EXPERIMENT 43 PLASMA SPECTROSCOPY SAFETY FIRST In this experiment low power but high voltage radiofrequency (RF) electromagnetic radiation is used to produce a plasma inside an evacuated glass sphere. The radiofrequency power and voltages are such that even direct connection to high voltage plates surrounding the glass sphere is unlikely to be harmful. Access to radiofrequency power is restricted by using coaxial cables and enclosing the exposed high-voltage electrodes surrounding the sphere in an aluminium and Perspex box. Do not open this box or disconnect cables. Report any apparent damage to the lab technician and/or your tutor. There is a very small possibility that the spherical discharge vessel will implode. The aluminium and Perspex box will contain most of the glass splinters. Should this happen, turn off the vacuum pumps immediately. If you do not understand any of these points speak to a tutor before turning on any equipment
EXPERIMENT 43 PLASMA SPECTROSCOPY SAFETY FIRST In this experiment low power but high voltage radiofrequency (RF) electromagnetic radiation is used to produce a plasma inside an evacuated glass sphere. The radiofrequency power and voltages are such that even direct connection to high voltage plates surrounding the glass sphere is unlikely to be harmful. Access to radiofrequency power is restricted by using coaxial cables and enclosing the exposed high-voltage electrodes surrounding the sphere in an aluminium and Perspex box. Do not open this box or disconnect cables. Report any apparent damage to the lab technician and/or your tutor. There is a very small possibility that the spherical discharge vessel will implode. The aluminium and Perspex box will contain most of the glass splinters. Should this happen, turn off the vacuum pumps immediately. If you do not understand any of these points speak to a tutor before turning on any equipment
PREWORK Throughout sections 2 and 3 of these notes are interspersed questions designed to enhance your understanding the physics of plasmas and plasma spectroscopy. These questions should be attempted and preferably completed - BEFORE the start of each lab session. Some will require searching the scientific literature to locate data required to complete this question. The source of such data should be cited in your answer. 1. AIM Plasmas where the degree of ionization is small (typically <~ 1%) are referred to as Low Temperature Plasmas. These plasmas are extensively used in industry for a wide range of applications, from compact fluorescent lamps to machines for fabricating semiconductor chips. The properties of plasmas, be they space plasmas, high-temperature plasma for fusion, or lowtemperature plasmas, are difficult to measure without perturbing the plasma modifying its properties. In Experiment 12 Langmuir probes a fine wire is inserted into a plasma to measure its characteristics. In this experiment, by contrast, we measure the spectrum of the light emitted from the plasma to determine the characteristics of the plasma a technique that is applicable to the study of plasmas with a wide range of properties. This experiment will introduce you, not only to low-temperature plasmas, but the atomic and molecular spectroscopy that is crucial for extracting information about the plasma from the spectrum of the emitted radiation. 2. BASIC PLASMA PHYSICS CONCEPTS 2.1. Electron and ion temperatures Most macroscopic parameters (e.g. diffusion coefficient, mobility, collision frequencies, etc) of particles in a plasma can be derived from their speed distribution function f(v), with f(v)dv being the fraction of particles in the speed range of v to v + dv. This is because the probability of an interaction - scattering, excitation of an energy level of an atom - depends on the relative velocity of the interacting particles. The temperature of particles can only be defined when their ensemble in the body of a plasma exhibit a Maxwellian speed distribution: where m 3/2 f(v) = ( 2πk B T ) v = particle speed m = mass of particle 4πv 2 exp ( mv2 2k B T ) (2.1) T = temperature of the ensemble of particles (in K) k B = Boltzmann constant
