Absolute number density and kinetic analysis of CF, CF2 and ... | Study notes Data Acquisition | Docsity (2024)

Download Absolute number density and kinetic analysis of CF, CF2 and ... and more Study notes Data Acquisition in PDF only on Docsity! ERNST–MORITZ–ARNDT–UNIVERSITÄT GREIFSWALD Absolute number density and kinetic analysis of CF, CF2 and C2F4 molecules in pulsed CF4/H2 rf plasmas I n a u g u r a l d i s s e r t a t i o n zur Erlangung des akademischen Grades doctor rerum naturalium (Dr. rer. nat.) an der Mathematisch–Naturwissenschaftlichen Fakultät der Ernst–Moritz–Arndt–Universität Greifswald vorgelegt von: Sergey Stepanov geboren am 17. November 1980 in Sankt–Petersburg (Russland) Greifswald, 26. April 2010 Dekan: Prof. Dr. Klaus Fesser 1. Gutachter: Prof. Dr. Jürgen Meichsner 2. Gutachter: Prof. Dr. Uwe Czarnetzki Tag des Promotionskolloquiums: 09. Juli 2010 Abbreviations a-C:F amorphous fluorocarbon (thin film or layer) AS Absorption Spectroscopy AFM Atomic Force Microscopy ATR–FTIR Attenuated Total Reflection Fourier Transform InfraRed CCP Capacitively Coupled Plasma c.w. continuous wave (plasma operation) D/A Digital–to–Analog (convertor) DC Direct Current ECR Electron Cyclotron Resonance EEDF Electron Energy Distribution Function FTIR Fourier Transform InfraRed (spectroscopy) HWHM Half–Width at Half–Maximum IC Integrated Circuit ICP Inductively Coupled Plasma IR InfraRed IR–TDLAS InfraRed Tunable Diode Laser Absorption Spectroscopy IR–QCLAS InfraRed Quantum Cascade Laser Absorption Spectroscopy LIF Laser Induced Fluorescence (spectroscopy) MCT Mercury Cadmium Telluride (HgCdTe) MFC Mass Flow Controller MS Mass Spectrometry MWI MicroWave Interferometry NIST National Institute of Standards and Technology OES Optical Emission Spectroscopy PE PolyEthylene PECVD Plasma Enhanced Chemical Vapor Deposition PTFE PolyTetraFluoroEthylene (TeflonTM) QCM Quartz Crystal Microbalance RIE Reactive Ion Etching RF Radio Frequency SNR Signal–to–Noise Ratio TDLAS Tunable Diode Laser Absorption Spectroscopy TTL Transistor–Transistor Logic iii Abbreviations UV UltraViolet VUV Vacuum UltraViolet XPS X–ray Photoelectron Spectroscopy iv List of symbols A Hönl-London factor A1,2 powered (grounded) electrode area β sticking coefficient B12,21 Einstein coefficients for absorption (stimulated emission) by an absorbing transition between levels ”1” and ”2” c light speed (≈ 2.998 · 108 m s−1) C1,2 powered (grounded) electrode sheath capacitance D diffusion coefficient De dissociation energy ε0 vacuum permittivity (≈ 8.854 · 10−12 A s V−1 m−1) e elementary charge (≈ 1.602 · 10−19 C) E energy level; electron energy; energy f(E) electron energy distribution function (EEDF) fD Doppler (Gaussian) spectral line profile fL Lorentzian spectral line profile fe electron plasma frequency fi ion plasma frequency frf rf voltage frequency (13.56 MHz) g statistical weight (degeneracy) h Planck constant (≈ 6.626 · 10−34 J s); height of the chamber (30 cm) h̄ reduced Planck constant (h̄ = h 2π ≈ 1.055 · 10−34 J s) Ĥ Hamiltonian i imaginary unit I moment of inertia I(ν) radiation intensity at wavenumber ν J rotational quantum number k̂ absolute rate coefficient (in cm3s−1) k effective rate coefficient (in s−1); dielectric constant K effective rate (in cm−3s−1) kB Boltzmann constant (≈ 1.381 · 10−23 J K−1) k(ν) absorption coefficient at wavenumber ν L angular momentum; absorption path length v General introduction of typical ne and Te values is shown in figure 0.1 by the grey bar. Besides, being a low-temperature plasma, considered discharges are weakly ionized and strongly non-thermal, i.e. ne ≈ ni ng and Te Ti ≈ Tg (index ”i” means ions, and ”g” – the neutral gas). Despite the fact, that the fluorocarbon reactive plasmas are nowadays widely applied in industry, many aspects of their plasma-chemistry are still not completely understood. In order to improve the knowledge in this field, further fundamental investigations on the kinetics of important species in these plasmas are necessary. This thesis presents a study focused on the kinetics of CF and CF2 radicals in CF4/H2 rf CCPs and that of C2F4 molecule which is formed in the discharges as a stable intermediate product. In the fluorocarbon plasmas, these species play an essential role in both volume and surface plasma-chemical reactions. Therefore, from the analysis of their kinetics, one can learn more about the elementary processes in the studied systems. The investigations discussed in the present work have been carried out in the framework of the Transregional Collaborative Research Centre ”Fundamentals of complex plasmas” (SFB/TRR24, project section B5) supported by the Deutsche Forschungsgemeinschaft (DFG). Scope of the thesis The first chapter of the thesis gives a brief overview on the different types and technical applications of the low-pressure discharges in fluorocarbon gases. Thereby, characteristic features and properties of the capacitively coupled plasmas are given in a separate section. Additionally, this chapter discusses plasma-chemical processes, taking place in the studied discharges, and possible methods to investigate these processes experimentally. Chapter 2 provides the basic principles of the molecular absorption spectroscopy in the mid-infrared spectral range, – the main experimental technique which was used for the measurements in this work. Both, vacuum part and optical unit of the experimental set-up, are described in details in chapter 3. Besides, the software and two methods of the data acquisition employed for the measurements are also discussed there. The next (fourth) chapter presents preliminary investigations which have been made to gain the relevant spectroscopic data necessary for the following experiments. The most important experimental results achieved in the present work will be reported in chapter 5. Thus, external parameters selected for the discharge operation and internal properties found for the studied plasmas will be briefly discussed at the 2 Scope of the thesis beginning of the chapter. Further, preliminary FTIR measurements of the parent molecule CF4 and the stable intermediate products C2F4, C2F6, C3F8, CHF3 and HF will be considered, in order to better characterize and specify the typical gas phase composition in the discharges. However, the main focus of the investigations reported in the chapter is still on CF, CF2 and C2F4, the three target species of the study. In particular, temporally resolved number density traces of the species, measured in pulsed CF4/H2 rf plasmas by means of the IR-TDLAS technique, will be presented and compared to each other. Moreover, in the frame of the kinetic analysis, effective rates and rate coefficients, defined for assumed production and loss processes, will be estimated from the fit of the measured density curves. Finally, in the last chapter of the thesis, the main results of the study will be summarized and a brief outlook on further research efforts will be given. 3 General introduction 4 1.2 Capacitively coupled RF discharges figure 1.1b, [2]. Additionally, fluorocarbon thin films have relatively low dielectric constants k ∼ 1.8 − 2.4 [11, 12] maintained by C–F bonds and show good thermal stabil- ity caused by C–C cross–linked structure [13]. Therefore, plasma deposited flu- orocarbon polymers used as interlevel dielectrics in ICs allow to reduce parasitic capacitances, in comparison to that of SiO2 (k ∼ 3.9). Such low-k materials became very important for the progress in the IC technology. However, in spite of the technical applications, many plasma–chemical processes within the discharges as well as mechanisms of the plasma–surface interaction are still not completely understood. Many complex industrial processes involving the fluorocarbon plasmas have been established due to empirically determined recipes. In order to optimize existing technologies and, ideally, to enable new ones, knowledge on the key plasma processes and their kinetics needs to be improved. Therefore, further fundamental investigations on the fluorocarbon rf discharges are required. 1.2 Capacitively coupled RF discharges Capacitively coupled rf plasmas considered in this work belong to the discharge type which is most often used for various technical applications and hence as a model system for fundamental investigations. Normally, a driving frequency frf applied for the generation of these discharges is 13.56 MHz (and its higher harmonics, e.g. 27.12 MHz). This value was specially allocated by the International Telecommunication Agreements (ITA) as a standard frequency used in commercial rf generators, in order to avoid any interference with existing communication channels. On the other hand, this frequency lies between the plasma frequency of ions fi and that of electrons fe: 1 2π √ nie2 miε0 = fi < frf < fe = 1 2π √ nee2 meε0 (1.1) where: e is the elementary charge, ε0 - the vacuum permittivity, and m and n are the mass and density of ions (index ”i”) or electrons (index ”e”), respectively. As follows from (1.1), ions in plasma are not able to respond to the fast alternating electric field and hence can not gain any energy from it. In contrast to them, electrons start to oscillate following the rf field. If no collisions had taken place, they would also gain no energy, since the electron acceleration during the first rf half-cycle would be compensated by breaking during the next one. However, due to elastic collisions with neutrals, electrons change their direction randomly, which leads to an effective increase of their energy over an rf period and therefore forms a strongly non-thermal system of energetic electrons and cold ions and neutrals. 7 1 Fluorocarbon RF plasmas matching network rf electrode sheath plasma bulk wall sheath+ + + + + + + + + + + ++ + +- - --- - - + + + + RF A1 A2 rf generator RF D1 R1 D2 R2 Rplasma C1 C2 Figure 1.2: Scheme and equivalent circuit diagram of an asymmetric capacitively coupled rf discharge. The described mechanism of the energy coupling also known as ohmic heating of electrons (see e.g. [1]) is dominant in the rf plasmas considered in this work. It results in so called α-mode of the discharge operation (see [14] for details). Principally, there are two other energy transfer mechanisms possible: (i) heating by secondary electrons which results in so called γ-mode (see [14]) and may become important for high rf voltages, and (ii) stochastic electron heating due to reflection at the plasma sheaths, which dominates under extremely low pressure conditions (p ≤ 1 Pa, [1,15]). Much higher mobility of electrons in plasma, in comparison to that of ions, leads to a negative charging of the electrode surfaces with respect to the bulk plasma. This results in positive space charge regions, so called sheaths, between the plasma and electrodes, which hamper further electron fluxes towards the electrodes. Figure 1.2 shows this situation schematically. In this figure one can see also an equivalent circuit diagram of a capacitively coupled rf discharge between two electrodes, [16]. C1 and C2 represent the sheath capacitances which depend on the electrode areas A1 and A2. The high electron mobility is shown by diodes D1 and D2. Elements R1, R2 and Rplasma perform the ohmic resistance of both sheaths and bulk plasma, respectively. The rf generator gives a voltage U(t) = U0 sin(ωt) (ω = 2πfrf) (1.2) 8 1.2 Capacitively coupled RF discharges which is capacitively coupled to the driven electrode A1, by means of the matching network capacitors. Assuming a pure capacitive nature of the electrode sheaths (R1,2 Z1,2 = 1 ωC1,2 ), the circuit in figure 1.2 may be considered as a capacitive voltage divider, and hence the following plasma potential Uplasma can be found [16]: Uplasma(t) = Up + Up0 sin(ωt), Up0 = C1 C1 + C2 U0 (1.3) Furthermore, due to the diodes D1 and D2 in the scheme (i.e. high electron mobility), it must be always valid: Uplasma(t) ≥ U(t), i.e. comparing (1.2) and (1.3), Up > 0. On the other hand, because of the capacitive coupling of the rf power, no total current can flow over an rf period. Therefore, the voltage at the driven electrode is shifted by so called dc self–bias voltage [16]: Ubias = C1 − C2 C1 + C2 U0 (1.4) In the case of asymmetrical electrodes where A1 < A2 (see figure 1.2), the Ubias value will be negative, since C1 < C2 in (1.4). The described situation is shown in figure 1.3 quantitatively, where C1 = 0.1C2 was taken for the calculations. As one can see, due to the negative Ubias, the voltage between the driven electrode and plasma remains negative over the whole rf period: (Urf − Uplasma) < 0. That means, that the (modulated) electric field in the sheath is always directed toward the rf electrode, and hence accelerates positive ions from plasma in this direction. At the same time, electrons are ”trapped” in the plasma volume for the most of the rf cycle. 