Emission kinetics of a HgBr discharge excilamp

PLASMAS AND GASES V.V. DATSYUK,1 I.A. IZMAILOV,2 V.V. NAUMOV 2 Taras Shevchenko National University of Kyiv, Faculty of Physics (64, Volodymyrs’ka Str., Kyiv 01601, Ukraine; e-mail: datsyuk@univ.kiev.ua) 2 V.E. Lashkaryov Institute of Semiconductor Physics, Nat. Acad. of Sci. of Ukraine (41, Prosp. Nauky, Kyiv 03028, Ukraine) 1 PACS 42.72.Bj, 52.80.Yr EMISSION KINETICS OF A HgBr DISCHARGE EXCILAMP A kinetic model of the working medium of a discharge excilamp on the B–X transition of mercury bromide, HgBr, excimer molecules has been proposed. The model explains the nonmonotonic dependence of the excilamp radiation intensity on the partial pressure of mercury dibromide molecules by the attachment of electrons to these molecules. HgBr(X) molecules were found to transit into the HgBr(B) excited state due to their collisions with high-energy electrons, thereby improving the excilamp characteristics. K e y w o r d s: excilamp, gas discharge plasma, kinetics, excimer radiation, mercury halides. 1. Introduction Excimer lamps (excilamps) are sources of radiation in the UV and visible spectral ranges. They have been intensively studied within the last three decades [1ҫ 13]. In order to create a working medium of excilamps, the gas discharges similar to discharges in excimer lasers are used [1]. However, unlike the latter, excilamps produce cheaper polychromatic radiation intended for the illumination of large areas and volumes. In comparison with ordinary lamps, excilamps have a higher spectral density of radiation power: more than 80% of the total power is emitted in a narrow band 2 to 5 nm in width. Owing to these advantages, excilamps are widely applied in modern photophysics, photochemistry, and photobiology [3ҫ5]. Excilamps based on mercury monohalides are promising to be used in the visible spectral range. Their radiation emission occurs owing to electronicvibrational transitions in HgBr∗ (� = 502 nm) and/or HgCl∗ (� = 557 nm) excimer molecules. The working mixture HgX2 -M, where X = Br or Cl, and M = Ne, He, or Xe, is excited with pulse-periodic discharges. c V.V. DATSYUK, I.A. IZMAILOV, V.V. NAUMOV, 2015 ○ 416 Typical kinetic models [6, 9, 10, 13], which involve the kinetics of a gas discharge plasma, dissociative excitation of HgX2 molecules, and deactivation and radiation emission of HgX(B) molecules cannot explain the experimental dependence of the energy emitted by HgX(B) molecules on the partial pressure of HgX2 . In experiments, when the HgBr2 vapor pressure, �HgX2 , increased from a few tenths to 0.5ҫ1 kPa, the emission intensity � grew by an order of magnitude. The further increase of �HgX2 to 1.5 kPa made � approximately half as high [6, 8]. However, ordinary theoretical models predict that the increase of �HgX2 should be accompanied by a monotonic growth of both the generation rate of HgX∗ molecules and the excilamp eiciency. Our work difers from the previous ones as follows: 1) we calculate the coeicient of electron losses that characterizes the excilamp eiciency reduction associated with the electron attachment to HgX2 molecules, and 2) we consider the excitation of electron states in HgX(B) molecules as a result of the collisions between HgX(X) molecules and electrons of the gas discharge plasma. The calculations were carried out without adjustable parameters. The theoretical prediction agrees well, both qualitatively and quantitaISSN 2071-0194. Ukr. J. Phys. 2015. Vol. 60, No. 5 Emission Kinetics of a HgBr Discharge Excilamp tively, with the measured dependences of � on the partial pressure of HgX2 molecules. 