This equation relates the average thermal energy of the particles to their temperature. Although the electrons and ions in a plasma may both have Maxwellian speed distributions, the temperatures that define these distributions may be different for ions and electrons. For a typical low temperature plasma, the electron temperature T e 1 may be ~ 1-5 ev, while the ion temperature could be as low as 0.05 ev. The assumption of a Maxwellian velocity distribution for ions and electrons in a plasma is an approximation in low temperature plasmas: the distribution function can deviate from Maxwellian. It is this assumption that must be kept in mind when analysing experimental data to determine the temperatures of various species of particles. Pre-work question 2.1: (a) From equation 3.1, derive an expression for the average thermal speed, < v >, and the RMS speed, v rms. (b) Calculate < v > and v rms of He ions with an electron temperature of 0.25 ev. What is their temperature in kelvin? 3. OPTICAL EMISSION SPECTROSCOPY OF LOW-TEMPERATURE PLASMAS Optical emission spectroscopy (OES) is a well-established and essential diagnostic tool for lowtemperature plasmas. OES is non-invasive, providing measurements of a wide range of collisional processes and plasma macroscopic parameters without affecting the plasma characteristics. The versatility of this diagnostic tool makes it valuable for various plasma-assisted applications, ranging from material processing to nuclear fusion. Using a spectrometer, the radiation emitted by excited atoms, molecules and their ions is collected and decomposed into an emission spectrum, i.e. several radiative lines or bands with well-defined central wavelengths. The spectral fingerprint of each spectrum is exclusively dependent on the gas used to generate the plasma. The collisional and radiative mechanisms that take place in the plasma govern the relative intensity and spectral profile of the different emission lines and bands. 3.1. Basics of atomic and molecular spectroscopy The discharge emission in the visible spectral range originates from transitions between electronically excited atoms and molecules. Analysis of the emission spectrum allows determination of the atomic and molecular species that populate the plasma, which can in turn be correlated with their mechanisms of excitation and various plasma macroscopic parameters. 1 In plasma physics temperatures are mostly given as the energy k BT in units of ev. Thus, for a temperature T in K, T(eV) = k BT/e.
3.1.1. Electronic transitions in atoms The atomic structure of an atom, A, is commonly represented using energy level diagrams and the electronic energy levels are usually written in the spectroscopic notation A(n 2S+1 L). The labels n, L, and S correspond to the principal, orbital angular momentum, electron spin quantum numbers Figure 1.1. Energy level diagram for helium. respectively. Figure 1 shows an example of an energy level diagram for helium. Note that levels are shown separated by their spin multiplicity 2S + 1, i.e. into the single (S = 0) and triplet (S = 1) systems while the orbital angular momentum is given by the letters S, P, S, F for L = 0, 1, 2, 3, respectively. Since the total orbital angular momentum and the total spin momentum are coupled by weak magnetic forces, more than one radiative transition can occur between a pair of principal quantum numbers. The allowed dipole transitions are governed by the selection rules
ΔS = 0; ΔL = 0 or ± 1; ΔJ = 0 or ± 1 (3.1) where J = L + S; L + S 1; ; L S is the total (electron) angular momentum quantum number. The central wavelength, λ i j, for a given atomic radiative transition i j < i is related to the energy gap between the upper i A(n 2S+1 L) and the lower j A(n 2S +1 L ) states: λ i j = hc E i E j (3.2) where E i and E j are the energies of the upper and lower levels, h the Planck s constant and c the speed of light. The radiative intensity of a given line is proportional to the number density of the upper (emitter) state, N i, and given by: ε i j N i A i j hc λ i j (3.3) with A i j the Einstein coefficient (or transition probability) for the spontaneous radiative emission i j. Pre-work question 3.1. (a) The transition shown in red in Figure 1 is allowed. Show that it satisfies the relevant selection rules for S and L. (b) Using the energy level data available in the NIST online database calculate the wavelength for the