0 2 0 4 0 6 0 8 0 1 0 0 0 0 U b i a s U b i a s U r f U p l a s m a U r f - U p l a s m a Vo lta ge , a .u. T i m e , n s Figure 1.3: Potential of the driven electrode Urf shifted by a dc self-bias voltage Ubias and plasma potential Uplasma calculated for C1 = 0.1C2. 9 1 Fluorocarbon RF plasmas Table 1.1: List of the main electron impact reactions with CF4 and H2 precur- sor molecules and coefficients of their rate constants in Arrhenius form (1.6), according to [29]. reaction channel B γ Ea/kB (cm3s−1) (105 K) dissociative ionization (1) CF4 + e− → CF+ 3 + F + 2e− 2.90 · 10−9 1.35 1.570 (2) CF4 + e− → CF+ 2 + 2F + 2e− 1.54 · 10−8 0 2.851 (3) CF4 + e− → CF+ + 3F + 2e− 1.94 · 10−8 0 4.008 (4) CF4 + e− → C+ + 4F + 2e− 1.73 · 10−8 0 4.584 e− dissociation (5) CF4 + e− → CF3 + F + e− 9.43 · 10−10 0 1.937 (6) CF4 + e− → CF2 + 2F + e− 1.30 · 10−10 0 2.038 (7) CF4 + e− → CF + 3F + e− 3.72 · 10−10 0 3.295 (8) H2 + e− → 2H + e− 9.40 · 10−12 2.38 0.947 e− dissociative attachment (9) CF4 + e− → CF3 + F− 2.03 · 10−9 −2.37 1.656 As clearly seen in figure 1.5, even a relatively small variation of the electron tem- perature may significantly affect both the absolute values of the rate coefficients and the ratio between them. Thus, at Te lower than 2 eV, the dissociative ionization of CF4 forming CF+ 3 ion (channel (1) in table 1.1), the electron impact dissociation of H2 (channel (8) in table 1.1) and the dissociative electron attachment to CF4 (chan- nel (9) in table 1.1) have notably higher rate coefficients than other electron induced processes listed in the table. However, at higher electron temperatures, the dissocia- tive ionization of CF4 forming CF+ 2 ion and electron impact dissociation giving CF3 radical (channel (2) and (5), respectively) become comparable with those reactions. Therefore, the mean energy of electrons in plasma is an essential parameter which determines all electron induced plasma-chemical processes and hence influences the kinetics of species in the discharge. Further, the fragment species formed in the electron impact reactions from the feed gas molecules in return can interact with electrons in plasma. Thus, the partial cross–sections σ(E) for the electron impact ionization of CF, CF2 and CF3 radicals (CFx + e− → CF+ x + 2e−) have been experimentally obtained in [30]. Also the dis- sociative ionization of the species forming neutral and positively charged fragments like C, F, CFx, F+ and CF+ x (x = 1− 3) was investigated in [31]. Beside the electron induced processes, CF2 and CF3 radicals can recombine with 12 1.3 Gas phase processes in fluorocarbon plasmas 1.0 1.5 2.0 2.5 3.0 10-20 10-18 10-16 10-14 10-12 10-10 (9) (7) (6) (5) (4) (2) (3) (1) R at e co ef fic ie nt k( T e), c m 3 s-1 Te, eV (8) Figure 1.5: Rate coefficients k̂ of the electron induced processes listed in table 1.1 calculated with formula (1.6) at various electron temperatures Te. Solid lines show three reaction channels with the highest rate coefficients. Table 1.2: Recombination reactions between fluorocarbon radicals and their rate co- efficients k̂ at room temperature. reaction channel rate coefficient reference k̂ (cm3s−1) CF2 + CF2 + M → C2F4 + M 4.01 · 10−14 [32] 4.25 · 10−14 [33] 2.85 · 10−14 [34] (2− 3) · 10−14 [35] CF3 + CF3 + M → C2F6 + M 1.10 · 10−11 [36] 1.04 · 10−11 [37] 3.90 · 10−12 [38] CF2 + CF3 + M → C2F5 + M 8.80 · 10−13 [39] each other (see table 1.2). However, these channels appear to be rather of minor importance, since they need a third collision partner M in the gas phase, unless the reactor wall acts as M. CFx radicals formed in plasma can react also with other species, e.g. with atomic and molecular fluorine. These reactions lead to consumption of CFx radical and 13 1 Fluorocarbon RF plasmas Table 1.3: List of the main recombination reactions of of fluorocarbon radicals with atomic and molecular fluorine, and their rate coefficients k̂ at room temperature. reaction channel rate coefficient reference k̂ (cm3s−1) CF3 + F + M → CF4 + M (1.1− 1.7) · 10−11 [40] 4.40 · 10−11 [41] CF2 + F + M → CF3 + M (0.4− 2.3) · 10−12 [40] 4.15 · 10−11 [41] CF + F + M → CF2 + M < 1.0 · 10−13 [42] CF3 + F2 → CF4 + F 7.0 · 10−14 [40] 2.31 · 10−14 [43] CF2 + F2 → CF3 + F < 2.0 · 10−15 [40] 8.32 · 10−14 [44] CF + F2 → products 3.9 · 10−12 [45] Table 1.4: Reactions between atomic and molecular fluorine and hydrogen, and their rate coefficients k̂ at room temperature. reaction channel rate coefficient reference k̂ (cm3s−1) F + H2 → H + HF 2.6 · 10−11 [46] 2.8 · 10−11 [47] F2 + H → F + HF 4.3 · 10−12 [48] 1.4 · 10−12 [49] production of CFx+1 molecule (see table 1.3). However, in presence of hydrogen, a fairy stable HF molecule is produced in plasma, due to reactions shown in table 1.4, which decreases the density of fluorine available for reactions with CFx radicals. On the other hand, atomic hydrogen may also react with CFx radicals, tearing one F atom away or forming CHFx molecule (see table 1.5). Although reactions with molecular hydrogen have much lower rate coefficients, they can also play a certain role in the radical kinetics, since H2 molecules are continuously fed into the reactor as precursor gas. Hence, an admixture of H2 to the fluorocarbon feed gas can significantly influ- ence density of free CFx radicals in plasma, what was observed in various types of 14 1.5 Diagnostic methods for gas phase analysis in fluorocarbon plasmas in reactions like A + B + M → AB + M. For each species, the overall efficiency of the surface reactions can be expresses by so called sticking coefficient β, which obviously depends on the material that the surface is made of. Thus, experimental studies on the sticking coefficients of CF and CF2 radicals on various materials, e.g. stainless steel, copper, aluminium or silicon, can be found in papers by the groups of Booth [64] and Czarnetzki [65]. On the other hand, the surface condition is also essential for the plasma kinetics. For instance, in the reactor with ”clean” stainless steel walls, i.e. without fluorocar- bon layer, sticking on the surface is fairly dominant process in the kinetics of CF2 radical, whereas it becomes negligible in case of the previously passivated reactor walls. The reason for such drastic change in the kinetics is CF2 sticking coefficient β which is much higher for stainless steel than that for the fluorocarbon layer [17,35]. Generally, the efficiency of the surface reactions, i.e. their rate coefficients k̂ and hence the overall sticking coefficient β, depends also on the surface temperature T . The dependencies k̂(T ) and β(T ) can obviously be expressed in the Arrhenius form, i.e. by equation (1.6) which describes their increase with temperature. Finally, possible influence of the plasma radiation over the fluorocarbon layers should be mentioned as a further kind of the plasma–surface interaction. Indeed, photons from the ultra violet (UV) or vacuum ultra violet (VUV) spectral ranges have their energies comparable with those of the C–C, C–F or C=C chemical bonds in the fluorocarbon films (several eV) and can penetrate quite deep into the layer (up to a few tens of nm), [72,73]. Therefore, they can break the bonds, which may release CFx or F radicals into the gas phase, activate the surface or change the chemical structure (cross–linking) and/or porosity of the films. Treatment of various polymer films or organic substances by the UV- or VUV photons coming from plasma or separate radiation sources was considered in many studies, e.g. [74–78]. 1.5 Diagnostic methods for gas phase analysis in fluorocarbon plasmas In order to analyze numerous processes in fluorocarbon plasmas and hence to pro- vide a better understanding of the plasma chemistry in these discharges, a number of experimental techniques have been established in the last decades to probe the concentrations and kinetics of the reactive species of interest. Certainly, all of them have their advantages and disadvantages and should be chosen according to charac- teristic features of the studied process, e.g. its typical time scales or detection limits of the target species. This section gives a brief overview of the main experimental methods usually applied for the fluorocarbon plasma diagnostics. 17 1 Fluorocarbon RF plasmas Laser Induced Fluorescence spectroscopy (LIF) is a common laser spectroscopic technique which has been successfully used by many working groups for measure- ments on CF and CF2 radicals in various fluorocarbon discharges [8,13,62,65,79–82]. Due to the typically high signal–to–noise ratio (SNR) of the fluorescence, this method provides a good sensitivity in detection of rotational lines of the species. Therefore, CFx rotational temperatures in plasma can be evaluated from the LIF measurements over a certain range of rotational lines [82]. A further important advantage of the LIF technique is its inherently high temporal and spatial resolution, which enables measurements of CFx spatial profiles in the reactor. These profiles provide useful information on fluxes, sources and sinks of the radicals and hence on the discharge processes related to both the gas phase and reactor surfaces. For instance, CFx diffusion coefficients and sticking probabilities can be derived from the spatially resolved LIF measurements [64,65]. However, only relative concentrations can be measured by means of LIF. There- fore, reliable calibration procedures are required to gain the absolute number den- sities of the species. It can be reached by comparing the LIF signal amplitude with that from a known concentration of some reference molecules, or by applying an- other (optical) experimental technique which enables direct measurements of the absolute concentration. Thus, the broadband absorption spectroscopy in the ultra- violet spectral range (UV–AS) was used in [64] to calibrate the LIF measurements of CF2. Clearly, UV–AS or VUV–AS (AS in the vacuum ultraviolet) can be applied by itself to measure absolute number densities of CFx [83, 84] or F [85] radicals in fluorocarbon discharges, though without spatial resolution. Optical Emission Spectroscopy (OES) is a further experimental technique suitable to study fluorine and fluorocarbon radicals in plasmas, see e.g. [65, 86–88]. Similar to LIF, OES provides only relative measurements which then, under certain model assumptions, can be put on an absolute scale. Beside the mentioned