Merle E. Riley

Approximations for the exchange potential in electron scattering

Four new exchange potentials (the semiclassical exchange approximation, the asymptotically adjusted free‐electron–gas exchange approximation, the second‐order free‐electron–gas exchange approximation, and the high‐energy exchange approximation) are derived. Calculations are performed for elastic electron scattering from helium and argon. The results are compared to one another and to calculations using Hara’s free‐electron–gas approximation and the exact nonlocal exchange potential. Three of the approximations to exchange are in good agreement with the exact exchange —except at very low energy— but are much easier to use. Thus they should be very useful in electron–atom and electron–molecule scattering calculations.

Bremsstrahlung energy spectra from electrons of kinetic energy 1 keV ≤ T1 ≤ 2000 keV incident on neutral atoms 2 ≤ Z ≤ 92

Abstract A tabulation is presented of theoretical predictions for the electron bremsstrahlung energy spectrum from neutral atoms as a function of atomic number Z, incident electron kinetic energy T1, and fraction of energy radiated k T 1 . Tabulated values were obtained by interpolation from a smaller set of calculated data points. These calculated points were obtained by describing bremsstrahlung as a single-electron transition in a relativistic self-consistent screened potential and, after expansions in partial waves, by performing a numerical evaluation for radial wavefunctions and matrix elements.

Dynamics of collisionless rf plasma sheaths

The behavior of rf plasma sheaths has been the subject of much scientific study and also is technologically important for plasma etching and deposition in the manufacture of integrated circuits. This paper presents a semianalytic model of rf sheaths and describes an experiment that tested the model. An approximation to the first integral of the Poisson equation allows solving for the response of plasma sheaths to an imposed rf bias voltage. This approximation enables the plasma sheaths to be included within an electrical model of the plasma and external rf circuit components, and affords a prediction of the ion energy distributions impacting the electrodes, which are in contact with the plasma. The model is a significant advance beyond previous sheath models because it has no restriction on the ratio of the rf period to the ion transit time across the sheath. The model is applicable to those high-density, low-pressure plasmas in which the Debye length is a small fraction of the ion mean-free path, which i...

Ion energy and angular distributions in inductively coupled radio frequency discharges in argon

We report measurements of the energies and angular distributions of positive ions in an inductively coupled argon plasma in a Gaseous Electronics Conference Reference Cell. Use of two separate ion detectors allowed measurement of ion energies and fluxes as a function of position as well as ion angular distributions on the discharge centerline. The inductive drive on our system produced high plasma densities (up to 1012/cm3 electron densities) and relatively stable plasma potentials. As a result, ion energy distributions typically consisted of a single feature well separated from zero energy. Mean ion energy was independent of rf power and varied inversely with pressure, decreasing from 29 to 12 eV as pressure increased from 2.4 to 50 mTorr. The half‐widths of the ion angular distributions in these experiments varied from 5° to 9°, or equivalently, the transverse temperatures varied from 0.18 to 0.29 eV with the distributions broadening as either pressure or rf power was increased.

A velocity reset method of simulating thermal motion and damping in gas–solid collisions

We present a velocity reset procedure for the approximate description of the molecular dynamics of a tractable subset of the atoms composing a macroscopic solid which is subjected to collisions. The coupling of the subset to the remainder (the reservoir) is taken into account in a stochastic manner by periodically resetting the velocities of subset particles which interact with the reservoir. The Cartesian velocity components are reset to vnew =(1−θ)1/2vold +θ1/2vT, where vold is the previous velocity, vT is a random velocity chosen from a Maxwellian distribution at temperature T, and θ is a parameter which controls the strength of the reset. In the limit θ=1 and all subset particles are reset, the method is similar to Andersen’s thermostat procedure [J. Chem. Phys. 72, 2384 (1980)]. In the double limit that θ→0 and the interval between resets Δtrs →0 such that β=θ/2Δtrs is fixed, the equations of motion for the subset reduce to Langevin form, where β is the frictional damping rate. This partial velocity ...

