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NASA NTRS2008

Electron Impact Ionization: A New Parameterization for 100 eV to 1 MeV Electrons

Low, medium and high energy electrons can penetrate to the thermosphere (90-400 km; 55-240 miles) and mesosphere (50-90 km; 30-55 miles). These precipitating electrons ionize that region of the atmosphere, creating positively charged atoms and molecules and knocking off other negatively charged electrons. The precipitating electrons also create nitrogen-containing compounds along with other constituents. Since the electron precipitation amounts change within minutes, it is necessary to have a rapid method of computing the ionization and production of nitrogen-containing compounds for inclusion in computationally-demanding global models. A new methodology has been developed, which has parameterized a more detailed model computation of the ionizing impact of precipitating electrons over the very large range of 100 eV up to 1,000,000 eV. This new parameterization method is more accurate than a previous parameterization scheme, when compared with the more detailed model computation. Global models at the National Center for Atmospheric Research will use this new parameterization method in the near future.

Fang, Xiaohua↗
NASA NTRS1982

Venus nightside ionosphere - A model with KeV electron impact ionization

The impact of keV electrons is proposed as the strongest source of ionization in a full-up Venus nightside ionosphere model for the equatorial midnight region. The electron impacts lead to a peak ion density of 100,000/cu cm, which was observed by the PV-OIMS experiment on several occasions. In addition, the observed altitude profiles of CO2(+), O(+), O2(+), H(+), and H2(+) can be reproduced by the model on condition that the available keV electron flux is approximated by a reasonable extrapolation from fluxes observed at lower energies.

Kumar, S.↗
NASA NTRS1982

Impact ionization study

The impact ionization phenomenon which was observed on certain spacecraft was studied. The phenomenon occurs when a neutral atom, molecule, or ion strikes a surface with sufficient kinetic energy that either the incident neutral or atoms on the surface are ionized, with subsequent escape of ions and/or electrons. The released ions and electrons can interfere with measurements on the spacecraft by confusing interpretation of the data. On the other hand, there is the possibility that the effect could be developed into a diagnostic tool for investigating neutral atmospheric species or for studying physical processes on spacecraft surfaces.

Whipple, E. C., Jr.↗
NASA NTRS1989

The effect of electron temperature and impact ionization on Martian return AOTV flowfields

Various electron impact ionization models in conjunction with a quasi-equilibrium electron temperature model have been investigated and applied to the stagnation region of a hypothetical 2.3 m nose radius Martian return AOTV. For the conditions considered, U = 12 km/sec at 80 km, both multi-temperature inviscid and viscous results indicate that a two-step ionization impact model predicts ionization distances in agreement with experimental data, that nonequilibrium chemistry and radiation effects are important throughout the stagnation zone, and that the quasi-equilibrium electron temperature model is reasonable. Also, using a non-grey emission-absorption radiation step model, it is shown that nonequilibrium causes a reduction in radiative heating from that predicted for equilibrium conditions and that compared to an adiabatic wall a cool wall (1650 deg K) results in a 28 to 45 percent reduction in radiative heating due to absorption near the wall.

Carlson, Leland A.↗
NASA NTRS1993

Oxygen ionization rates at Mars and Venus - Relative contributions of impact ionization and charge exchange

Oxygen ion production rates above the ionopauses of Venus and Mars are calculated for photoionization, charge exchange, and solar wind electron impact ionization processes. The latter two require the use of the Spreiter and Stahara (1980) gas dynamic model to estimate magnetosheath velocities, densities, and temperatures. The results indicate that impact ionization is the dominant mechanism for the production of O(+) ions at both Venus and Mars. This finding might explain both the high ion escape rates measured by Phobos 2 and the greater mass loading rate inferred for Venus from the bow shock positions.

Zhang, M. H. G.↗
NASA NTRS1987

Tunneling-assisted impact ionization for a superlattice

Tunneling-assisted impact ionization across the conduction-band-edge discontinuity of quantum-well heterostructures is investigated and applied to a new superlattice structure. Multiquantum-well structures where the quantum-well regions are heavily doped and the undoped barrier regions are essentially insulating were considered. Incident hot electrons due to the applied electric field perpendicular to the heterointerface interact with the two-dimensional electrons confined to the quantum wells through Coulomb force. The resultant electrons can either have enough energy to get out of the wells or to tunnel through the triangular barriers. A new analytical approximation for the impact ionization rate is given which compares favorably with numerical results. The tunneling-assisted impact ionization rates and the ionization coefficients are calculated. It is shown that the tunneling effect reduces the ionization threshold and enhances the ionization rate significantly.