absorption spectroscopy, actinometry technique established in [89, 90] is commonly used for this purpose. This method is based on adding a small amount of an ”actinometric” gas (Ar or N2) and following comparison of its emission intensity with that from the species of interest. In addition, this approach provides information about the distri- bution of energetic electrons in the discharge [65]. It can be also noted, that OES is technically less complicated than LIF, but offers rather poor spatial resolution. Apart from F and CFx radicals, many other neutral and charged CxFy (x, y ≥ 2) species are present in fluorocarbon plasmas. In order to detect them, various Mass Spectrometry (MS) techniques can be applied, e.g. the most commonly used electron beam ionization at the entrance of a Quadrupole Mass Spectrometer 18 1.5 Diagnostic methods for gas phase analysis in fluorocarbon plasmas (QMS, [91,92]), Threshold Ionization MS (TIMS, [53,93–95]), Electron Attachment MS (EAMS, [96,97]) or positive Ion Attachment MS (IAMS, [98]). Although no spa- tially resolved measurements are possible in this case, density of the studied species can be determined absolutely and with relatively good temporal resolution [95]. Alternatively, large CxFy neutral species in plasma can be measured by means of Fourier Transform InfraRed (FTIR) spectroscopy [99–103]. This technique involves a broad band spectral region and therefore can offer only limited temporal and spectral resolution. The latter is usually of 1–10 cm−1 and thus much larger than typical width of an absorption line. This is however less critical for large CxFy molecules, since their numerous absorption lines are normally located closely to each other and hence are mostly overlapped. Besides, a gas mixture consisted of various fluorocarbon species can be deconvoluted and quantified, using previously recorded reference FTIR–spectra of its individual components [104]. In contrast to FTIR, InfraRed Laser Absorption Spectroscopy (IR–LAS) can mea- sure within a very narrow spectral range, but then offers much better temporal and sub–Doppler spectral resolution. Moreover, absolute concentrations of the studied species can be acquired in a relatively easy way [105]. These advantages make IR– LAS technique very suitable for investigations on the kinetics of small transient species, e.g. CFx radicals, which normally have separate absorption lines in the infrared spectral region. IR–LAS based on lead salt Tunable Diode Lasers (IR–TDLAS) and applied in this work (see chapter 3 for details) has been intensively used also by many other working groups for temporally resolved measurements of CFx radicals in various fluorocarbon discharges, e.g. [54–57,66,106]. On the other hand, Quantum Cascade Lasers (QCL) developed as alternative IR light sources [107,108] were recently applied for the IR– LAS measurements in CF4/H2 rf plasmas using the same experimental set–up as that in the present work [103,104,109]. However, irrespective of the laser type, measured absorption results from the averaging over the line–of–sight of the IR beam. Therefore, in a common case of cylindrical configuration, a good radial resolution can be hardly achieved by means of this technique, especially if the beam is guided through the reactor in a multi– path way (e.g. in a multi–path cell). Nevertheless, axial density profiles can still be resolved [54,106]. Finally, density and temperature of electrons are two further important parameter which influence all electron induced processes in plasma (see section 1.3). In case of ”clean” plasmas in inert gases, they can be trivially measured by means of classical Langmuir probe techniques, e.g. [110, 111]. However, in reactive gas plasmas, e.g. in fluorocarbon plasmas, it becomes particularly difficult, because of the insulating 19 1 Fluorocarbon RF plasmas Wavenumber, cm-1 1400 1200 1000 FTIR 0 2 4 10 -3 ab so rb an ce u ni ts 296 292 288 284 280 XPS co un t ra te , a. u. Binding energy, eV CF3 CF2 CF Figure 1.6: FTIR (C–F stretching vibrations) and XPS (C 1s) spectra of a polyethy- lene sample modified in CF4 rf discharge (50 Pa, effective voltage Ueff = 225 V, ttreatment = 5 s), after [123]. 22 2 Basics on molecular spectroscopy This chapter discusses structure of molecular energy spectra and basic principles of the absorption spectroscopy, an experimental diagnostic technique which employs these spectra to estimate absolute concentrations of the molecules. 2.1 Structure of molecular spectra Theory of molecular spectra, their nature and methods of their mathematical de- scription are discussed in literature in detail, e.g. in books by Herzberg [130–132], Duxbury [133], Svanberg [134] or Thorne et al. [135]. Therefore, only a brief overview on the structure of molecular spectra will be given here. Generally, each molecule consisting of two or more atoms can be considered as a quantum-mechanic system and hence treated by use of the Schrödinger equation: ih̄ ∂ ∂t Ψ(r, t) = ĤΨ(r, t) (2.1) where i is the imaginary unit, h̄ is the reduced Planck constant, Ψ(r, t) is the wave function, which is the probability amplitude for different configurations of the sys- tem, and Ĥ is the Hamiltonian. According to the Born-Oppenheimer approximation [136], the motion of electrons and that of nuclei in the molecule can be considered to occur independently. Further- more, in most cases, vibration of the molecule and its rotation may be also treated as two separate kinds of movement. Under these assumptions, the Hamiltonian Ĥ in equation (2.1) is expanded in terms of the electronic, vibrational and rotational Hamiltonians as Ĥ = Ĥel + Ĥvib + Ĥrot (2.2) and the complete wave function Ψ can be rewritten as a product: Ψ = Ψel ·Ψvib ·Ψrot (2.3) Eigenvalues of the Hamiltonian Ĥ in form (2.2) give the electronic, vibrational and rotational energy levels of the molecule, schematically shown in figure 2.1. Normally, absorption (or emission) lines related to transitions between two differ- ent electronic levels are located in the ultraviolet (UV) or visible (optical) spectral 23 2 Basics on molecular spectroscopy vibrational states rotational states en er gy excited electronic state electronic ground state ~ 0. 1 eV ~ 0. 00 1 eV Figure 2.1: General scheme of electronic, vibrational and rotational energy levels of a molecule. range (see figure 2.2). They are usually employed for UV-absorption spectroscopy, optical emission spectroscopy (OES) or LIF diagnostic technique. Vibrational-rotational transitions within the same electronic state of the molecule yield spectral lines of much longer wavelengths which are typically located in the near- or mid infrared region. This class of the absorption lines will be employed for the IR-TDLAS measurements in the present work, since species of interest in the studied plasmas mostly remain in the ground electronic state. Finally, absorption (or emission) lines related to a change of the rotational state, without any changing in vibration, form the far infrared part of molecular spectra. 2.1.1 Vibrational energy levels and transitions Typical structure of vibrational energy levels can be considered on example of a diatomic molecule treated as an anharmonic oscillator [130]. In this case, poten- tial energy of the system can be described by the Morse potential function (see figure 2.3): V (r) = De ( 1− e−α(r−re) )2 (2.4) where r is the distance between two atoms, re is the equilibrium bond distance, De is the dissociation energy and α controls the ”width” of the potential profile. The Schrödinger equation with potential function (2.4) can be solved, which gives 24 2.1 Structure of molecular spectra v1 v3 v2 x y z v2 Figure 2.4: Four vibrational modes of a linear CO2 molecule: ν1 – symmetric stretching, ν3 – anti-symmetric stretching and two ν2 – bending in XY– and in ZY–planes. 2.1.2 Rotational energy levels and transitions Rotational motion of a diatomic molecule can be described considering the molecule as a classical rigid rotator with a moment of inertia I. In this case, the angular momentum −→ L = I−→ω , and energy of rotation Erot = 1 2 Iω2, i.e. Erot = L2 2I (2.7) (ω is the angular velocity of rotation). Taking (2.7) into account, the Schrödinger equation can be solved yielding rota- tional energy levels of the rigid rotator (see e.g. [130,137,138]): E(J) = h̄2J(J + 1) 2I (2.8) where J = 0, 1, 2, . . . is the rotational quantum number, and each level E(J) is (2J + 1)-fold degenerate. Determining rotational constant B: B = h 8π2cI (2.9) equation (2.8) can be rewritten as E(J) = hcBJ(J + 1) (2.10) As follows from the selection rules, during absorption (or emission) transitions J ′ → J ′′, the quantum number J has to change by unity, i.e. ∆J = J ′′ − J ′ = ±1. Besides, location of the lines in rotational spectra is given by differences: hν = E(J ′′)− E(J ′) = hcB [J ′′(J ′′ + 1)− J ′(J ′ + 1)] (2.11) For instance, considering transitions J → (J + 1), equation (2.11) yields 27 2 Basics on molecular spectroscopy ν = 2Bc(J + 1), J = 0, 1, 2, . . . (2.12) i.e. equidistant spectral lines with an energy gap of 2Bc between them. In the case of a real molecule (non-rigid rotator), the centrifugal force pulls the atoms apart. Hence, the molecule moment of inertia I increases, decreasing the rotational constant B. This centrifugal distortion can be taken into account by adding of a correction term into equation (2.10) [130]: E(J) = hc [ BJ(J + 1)−GJ2(J + 1)2 ] (2.13) (G is the centrifugal distortion constant). Accordingly, spectral positions of the transition lines also become corrected. Thus, equation (2.12) for transitions J → (J + 1) changes to: ν = [ 2B(J + 1)− 4G(J + 1)3 ] c, J = 0, 1, 2, . . . (2.14) Polyatomic molecules A linear polyatomic molecule (e.g. HCN, CO2 or C2H2) has a rotational spectrum closely analogous to that of a diatomic molecule. One should only take into account more complicated form of the moment of inertia I about the molecular axis, which defines rotational constant B. A nonlinear molecule has three moments of inertia, – IA, IB and IC , – about three principal axes of the molecule. Then, equation (2.7) for the classical rotational energy Erot takes the form Erot = L2 A 2IA + L2 B 2IB + L2 C 2IC (2.15) where LA, LB and LC are the components of the angular momentum L about the corresponding principal axes. Furthermore, three rotational constants A, B and C can be defined for the molecule, analogically to that in (2.9): A = h 8π2cIA , B = h 8π2cIB , C = h 8π2cIC (2.16) Finally, rotational energy levels of a polyatomic molecule can be found as eigenval- ues of the Hamiltonian with Erot expanded into the form (2.15); here, depending on its geometry, the molecule may be often considered as a symmetric top (see [131,137] for details). 