Ion energy and angular distributions in inductively driven radio frequency discharges in chlorine

In this article, we report values of ion energy and angular distributions measured at the grounded electrode of an inductively coupled discharge in chlorine gas. The inductive rf drive in our cell produced high plasma densities (1011/cm3 electron densities) and stable plasma potentials. As a result, ion energy distributions typically consisted of a single peak well separated from zero energy. Mean ion energy varied inversely with pressure, decreasing from 13 to 9 eV as the discharge pressure increased from 20 to 60 mTorr. Half-widths of the ion angular distributions in these experiments varied from 6° to 7.5°, corresponding to transverse energies from 0.13 to 0.21 eV. During the course of the experiment, ion energies gradually decreased, probably due to the buildup of contaminants on the chamber walls. Cell wall temperature also was an important variable, with ion fluxes to the lower electrode increasing and the ion angular distribution narrowing as the cell temperature increased.

Absolute Intensities of the Vacuum Ultraviolet Spectra in a Metal-Etch Plasma Processing Discharge

In this paper we report absolute intensities of vacuum ultraviolet and near ultraviolet emission lines (4.8 eV to 18 eV ) for aluminum etching discharges in an inductively coupled plasma reactor. We report line intensities as a function of wafer type, pressure, gas mixture and rf excitation level. IrI a standard aluminum etching mixture containing C12 and BC13 almost all the light emitted at energies exceeding 8.8 eV was due to neutral atomic chlorine. Optical trapping of the WV radiation in the discharge complicates calculations of VUV fluxes to the wafer. However, we see total photon fluxes to the wailer at energies above 8.8 eV on the order of 4 x 1014 photons/cm2sec with anon- reactive wafer and 0.7 x 10 `4 photons/cm2sec with a reactive wtier. The maj ority of the radiation observed was between 8.9 and 9.3 eV. At these energies, the photons have enough energy to create electron-hole pairs in Si02, but may penetrate up to a micron into the Si02 before being absorbed. Relevance of these measurements to vacuum-W photon-induced darnage of Si02 during etching is discussed.

Effects of the Pauli principle on electron scattering by open-shell targets

The semiclassical exchange approximation and two free‐electron–gas exchange approximations are applied to electron scattering from the hydrogen atom. In the triplet spin state the results are similar to our previous findings [M. E. Riley and D. G. Truhlar, J. Chem. Phys. 63, 2182 (1975)] for electron scattering by closed‐shell atoms. However these results, already of useful accuracy, are improved by the inclusion of one‐electron exchange terms or an orthogonality constraint. For the singlet spin state it is essential to include the one‐electron exchange terms except at high impact energies (greater than about 50 eV). The approximation of Lippmann, Schey, Burke, and Chandra for treating exchange in closed‐shell systems is tested and found to be less accurate than the present approximations.

Ion distribution functions in inductively coupled radio frequency discharges in argon–chlorine mixtures

We report on measurements of positive ion energies, current densities, and angular distributions at the grounded electrode of inductively coupled discharges in mixtures of argon and chlorine. We also report on ion species and Langmuir probe measurements for these discharges. The inductive drive in our gaseous electronics conference reference cell produced high plasma densities (1011–1012/cm3) and stable plasma potentials. As a result, ion energy distributions consisted of a single peak well separated from zero energy. At pressures of 2.5–20 mTorr and constant rf power, the addition of Cl2 to an Ar discharge lowered ion current densities, reduced ion energies, and reduced the width of the ion energy distributions. Half-widths of the ion angular distributions ranged from 4.5° to 8.5° with the distributions broadening with increases in pressure or rf power. The addition of Cl2 to Ar discharges made the angular distributions less sensitive to total pressure. Cl+ replaced Ar+ as the dominant ionized species wh...

Ion energy distributions at rf-biased wafer surfaces

We report the measurement of ion energy distributions at a radio frequency (rf)-biased electrode in inductively driven discharges in argon. We compare measurements made with a gridded energy analyzer and a commercial analyzer that contains a mass spectrometer and energy analyzer in tandem. The inductive drive and the rf bias in our Gaseous Electronics Conference reference cell were both at 13.56 MHz. By varying the plasma density, we were able to examine the transition region between the “low frequency limit” for rf bias and the intermediate frequency region where, at fixed bias frequency, the ion energy distribution width varies with the plasma density. We find that the experimental ion energy distributions become narrower as the time for ion transit through the sheath approaches the rf period, but that the ion distributions still have widths which are ∼90% of their low frequency limit when the ion transit time is 40% of the rf period. Space-charge-induced beam broadening inside our analyzers appears to ...