensive mathematical model of the MFSFET. The model takes into account the hysteresis nature of the MFSFET and the time dependent decay as well as the effects of partial polarization. This model defines the Drain current based on calculating the degree of polarization from previous gate pulses, the present Gate voltage, and the amount of time since the last Gate volta-e pulse.

MacLeod, Todd C.↗
NASA NTRS1985

Theoretical Thermodynamics of Mixtures at High Pressures

The development of an understanding of the chemistry of mixtures of metallic hydrogen and abundant, higher-z material such as oxygen, carbon, etc., is important for understanding of fundamental processes of energy release, differentiation, and development of atmospheric abundances in the Jovian planets. It provides a significant theoretical base for the interpretation of atmospheric elemental abundances to be provided by atmospheric entry probes in coming years. Significant differences are found when non-perturbative approaches such as Thomas-Fermi-Dirac (TFD) theory are used. Mapping of the phase diagrams of such binary mixtures in the pressure range from approx. 10 Mbar to approx. 1000 Mbar, using results from three-dimensional TFD calculations is undertaken. Derivation of a general and flexible thermodynamic model for such binary mixtures in the relevant pressure range was facilitated by the following breakthrough: there exists an accurate nd fairly simple thermodynamic representation of a liquid two-component plasma (TCP) in which the Helmholtz free energy is represented as a suitable linear combination of terms dependent only on density and terms which depend only on the ion coupling parameter. It is found that the crystal energies of mixtures of H-He, H-C, and H-O can be satisfactorily reproduced by the same type of model, except that an effective, density-dependent ionic charge must be used in place of the actual total ionic charge.

Hubbard, W. B.↗
NASA NTRS1985

Statistical mechanics of light elements at high pressure. VIII - Thomas-Fermi-Dirac theory for binary mixtures of H with He, C, and O

We present three-dimensional Thomas-Fermi-Dirac calculations of lattice mixing energies of hydrogen with carbon and oxygen atoms, respectively. The results are used to derive effective interatomic potentials for use in liquid-state mixture calculations. We then use the potentials to derive analytic expressions for binary mixture-free energies and to map out the phase diagrams of mixtures of hydrogen with, respectively, helium, carbon, and oxygen, over a pressure range of about 5 to about 10 to the 3rd Mbar. Within this pressure range, all three of the latter elements are found to have unlimited solubility in metallic hydrogen over a temperature range which lies above their pure-element melting temperatures, and which includes likely interior temperatures in the Jovian planets.

Hubbard, W. B.↗
NASA NTRS1998

Modeling of Metal-Ferroelectric-Semiconductor Field Effect Transistors

The characteristics for a MFSFET (metal-ferroelectric-semiconductor field effect transistor) is very different than a conventional MOSFET and must be modeled differently. The drain current has a hysteresis shape with respect to the gate voltage. The position along the hysteresis curve is dependent on the last positive or negative polling of the ferroelectric material. The drain current also has a logarithmic decay after the last polling. A model has been developed to describe the MFSFET drain current for both gate voltage on and gate voltage off conditions. This model takes into account the hysteresis nature of the MFSFET and the time dependent decay. The model is based on the shape of the Fermi-Dirac function which has been modified to describe the MFSFET's drain current. This is different from the model proposed by Chen et. al. and that by Wu.

Duen Ho, Fat↗
NASA NTRS1983

Statistical mechanics of light elements at high pressure. V Three-dimensional Thomas-Fermi-Dirac theory

A numerical technique for solving the Thomas-Fermi-Dirac (TED) equation in three dimensions, for an array of ions obeying periodic boundary conditions, is presented. The technique is then used to calculate deviations from ideal mixing for an alloy of hydrogen and helium at zero temperature and high presures. Results are compared with alternative models which apply perturbation theory to calculation of the electron distribution, based upon the assumption of weak response of the electron gas to the ions. The TFD theory, which permits strong electron response, always predicts smaller deviations from ideal mixing than would be predicted by perturbation theory. The results indicate that predicted phase separation curves for hydrogen-helium alloys under conditions prevailing in the metallic zones of Jupiter and Saturn are very model dependent.

Macfarlane, J. J.↗
NASA NTRS1984

Statistical mechanics of light elements at high pressure. VI - Liquid-state calculations with Thomas-Fermi-Dirac theory

A model free energy is developed for hydrogen-helium mixtures based on solid-state Thomas-Fermi-Dirac calculations at pressures relevant to the interiors of giant planets. Using a model potential similar to that for a two-component plasma, effective charges for the nuclei (which are in general smaller than the actual charges because of screening effects) are parameterized, being constrained by calculations at a number of densities, compositions, and lattice structures. These model potentials are then used to compute the equilibrium properties of H-He fluids using a charged hard-sphere model. The results find critical temperatures of about 0 K, 500 K, and 1500 K, for pressures of 10, 100, and 1000 Mbar, respectively. These phase separation temperatures are considerably lower (approximately 6,000-10,000 K) than those found from calculations using free electron perturbation theory, and suggest that H-He solutions should be stable against phase separation in the metallic zones of Jupiter and Saturn.

Macfarlane, J. J.↗
NASA NTRS1992

Theoretical investigation of gas-surface interactions

The investigation into the appearance of intruder states from the negative continuum when some of the two-electron integrals were omitted was completed. The work shows that, provided all integrals involving core contracted functions in an atomic general contraction are included, or that the core functions are radially localized, meaningful results are obtained and intruder states do not appear. In the area of program development, the Dirac-Hartree-Fock (DHF) program for closed-shell polyatomic molecules was extended to permit Kramers-restricted open-shell DHF calculations with one electron in an open shell or one hole in a closed shell, or state-averaged DHF calculations over several particle or hole doublet states. One application of the open-shell code was to the KO molecule. Another major area of program development is the transformation of integrals from the scalar basis in which they are generated to the 2-spinor basis employed in parts of the DHF program, and hence to supermatrix form. Particularly concerning the omission of small component integrals, and with increase in availability of disk space, it is now possible to consider transforming the integrals. The use of ordered integrals, either in the scalar basis or in the 2-spinor basis, would considerably speed up the construction of the Fock matrix, and even more so if supermatrices were constructed. A considerable amount of effort was spent on analyzing the integral ordering and tranformation for the DHF program. The work of assessing the reliability of the relativistic effective core potentials (RECPs) was continued with calculation of the group IV monoxides. The perturbation of the metal atom provided by oxygen is expected to be larger than that provided by hydrogen and thus provide a better test of the qualification of the RECPs. Calculations on some platinum hydrides were carried out at nonrelativistic (NR), perturbation theory (PT) and DHF levels. Reprints of four papers describing this work are included.

Dyall, Kenneth G.↗