28 2.2 Basic principles of absorption spectroscopy 2.1.3 Vibrational-rotational transitions A combination of vibrational and rotational motion of a molecule results in a rotating oscillator. It should be emphasized, that vibration of the molecule influences its rotation, due to the changing of the moment of inertia I and hence of the rotational constants A,B,C. In return, rotational motion may influence molecular vibrations. Therefore, vibrational-rotational spectrum is not just a simple sum of both ”pure” spectra, but their combination where some interaction terms have to be taken into account (see [130,131] for details). As discussed above, following restrictions (selection rules) are imposed on the vibrational-rotational transitions v′, J ′ → v′′, J ′′: ∆J = ±1, ∆v = 0,±1,±2,±3, . . . However, if the molecule has nonzero electronic orbital angular momentum, i.e. is a nonlinear polyatomic or a non-Σ diatomic molecule, transitions with ∆J = 0 are also allowed (see e.g. [137,139]). Depending on the ∆J value, absorption (or emission) lines in molecular spectra are usually grouped into three branches within each fundamental vibrational mode of the molecule: ∆J = −1, P–branch ∆J = 0, Q–branch (not always allowed) ∆J = +1, R–branch Thus, figure 2.5 shows two examples: (i) the ν3 fundamental band of CF2 radical which was calculated in [17] and consists of P–, Q– and R–branch, and (ii) the (v = 0 → 1) fundamental band of CO molecule which was measured in a reference cell by means of a FTIR spectrometer and consists only of P– and R–branch; the Q–branch is absent, since vibrational-rotational transitions with ∆J = 0 are not allowed in this case. 2.2 Basic principles of absorption spectroscopy Absorption Spectroscopy (AS) is an experimental diagnostic tool based on the in- teraction of electromagnetic radiation with molecules of matter. In particular, it employs allowed vibrational-rotational transitions which may occur within the in- frared active bands of the molecules due to absorption of the radiation. In this work, the linear AS theory was applied, where absorption of the electro- magnetic waves does not depend on their intensity, and possible influence of the radiation on the distribution of considered species over their energy levels is negli- gible. These assumptions were valid because of the low power of the applied laser diodes, which normally did not exceed a few tenth of mW. 29 2 Basics on molecular spectroscopy Natural and pressure broadening The well-known Heisenberg uncertainty principle [141] relates the lifetime ∆t of an excited state of a molecule with the uncertainty of its energy ∆E: ∆E∆t ≥ h̄/2 (2.19) Spontaneous (radiative or radiationless) transitions from considered energy level lead to its finite lifetime ∆t. Hence, this energy level will be blurred according to (2.19), which immediately results in a natural broadening of each spectral line. The lifetime ∆t can be reduced further due to collisions with other particles, causing an additional broadening of the line (so called pressure broadening). Both natural and pressure broadening mechanisms form a Lorentzian line profile with the ”full-width-at-half-maximum” (FWHM) γL centered at the wavenumber ν0: fL(ν − ν0) = 1 π γL/2 (ν − ν0)2 + (γL/2)2 (2.20) Normally, the natural line broadening is much narrower than the pressure broad- ening and can be therefore neglected. Then, the linewidth γL is given by pressure p and temperature T : γL = γL,0 p p0 ( T0 T )α (2.21) where γL,0 is the linewidth under normal conditions (p0 = 1 atm, T0 = 0◦C) and α has a value of ∼ 0.5 [142]. Typically, γL values lie between 10−5 and 10−2 cm−1, depending on the pressure p (see (2.21)). Doppler (thermal) broadening The gas particles, which absorb the radiation, have a distribution of their velocities. Obviously, this distribution is the wider, the higher the temperature T of the gas. Due to the Doppler effect, each absorbing photon will be ”red”- or ”blue”-shifted, depending on its velocity relative to the gas particle. Since the spectral line is a combination of all of these absorbed photons, the actual line profile will be broadened out by means of their distributed Doppler shifts. Assuming a Maxwellian velocity distribution with a gas temperature T , the Doppler broadening effect can be described by a Gaussian line profile centered at the wavenumber ν0 fD(ν − ν0) = 1√ 2πνD e − (ν−ν0)2 2νD 2 (2.22) 32 2.2 Basic principles of absorption spectroscopy with a Doppler linewidth (FWHM) γD γD = 2 √ 2ln2 νD = 2 ν0 c √ kBT M 2ln2 (2.23) where M is the mass of the gas particles, kB – the Boltzmann constant, and c – the speed of light. Normally, under low pressure conditions (p < 3 mbar), the Doppler broadening dominates over the natural and pressure broadening (γD γL), and the absorption lines in the infrared spectral range have their typical width values between 1 and 10−3 cm−1. Voigt line profile A general considering of both described broadening mechanisms leads to so called Voigt line profile, which is a combination of the Gaussian and Lorentzian profiles. Mathematically, it is a convolution of (2.22) and (2.20): f(ν, γD, γL) = ∫ +∞ −∞ fD(ν ′, γD)fL(ν − ν ′, γL)dν ′ (2.24) where ν0=0 was taken for simplicity. Instrumental broadening The further broadening mechanism is called instrumental broadening and relates to the finite linewidth of the absorbing laser beam and the influence of the optical elements involved into the measurement, i.e. to the apparat function of the measur- ing system. Its contribution γinstrum to the total linewidth γtotal can be calibrated experimentally, using a spectral line of a reference gas under known pressure, and then considered in further measurements as follows: γtotal = √ γ2 D,L + γ2 instrum (2.25) 2.2.3 Linestrength The physical matter and properties of the linestrength S defined as the proportional coefficient in equation (2.18) can be discussed using a simple example of an absorbing transition between two energy states ”1” and ”2” which have an energy gap of hν12 = E2 − E1 between them (see figure 2.7). The formulas necessary for this can be found, e.g., in [131]. If n1 and n2 are the populations of the considering states, then the linestrength of the transition ”1”→”2” is: 33 2 Basics on molecular spectroscopy n2, g2 n1, g1 hν12 B12 B21 E1 E2 Figure 2.7: Scheme of an absorbing transition between two energy states. Ei, ni and gi are the energy, population and degeneracy of the state i, respectively (i=1,2). S1→2 = hν12 n (B12n1 −B21n2) (2.26) where n is the absolute number density of the absorbing particles; B12 and B21 are the Einstein coefficients of the absorption and stimulated emission, respectively (see figure 2.7). In case of the assumed thermodynamic equilibrium, the B12 and B21 coefficients are related to each other through the statistical weights, or degeneracies, g1 and g2 of the states: g1B12 = g2B21 (2.27) On the other hand, defining a specific Hönl-London-Factor A for the down state ”1”, the B12 coefficient is also often related to the transition dipole moment µ, which is a characteristic constant for the considering species and vibrational mode: B12 = 8π3 3h2c Aµ2 (2.28) Besides, the equilibrium state populations ni are distributed according to the Boltz- mann distribution with a total partition function usually signed with Q: ni = gi n Q e − Ei kBT (2.29) Hence, taking (2.27), (2.28) and (2.29) into account, equation (2.26) may be rewritten as: S1→2 = 8π3 3hc ν12 g1 Q e − E1 kBT Aµ2 ( 1− e− hcν12 kBT ) (2.30) 34 Figure 3.1: Photo of the experimental set-up used in the present work. 3 Experimental set-up and data acquisition This chapter describes the main parts of the experimental set-up and data acquisition methods, which were applied to carry out all measurements presented in this work. The set-up shown in figure 3.1 consists of two principal components: (i) vacuum chamber, where investigated discharges have been produced, and (ii) optical unit, or IR-TDLAS system, which provided the experimental technique applied for the investigations. Besides, there is a rack with all devices and controllers used for the plasma operation. 3.1 Vacuum apparatus The plasma reactor shown in figure 3.2 was a cylindrical vacuum chamber made of stainless steal. It had both an inner diameter and a height of about 30 cm, resulting in a volume of about 20 liter. The powered electrode designed as a cylindrical copper 37 3 Experimental set-up and data acquisition CxFy H2 matching network rf generator (13.56 MHz) TTL trigger rf electrode MFC MFC pump Figure 3.2: Vacuum part of the experimental set-up: vacuum chamber and technical devices used for creation and operation of the studied rf discharges. block of 8 cm in diameter was placed in the center of the chamber and coupled to the 13.56 MHz rf power generator capacitively by means of a matching network. Before a measurement was started, two variable capacitor batteries of the network had to be matched to optimize the rf power transfer into the plasma. Then, during the measurement, these batteries were fixed at their optimal positions. In order to pulse the discharge, i.e. to form ”plasma-on” and ”plasma-off” phases, the rf power generator was triggered by means of a corresponding TTL-signal from the digital pulse/delay generator. To cool the powered electrode and keep its temperature constant during the plasma operation, a water cooling cycle with a thermostat was mounted onto the copper block. The walls of the reactor were grounded and had much higher area than the powered electrode. Therefore, a highly asymmetrical capacitively coupled rf discharge was ignited in the chamber, resulting in a high negative potential drop Ubias within the rf sheath between the plasma and the powered electrode (see section 1.2). The process gases (CF4 and H2) were fed into the reactor through many small holes in the shielding placed around the center electrode (see figure 3.3). Therefore, a continuous fresh gas supply directly to the powered rf electrode was provided during the discharge operation. The total pressure in the chamber and the feed gas flows were regulated indepen- 38 3.1 Vacuum apparatus rf electrode feed gases Figure 3.3: Scheme of the shielding placed around the rf electrode. Holes in the shielding served for feeding the gas into the chamber. dently by means of a capacitance manometer, mass flow controllers, a throttle valve controller and a sliding vane rotary pump which was able to evacuate the reactor down to the pressure less than 0.1 Pa. Two flanges, each of about 25 mm in inner diameter, were placed at the chamber sides and provided the probing infrared beam in a double path way through the re- actor, about of 55 mm above the rf electrode (see section 3.2.2). Potassium bromide (KBr) was used as a material for the side windows, since it has a high transmittance of about 90% in the spectral range from 500 to 2500 cm−1 (see figure 3.4), i.e. in the mid infrared region where absorption features of the studied species are located (see figure 3.10 in section 3.2.2 below). All technical devices and units applied for the plasma creation, discharge operation and keeping the constant pressure and gas flow conditions are listed in Appendix, see section A.3. 2500 2000 1800 1600 1400 1200 1000 800 600 400 250 4.0 5.0 6.0 7.0 8.0 9.0 10 12 14 16 20 30 40 Wavenumber, cm-1 Wavelength, μm Tr an sm itt an ce , % 0 20 40 60 80 100 Figure 3.4: Transmittance of potassium bromide (KBr) in the infrared spectral range [143]. 