H. Deutsch

The energy balance at substrate surfaces during plasma processing

Abstract A summary is given of different elementary processes influencing the thermal balance and energetic conditions of substrate surfaces during plasma processing. The discussed mechanisms include heat radiation, kinetic and potential energy of charged particles and neutrals as well as enthalpy of involved chemical surface reactions. The energy and momentum of particles originating from the plasma or electrodes, respectively, influence via energy flux density (energetic aspect) and substrate temperature (thermal aspect) the surface properties of the treated substrates. The various contributions to the energy balance are given in a modular mathematical framework form and examples for an estimation of heat fluxes and numerical values of relevant coefficients for energy transfer, etc. are given. For a few examples as titanium film deposition by hollow cathode arc evaporation, silicon etching in CF 4 glow discharge, plasma cleaning of contaminated metal surfaces, and magnetron sputtering of aluminum the energetic balance of substrates during plasma processing will be presented. Furthermore, the influence of the resulting substrate temperature on characteristic quantities as etching or deposition rates, layer density, microstructure, etc. will be illustrated for some examples, too.

Theoretical determination of absolute electron-impact ionization cross sections of molecules

Abstract Much emphasis has been devoted recently to the experimental determination of absolute electron-impact ionization cross sections of molecules and radicals because of the importance of these cross sections in many applications (e.g. as input parameters to modeling codes for various purposes). Supporting theoretical calculations have been lagging behind to some extent. Because of the inherent complexity of such calculations, simplistic additivity rules and semiempirical methods have often been used in place of more rigorous calculation schemes, particularly in applications where a larger number of cross section data were needed with reasonable precision. Although these methods have often proved to be quite successful as descriptive tools (i.e. reproducing existing experimental ionization cross sections reasonably well), their ability to calculate cross sections for species for which no experimental data are available (predictive capabilities) tend to be limited or questionable. This topical review describes recent progress in the development of more rigorous approaches for the calculation of absolute electron-impact molecular ionization cross sections. The main emphasis will be on the application of the semiclassical Deutsch–Mark (DM) formalism, which was originally developed for the calculation of atomic ionization cross sections, to molecular targets, and on the binary–encounter–Bethe (BEB) method of Kim and Rudd. The latter is a simpler version of the more rigorous binary–encounter–dipole (BED) theory, which was also first developed for the calculation of atomic ionization cross sections, and based on the methods developed by Khare and co-workers. Extensive comparisons between available experimental cross sections and the predictions of these theoretical models will be made for 31 molecules and free radicals (H 2 , N 2 , O 2 , S 2 , C 2 , C 3 , O 3 , H 2 O, NH 3 , CO 2 , CH 4 , CH 3 , CH 2 , CH, CF 4 , CF 3 , CF 2 , CF, NF 3 , NF 2 , NF, SiF 3 , SiF 2 , SiF, TiCl 4 , C 2 H 2 , C 2 H 6 , C 6 H 6 , SiF 6 , C 2 F 6 , CH 3 OH).

A semiclassical approach to the calculation of electron impact ionization cross-sections of atoms: from hydrogen to uranium

Abstract Absolute ionization cross-sections for single ionization by electron impact (from threshold up to 200 eV) of free gaseous atoms have been calculated by utilizing a recently proposed semiclassical approach (DM formulation). The formula used here is derived within the framework of classical and quantum mechanical approximations, and the necessary input parameters are determined and discussed. Where possible the calculated ionization cross-section functions are compared with experimental data sets and with the most widely used previous formulae such as the Gryzinski and Lotz formulae. It is concluded that the present approach leads on average to a better agreement with experimental results than previous classical, semiclassical and empirical treatments.

Energy influx from an rf plasma to a substrate during plasma processing

The energy influx delivered by an rf plasma to a metal substrate has been studied by a calorimetric method with a thermal probe. By changing the substrate voltage, the influence of the kinetic energy of the charge carriers to the thermal power could be determined. The measured energy influx for an argon plasma can be explained mainly by ions, electrons, and their recombination. In the case of an oxygen plasma, where the energy influx is under comparable conditions about 50% higher, also other transfer mechanisms such as surface-aided atom association and relaxation of rovibrational states have to be taken into consideration.

Electron impact ionization cross sections of molecules: Part II. Theoretical determination of total (counting) ionization cross sections of molecules: a new approach

Cross sections for single ionization of molecules by electrons (threshold ⩽ E ⩽ 200 eV) have been calculated using a newly developed semiclassical formula. The formula is a combination of the classical binary encounter approximation, the Born-Bethe approximation and the additivity rule. This formula has been applied to H2, N2, O2, H2O, CO2, C2H2, NH3, CH4, CF4, C2H4, CH3OH, SF6, UF6, C2H6 and C6H6 and the cross sections obtained have been compared with results from the classical binary encounter approximation (Gryzinski formula), the semiclassical Jain-Khare approach, and reliable experimental data. The main advantage of the present treatment is that ionization cross sections can be described by a simple analytical formula (depending only on basic atomic properties), which yields results in better agreement with experimental data than the classical formulae.