Chuang, S. L.↗
NASA NTRS1995

Electron impact ionization rates for interstellar neutral H and He atoms near interplanetary shocks: Ulysses observations

During average solar wind flow conditions at 1 AU, ionization rates of interstellar neutrals that penetrate into the inner heliosphere are dominated by charge exchange with solar wind protons for H atoms, and by photoionization for He atoms. During occurrences of strong, coronal mass ejection (CME)-driven interplanetary shock waves near 1 AU, electron impact ionization can make substantial, if not dominating, contributions to interstellar neutral ionization rates in the regions downstream of the shocks. However, electron impact ionization is expected to be relatively less important with increasing heliocentric distance because of the decrease in electron temperature. Ulysses encountered many CME-driven shocks during its journey to and beyond Jupiter, and in addition, encountered a number of strong corotating interaction region (CIR) shocks. These shocks generally occur only beyond approximately 2 AU. Many of the CIR shocks were very strong rivalling the Earth's bow shock in electron heating. We have compared electron impact ionization rates calculated from electron velocity distributions measured downstream from CIR shocks using the Ulysses SWOOPS experiment to charge-exchange rates calculated from measured proton number fluxes and the photoionization rate estimated from an assumed solar photon spectrum typical of solar maximum conditions. We find that, although normally the ratio of electron-impact ionization rates to charge-exchange (for H) and to photoionization (for He) rates amounts to only about one and a few tens of percent, respectively, downstream of some of the stronger CIR shocks they amount to more than 10% and greater than 100%, respectively.

Feldman, W. C.↗
NASA NTRS1994

Semiclassical Study of the Wave Vector Dependence of the Interband Impact Ionization Rate in Bulk Silicon

We present calculations of the interband impact ionization rate calculated using a wave vector dependent (k-dependent) semiclassical formulation of the transition rate. The transition rate is determined using Fermi's golden rule from a two-body screened Coulomb interaction assuming energy and momentum conservation. The transition rate is calculated for the first two conduction bands of silicon by numerically integrating over the full Brillouin zone. The overlap integrals in the expression for the transition rate are determined numerically using a 15 band k-p calculation. It is found that the transition rate depends strongly on the initiating electron wave vector (k vector) and that the transition rate is greatest for electrons originating within the second conduction band than the first conduction band. An ensemble Monte Carlo simulation, which includes the numerically determined ionization transition rate as well as the full details of the first two conduction bands, is used to calculate the total impact ionization rate in bulk silicon. Good agreement with the experimentally determined electron ionization rate data is obtained.

Wang, Yang↗
NASA NTRS1995

Theoretical study of hole initiated impact ionization in bulk silicon and GaAs using a wave-vector-dependent numerical transition rate formulation within an ensemble Monte Carlo calculation

In this paper, calculations of the hole initiated interband impact ionization rate in bulk silicon and GaAs are presented based on an ensemble Monte Carlo simulation with the inclusion of a wave-vector-dependent numerical transition rate formulation. The ionization transition rate is determined for each of the three valence bands, heavy, light, and split-off, using Fermi's golden rule with a two-body, screened Coulomb interaction. The dielectric function used within the calculation is assumed to be wave-vector-dependent. Calculations of the field-dependent impact ionization rate as well as the quantum yield are presented. It is found from both the quantum yield results and examination of the hole distribution function that the effective threshold energy for hole initiated impact ionization is relatively soft, similar to that predicted for the corresponding electron initiated ionization events occur more frequently than either heavy or split-offf initiated ionization events in bulk silicon over the applied electric field strengths examined here, 250-500 kV/cm. Conversely,in GaAs, the vast majority of hole initated ionization events originate from holes within the split-off band.

Oguzman, Ismail H.↗
NASA NTRS1982

Threshold law for electron-atom impact ionization

A derivation of the explicit form of the threshold law for electron impact ionization of atoms is presented, based on the Coulomb-dipole theory. The important generalization is made of using a dipole function whose moment is the dipole moment formed by an inner electron and the nucleus. The result is a modulated quasi-linear law for the yield of positive ions which applies to positron-atom impact ionization.

Temkin, A.↗
NASA NTRS1994

Numerical Study of the Wave-Vector Dependence of the Electron Interband Impact Ionization Rate in Bulk GaAs

Ensemble Monte Carlo calculations of the electron interband impact ionization rate in bulk GaAs are presented using a wave-vector (k)-dependent formulation of the ionization transition rate. The transition rate is evaluated through use of numerically generated wavefunctions determined via a k-p calculation within the first two conduction bonds at numerous points within a finely spaced three-dimensional grid in k space. The transition rate is determined to be greatest for states within the second conduction band. It is found that the interband impact ionization transition rate in bulk GaAs is best characterized as having an exceedingly "soft" threshold energy. As a consequence, the dead space, defined as the distance over which the ionization probability for a given carrier is assumed to be zero, is estimated to be-much larger than that estimated using a "harder" threshold. These results have importance in the design of multiquantum-well avalanche photodiodes.

