Function Of Average Electron Energy Research Articles

Determination of relative ion chamber calibration coefficients from depth-ionization measurements in clinical electron beams

A method is presented to obtain ion chamber calibration coefficients relative to secondary standard reference chambers in electron beams using depth-ionization measurements. Results are obtained as a function of depth and average electron energy at depth in 4, 8, 12 and 18 MeV electron beams from the NRC Elekta Precise linac. The PTW Roos, Scanditronix NACP-02, PTW Advanced Markus and NE 2571 ion chambers are investigated. The challenges and limitations of the method are discussed. The proposed method produces useful data at shallow depths. At depths past the reference depth, small shifts in positioning or drifts in the incident beam energy affect the results, thereby providing a built-in test of incident electron energy drifts and/or chamber set-up. Polarity corrections for ion chambers as a function of average electron energy at depth agree with literature data. The proposed method produces results consistent with those obtained using the conventional calibration procedure while gaining much more information about the behavior of the ion chamber with similar data acquisition time. Measurement uncertainties in calibration coefficients obtained with this method are estimated to be less than 0.5%. These results open up the possibility of using depth-ionization measurements to yield chamber ratios which may be suitable for primary standards-level dissemination.

One-dimensional modelling of a capacitively coupled rf plasma in silane/helium, including small concentrations of O2 and N2

Functional coating deposition using plasma is broadly used in industrial application working at a pressure ranging from low pressure discharges (a few Pascals) to atmospheric plasmas. The active gas (silane is selected for this study) is often diluted in a gas that helps in stabilizing the discharge like helium or argon. In addition, the discharge can be polluted by uncontrolled external gas source like air or oxygen coming from water adsorbed in reactor walls. In this paper, we study the interactions taking place within the bulk of a capacitively coupled plasma and study the impact of these reactions on the flux of species moving towards the substrate and so the impact on the composition of deposited film. A one-dimensional fluid model is presented for the modelling of radio frequency capacitively coupled plasmas in a mixture of silane/helium, including small concentrations of O2 and N2. In total, 48 different species (electrons, ions, neutrals, radicals and excited species) are considered in the model. After a sensitivity study, 27 electron–neutral and 76 chemical reactions (i.e. ion–neutral and neutral–neutral reactions) were maintained in the fluid model. The fluid model itself consists of a set of mass balance equations (i.e. one for every species), the electron energy equation and the Poisson equation. The reaction rate coefficients of the electron–neutral reactions, as a function of average electron energy, are obtained from a Boltzmann model. The reaction rate coefficients of the ion–neutral and neutral–neutral reactions are assumed to be constant. It is found that helium does not affect the silane plasma chemistry drastically. The incorporation of small amounts of air (containing about 82% N2 and 18% O2) in a silane/helium plasma, however, influences the plasma chemistry to a large extent. A large number of nitrogen species (i.e. N2, N, N2+), and species containing oxygen (i.e. SiH3O SiO, OH and others), are present in the discharge at relatively high densities (i.e. of the order of 1014–1017 m−3).

Modeling of plasma-etch processes using well stirred reactor approximations and including complex gas-phase and surface reactions

A 0-D or well stirred reactor model determines spatially and time-averaged species composition in plasma-etch reactors, through solution of species, mass, and electron-energy balance equations. The use of well stirred reactor approximations reduces the computational expense of detailed kinetics calculations and allows investigation of the dependence of plasma chemistry on etch-process parameters. The reactor is characterized by a chamber volume, surface area, net mass flow or residence time, pressure, energy loss to surroundings, power deposition, and inlet-gas composition. The electron-energy equation includes a detailed power balance with losses to ions and electrons through the sheath, as well as inelastic and elastic collision losses. The model employs reaction-rate coefficients for electron-impact reactions, which require an assumption of the electron energy distribution function (EEDF). We compare model results using Maxwellian EEDF's, as well as reaction-rate coefficients determined as a function of average electron energy through solution of the Boltzmann equation, for chlorine chemistry. The Boltzmann rates are determined by time-lagging the equilibration of electrons with applied electric fields. The Maxwellian reaction rates give higher ionization fractions than the Boltzmann rates, affecting the predicted electronegativity and positive ion composition for chlorine plasmas. The model also shows a strong sensitivity of the plasma composition to the assumed surface-recombination probability of atomic chlorine. >

Hydrodynamic hot-electron transport model with Monte Carlo-generated transport parameters

A unique hot-electron transport model suitable for studying submicron GaAs device structures is presented. The model is based on the semiclassical “hydrodynamic” conservation equations for the average electron density, momentum, and energy. The model includes electron relaxation times, momentum relaxation times, energy relaxation times, electron temperature tensors and heat flow vectors as a function of average electron energy for the Γ, X and L valleys of GaAs. The relaxation times represent rates of exchange of electrons between valleys and rates of loss of average momentum and average energy between and within the individual valleys. The electron temperature tensor and heat flow vector depend on the electron velocity distribution about the average electron velocity and ultimately affect transport when spatial variations in average velocity and average energy exist. Transport parameters are calculated using the Monte Carlo method and the ergodic principle applied directly to the integral definitions for the parameters. Therefore, the model includes nonequilibrium transport effects such as velocity overshoot and nonuniform average electron energy. The new model should prove instrumental in optimizing electron transport through submicron structures for high-speed device applications.

Theoretical analysis of the DC avalanche breakdown in GaAs MESFET's

The channel avalanche breakdown in GaAs MESFET's has been investigated using nonstationary electron dynamics and an ionization coefficient taken as a function of average electron energy. Stationary high-field domains of different shapes and peak-field localization are calculated at the breakdown, depending on technological parameters, device geometry or gate bias. Design rules are given to obtain maximum saturated output power and a full-channel current breakdown voltage comparable to the one near pinchoff. In particular, it is found that both a recessed channel geometry and an increased gate-drain distance should yield the best device performances with a doping level not higher than about 1.2-10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">17</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> and a channel current I <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dss</inf> between 275 and 330 mA/mm.