Microcalorimetry of dust particles in a radio-frequency plasma

The internal temperature of rhodamine B-dyed dust particles (2rp=1.2 μm) immersed in radio-frequency (rf) plasmas has been measured for various plasma conditions. For this purpose, the dye has been excited with an argon-ion laser and the fluorescent emission of the particles has been recorded with an optical multichannel analyzer system. The temperature has been determined after comparison with calibration curves. In argon, the particle temperature increases with rf power and is independent of pressure. In oxygen, an increase with rf power is observed, too. However, the energy flux towards the particles includes also heating by atom recombination (association) and exothermic combustion reactions. These temperature measurements have been compared with calculations based on the thermal balance, where measurements of gas temperature, electron density, and electron temperature have been used. A good agreement between theory and experiment has been found.

Absolute total and partial electron impact ionization cross sections of hexamethyldisiloxane

Abstract We studied the electron impact ionization of hexamethyldisiloxane (HMDSO), Si 2 O(CH 3 ) 6 , which is widely used in plasma-enhanced polymerization applications. Appearance energies and absolute partial cross sections for the formation of fragment ions with relative intensities >1% of the most abundant ion, the Si 2 O(CH 3 ) 5 + fragment ion, were measured in a high resolution double focusing sector field mass spectrometer with a modified ion extraction stage for electron energies from threshold to 100 eV. Dissociative ionization was found to be the dominant process. The main ionization channel removes a complete methyl group to produce the fragment ion Si 2 O(CH 3 ) 5 + with a cross section of 1.7 × 10 −15 cm 2 at 70 eV. The stoichiometric and isotope composition of the various fragment ions was determined by using the high resolution ( m /Δ m = 40,000) of the mass spectrometer used in these studies. The methyl ion is formed with considerable excess kinetic energy, whereas all other fragment ions are formed with essentially no excess energy. The experimental total single ionization cross section of HMDSO (2.2 × 10 −15 cm 2 at 70 eV impact energy) is in good agreement with the result of a semiempirical calculation (2.1 × 10 −15 cm 2 at the same energy).

A MODIFIED ADDITIVITY RULE FOR THE CALCULATION OF ELECTRON IMPACT IONIZATION CROSS-SECTION OF MOLECULES ABN

Abstract This paper describes a modified additivity rule for the calculation of electron impact ionization cross-sections of molecules and radicals of the form AB n ( n = 1–6). This additivity rule incorporates weighting factors for the contributions to the molecular ionization cross-sections from the ionization cross-sections of the constituent atoms, which depend explicitly on the atomic radii and the effective number of atomic electrons. In a few special cases (hydrides where the other constituent atom has a radius smaller than the radius of the H atom and species where both constituent atoms have radii smaller than the radius of the H atom), the weighting factors can be simplified, so that they depend only on the atomic radii, i.e. on geometric effects. A comprehensive comparison of the predictions of this new modified additivity rule with available experimental data and with other theoretical predictions is presented.

Dissociative ionization of silane by electron impact

Abstract We studied the electron impact ionization of silane (SiH4) which is widely used in the plasma deposition of different siliconcontaining thin films. Absolute partial cross-sections for the formation of all fragment ions were measured in a high resolution double focusing sector field mass spectrometer with a modified ion extraction stage for electron energies from threshold to 100 eV. No evidence for the formation of stable parent SiH4+ ions was found in agreement with previous experimental investigations. The single positive fragment ion formation is the dominant ionization process. We observed the following product ions: SiH3+, SiH2+, SiH+, Si+, H2+, and H+. The agreement between our measured absolute partial ionization crosssections and two earlier data sets obtained by different techniques is generally good for the silicon-containing fragment ions taking into account quoted uncertainties of ± 10% to ± 20%, but less satisfactory for the formation of atomic and molecular hydrogen ions which were found to be produced with significant excess kinetic energies, particularly in the case of H+. A comparison of the total SiH4 ionization cross-section derived from the measured partial ionization cross-sections and a calculated cross-section based on the Binary-Encounter-Bethe (BEB) model showed excellent agreement in the energy range above 30 eV.

Partial cross sections for positive and negative ion formation following electron impact on uracil

We report absolute partial cross sections for the formation of selected positive and negative ions resulting from electron interactions with uracil. Absolute calibration of the measured partial cross sections for the formation of the three most intense positive ions, the parent C4H4N2O+2 ion and the C3H3NO+ and OCN+ fragment ions, was achieved by normalization of the total single uracil ionization cross section (obtained as the sum of all measured partial single ionization cross sections) to a calculated cross section based on the semi-classical Deutsch–Mark formalism at 100 eV. Subsequently, we used the OCN+ cross section in conjunction with the known sensitivity ratio for positive and negative ion detection in our apparatus (obtained from the well-known cross sections for SF+4 and SF−4 formation from SF6) to determine the dissociative attachment cross section for OCN− formation from uracil. This cross section was found to be roughly an order of magnitude smaller, about 5 × 10−22 m2 at 6.5 eV, compared to our previously reported preliminary value. We attribute this discrepancy to the difficult determination of the uracil target density in the earlier work. Using a reliably calculated cross section for normalization purposes avoids this complication.