transitions 3 3 S 2 3 P, 3 1 S 2 1 P, 3 3 P 2 3 S, 3 1 P 2 1 S, 4 3 S 2 3 P, 4 1 D 2 1 P, 5 3 D 2 3 P. 3.1.2. Electronic and vibrational transitions in diatomic molecules The emission spectra and the energy level diagrams of diatomic molecules are rather more complex. As in atoms, the molecular electronic states can also be specified by their molecular term symbols M(n 2S+1 Λ +, u,g ) with Λ = 0, ±1, ±2, ±3 (corresponding to the Greek symbols Σ, Π, Δ, Φ) describing the overall angular momentum on the internuclear axis. For the Σ states, the right-hand superscripts +, indicate if the wave function is symmetric (+) or anti-symmetric ( ) with respect to reflection at any plane, including the internuclear axis. The subscripts u, g denote whether if the wave function is symmetric (g) or anti-symmetric (u) with respect to inversion through the centre of symmetry
of the molecule. For instance, the ground electronic state of N2 is X 1 Σ g + with n = X. The selection rules for electric dipole radiation of excited molecules require: ΔS = 0; ΔΛ = 0 or ± 1; g u (3.4) Figure 1.2. Energy diagram of a diatomic molecule. Diatomic molecules have additional degrees of freedom and quantization of their energy levels varies greatly from the atomic case. The atomic nuclei in a molecule are allowed to vibrate (i.e. stretch and compress) about an equilibrium separation and thus the energy associated with this movement cannot be neglected. In addition, the whole molecule can also rotate about its centre of mass. For each electronic state, the total potential energy of the molecule depends on the internuclear distance, giving rise to multiple bound vibrational states for a given electronic configuration. In turn, multiple bound rotational states can also exist for each vibrational state. Therefore, the total energy of a diatomic molecule for a given electronic state, E, is given by: E = E e + E υ + E r (3.5)
where E e is the minimum energy of each electronic state, E ν is the vibrational energy and E r the rotational energy. Figure 2 shows an example of a potential energy curve as a function of the internuclear distance for two electronic states. The vibrational energy for each vibrational level is given at the first order by 2 : E υ = ħω e (υ + 1 2 ) (3.6) with ω e = β 2D e μ the fundamental frequency of the vibration, β a constant associated with the force constant of the bond at equilibrium, De the dissociation energy of the molecule in the given electronic state, μ the reduced mass of the molecule and ν the vibrational quantum number. Pre-work question 3.2 (a) Derive an expression for the wavenumber, υ = 1/λ, associated with an electronic transition between two pairs of vibrational levels υ υ. Neglect contributions from the rotational components. (b) In this work, we study the emission spectrum of a discharge maintained in N2. One of the most intense spectral bands occurs due to transitions between the two electronic states C 3 Π u B 3 Π g, the so-called second positive system (SPS). Using the data provided in table 1, estimate the wavelength associated with vibrational transitions in the SPS for υ = υ υ = 2 with υ = 0, 1, 2, 3, 4. Electronic state E e (ev) ω e (x10 13 s -1 ) C 3 Π u 11.052 38.562 B 3 Π g 7.392 32.651 Table 1. Coefficients for the N2 SPSP 3.1.3. Thermodynamic equilibrium in a plasma Plasma systems in complete thermodynamic equilibrium (CTE) are uniform and homogenous plasmas in which kinetic, chemical equilibrium and all the plasma properties are unambiguous functions of a single temperature. In CTE conditions, this temperature is homogeneous and the same for all the degrees of freedom. Moreover, the electromagnetic radiation of the plasma can be considered as a black body radiation with this temperature. However, plasmas in CTE conditions cannot be practically realized in the laboratory. Most plasmas are optically thin 3 over a wide range of wavelengths and, as result, the plasma radiation can no longer be considered as a black body 2 Note that this is a solution for the harmonic oscillator, which in this case is only a first order approximation used to describe the molecular potential curves for low vibrational quanta. 3 For an optically thin plasma the emitted radiation escapes from the plasma without further interaction.
