Electron Scattering on Triatomic Molecules: The Need for Data

Transcription

1 Japanese Journal of Applied Physics Vol. 45, No. 0B, 2006, pp #2006 The Japan Society of Applied Physics Electron Scattering on Triatomic Molecules: The Need for Data Grzegorz P. KARWASZ, Tomasz WRÓBLEWSKI, Roberto S. BRUSA and Eugen ILLENBERGER 2 Institute of Physics, Pomeranian Pedagogical Academy, Slupsk, Poland Dipartimento di Fisica, Università di Trento, Povo, Italy 2 Institut für Chemie und Biochemie Physikalische und Theoretische Chemie, Freie Universität, Berlin, Germany (Received February 9, 2006; accepted April 23, 2006; published online October 24, 2006) We review data sources for electron molecule scattering cross sections, paying particular attention to triatomic molecules, such as CO 2, O, and OCS. Experimental cross sections obtained by beam techniques are compared with those obtained by swarm-data modeling. The need for measurements of inelastic processes, particularly electronic excitation and dissociation, is stressed. [DOI: 0.43/JJAP ] KEYWORDS: electron scattering, cross sections, ionization, dissociation, resonances, swarm methods. Introduction Cross sections are the basis of plasma and gas-discharge modeling. Molecular gases are targets of main technological interest, but compared with those atomic gases, their numerous possible inelastic channels (e.g., rotational, vibrational and electronic excitations, parent and dissociative ionization, dissociation into neutrals and electron attachment) make modeling tedious. In this study, particular attention is given to quasi-homonuclear triatomic molecules, such as linear CO 2, O (isoelectronic with CO 2 ), OCS (a heavier chemical analog of CO 2 ), and bent NO 2 (with a 34 bend angle), SO 2 (9 ) and O 3 (7 ). All these molecules except CO 2 are polar with permanent moments of 0.67 D for O, 0.36 D for NO 2, 0.72 D for OCS,.63 D for SO 2 and 0.53 D for O 3. ) CO 2 becomes polar in bending and asymmetric stretching vibrational states. Electron scattering in the case of CO 2, O, NO 2,O 3, SO 2, and OCS is characterized by the presence of resonant states which lead to an enhancement of vibrational excitation and dissociative attachment. In the case of linear molecules, these resonances are observed as narrow peaks in total cross section. The positions of these peaks shift to lower energies (and their amplitudes increase) with increasing dipole moment (Fig. ). For bent molecules, such as SO 2, overlapping resonances are present, which produce broader maxima. In the limit of high energies, total cross section depends on the total number of electrons in the target 2) and therefore merge for CO 2, O, and NO 2 (Fig. ). 892 Total cross section (0-6 cm 2 ) CO 2 6 O NO 2 4 OCS SO 2 CO 2 - vibr. 2 0, Electron energy (ev) Fig.. Comparison of total cross sections (recommended values from ref. ) of triatomic molecules. The squares are vibrational cross sections of CO 2, ref. 2. The straight line indicates the /E dependence of the maxima in the total cross sections in OCS, O, and CO Reviews of Electron-Scattering Cross Sections Numerous reviews and recommended sets of cross sections that include those of triatomic molecules have been published in recent years. These sets were obtained mainly from swarm data; we quote here the review by Hayashi 3) for as many as 40 atomic and molecular targets, starting from noble gases and metal vapors, and ending with hydrides and fluorides used in semiconductor industries. The difficulty in such an approach is that, owing to the obvious lack of space, no sufficient justification for the data choice is given. More recently, Hayashi has completed extensive (more than 000 items) bibliographic lists for separate targets, such as CO 2. 4) Reviews on single targets, such as H 2, 5) O 2, 6) H 2 O 7) and a series of papers by Christophorou and Olthoff 8) on chlorofluorocarbons all give details but make the search for analogies between targets difficult. Two of the present authors, for small polyatomic molecules, including triatomic molecules 9) and industrialinterest molecules, 0) have made a summary of the existing total and partial cross sections, but rather refrained from giving recommended values. An example of such an analysis of partial cross sections is given in Fig. 2 for SO 2. Recommended values for the elastic, total, momentum transfer, electronic excitation, vibrational excitation, ionization and photoabsorption cross sections in approximately 40 targets are given in the monograph edited by Itikawa. ) Such a comparison shows, in an excellent manner, existing analogies between targets, but again due to space restrictions gives cross sections only at selected energies, for example, Fig. 3, for O. 3. Beam, Swarm, and Semiempirical Methods Experiments with monoenergetic electron beams perform best at energies higher than a few tenths of an electronovolt and, therefore, give direct insight into resonant states. Recent beam data indicate that the contribution from vibrational excitation in gases like O 2) 3) and CO 2 is very high, probably as much as /3 of the total cross section (Fig. ).