Wang, Yang↗
NASA NTRS1994

Numerical study of the wave-vector dependence of the electron interband impact ionization rate in bulk GaAs

Ensemble Monte Carlo calculations of the electron interband impact ionization rate in bulk GaAs are presented using a wave-vector (k)-dependent formulation of the ionization transition rate. The transition rate is evaluated through the use of numerically generated wavefunctions determined via a k-p calculation within the first two conduction bands at numerous points within a finely spaced three-dimensional grid in k space. The transition rate is determined to be greatest for states within the second conduction band. Is is found that the interband impact ionization transition rate in bulk GaAs is best characterized as having an exceedingly soft threshold energy. As a consequence, the dead space, defined as the distance over which the ionization probability for a given carrier is assumed to be zero, is estimated to be much larger than that estimated using a harder threshold. These results have importance in the design of the multiquantum-well avalanche photodiodes.

Wang, Yang↗
NASA NTRS1994

Theoretical Investigation of Wave-Vector-Dependent Analytical and Numerical Formulations of the Interband Impact-Ionization Transition Rate for Electron in Bulk Silicon and GaAs

The electron interband impact-ionization rate for both silicon and gallium arsenide is calculated using an ensemble Monte Carlo simulation with the expressed purpose of comparing different formulations of the interband ionization transition rate. Specifically, three different treatments of the transition rate are examined: the traditional Keldysh formula, a new k-dependent analytical formulation first derived by W. Quade, E Scholl, and M. Rudan, and a more exact, numerical method of Y. Wang and K. F. Brennan. Although the completely numerical formulation contains no adjustable parameters and as such provides a very reliable result, it is highly computationally intensive. Alternatively, the Keldysh formula, although inherently simple and computationally efficient, fails to include the k dependence as well as the details of the energy band structure. The k-dependent analytical formulation of Quade and co-workers overcomes the limitations of both of these models but at the expense of some new parameterization. It is found that the k-dependent analytical method of Quade and co-workers produces very similar results to those obtained with (he completely numerical model for some quantities. Specifically, both models predict that the effective threshold for impact ionization in GaAs and silicon is quite soft, that the majority of ionization events originate from the second conduction band in both materials, and that the transition rate is k dependent. Therefore, it is concluded that the k-dependent analytical model can qualitatively reproduce results similar to those obtained with the numerical model yet with far greater computational efficiency. Nevertheless, there exist some important drawbacks to the k-dependent analytical model of Quade and co-workers: These are that it does not accurately reproduce the quantum yield data for bulk silicon, it requires determination of a new parameter, related physically to (he overlap integrals of the Bloch state which can only be adjusted by comparison to experiment, and fails to account for any wave-vector dependence of the overlap integrals. As such [he transition rate may be overestimated at those points for which "near vertical," small change in k, transitions occur.

Kolnik, Jan↗
NASA NTRS1994

Theoretical investigation of wave-vector-dependent analytical and numerical formulations of the interband impact-ionization transition rate for electrons in bulk silicon and GaAs

The electron interband impact-ionization rate for both silicon and gallium arsenide is calculated using an ensemble Monte Carlo simulation with the expressed purpose of comparing different formulations of the interband ionization transition rate. Specifically, three different treatments of the transition rate are examined: the traditional Keldysh formula, a new k-dependent analytical formulation first derived by W. Quade, E. Scholl, and M. Rudan (1993), and a more exact, numerical method of Y. Wang and K. F. Brennan (1994). Although the completely numerical formulation contains no adjustable parameters and as such provides a very reliable result, it is highly computationally intensive. Alternatively, the Keldysh formular, although inherently simple and computationally efficient, fails to include the k dependence as well as the details of the energy band structure. The k-dependent analytical formulation of Quade and co-workers overcomes the limitations of both of these models but at the expense of some new parameterization. It is found that the k-dependent analytical method of Quade and co-workers produces very similar results to those obtained with the completely numerical model for some quantities. Specifically, both models predict that the effective threshold for impact ionization in GaAs and silicon is quite soft, that the majority of ionization events originate from the second conduction band in both materials, and that the transition rate is k dependent. Therefore, it is concluded that the k-dependent analytical model can qualitatively reproduce results similar to those obtained with the numerical model yet with far greater computational efficiency. Nevertheless, there exist some important drawbacks to the k-dependent analytical model of Quade and co-workers: These are that it does not accurately reproduce the quantum yield data for bulk silicon, it requires determination of a new parameter, related physically to the overlap intergrals of the Bloch state which can only be adjusted by comparison to experiment, and fails to account for any wave-vector dependence of the overlap integrals. As such the transition rate may be overestimated at those points for which 'near vertical,' small change in k, transitions occur.

Kolnik, Jan↗
NASA NTRS1977

Angular distribution of Auger electrons due to 3d-shell impact ionization of krypton

Cross sections for electron impact ionization of krypton due to ejection of a 3d-shell electron have been calculated using screened hydrogenic and Hartree-Slater wavefunctions for the target atom. While the total ionization cross sections in the two approximations are within 10% of each other, the Auger electron angular distribution, related to cross sections for specific magnetic quantum numbers of the 3d electrons, are widely different in the two approximations. The angular distribution due to the Hartree-Slater approximation is in excellent agreement with measurement. The physical reason for the discrepancies in the two approximations is explained.

Omidvar, K.↗