radiation. Plasma non-uniformity also leads to irreversible losses related with conduction, convection, and diffusion, which also disturbs the complete thermodynamic equilibrium. A more realistic approximation is the so-called local thermodynamic equilibrium (LTE) approach. Here, the plasma is considered optically thin and thus the radiation is not required to be in equilibrium. However, the collisional processes can be locally in equilibrium at a given temperature, which can differ from point to point in space and time. In many low-temperature plasmas the electrons may be in LTE at temperature Te and the ions and neutrals in LTE at a common temperature Ti as energy is provided directly to the electrons from an applied electric field, and is only slowly transferred to the ions and neutral species present through electron collisions. In order for the electron velocity distribution to be Maxwellian it is necessary for the electrons to undergo many collisions in a period of time short compared with the characteristic heating time or the time it takes to transfer energy to the other species present or they are otherwise lost from the plasma. Translational energy will rapidly be transferred between ions and neutral species present so that in most low temperature plasmas Maxwellian velocity distributions will be achieved for the heavy particles present. For weakly ionized gases their temperature will be close to room temperature and orders of magnitude less than the temperature of the electrons. 3.1.4. Excitation temperature of an atomic population For a plasma in thermal equilibrium statistical mechanics gives the population, n i, of an excited state i of energies E i relative to the ground state population n 0 4 E i g i n i = n 0 exp ( ) (3.7) g 0 k B T exc Where g 0 is the statistical weigh of the ground state and g i is the statistical weight of level i, k B is the Boltzmann constant. The statistical weights g account for the degeneracy of the levels, which gives the number of states within an energy level corresponding to a given quantum number.this expression, the Boltzmann distribution, will also give the relative population of energy levels of atoms in an LTE plasma provided the electron velocity distribution is Maxwellian, the collision rates are such that the time between collisions is much less than the radiative lifetime of the excited states, and the states are sparsely populated. Practically, this means that equation (3.7) rarely applies to the first excited state, may exclude other low-lying energy states, and thus n0 must be replaced by an arbitrary constant C. Thus, we can determine a temperature to the populations from the populations of higher energy excited states using equation (3.7). This temperature, the excitation temperature, Texc is close to, but not necessarily equal to, the electron temperature. 4 The number of atoms in excited states is usually much less than those in the ground state. Consequently, n 0 is very closely equal to the total density of atoms
The population n i of a specific excited state may be determined from the intensity I i of a spectral line originating from that state I j j n i = S i λ i ξ(λ j j i )g i A (3.8) i where S is a calibration factor which must be determined if an absolute measurement of n i is required, I j j i is the line intensity recorded by the spectrometer of a spectral line of wavelength λ i emitted when the atom decays from level i to level j, ξ is the relative spectral responsivity of the spectrometer, gi is spectral weight of level i and recorded by the spectrometer and A j i (see Appendix section) is the Einstein emission coefficient for the transition. The excitation temperature can thus be determined experimentally. from the slope of a plot of the logarithms of a set of relative spectral line intensities, plotted as a function of the excitation energy of the upper (emitter) state, E i : I j j ln ( i λ i ξ(λ j j i )g i A ) = C E i (3.9) k i B T exc 4.1.2. Vibrational temperature of molecules The vibrational and rotational processes play a fundamental role in a plasma. Rotational excitations play the role of plasma thermometer, whereas the vibrational excitations due to its adiabatic character can trap energy and play the role of energy reservoir, due to which the