39 3 Experimental set-up and data acquisition technical applications, the semiconductor materials are usually doped with atoms that must either accept an extra electron from the crystal or donate an extra electron to the crystal thus allowing its natural participation in the valence bonds between adjacent atoms. When an excess of either acceptor or donor atoms is present, the crystal is said to be p-type or n-type, respectively. Normally, the n-type materials are designed so that the Fermi energy EC F , which characterizes the Fermi-Dirac energy distribution of electrons, is shifted into the conduction band [133, 151], and thus electrons partially occupy this band (see fig- ure 3.6a). Similarly, the energy EV F of the Fermi level in the p-type materials is shifted into the valence band and thus holes partially occupy energy states within this band. At thermal equilibrium the Fermi energy level applicable to the p-type part of the crystal must coincide, across the p-n junction, with that of the n-type part, i.e. EC F = EV F . Thus, the energy bands structure of the n-type material is dis- placed downward relative to that of the p-type material, forming a potential barrier for electrons on the way from the n-type part into the p-type part (see figure 3.6a). In case of a positive voltage connected to the p-type face of the crystal, i.e. +U in figure 3.5, the energy bands configuration changes to that sketched in figure 3.6b. This results in a decrease of the potential barrier for electrons and an increase of the Fermi energy EC F which becomes higher than EV F . Furthermore, the voltage U causes electrons from the n-type material and holes from the p-type material to be simultaneously injected into the region of the p-n junction (so called active zone). Here they may recombine, i.e. the electron may re-occupy the energy state of the hole, emitting a photon with energy equal to the difference between the electron and hole states involved: hν ≈ Eg (see figure 3.6b). Next, this photon may either be absorbed (forming an electron-hole pair again) or cause recombination of a further electron with a hole accompanied by a stimulated emission. This generates another photon of the same frequency, traveling in the same direction, with the same polarization and phase as the first one. Therefore, stimulated emission causes gain in an optical wave within the active zone of the crystal. Like in other lasers, the gain region should be surrounded with an optical cavity to provide generation. For this purpose, two end faces of the crystal are cleaved forming perfectly smooth, parallel edges, which works as a Fabry-Pérot resonator (see figure 3.5). Photons emitted in the active zone travel along the waveguide and are reflected several times from each end face before they leave the resonator. Thus, each time the wave passes through the cavity, it is amplified by the stimulated emission. Finally, when this amplification exceeds the losses due to absorption, incomplete reflection from the end facets, ohmic losses etc., the laser action starts. Mathematically, that means (i) EC F −EV F > Eg (the population inversion for electrons 42 3.2 IR Tunable Diode Laser Absorption Spectroscopy (IR–TDLAS) system Figure 3.7: Dependence of the diode laser frequency on the chemical composition, on example of four different lead salt lasers [151]. and holes) and (ii) eU > Eg (threshold condition for the applied voltage). On the other hand, the length l of the optical cavity and the refractive index n of the semiconductor in the active zone determine the number of axial cavity modes allowed for the radiation of a wavelength λ leaving the resonator: N ( λ 2 ) = nl, N = 1, 2, 3... (3.1) As mentioned above and shown in figure 3.6b, the emission occurs at frequencies ν ≈ Eg/h, whereas the band gap energy Eg of semiconductors mainly depends on their chemical composition. Therefore, to meet a desired spectral range, the corresponding crystal must first be specially composed, for instance, like it shown in figure 3.7. Then, the laser frequency ν can be roughly tuned by means of heating or cooling of the crystal, i.e. by varying its temperature T , which changes the refractive index n and hence the optical length of the cavity. Further fine tuning of ν can be achieved by a slight modulation of the voltage U , whereby the temperature T of the diode will be also slightly modulated, altering the optical length of the resonator again. Lead salt diode lasers used for the measurements in the present work have been controlled as described above, i.e. by means of the diode temperature and diode 43 3 Experimental set-up and data acquisition 1430 1440 1450 1460 1470 1480 780 683 585 488 390 Wavenumber, cm-1 D io de c ur re nt , m A T = 80.0 K m od e ho p m ul tim od e be ha vi or Figure 3.8: Typical mode structure diagram of a lead salt diode laser at a fixed temperature T. current variation (see section 3.2.2). Normally, these lasers are supplied with so called mode structure diagrams, which characterize spectrum of the emitted radia- tion (see figure 3.8). Particularly, there may be regions where a step-like change of the emission wavenumber occurs (so called ”mode hops”), or vice versa, many laser modes are emitted simultaneously (multimode behavior). 3.2.2 Optical table, laser tuning and beam guidance The optical component of the experimental set-up (the IR-TDLAS system) was designed and made at the Fraunhofer IPM in Freiburg [152]. It consists of an optical table with necessary optical arrangement on it, and a computer with special modules and software for the laser controlling, spectra recording and data acquisition. The scheme of the optical table is shown in figure 3.9. The probing IR radiation was produced by means of a Tunable lead salt multimode Diode Laser (TDL) placed in the laser station at the cooling head (Leybold, RGD 1245). The cooling head had a forcer inside which was moving with a frequency of 2 Hz whereas the liquid helium was pumped under the pressure of 20 bar through a closed cycle between the head and water cooled compressor (Leybold, ARW 4000 EU). The regular expansion of the helium resulted in a cooling of the cooling head and hence of the leaser diode station connected to the head by means of a heat-conducting copper contacts. In order to prevent the heat exchange with environment, the inside of the cooling head has been previously evacuated down to the pressure less than 10−5 mbar. After the cooling of the system was completed, the temperature in the laser station reached 44 3.2 IR Tunable Diode Laser Absorption Spectroscopy (IR–TDLAS) system 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 las er on las er off ν+δν W av en um be r, cm -1 Cu rre nt, m A T i m e , µs ν las er on las er on las er off Figure 3.11: Laser current ramps and their conversion into the emission spectral range [ν, ν + δν]. wavenumbers ν shows a strongly non-linear behavior. Hence, so called (non-linear) ”tuning rate function”had to be calibrated experimentally, using a germanium etalon with known free spectral range (see below). The radiated IR laser beam left the laser station through a KBr window. Due to a very small emitting area of the laser, the beam was strongly divergent and had the radiation angle wider than 50◦. Therefore, it was collimated by a mirror lens placed directly at the laser station and then guided onto a grid monochromator with a grid constant of 1/90 mm, where as far as possible a single mode was selected. The next element on the optical table was a beam splitter. Here, a small part of the radiation was guided into the reference channel, where a glass cell with a reference gas (e.g. N2O, CH4, C2H4) was placed to identify measured absorption spectra. Absorption lines of the reference gas measured in the cell were arranged according to that calculated by means of a special software IgorPro (WaveMetrics Inc., [163]). Besides, a three-inch germanium etalon (neoplas Control GmbH) was placed in the reference channel to find the non-linear tuning rate function experimentally. This procedure was based on the known distance between two maxima (or minima) in the signal intensity giving by the etalon, - so called ”etalon free spectral range”, - see figure 3.12. Within the IR spectral range considered in this work, it was about of 0.0158 cm−1 [164]. The rest of the radiation was guided from the beam splitter into the main channel. 47 3 Experimental set-up and data acquisition 0 5 0 1 0 0 0 . 0 1 5 8 c m - 1 las er off Sig na l In ten sity ( I ), a.u . W a v e n u m b e r ( n o n - l i n e a r s c a l e ) m e a s u r e d s i g n a l e t a l o n m a x i m a 0 . 0 1 5 8 c m - 1 Figure 3.12: Signal intensity measured from the three-inch germanium etalon to calibrate the non-linear wavenumber scale. The etalon free spectral range, i.e. the distance between two maxima (or minima), is about of 0.0158 cm−1. Here the beam was first squeezed to a diameter of about 4 – 5 mm by means of a telescope (two spherical mirrors on the table) and then directed through the vacuum chamber in a double path way (see figure 3.9). Obviously, an increase of the beam path inside the reactor would be highly favorable for the applied diagnostics. However, small diameter of the KBr side windows hampered any further passing of the laser beam through the chamber. An alternative usage of an optical multi-path cell placed in the reactor (see e.g. [165]) was also not feasible, because of the massive thin film deposition taking place in the studied plasmas. The intensity of the transmitted radiation was measured at the end of both chan- nels by means of two photovoltaic Mercury Cadmium Telluride (HgCdTe, MCT) detectors (InfraRed Associates Inc.) which had to be cooled with a liquid nitrogen in order to reduce the background noise. The measured (analog) signals were then amplified by means of two pre-amplifiers (MCT-1000, Infrared Systems Develop- ment Corp.) and sent onto the analog-digital (A/D) converter (BNC-2090, National Instruments GmbH) at the PC for further data acquisition by the software. The A/D converter had totaly 940 channels and a maximal sampling rate of 1 MHz, which gave an absolute limit of the temporal resolution for the system. Thus, if an absorption spectrum is measuring using 200 channels, it is possible to record not more than 106/200 = 5000 spectra per second, i.e. the best temporal resolution in 48 3.3 Data acquisition and TDLWintel software 0 1 0 0 2 0 0 3 0 0 4 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 w i t h o u t P E 1 l a y e r P E 2 l a y e r s P E 4 l a y e r s P E Int en sity wi th PE film , a .u. I n t e n s i t y w i t h o u t P E f i l m , a . u . Figure 3.13: Test for the non-saturation regime of the MCT detector. The signal intensity was measured over the laser ramp: first, without polyethylene (PE) film, and then with one, two or four PE layers in the beam path. this case is so small as 200 µs. Finally, the optical elements of the TDLAS system have been carefully adjusted to maximize the intensity of the signal coming onto the detectors and, therefore, to provide the best possible signal-to-noise ratio (SNR). However, in order to apply the measured intensities for further calculations correctly, it was very important to make sure that both detectors were not saturated. Otherwise, the system should be slightly de-adjusted taking the detectors back into the proper linear regime. The simplest test for that was to put a few layers of a polyethylene (PE) film, which has a broadband absorption in the IR spectral range, on the beam path and check, if the signal attenuation remains constant over the actual intensity range. Figure 3.13 shows this test graphically revealing the non-saturation (linear) regime of the detector. 3.3 Data acquisition and TDLWintel software The diode lasers have been controlled using a special software TDLWintel (Aerodyne Research Inc., [166]). At the same time, this program was also used for the data acquisition process, giving a possibility to measure up to three different absorption lines in the target spectral range. Therefore, the absolute number density monitoring 49 3 Experimental set-up and data acquisition 0 2 4 6 8 0 . 0 2 . 0 4 . 0 6 . 0 8 . 