2 Jpn. J. Appl. Phys., Vol. 45, No. 0B (2006) Cross section (0-20 m 2 ) 0 SO 2 σ m : Tice Elastic: Orient Gulley Trajmar Raj Ionization: Orient Cadez Basner Kim Attachment: Cadez Vibrational: Simon Born x00 Total: Dababneh Szmytkowski Szmytkowski 96 Wan Zecca Raj Excitation: Vuskovic Fig. 2. Experimental total and partial cross sections for electron scattering on SO 2 molecule. All data are experimental, apart from those of Raj et al. which are from the semiempirical additivity rule. See ref. 9. 0,0 0, Electron Energy (ev) 0 Total momentum elastic Cross section (0-6 cm 2 ) 0, O x0 D Σ + C Π attachment (00) (00) O + + NO + O( S ) Fig. 3. Recommended total and partial cross sections for electron scattering on O molecule; data are from ref.. 0,0 0, Electron energy (ev) This contribution is approximately double that of the prominent 2 g resonance in, where the vibrational cross section is about /6 of the total cross section. Note that the enhancement of molecular vibrations represents an essential energy loss channel in plasma, depleting the electron-energy distribution function only around energies corresponding to resonance energies. 4) At sub-ev energies, the reliability of beam experiments is lower and the analysis of diffusion coefficients (i.e., transverse drift, longitudinal drift, and drift velocity) is of great help in obtaining cross sections. Both Boltzmann and Monte-Carlo codes can be used in deriving cross sections from diffusion coefficients. 5) An example of a successful prediction of cross sections is reported in ref. 6 for NO, where from a particularly deep structure in the transverse diffusion coefficient, see Fig. 4(a), large vibrational cross sections for two low-energy resonances were derived, Fig. 4(b). Large cross sections for resonant vibrational excitation (and also for the very low energy, fine-structure electronic 3=2 $ =2 transition) have also been recently found in NO by beam experiments. 7,8) Another example of the successful swarm prediction of cross sections of a triatomic molecule (CO 2 ) is the work by 893 Wróblewski et al., 9) where the near-to-threshold peak of the vibrational cross section has been predicted, and is in agreement with that found in a recent beam experiment. 20) Unfortunately, at present, very few results are produced by swarm experiments. 4. Data for Plasma Processing Low-energy resonances and cross sections influence the energy distribution of electrons in plasma and, therefore, determine the effective electronic temperature. However, such an analysis does not give insight into the chemical processes; cross sections for the formation of ionized and neutral species are needed. In this sense, only ionization cross sections are considered to be sufficiently well documented, even if targets of essential industrial importance, like CCl 4 or WF 6, have only been studied recently. 2) However, on the contrary, electronic excitations and dissociations into neutrals are poorly known, even for simple targets, such as H 2 (Fig. 5). 4. Ionization Until recently, few laboratories have worked systematically on electron-impact ionization. We cite here Inns-

3 Jpn. J. Appl. Phys., Vol. 45, No. 0B (2006) D T /µ[ev] σ [0-6 cm 2 ] 0 0, NO Bailey Skinker Lakshminarasimha ZLJP 2-res. model 0,0 0, , 0,0 E-3 E/N[Td] NO,0 2,0 Energy [ev] Fig. 4. Analysis of swarm data as a tool of deriving cross sections in NO. A prominent dip in transverse diffusion coefficient can be explained by enhancement in the vibrational cross section. A two-resonance model assumes that the v ¼ and 2 vibrational cross sections are almost as large as that in the resonant elastic scattering. Adopted from ref. 6. bruck 22) and Pasadena 23) laboratories and the pioneering measurements by Rapp and Englander-Golden, 24) which are still one of the most complete. New techniques have recently been developed, like fast-neutral-beam experiments. 