plasma becomes chemically reactive. Vibrational levels of diatomic molecules are not degenerated (i.e. g i = 1 for all i) and the number density of molecules, N(υ ), with a given vibrational quanta υ should follow a Boltzmann distribution at a vibrational temperature T υ : N(υ ) = N(0)exp ( E υ k B T υ ) (3.10) 4.1.3. Rotational temperature of molecules Because the rotational quanta are generally small (see Figure 2), energy transfer (relaxation) in rotational-rotational (RR) and rotational-translational (RT) collisional processes within molecules are usually non-adiabatic. In general RT relaxation is a fast process usually requiring only several collisions. In most systems the rates of the rotational relaxation processes are comparable with the rate of thermalization, i.e. translational-translational (TT) relaxation. Consequently, the rotational and translational degrees of freedom of N 2 molecules can usually be assumed in thermal equilibrium with each other, and the rotational temperature, Trot, is assumed to represent the gas temperature, Tg. When the spectral resolution of the spectrometer is sufficiently high to separate the different rotational structures (δλ 0.02 nm), Trot can be calculated using a Boltzmann plot or
by appropriately fitting the ro-vibrational band-head envelope. However, this approach is limited when lower resolution spectrometers are used to record the discharge emission. Alternatively, the rotational temperature can be determined by considering the strong dependence of the emission intensity of band-heads in the nitrogen first positive system (FPS), B 3 Π g A 3 Σ u + with Trot. This method compares experimentally measured and theoretical spectra of the band head of the FPS (2-0) at a given spectral resolution and proposes a semi-empirical formula for Trot that depends on the ratio of the emission intensities related with the band sub-heads at 774.3 nm and 775.8 nm (see appendix): T rot [K] = 195 [I(775.8 nm) I(774.3 nm) ] 0.52 (3.11) Figure 1.3. An example of two ro-vibrational bands associated with transitions between two pairs of vibrational levels in two different electronic states of the nitrogen second positive system (C 3 Π u B 3 Π g ). This spectrum was acquired with a high resolution spectrometer (<0.02 nm). 4. EXPERIMENTAL APPARATUS Vacuum system A diagram of the vacuum system is given in a bench file and you should refer to this.
The vacuum vessel, a glass flask, is connected to a diffusion pump and rotary mechanical pump, which can achieve a lowest pressure of ~10-4 Torr. The pressure gauge is connected to a Pirani sensor, giving a wide pressure range 10 3 Torr to 10-4 Torr, and a cold cathode gauge head which operates in the range 10-3 Torr to 10-7 Torr. The readout switches between sensors automatically as the pressure changes. Gas (He, CO2 or N2, depending on the tap settings of the manifold mounted on the wall) is admitted via a needle valve (the gas bottles are behind the wall). For operation, the tap between the flask and the pump is kept fully open and the pressure is varied by adjusting the needle valve. RF source The discharge power source is composed by a radio frequency oscillator (Hewlett Packard) that operates at ~31 MHz and it is connected to a linear amplifier (Kenwood). The radio frequency signal is applied between two aluminum plates on either side of the vacuum flask. Power is coupled into the discharge capacitively. The power level (RF voltage) is controlled by a dial on the front panel of a linear amplifier. Spectrometer The radiation emitted by the plasma is captured by an optical fiber that is coupled to an Ocean Optics HR 4000 spectrometer with a nomminal resolution of δλ 0.2 nm and wavelength range of 200 1000 nm. The proprietary software, OceanView, is used for acquisition and analysis of spectra. 5. MEASUREMENTS Switch on the vacuum gauge. Start the backing pump, first closing the air inlet valve. Making sure that the needle valve in the gas supply line is closed, close the plate valve and the backing valve and open the bypass valve and isolating valve. Wait until the pressure drops to a few 10-2 Torr. When this pressure has been achieved, get a tutor to turn on the cooling water to the diffusion pump and turn on the diffusion pump heater. Wait about 15 minutes.