0 ( a ) r a w d a t a ( b ) a v e r a g e d CF de ns ity, 1 011 cm -3 T i m e , s Figure 3.15: CF radical density in a pulsed plasma: (a) – ”raw” measurement in the ”stream mode”, (b) – averaging over 50 plasma pulses. section 3.2.2), but mainly by the time, that the fit and calculation procedure took. Depending on the complexity of the fitted spectra, the temporal resolution, which could be achieved practically, was not better than 30− 40 ms. Nevertheless, even at such temporal resolutions, the measured density traces were quite noisy. Therefore, they were recorded over many successive plasma pulses (typically, over 50) and then averaged. The efficiency of the averaging can be seen on the example in figure 3.15. Thus, the ”stream mode” was suitable for a continuous real time analysis of the density traces of that particles, whose kinetics in the studied plasmas was relatively slow, e.g. stable fluorocarbon molecules, like C2F4, or transient species with a relatively long life time, like CF2 radical. For the species with a fast kinetics, like CF radical, the ”stream mode” was only used to measure the ”overview” density traces roughly. To follow their concentration more precisely, e.g. in the early afterglow or at the beginning of plasma pulse, the ”burst mode” had to be applied. 3.3.2 ”Burst-Mode” approach The ”burst mode” allowed the TDLWintel to collect the raw absorption spectra for a relatively short time period (up to few seconds) and fit them returning molecular concentrations afterwards. In this case, the time, which the fit and calculation 52 3.3 Data acquisition and TDLWintel software procedure took, did not influence the temporal resolution limit, like it was upon the ”stream mode”. That resulted in a much higher temporal resolution, the density traces could be measured with. Normally, absorption spectra in the ”burst mode” have been measured using all 940 D/A convertor channels, resulting in an absolute temporal resolution of 940 µs (see section 3.2.2). In order to synchronize the measurements with the plasma operation, the TTL signal from the pulse/delay generator, which was pulsing the plasma, was used to trigger the ”burst mode”. Thus, the highly resolved density measurements could be made for a short time period directly at the beginning of the plasma pulse or just after the plasma was switched off. However, during the calculation routine was running for one sequence of accumulated spectra, the further spectra collection was paused and the next burst could not be triggered. In other words, the plasma pulses analyzed in the ”burst mode” were not successive. Obviously, the density traces measured in this mode were even more noisy than that obtained upon the ”steam-mode”. Therefore, their averaging over many plasma pulses (typically, over 50) was made here as well. 53 3 Experimental set-up and data acquisition 54 4.1 Spectroscopic data of CF radical Table 4.1: The CF radical absorption lines considered in this work and their spec- troscopic data. The values taken for the measurements in this work are marked with bold font. electronic state line position linestrength reference ν (cm−1) (10−19cm/mol.) 2Π1/2 R (7.5) f 1308.5020 3.49 [17,35] 1308.5020 – [55] 1308.5032 – [159] R (7.5) e 1308.4946 3.49 [17,35] 1308.4947 – [55] 1308.4959 – [159] 2Π3/2 R (7.5) f 1308.6706 2.34 [17] 1308.6702 – [55,169] 1308.6722 – [159] R (7.5) e 1308.6700 2.34 [17] 1308.6702 – [55,169] 1308.6722 – [159] 2Π1/2 R (4.5) f 1301.0107 2.90 [17] 1301.0117 2.27 [170] 1301.0115 – [159] R (4.5) e 1301.0028 2.90 [17] 1301.0034 2.43 [170] 1301.0035 – [159] 2Π3/2 R (4.5) f 1300.9326 1.88 [17] 1300.9320 – [57,169] 1300.9339 – [159] R (4.5) e 1300.9323 1.88 [17] 1300.9320 – [57,169] 1300.9339 – [159] of the atmospheric water vapors in this region, which were always presented in the laboratory air and influenced the measured transmitted signal I(ν). However, due to a constant H2O concentration and a very wide broadening of its lines under at- mospheric pressure, this influence was treated as a permanent deformation of the baseline I0(ν). 57 4 Preliminary investigations on relevant spectroscopic data of the target molecules 1 3 0 8 . 5 1 3 0 8 . 6 1 3 0 8 . 7 0 . 9 1 . 0 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 R ( 7 . 5 ) , 2 Π 3 / 2 : 1 3 0 8 . 6 7 0 0 c m - 1 . 6 7 0 6 c m - 1 W a v e n u m b e r , c m - 1 H 2 O R ( 7 . 5 ) , 2 Π 1 / 2 : 1 3 0 8 . 4 9 4 6 c m - 1 . 5 0 2 0 c m - 1 13 08 .55 1c m-1 Tra ns mi tta nc e, I / I 0 C H 4 13 08 .53 0c m-1 13 08 .69 2c m-1 13 08 .64 9c m-1 13 08 .51 0c m-1 13 08 .58 2c m-1 13 08 .57 8c m-1 13 08 .71 7c m-1 13 08 .48 1c m-1 N 2 O Figure 4.2: Transmittance spectra of N2O and CH4 reference gases (pressure p = 15 mbar, optical length L = 15 cm) and that of the atmospheric H2O vapor (p = 1013 mbar, L = 300 cm) calculated within the target spectral range. Vertical dashed lines show positions of CF absorption lines used for the measurements in the present work. Figure 4.3 shows the 2Π1/2 R(7.5) CF doublet and the N2O reference lines measured at 1308.50 cm−1. As mentioned above, due to the Λ-type dou- bling, this CF doublet is split into two absorption lines with equal strengths of 3.49 · 10−19 cm/molecule (see table 4.1). Therefore, it was fitted with two Voigt profiles independently. In contrast to that, the second 2Π3/2 R(7.5) CF doublet at 1308.67 cm−1, which also consists of two components, could not be experimen- tally resolved, since the gap between its two lines is much narrower than their Doppler broadening (see figure 4.4). Therefore, this doublet was always fitted with a single Voigt profile of the double linestrength S = 2 × (2.34 · 10−19) = 4.68 · 10−19 cm/molecule. 58 4.1 Spectroscopic data of CF radical 1 3 0 8 . 4 8 1 3 0 8 . 5 0 - 0 . 1 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 1 3 0 8 . 4 9 1 3 0 8 . 5 0 1 3 0 8 . 5 1 - 0 . 0 0 2 0 . 0 0 0 0 . 0 0 2 0 . 0 0 4 0 . 0 0 6 N 2 ON 2 O C F Ab so rba nc e W a v e n u m b e r , c m - 1 Figure 4.3: The resolved 2Π1/2 R(7.5) CF doublet and N2O reference lines measured at 1308.50 cm−1. 1 3 0 8 . 6 0 1 3 0 8 . 6 5 1 3 0 8 . 7 0 1 3 0 8 . 7 5 0 . 0 0 0 . 0 3 0 . 0 6 - 0 . 0 0 2 0 . 0 0 0 0 . 0 0 2 0 . 0 0 4 0 . 0 0 6 1 3 0 8 . 6 6 1 3 0 8 . 6 7 1 3 0 8 . 6 8 N 2 ON 2 ON 2 O Ab so rba nc e W a v e n u m b e r , c m - 1 C F C F Figure 4.4: The unresolved 2Π3/2 R(7.5) CF doublet and N2O reference lines mea- sured at 1308.67 cm−1. Since the strength S of the unresolved doublet is comparable with that of each component within the resolved one, fairly similar absorbance and signal-to-noise ratio are expected for both selected doublets (compare figures 4.3 and 4.4). Hence, neither of them would be evidently preferable for further CF density measurements. 59 4 Preliminary investigations on relevant spectroscopic data of the target molecules 1 0 0 1 0 1 1 0 2 1 0 3 0 2 0 4 0 6 0 8 0 1 0 0 C 2 F 4 C 3 F 6 C 4 F 8 We igh t p erc en t o f p rod uc ts, % P r e s s u r e , T o r r Figure 4.6: Gaseous products composition for the polytetrafluoroethylene (PTFE) pyrolysis under 600◦C (according to data from [173]). 600◦C by Lewis et al. [173]. As one can see, at low pressures (p < 10 Torr), the C2F4 content in the products mixture is very high (up to 95–97%). An increase of the process pressure immediately leads to a drop of the C2F4 gain, whereas two further monomers, – C3F6 and C4F8, – are formed. Furthermore, it was found, that increasing of the temperature up to 700◦C has only a minor effect on the composi- tion of the products gas mixture. However, far higher temperatures lead again to considerable admixtures of C3F6 and C4F8 reducing the rate of the C2F4 [177]. Hence, fairly pure C2F4 gas is expectable as a sole product of the PTFE thermal decomposition at very low pressures and temperatures of about 550–600◦C. Experimental equipment used for the pyrolysis of the polytetrafluoroethylene in this work is shown in figure 4.7. Quartz tube /1/ filled with a certain amount of crumbed TeflonTM was placed in the vacuum chamber /2/, which was then evacuated using a diffusion pump /3/. The pressure in the system was measured by means of a capacitance manometer /4/. An electrical resistance wolfram coil /5/ was fixed at the quartz tube to heat it up to desired process temperature which was measured by means of a previously calibrated Fe-Co thermocouple /6/ placed into the tube. The PFTE thermal decomposition took place under initial pressure p < 10−3 mbar and temperature t◦ = (580 ± 10)◦C. Any gaseous output, formed in the chamber before the stationary process conditions are established, was drained. Next, the valve /7/ was opened and the actual degradation products were piped into a liquid nitrogen trap /8/, where they stayed frozen on the walls. Finally, after the pyrolysis process was completed, the product mixture was released from the walls by warming 62 4.3 Spectroscopic data of the stable reaction product C2F4 to pump to pump 1 2 3 4 5 5 6 7 8 9 10 Figure 4.7: Experimental apparatus for the PTFE thermal decomposition: /1/ − quartz tube, /2/ − vacuum chamber, /3/ − diffusion pump, /4/, /10/ − capacitive manometer, /5/ − resistance wolfram coil, /6/ − Fe-Co thermocouple, /7/ − valve, /8/ − liquid nitrogen trap, /9/ − storage vessel. the trap, and a storage vessel /9/ was filled with the gas up to a pressure of about 3.5 mbar, for further analysis. Purity of the produced C2F4 Since the C2F4 produced by the pyrolysis was intended to be used as a reference gas for calibration, its purity was of particular importance. Therefore, the composition of the gained gas mixture was analyzed by means of two different methods. First, the mass spectrum of the mixture was recorded using a quadrupole mass spectrometer (HIDEN EPIC IV). Here, the signal intensity of positive ions, formed in electron collisions with the gas molecules, was analyzed, comparing to their mass- to-charge ratio m/z. Figure 4.8 shows this spectrum and that representing the ion distribution for pure C2F4 [162]. As expected, they are in a very good agreement with each other. Certainly, a small admixture of other monomers with higher molecular weight was also detected in the sample, namely, C3F6 (C3F+ 5 ions at 131 amu) and C4F8 (C3F+ 6 peak at 150 amu), but no C2F6 was measured (absence of C2F+ 5 signal at 119 amu). Nevertheless, a fairly low intensity of the impurity peaks comparing to that of the main peaks indicates a very high C2F4 content in the mixture. Alternatively, the gas mixture was analyzed by means of the Fourier Transform Infra-Red (FTIR) technique. For this purpose, a cylindrical reference glass cell (15 cm long and 5 cm in diameter) with KBr windows was filled with the sample gas at pressure p = 50 Pa. Curve (a) in figure 4.9 shows the FTIR spectrum of this 63 4 Preliminary investigations on relevant spectroscopic data of the target molecules 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 0 3 1 0 4 1 0 5 1 0 6 1 0 7 1 0 3 1 0 4 1 0 5 1 0 6 1 0 7 C F 3 + m / z , a m u ( b ) int en sity , c ps C 3 F 6 +C 3 F 5 + C 3 F 3 + int en sity , c ps F + C F + C 2 F + C F 2 + C 2 F 2 + C 2 F 3 + C 2 F 4 +C F + C 2 F + C F 2 + C 2 F 2 + C F 3 + C 2 F 3 + C 3 F 3 + C 2 F 4 + F + C F + C 2 F + C F 2 + C 2 F 2 + C F 3 + C 2 F 3 + C 2 F 4 + ( a ) Figure 4.8: Mass spectrum of (a) – gas mixture gained by the PTFE pyrolysis and (b) – pure C2F4 gas [162]. sample measured with a spectral resolution of about 0.25 cm−1. In the same figure one can also see two further FTIR spectra taken from C2F4 patterns by others, with a spectral resolution of about 4 cm−1 [162] and 0.0019 cm−1 [158], respectively. All three spectra are in a very good agreement with each other and indicate the most intense CF2-stretching bands within the C2F4 molecule: the ν9 asymmetrical stretching band centered at 1339.9 cm−1 and the ν11 symmetrical stretching band at 1187.6 cm−1. Furthermore, the FTIR spectrum obtained from the reference cell (curve (a)) confirmed the conclusion that possible impurities of other monomers with higher molecular weight (C2F6, C3F6 or C4F8) can be neglected. Hence, according to the sample analysis, the gas produced by means of the vacuum pyrolysis of polytetrafluoroethylene was found to be pure C2F4 by far, and therefore, suitable for the following calibration procedure. 