2. Kinetic Model of Excilamp Plasma In the proposed kinetic model, we consider the gas discharge plasma in the HgBr2 ҫNe mixture as a set of two subsystems. One of them contains free electrons, and the other heavy particles: molecules, atoms, and ions. Diferent characteristic times are required for the equilibrium to be established in these subsystems. Relaxation in the electron subsystem is the most rapid, and we assume that, within the time interval much shorter than the discharge one, the Maxwellian distribution of electrons over their velocities characterized by the temperature �� is established. If �� and the time dependence of the electron concentration, �(�), are known, the equations of physico-chemical kinetics can be used to calculate the concentration of heavy particles and the radiation power emitted by HgX(B) molecules. The electron concentration �(�) can be determined on the basis of the data of experiments, in which the current density in the gas discharge, �(�), is measured. However, it should be noted that, while measuring �(�), we cannot register all electrons formed in the electric discharge. This circumstance is related to the fact that some of the created electrons attach to electronegative molecules; in our case, HgX2 : � a � + HgX2 + (M) −→ HgX− 2 + (M). (1) Since reaction (1) withdraws electrons from the sequence of processes resulting in the formation of HgX(B) molecules, the eiciency of a light source diminishes. This reduction was studied by calculating the coeicient of electron losses introduced in this work for the ҥrst time. Calculations in the framework of the proposed kinetic model were carried out in two stages. At the ҥrst stage, a formula for the total rate of conduction electron generation in the gas discharge, �(�), was postulated. Using �(�), the electron concentration �(�) was calculated analytically within the operational method. The obtained dependence �(�) enabled the assumption about the form of �(�) to be veriҥed, because now the current density �(�) = = ���(�), where � is the electron charge, and � is the drift vector of electrons, is known: this is a quantity that can be measured experimentally. At the ISSN 2071-0194. Ukr. J. Phys. 2015. Vol. 60, No. 5 second stage, the determined �(�) dependence was used to solve numerically a system of kinetic equations for the concentrations of heavy particles. As a result, we obtained the radiation emission intensity by HgX(B) molecules, �(�). This dependence is also known from experiments. Hence, a comparison of the calculated and experimental dependences �(�) and �(�) allows one to verify the proposed kinetic model. In the framework of this approach, a number of speciҥc features inherent to electric discharges in the mixtures of inert gases with HgX2 can explained. In particular, ︀a non-monotonic dependence of the emitted energy �(�)�� on the HgX2 concentration is explained. 3. Coefficient of Electron Losses Let the rate of electron generation �(�) and the electron concentration �(�) be related to each other by the kinetic equation �� = �(�) − �� �. �� (2) Here, we denote the rate of electron attachment to electronegative HgX2 molecules in reaction (1) by �� ≡ �� [HgX2 ], where �� is the constant of electron attachment, and [HgX2 ] the concentration of HgX2 molecules. ︀� Let us introduce the quantity �0 (�) = 0 �(�)�� equal to the number of electrons generated in a unit volume and rewrite Eq. (2) in the form �(�) + �� ︁� �(�) �� = �0 (�). (3) 0 The solution of Eq. (3) can be found, by using the operational method. Let the direct Laplace transformation of �0 (�) give �0 (�). Then, from Eq. (3), we get the Laplace transform of �(�): � (�) = � �0 (�). � + �� (4) Formula (4) can be used to recover the original function �(�) for any �0 (�). The calculated dependences �(�) agree well with the experimental ones, if ︃0, ︂ ︂ ︂ � < 0, ︂ �0 = �m 2 exp − �−�0 − exp − 2 �−�0 , � > 0, (5) � � 417 V.V. Datsyuk, I.A. Izmailov, V.V. Naumov n η 1 a) n0 0.5 1 4. Kinetics of Heavy Particles b b) b b 0.5 n b 0 0 0 200 400 t(ns) 0 1 2 3 4 z Fig. 1. Concentration of generated electrons and those survived in the discharge: curves n0 and n were determined using Eqs. (5) and (6), respectively (a). t0 = 30 ns and z = 