Close the bypass valve and open the plate valve. Wait until the pressure inside the glass bulb to drop below 10-3 Torr. Open the OceanView software while you wait for the pressure to drop. Click on the Quick View icon. Set the integration time to 300 ms and 10 scans to average in the Acquisition Group Window (left sidebar) and wait about 5 minutes. Create a new dark background spectrum by clicking in the dark lamp icon situated in the toolbar above the graph window this will open a new window with a background-subtracted spectrum. Any changes to the optical set-up or ambient light in the laboratory should be corrected using this feature before recording a spectrum. If you have any concerns about the OceanView software you can refer to the user manual or ask a tutor. 5.1. Measurement of the excitation temperature in a helium plasma 1. Selected He on the gas manifold unit. This step should be performed under the supervision of a tutor. 2. Gently open the needle valve until the pressure is about 0.04 Torr. Further increase the pressure inside the bulb to 0.1 Torr by manipulating the isolation valve. 3. Turn on the RF oscillator and the amplifier. Turn the Plate knob until a breakdown of the gas in the bulb is achieved. A visible glow should be apparent in the flask. Note: make sure that the spectrum on the OceanView is fully background-subtracted before generating the plasma. 4. Without saturating the spectra, maximize the signal-to-noise ratio by tuning the acquisition parameters of the spectrometer in OceanView. 5. Record and plot the helium plasma spectrum. 6. Record the emission intensity of atomic lines related with the same radiative transitions between different helium excited states calculated in the pre-work question 3.1(b). 7. Estimate the helium excitation temperature for the helium emitter states. Based on reported values for the electron temperature in helium plasmas, discuss in your report if the plasma is in local thermodynamic equilibrium. 8. Plot the emission intensity of the atomic lines in step 6 as function of the RF voltage at two different pressures.
5.2. Measurement of the vibrational and rotational temperatures of a nitrogen plasma Select N2 on the gas manifold unit. This step should be performed under the supervision of a tutor. Set the pressure in the bulb to about 0.07 Torr. Record and plot the nitrogen plasma spectrum. Discuss in your logbook the main features that differentiate atomic and molecular emission spectra. Identify and plot in your logbook the emission bands associated with transition within the nitrogen second positive system, C 3 Π u B 3 Π g. How do you compare the wavelength of the band-heads calculated in the pre-work and those obtained experimentally? Discuss. Record the emission intensity associated with the C 3 Π u B 3 Π g transitions with ν = 2. Estimate the vibrational temperature of the C 3 Π u nitrogen levels. Estimate the rotational temperature for nitrogen. How do you compare this value with the vibrational temperature and the excitation temperature found for helium? Discuss this in your logbook. Plot the emission intensity associated with the C 3 Π u B 3 Π g transitions with ν = 2 as function of the RF voltage at two different pressures. Estimate the rotational temperature for nitrogen as a function of the RF voltage at two different pressures. Discuss the results in your logbook. References R. Eisberg and R. Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, John Wiley and Sons (New York, 1985) A. Fridman and L. A. Kennedy, Plasma Physics and Engineering, Taylor & Francis (New York, 2004)
F. R. Gilmore, R. R. Laher and P. J. Espy, Franck-Condon Factors, r-centroids, Electronic Transition Moments, and Einstein Coefficients for Many Nitrogen and Oxygen Band Systems, J. Phys. Chem. Ref. Data, Vol. 21 (5), 1992 M. Mavadat, A. Ricard, C Sarra-Bournet and G Laroche, Determination of Ro-Vibrational Excitations of N 2 ( B, v ') and N 2 ( C, v ') States in N 2 Microwave Discharges Using Visible and IR Spectroscopy, J. Phys. D: App.l Phys., Vol. 44 (15), 201 National Institute of Standards and Technology, Atomic Spectra Database Lines Form 2017, http://physics.nist.gov/physrefdata/asd/lines_form.html 6. APPENDIX Table 2. Statistical weights and Einstein coefficients for helium excited states. Transition j i g j A j i (s -1 ) 3 3 S 2 3 P 3 1.55x10 7 3 1 S 2 1 P 1 1.83x10 7 3 3 P 2 3 S 9 9.50x10 6 3 1 P 2 1 S 3 1.34x10 7 4 3 S 2 3 P 3 1.06x10 7 4 1 D 2 1 P 5 1.99x10 7 5 3 D 2 3 P 15 1.16x10 7 Table 3. Einstein coefficients for nitrogen C 3 Π u B 3 Π g transitions with υ = υ υ = 2 Transition υ υ υ A υ (s -1 ) 0 2 3.56x10 6 1 3 4.93x10 6 2 4 4.04x10 6 3 5 2.35x10 6 4 6 1.74x10 6