4.3.2 Calibration of the C2F4 absorption structure at 1337.11 cm−1 The C2F4 measurements in this work were carried out using a lead salt diode laser which emits in a spectral range from 1310 up to 1340 cm−1, i.e. where the P-branch of the ν9 stretching band is located (see figure 4.9). As it has been expected, trial measurements on the produced C2F4 gas in the reference cell showed no separate 64 4.3 Spectroscopic data of the stable reaction product C2F4 Table 4.2: Eight fictitious lines used for fit of the C2F4 absorption structure. line position (cm−1) linestrength (cm/molecule) 1337.0970 1.50 · 10−22 1337.1020 1.50 · 10−22 1337.1061 6.25 · 10−23 1337.1075 2.30 · 10−22 1337.1104 3.30 · 10−22 1337.1139 5.00 · 10−22 1337.1223 8.45 · 10−23 1337.1282 3.45 · 10−23 purity from the known gas pressure (50 Pa) and length of the reference cell (15 cm). In this work, the obtained spectroscopic data were used for further measurements of C2F4 absolute number density in the studied plasmas. 67 4 Preliminary investigations on relevant spectroscopic data of the target molecules 68 5 Absolute number density and kinetics of the target species in pulsed CF4/H2 rf plasmas This chapter primarily concerns the absolute number density traces of the target transient and stable species measured in pulsed CF4/H2 rf plasmas by means of the IR-TDLAS technique. In particular, correlations in the behavior of CF, CF2 and C2F4 concentrations, as well as kinetics of the species during the ”plasma-on” and ”plasma-off” phase will be extensively analyzed below. From this analysis, the dominant production and loss processes can be suggested for the molecules. But before, one should briefly describe the discharge operation parameters selected for the measurements and characterize internal properties of the studied plasmas. Besides, it is worth to consider preliminary FTIR measurements which have been carried out in order to detect and specify the stable products formed in the chamber in addition to the target species. 5.1 Plasma process parameters selected for investigations Using the technical equipment shown in the scheme of the experimental set-up in figure 3.2, many external operation parameters might be varied during the discharge, resulting in a strong impact on the plasma chemistry in the chamber. Indeed, as known from literature and own measurements, (i) the total pressure variation may grow either surface or gas phase reactions in importance, (ii) the rf power and the ratio between the precursor gases may influence the absolute number density of the key species formed in plasma, as well as the deposition (etching) of the a-C:F thin films at the reactor walls, e.g. [35,66,178], (iii) the plasma pulsing regime (pulse length and duty cycle) may affect the cross-linking and other properties of the a-C:F layers, e.g. [68–70], et cetera. Therefore, to analyze kinetics of the relevant species and reveal the dominant processes in the studied plasmas, absolute number density traces of the species have to be measured under identical plasma conditions and then compared. In order to settle the processes in the chamber and hence to assure identical conditions for the measurements, all studied discharges have been previously operated under selected parameter settings, during a few hundreds pulses before the measurement was started. 69 5 Absolute number density and kinetics of the species in pulsed CF4/H2 rf plasmas 0 1 0 2 0 3 0 4 0 5 0 6 0 - 1 0 1 2 3 4 5 6 etc hin g De po siti on / e tch ing ra te, n m/ mi n H 2 a d m i x t u r e , % de po siti on Figure 5.2: Deposition (etching) rate measured at the powered rf electrode under various H2 admixtures in pulsed plasmas (50 Pa, 10 sccm total gas flow, 50 W, 5 s on / 5 s off). The dashed line is a guide for the eye in the region of H2 admixtures higher than 20%. Own measurements by means of in–situ ellipsometry [35]. gas exchange in the chamber. In the case of V = 20 l, Φ = 10 sccm and considered pressures between 3 and 100 Pa, equation (5.1) yields τres = 5− 120 s. 5.2 Characterization of the pulsed discharge mode By means of a fast digitizing oscilloscope (WR 104Xi, LeCroy) connected to a corre- sponding output at the matching network, it was possible to measure the rf voltage at the powered electrode during the discharge operation. Figure 5.3 shows a typical rf sample at the beginning of the ”plasma-on” phase obtained by averaging over 25 successive plasma cycles. As one can see, ∼ 1 ms after the initial trigger to the rf power generator, a short and unstable plasma burst was observed, followed by ∼ 0.5 ms where the plasma was absent. A second onset, ∼ 1.5 ms after the initial trigger, led to stable discharge conditions. Thus, the time resolution of 940 µs mostly taken in the ”burst mode” was quite suitable for the measurements. And although the second measuring point might be recorded either during the unstable ”on-splash” or short ”off-gaps” at the beginning of the plasma pulse (see figure 5.3), its actual value was balanced due to the further averaging over a number of measured plasma cycles, and did not influenced the following data acquisition process. 72 5.2 Characterization of the pulsed discharge mode Figure 5.3: Typical rf voltage sample measured at the powered electrode at the be- ginning of the ”plasma-on” phase (10 Pa, 7 sccm CF4 / 3 sccm H2, 100 W, 1 s on / 2 s off). 0 1 2 3 - 5 0 0 - 4 0 0 - 3 0 0 - 2 0 0 - 1 0 0 0 1 0 0 2 0 0 W p l a s m a o f f U BIA S , V T i m e , s p l a s m a o n 1 0 0 W Figure 5.4: DC self-bias voltage Ubias measured at the driven electrode under var- ious rf powers in pulsed plasma (10 Pa, 7 sccm CF4 / 3 sccm H2, 1 s on / 2 s off). As mentioned above, due to the very different areas of the powered and grounded electrodes, a negative dc self-bias voltage Ubias is formed at the driven electrode in considered capacitively coupled discharges. Its values could be also measured during the plasma operation (see example in figure 5.4). 73 5 Absolute number density and kinetics of the species in pulsed CF4/H2 rf plasmas 0 5 0 1 0 0 1 5 0 2 0 0 - 5 0 0 - 4 0 0 - 3 0 0 - 2 0 0 - 1 0 0 0 5 0 P a 1 0 P a U BIA S , V R F p o w e r , W Figure 5.5: DC self-bias voltage Ubias measured at the driven electrode during the ”plasma on” phase under various rf powers and pressures of 10 and 50 Pa (7 sccm CF4 / 3 sccm H2, 1 s on / 2 s off). Figure 5.5 shows Ubias voltage measured at the driven electrode under various process parameters (pressure and rf power) selected for investigations in this work (see table 5.1). Two following trends can be clearly seen there: (i) the Ubias values are practically inversely proportional to the total pressure p: Ubias ∝ p−1, and (ii) |Ubias| increases nearly linear with increase of the rf power at the electrode (except for the low pressures and rf powers, where this increase becomes nonlinear). Such behavior of the self-bias voltage is quite typical for asymmetrical capacitively coupled discharges and was observed also by others, see e.g. [179]. As also seen in figure 5.5, at rf power of 100 W which was typically taken for the measurements presented below, the Ubias value varies over almost an order of magnitude, between −220 and −30 V, depending on the pressure p. Ultimately, this determines the energy of positive ions accelerated from plasma to the rf electrode by the self-bias voltage. 5.3 Broad band FTIR spectroscopy of stable gaseous reaction products Before considering the kinetics of the target CF, CF2 and C2F4 molecules, it may be useful to determine and specify other (stable) species formed in the studied plasmas. For this purpose, a previously evacuated cylindrical glass cell of length L = 15 cm 74 5.3 Broad band FTIR spectroscopy of stable gaseous reaction products 3600 3700 3800 3900 0 2 4 6 8 gas phase sample (HF absorption lines) A bs or ba nc e / 1 0-3 Wavenumber, cm-1 3860 3870 3880 3890 3900 0 2 4 6 8 A bs or ba nc e / 1 0-3 Wavenumber, cm-1 gas phase sample (HF absorption line) Gaussian fit profile Figure 5.7: Top: HF absorption lines detected within the measured FTIR spectrum of the discharge gas phase sample (10 Pa, 7 sccm CF4 / 3 sccm H2, 100 W, 1 s on / 2 s off, absorption length L = 15 cm). Bottom: Single HF absorption line measured at 3877.707 cm−1 and fitted with a Gaussian profile. Thus, more than 85% of the stable species in the gas phase of the studied plasmas could be detected and specified by means of the described FTIR measurements. Apparently, the rest must be attributed to H2 molecules which were continuously fed into the chamber, but could not be detected, since H2 has no absorption lines in the examined spectral range. 77 5 Absolute number density and kinetics of the species in pulsed CF4/H2 rf plasmas Finally, it is worth to note, that this estimation correlates with the balance of hydrogen in the reactor. Indeed, about of 9% from the initial 30% of H2 (3 of 10 sccm) were found to be converted into HF and CHF3 molecules measured in the gas phase, whereas a certain (currently unknown) amount of hydrogen might also be accumulated in the polymer thin film deposited at the reactor surfaces. 5.4 Target species and general approach to analysis of their reaction kinetics Different gas phase and surface processes discussed in sections 1.3 and 1.4 determine behavior and kinetics of the species in the studied CF4/H2 plasmas. For the sake of simplicity, these complex interactions during the discharge may be illustrated by the schematic diagram shown in figure 5.8. Thus, due to the electron impact reactions with molecules of the precursor gases, various neutral and charged dissociation products are formed in the plasma. These fragments may then react with each other (or again with the parent molecules) and produce fluorocarbon species of a higher molecular weight that can in return take part in the electron involved and chemical reactions. On the other hand, due to the strong interaction between the plasma and reactor surfaces, a fluorocarbon thin film may cover the chamber walls and rf electrode. In this case, the a-C:F layer can serve as an essential additional source or sink for the plasma species. As known from literature, CF and CF2 radicals and an intermediate product C2F4 play a key role in the gas phase plasma kinetics. Moreover, they are also held to be responsible for the fluorocarbon thin film formation at the reactor surfaces. Therefore, in the present work, the kinetic analysis will be primarily focused on these species. In the following sections, absolute number density traces of the target molecules measured in the pulsed plasmas under identical conditions will be analyzed, both in ”plasma-on” and ”plasma-off” phase. In particular, a balance equation will be written for each species to take into account relevant production and consumption channels, and hence to describe the measured kinetics mathematically. Thus, considering a bimolecular reaction A + B→ C + D (5.2) as an example production channel for species C, the corresponding contribution of the process to the balance equation for C can obviously be written as follows: d[C] dt = k̂+C[A][B] (5.3) 78 5.4 Target species and general approach to analysis of their reaction kinetics electron impact dissociation products CF4 H2 precursor gases C2F5 C2F6 C3F8 C2F4 C4F8 intermediate reaction products HF CHF3 e- H F F¯ fluorocarbon a:C-F thin layer at the reactor walls and rf electrode