25) The mutual agreement between data from different laboratories is good, yielding not only total but also partial ionization cross sections (Fig. 3 for O). Several semiempirical models have been developed to v0 v v2 v3 predict ionization cross sections 26,27) their results agree well with experimental data. However, these models rarely predict partial cross sections, i.e., the ionization pathways. 4.2 Dissociative electron attachment The formation of negative ions is usually a resonant process, even if energy dependences can exhibit large peaks similar to those for the production of H from H 2 around 0 and 4 ev (see for example Fig. 7 in ref. 28. Recent reviews on this subject were carried out, among others, by Illenberger and coworkers. 29) For electron attachment resonances, Christophorou et al. 30) noted that the maxima of their peaks diminish with their energy. This dependence is similar to the dependence of the amplitude of resonant maxima in total cross sections reported by March et al. 3) (Fig. ). Cross sections for electron capture in molecules such as SF 6, CCl 4 and C 6 F 6 increase towards zero energy, following simple quantum mechanical dependences, and, in the limit of zero energy, are proportional to E =2. In particular we recall precise measurements of dissociative attachment by pulsed radiolysis at very low energies by Shimamori et al. 32) If a molecular negative ion is stabilized, for example, via sharing energy with vibrational excitation of a molecule (or cluster) or by collisions with buffer gas, then the stable parent X ions are observed. This is, for example, the case of NO ions appearing from (NO) n clusters. 33) The contribution from dissociative attachment to resonant scattering in triatomic molecules is relatively large. In CO 2 at 4.4 ev this contribution amounts to 0.%, 9) in Oat 2.2 ev to 0.3%, in NO 2 at.5 ev to 0.3%, 34) in OCS at.3 ev to 0.5%, in SO 2 at 4.5 ev to 0.3%, 9,35) and in O 3 at.5 ev to as much as % of the total cross section. 34) 4.3 Electronic excitation Electronic excitation is an important energy loss channel in plasma, even if emitted light from optically allowed transitions has a high probability re-absorption. Optically allowed and forbidden processes can be distinguished from the energy dependence of the integral cross section optically allowed cross sections fall slowly with energy after their maxima (Fig. 5 for H 2 ). Also, angular distributions of scattered electrons differ for optically allowed and forbidden excitations: optically allowed transitions are Integral cross section (0-6 cm 2 ) 0, b 3 Π + u Nishimura Khakoo Hall Khakoo 94 Fliflet H 2 Integral cross section (0-6 cm 2 ) 0, Khakoo Srivastava Shemansky Fliflet B Σ + u Fig. 5. Comparison between optically forbidden b- state and optically allowed B-state electron-excitation cross sections in H 2. The data are from electron energy-loss measurements, apart from those of Hall et al., which are from metastable yield experiments; the lines are from theory. Adopted from ref Energy (ev) 0 00 Energy (ev) 894

4 Jpn. J. Appl. Phys., Vol. 45, No. 0B (2006) forward-centered. 36) Optically forbidden excitations produce metastable states or lead to molecular dissociation; these cross sections are essential for understanding, for example, afterglows. 37) The knowledge of electronic excitation cross sections is extremely poor, except for a few targets, like NO, for which extensive studies have been performed recently. 36) The difficulty in determining integral cross sections remains because of the necessity of measuring the signal of scattered electrons over a wide angular range and the subsequent integration. For example, a recent study of the ev ( þ u and u ) optical bands in CO 2 give differential cross sections and the probability of transition (general oscillator strength) but no integral cross sections. 38) Many electronic transitions lead to the dissociation molecules (for example the transition to the D state in O), and an alternative way to study these excitations is to detect the dissociation fragments. 