CF CF3CF2 CF+ CF3 +CF2 + CF3¯ C+ Figure 5.8: Schematic diagram of the reaction kinetics in CF4/H2 plasmas. Target species of the present study are marked with a grey background. Here, [A], [B] and [C] are the absolute number density (in cm−3) of molecules A, B and C, respectively; k̂+C is the absolute rate coefficient of the reaction (5.2) and has units of cm3s−1. However, the absolute concentration of one of the reactants in (5.2) may often be unknown. In this case, an effective rate coefficient k+C k+C = k̂+C[A] (5.4) which contains the unknown density [A] and hence has units of s−1 can be defined. This quantity may be reasonably used in the balance equation, when the kinetics of the species A is much slower than that of B or [A] [B]. An additional effective rate coefficient kdiff (also in s−1) can be assigned to describe diffusion of the species towards the electrode and the chamber walls. As mentioned above, not only the plasma-chemical reactions in the gas phase, but also production and loss processes taken place at the reactor surfaces may influence the number density of the considered species. Therefore, their contribution to the balance equation, should also be taken into account, e.g. using a total effective rate K+ (in cm−3s−1) defined for the surface production (or K− for the surface 79 5 Absolute number density and kinetics of the species in pulsed CF4/H2 rf plasmas 0 1 2 3 0 2 4 6 8 50 Pa 30 Pa 20 Pa 10 Pa plasma on A bs ol ut e C F 2 d en si ty , 10 13 c m -3 Time, s plasma off 0 10 20 30 40 50 0 2 4 6 8 0 2 4 6 8 0.0 0.2 0.4 0.6 0.8n0CF2 off n 0 C F 2of f , 1 013 c m -3 Pressure, Pa ksr k sr , 1 0-1 4 c m 3 s-1k-CF2 off k -C F 2of f , s-1 Figure 5.10: Top: CF2 number density decay measured during the plasma pulse at various total pressures (open symbols) and fitted to function (5.6) (solid lines) (7 sccm CF4 / 3 sccm H2, 100 W, 1 s on / 2 s off). Bottom: CF2 number density noff 0CF2 measured at the beginning of the plasma pause (squares); absolute self-recombination rate coefficient k̂sr (circles) and effective rate coefficient koff −CF2 (triangles) obtained from the fit. koff −CF2 values were always lower than 0.1 s−1, whereas the self-recombination rate coefficient k̂sr varied slightly around its mean value of 2.3 · 10−14 cm3s−1. Therefore, 82 5.5 Absolute number density traces of CF2 radical considering an estimation [CF2] ≥ 3 · 1013 cm−3, the first term of equation (5.5) appears to be at least an order of magnitude smaller than the second one, and thus can be neglected. In other words, under considered discharge conditions, CF2+CF2 recombination seems to be the dominant loss channel for the radical during the plasma pause, whereas diffusion and other first order consumption processes are rather of minor importance. Indeed, (i) in presence of hydrogen, the gas phase recombination of CF2 with fluorine may be neglected since fluorine is effectively bound in HF molecules, and (ii) CF2 surface losses must be very weak because of the fairly small sticking coefficient of the radical at the fluorocarbon layer which covers the reactor walls. Hence, the model function (5.6) for CF2 number density traces during the ”plasma off” phase can be rewritten in a more simple form (koff −CF2 → 0): [CF2](t) = noff 0CF2 1 + 2noff 0CF2 k̂sr(t− 1) (5.7) which will be used further in this work. Finally, it should be noted that the mean self-recombination rate coefficient k̂sr ∼ 2.3 · 10−14 cm3s−1 estimated above is in a good agreement with values known from literature (see also table 1.2). 5.5.2 CF2 radical in the ”plasma-on” phase Apart from the self-recombination which was found to be dominant during the plasma pause, the kinetic analysis of CF2 radical in plasma should obviously in- clude also other loss processes, like electron involved fragmentation, diffusion and chemical reactions with other species in plasma, as well as CF2 production channels, like electron impact dissociation of CF4 parent molecules, CF3 + e and CF3 + H reactions, see tables 1.1, 1.3 and 1.5 for details. Keeping the symbol k̂sr for the absolute rate coefficient of CF2+CF2 recombina- tion, the following differential equation can be written to describe CF2 behavior during the ”plasma–on” phase: d[CF2] dt = Kon +CF2 − kon −CF2 [CF2]− 2k̂sr[CF2][CF2] (5.8) Here, the effective rate Kon +CF2 (in cm−3s−1) considers all CF2 production channels during the plasma pulse, whereas kon −CF2 (in s−1) is the effective rate coefficient related to supposed CF2 consumption processes, other than the self-recombination treated in (5.8) separately. 83 5 Absolute number density and kinetics of the species in pulsed CF4/H2 rf plasmas Similarly to (5.5), equation (5.8) can be solved analytically (see section A.1.1 in Appendix), which gives the following expression for CF2 number density in plasma: [CF2](t) = Θ− kon −CF2 4k̂sr + [ C · exp(Θt)− 2k̂sr Θ ]−1 (5.9) where Θ = √( kon −CF2 )2 + 8Kon +CF2 k̂sr, and C is a constant defined by the absolute number density non 0CF2 of CF2 radical at the beginning of the ”plasma on” phase: [CF2](t = 0) = non 0CF2 ≈ 1.0 · 1013 cm−3 (see figure 5.9). Hence, function (5.9) was applied to fit CF2 density traces measured during the plasma pulse. Taking k̂sr = 2.3·10−14 cm3s−1 which was found in the previous section, the effective loss rate coefficients kon −CF2 and effective production rates Kon +CF2 have been obtained as parameters of the fit. The results are shown in figure 5.11. As expected, Kon +CF2 value increases with the total pressure, which indicates CF2 production mainly due to the plasma-chemical reactions in the discharge gas phase, e.g. due to CF4+e, CF3 + e and CF3+H assumed above. Since the increase of Kon +CF2 seems to be nearly linear with the total pressure p and thus with the total number density of CF4 in the chamber, one can suggest the electron impact dissociation of CF4 to be an essential channel of CF2 production in plasma: CF4 + e→ CF2 + 2F + e (5.10) In this case, the effective production rate Kon +CF2 defined in equation (5.8) can be written as follows: Kon +CF2 = k̂(5.10)[CF4]ne (5.11) where k̂(5.10) is the absolute rate coefficient for the reaction (5.10), and [CF4] and ne are the absolute number density of CF4 molecules and electrons, respectively. Thus, considering the slope of the trend line in figure 5.11 and taking 109 cm−3 as a typical value for ne in equation (5.11), one can estimate k̂(5.10) ∼ 6.9 · 10−11 cm3s−1, which is comparable with the value of 3.5 · 10−10 cm3s−1 given for the reaction channel in [180]. It may also be interesting to note, that two other reactions, CF3 + e and CF3 +H, have similar rate coefficients of 5.0 ·10−10 cm3s−1 [180] and 9.0 ·10−10 cm3s−1 [50,51], respectively. However, their contribution to the total production of CF2 during the plasma pulse appears to be relatively low, because CF3 and H number densities are definitely lower than that of CF4. 84 5.6 Absolute number density traces of the reaction product C2F4 fit - tau1-tau2 - CF-C2F4.opj 0 1 2 3 0 1 2 K+C2F4 on / k-C2F4 on n0C 2 F 4 on 30 Pa plasma off Ab so lu te C 2F 4 d en si ty , 10 14 c m -3 Time, s plasma on n0 C F4 on n∞ C2F4 on 0 1 2 3 0 1 2 3 4 10 Pa 20 Pa 30 Pa plasma off Ab so lu te C 2F 4 d en si ty , 10 14 c m -3 Time, s plasma on 50 Pa Figure 5.12: Top: Absolute C2F4 number density traces measured in pulsed plasma under various total pressures (7 sccm CF4 / 3 sccm H2, 100 W, 1 s on / 2 s off). Bottom: An example of C2F4 decay in plasma fitted to function (5.14). 87 5 Absolute number density and kinetics of the species in pulsed CF4/H2 rf plasmas In the following two sections, C2F4 behavior observed during and after the plasma pulse will be analyzed more in detail. 5.6.1 C2F4 behavior during the ”plasma-on” phase In order to describe C2F4 number density decays measured during the ”plasma on” phase and shown in figure 5.12, the following balance equation can be written: d[C2F4] dt = Kon +C2F4 − kon −C2F4 [C2F4] (5.13) Here, the effective production rate Kon +C2F4 (in cm−3s−1) considers all processes which result in production of C2F4 molecules, both in the gas phase and at the reactor surfaces. On the other hand, the effective rate coefficient kon −C2F4 (in s−1) relates to the channels of C2F4 consumption, e.g. electron impact fragmentation and diffusion of the species. Normally, the partial production of C2F4 due to CF2 + CF2 recombination has to be taken into account by an additional term k̂sr[CF2][CF2] in equation (5.13) (k̂sr is the absolute rate coefficient defined for the CF2 self-recombination above). However, function (5.9) obtained for [CF2] during the plasma pulse would not allow to solve the equation analytically. Therefore, within the present section, the contribution of this process is not treated separately, but effectively included in the overall rate coefficient Kon +C2F4 . Equation (5.13) is a first order linear differential equation, which can be easily solved as follows (see expression (A.8) in Appendix): [C2F4](t) = Kon +C2F4 kon −C2F4 + ( non 0C2F4 − Kon +C2F4 kon −C2F4 ) exp ( −kon −C2F4 t ) (5.14) where non 0C2F4 is the absolute concentration of C2F4 observed at the beginning of the plasma pulse: [C2F4](t = 0) = non 0C2F4 . Besides, the steady-state number density non ∞C2F4 of C2F4 molecules in plasma can be derived from equation (5.14) (t→∞): non ∞C2F4 = Kon +C2F4 kon −C2F4 (5.15) Further, C2F4 decay traces measured during the plasma pulse (see figure 5.12, top) were fitted to function (5.14). An example of the fit is shown in bottom of figure 5.12. Figure 5.13 shows Kon +C2F4 and kon −C2F4 values obtained from the fit (upper panel), as well as measured non 0C2F4 and calculated non ∞C2F4 number densities (lower panel). 88 5.6 Absolute number density traces of the reaction product C2F4 fit - tau1-tau2 - CF-C2F4.opj 0 10 20 30 40 50 0.0 0.5 1.0 1.5 2.0 0 5 10 15 20 Data: Data11_F Model: Parabola Equation: y = A + B*x + C*x^2 Weighting: y No weighting Chi^2/DoF = 3.5053E27 R^2 = 0.99268 A 0 ±0 B 0 ±0 C 630778845502.17859 ±22018875226.33177 K+C2F4 on K +C 2F 4on , 1 015 c m -3 s-1 Pressure, Pa k-C2F4 on Data: Data11_E Model: Parabola Equation: y = A + B*x + C*x^2 Weighting: y No weighting Chi^2/DoF = 0.30245 R^2 = 0.98013 A 6.01514 ±1.2508 B 0.25001 ±0.09708 C -0.00198 ±0.00155 k -C 2F 4on , s-1 0 10 20 30 40 50 0 1 2 3 4 0 1 2 Data: Data11_G Model: Parabola Equation: y = A + B*x + C*x^2 Weighting: y No weighting Chi^2/DoF = 1.4142E26 R^2 = 0.99499 A 0 ±0 B 3.1478E12 ±670242199688.03687 C 80738007908.61162 ±15566641481.67039 n0 C2F4 on Y =3.29444E13+7.24768E11 X+1.16925E11 X2 n 0 C 2F 4on , 1 014 c m -3 Pressure, Pa Data: Data11_B (RIGHT side) Model: Parabola Equation: y = A + B*x + C*x^2 Weighting: y No weighting Chi^2/DoF = 3.6594E25 R^2 = 0.99022 A 0 ±0 B 301898304042.17914 ±340947336897.03748 C 40957972759.22672 ±7918637412.08297 n 0 0 C 2F 4on , 1 014 c m -3n 00 C2F4 on neuer Fit - ~p2 ∞ ∞ Figure 5.13: Effective production rates Kon +C2F4 (boxes), loss rate coefficients kon −C2F4 (circles) and number densities non 0C2F4 (triangles) found from the fit of C2F4 decay traces shown in figure 5.12 to function (5.14). The steady- state densities non ∞C2F4 of C2F4 in plasma calculated by formula (5.15) are also given in the lower graph (diamonds). (7 sccm CF4 / 3 sccm H2, 100 W, 1 s on / 2 s off). While the total pressure increases, both effective loss rate coefficient kon −C2F4 and effective production rate Kon +C2F4 become also higher. Therefore, C2F4 losses due to the electron impact fragmentation and chemical reactions in the gas phase seem to dominate in the kinetics of the species during the plasma pulse, whereas diffusion 89