895 Fig. 6. Energy dependences of productions of CF 2 D þ and CO þ ions following ionization of fragments evaporated after electron irradiation of CF 3 COOH thin film. 46) 4.4 Dissociation into neutral fragments Neutral fragments (atoms or radicals) play an essential role in plasma processing. However, their measurements is extremely difficult, as far as absolute cross section is concerned. Few experiments have been performed and for almost every single gas a different, specific technique is used. For example, in CF 4, Nakano and Sugai 39) studied the formation of CF 3,CF 2, and CF radicals using a technique based on two electron beams: the first beam induced molecular dissociation, the second beam (at a fixed energy of 80 ev) ionized radicals, allowing their detection. Motlagh and Moore 40) used the tellurium mirror technique to study the dissociation of fluorocarbons and hydrocarbons (CH 3 F, CH 2 F 2, CHF 3, CH 4, CF 4, C 2 F 6, C 3 H 8 ); tellurium compounds formed with dissociation products are volatile. Motlagh and Moore noticed that the partial cross section for dissociation is proportional to the statistical pathway leading to the formation of a specific radical. For example, the cross section for the formation of a CF 3 radical from a CHF 3 molecule is /4 that for the formation of a CF 3 radical from a CF 4 molecule. In H 2 O, dissociation cross section has been determined from the laser-induced fluorescence of OH radicals: 4) the cross sections is as high as 2/7 the total cross section (this ratio comprises both H þ and H complementary formations). For O, LeClair and McConkey 42) studied the formation of metastable O ( S) atoms by detecting excimer radiation from XeO. The O ( S) atoms are produced together with groundstate molecules through the electronic excitation of O molecules to the purely repulsive D þ state. The O ( S) dissociation cross section reported by LeClair and McConkey 42) at 80 ev is one half (0: m 2 ) the electronic excitation cross section for the D þ state reported by Marinković et al. 43) A similar Xe excimer technique was used for OCS; 44) the maximum cross section for the production of S ( S) atoms was 0: m 2. All these techniques are specific for a given gas. A new setup has been recently developed in Berlin; it allows the immobilization of dissociation fragments and study of them after the primary irradiation. The technique consists of irradiation of a thin cryofilm (grown at 30 K) with lowenergy electrons and a successive gradual release of fragments by increasing the temperature of the film. 45) The evaporated fragments undergo an electron-impact ionization at a fixed energy (i.e., 90 ev) and are detected in a standard mass spectrometer. This resembles the technique of Nakano and Sugai, but offers a much higher sensitivity to different fragments. In a recent study of trifluoroacetic acid, 46) CO 2 fragments were observed, as in the case of HCOOH acid. 45) Additionally, some heavier fragments that evaporate at higher temperatures than CO 2 are produced in the electroninduced dissociation. These fragments give rise, among other things, to the production of CF 2 D þ ions in the mass spectrometer. When the energy of the electrons inducing the dissociation is changed, the CO þ 2 and CF 2 D þ signals show different dependencies [compare Figs. 6(a) and 6(b)]. The signal from CF 2 D þ ions falls rapidly with the energy of the electrons, whereas that of CO þ 2 ions is constant up to the highest energy studied. This resembles the differences between optically allowed and forbidden electronic excitations (Figs. 5 and 6). 5. Conclusions Establishing comprehensive cross sections sets for plasma modeling require the combination of different methods. Beam experiments in the gas phase give reliable results at energies above ev. Swarm measurements, combined with Boltzmann 6) or Monte Carlo 5) analysis, prove to be very useful at sub-ev energies. A proper account of inelastic channels in this energy range is essential in evaluating

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