1. Coeicient of electron losses η as a function of the parameter z. Points correspond to η(z) values found at calculations, whose results are shown in Fig. 2 (b) where � ≡ �0 / ln 2. In this case, we obtain ︂ � = 4 �m max 0; ︀ ︀ ︂ ︀ ︀ ︀ ︀ exp − �� 2 exp −2 �� � exp −� �� , − − (1 − �) (2 − �) (1 − �)(2 − �) (6) where � ≡ �� � . The plots of functions (5) and (6) are shown in Fig. 1, a. Equation (3) makes it possible to analyze the fraction of electrons that attach to molecules and, hence, leave the subsystem of light particles, reducing the excilamp eiciency. Let us introduce the coeicient of electron losses, which deҥnes a decrease of the concentration of electrons as a result of their attachment to electronegative molecules, �= ︁∞ −∞ �(�) �� ︂ ︁∞ �0 (�) ��. (7) −∞ If � = 1, process (1) does not reduce the light source eiciency. If � = 0, all free electrons attach to HgX2 molecules, so that the transformation of the electric discharge energy into the energy of light becomes impossible. The dependence of the coeicient � on the parameter � calculated for Eq. (5) is depicted in Fig. 1, b. According to the results of calculations, if � = 1, the excilamp eiciency becomes three times lower due to reaction (1). Under those conditions, the reduction of the maximum radiation power is not so large: the ratio between the maxima of �(�) and �0 (�) equals 0.7. 418 The kinetics of heavy particles in HgX2 ҫM plasma was simulated on the basis of the standard model describing a laser on the HgX(BҫX) transitions [1]. The following processes were taken into account (see Table). Process 1a is the creation of HgX(B) molecules as a result of the dissociation of HgX2 molecules at their collisions with electrons. The dissociation rate constant �� was evaluated using the data of work [15]. The quantum yield of the formation of a molecule in the state B 2 Σ+ 1/2 amounts to 0.2÷0.25 for the electron energy � = 5÷10 eV. Collisions between electrons and HgX2 molecules are also accompanied by the formation of HgX molecules in the ground state (reaction 1b) and the ionization (process 2). Electronically excited HgX(B) molecules transit into the ground state either by emitting a photon (process 10) or not (process 11). HgX(X) molecules can either dissociate at their collisions with the atoms of a bufer gas M (process 6) or form a three-atomic HgX2 molecule at their collisions with X2 halogen molecules (process 8). Besides direct reactions 6 and 8, we took inverse reactions 7 and 9 into account. The rate constants of dissociation reactions 6 and 13 are [17] (�) �AX = �AX ︂ � 1000 � ︂1/2 ︂ ︂ �AX (�) exp − �AX , �B � (8) where A = Hg or X, �HgX = 0.6×1024 cm− 3 , �HgX = = 0.48 eV [18], �X2 = 1024 cm−3 , �X2 = 1.97 eV [18], and � is the gas temperature measured in Kelvins. Reactions 1, 10, and 11 dominate in the electric discharge plasma [1,6,7,9,10,13]. Making allowance only for them, the radiation intensity � for the transition HgX(B) → HgX(X) in the quasistationary approximation is described by the formula �= 1 + �r ︀ ℎ� �d � [HgX2 ] ︀, �M [M] + �HgX2 [HgX2 ] (9) where ℎ� is the photon energy. According to Eq. (9), the intensity � increases with the concentration [HgX2 ] and approaches the constant value �s = ℎ� �d �. �r �HgX2 (10) Formula (10) makes it evident that, in order to explain the experimental data, the dependence of � on ISSN 2071-0194. Ukr. J. Phys. 2015. Vol. 60, No. 5 Emission Kinetics of a HgBr Discharge Excilamp Kinetics of heavy particles in HgX2 –M plasma a) No. Process Rate constant Formula or source 1.a, 1.b 2 3 4 5 ︀→ HgX(B) + X+ e e + HgX2 — → HgX(X) + X+ e e + HgX2 → HgX+ 2 + 2e − e + HgX2 → HgX− 2 → HgX(X) + X e + HgX(X) → HgX(B) + e e + HgX(X) ← HgX(B) + e kd = 2 × 10−9 cm3 /s κ kd , κ = 4 ki = 1.8 × 10− 9 cm3 /s ka ke ︁ ︁ ke exp EBT−EX 6 HgX(X) + M → Hg + X + M KHgX (d) (8) 7 HgX(X) + M ← Hg + X + M KHgX = 10− 32 cm6 /s (r) Estimation c ) 8 9 10 11 HgX(X) HgX(X) HgX(B) HgX(B) kx = 8 × 10− 11 сm3 /s ︀ ︀ 500 exp − 13100 kx T τr = 23 × 10−9 s kQ = 2,3 × 10−10 сm3 /s, Q = HgX2 kQ = 5 × 10− 13 сm3 /s, Q = Ne 12 X + X + M → X2 + M 13 X + X + M ← X2 + M Estimation b) [1] [14, 15] (12) (11) e + X2 → HgX2 + X + X2 ← HgX2 + X → HgX(X) + hν + Q → HgX(X) + Q (r) 2 (d) KX 2 [6] [16] [16] [16] KX = 3.5 × 10−33 сm6 /s (8) a) X stands for Br, J, or Cl, and M for Ne or He. Numerical values of rate constants are given for the mixture HgBr2 ҫNe; b) According to data of works [1, 6] for E/P = 2 V/(cm Torr); c) According to data of work [1]. [HgX2 ] has to be taken into account. In this work, this was done by calculating coeicient (7). We extended the standard kinetic model of a HgX(BҫX) lamp, by considering the excitation of the state HgX(B) in collisions of electrons with the HgX(X) molecules. A possibility for reaction 4 to be an additional channel for the creation of HgX(B) molecules was indicated in work [7]. A formula for the rate constant of electron-induced transitions in two-atom molecules was obtained in theoretical work [19] as ︂ ︂ √ 2 �X − �B 16 � |�BX | × exp �� = 3 � �0 2 � B �� ︂ ︂ �B − �X × �0 , 2 � B �� (11) where �0 = (2 �B �� �� )1/2 , �B is the Boltzmann constant, and �0 the modiҥed Bessel function. For the transition between the states HgBr(B) and HgBr(X), we have �B − �X = 23480 cm− 1 and �BX = 4 D; from whence, we ҥnd the rate constant �� = 2.9 × × 10− 7 cm3 /s if �� = 8 eV. The rate constant for the inverse reaction is 1.4 times higher. The rate constant of reaction (1) was determined by the formulas taken from work [20] and using the ISSN 2071-0194. Ukr. J. Phys. 2015. Vol. 60, No. 5 data of work [21]: ︂ ︂ ︂ 8 �⋆ �⋆ ∆� . exp − � � = �f � B �� � �� �B �� � B �� (12) Here, �f = 0.6 × 10− 17 cm2 , �⋆ = 3.7 eV, ∆� = = 0.5 eV, and �� is the electron mass. 5. Intensity of Radiation Emitted by HgX(B) In this work, the rate �(�) is assumed to weakly depend on the concentration of HgX2 molecules in the gas mixture. At the ҥrst stage, we selected �(�) and calculated �(�). Then, using the function �(�), we solved the system of equations determining the time dependences for the HgX2 , HgX(X), HgX(B), X, X2 , and Hg concentrations and calculated the radiation power emitted by HgX(B) molecules. The calculations were carried out for the following parameters: the bufer gas pressure � = 107 kPa, the temperature � varied from 365 to 465 K, �� = 8 eV, � = 2.7×106 cm/s, and �m = 4.62×1013 cm−3 . The pressure of saturated HgX2 vapor was determined using the following formula interpolating tabular values [22]: ︂ ︂ � 4470 . (13) + 11.50 − 0.05 lg � − lg �HgX2 = − � 40 419 a) 10 0 0 200 400 Time (ns) 10 b) 5 0 0 200 400 Time (ns) Peak Intensity (kW/cm3 ) 20 Emission Intensity (kW/cm3 ) Curent Density (A/cm2 ) V.V. Datsyuk, I.A. Izmailov, V.V. Naumov 10 b b c) 5 b b b b b 0 b 0 1 2 HgBr2 Pressure (kPa) Emission Energy (mJ/cm3 ) Fig. 2. Current (a) and emission intensity (b) pulses found for various HgBr2 pressures, and (c) the emission intensity as a function of the HgBr2 pressure. Points in Fig. 2, c mark the maximum values of intensities for curves in Fig. 2, b. The dashed curve demonstrates the results of calculations with ke = 0 rS b rS 1.0 rS rS b b 0.5 rS b rS b 0 b b b 0 1 2 HgBr2 Pressure (kPa) Fig. 3. Theoretical values of excilamp emission energy. Squares correspond to the experimental values of emission intensity (in arbitrary units) taken from Fig. 1.19 in work [6]. The dashed curve shows the results of calculations omitting reactions 4 and 5 Here, �HgX2 is the HgX2 pressure measured in Torr units (1 Torr = 133.3 Pa), and � the temperature in Kelvins. The system of kinetic equations for the concentrations was solved numerically, by using the Gear method. The results of calculations are shown in Fig. 2, where the current density in a gas discharge, �(�), and the speciҥc power of radiation, �(�), are compared. In addition, Fig. 2, c exhibits the peak intensity of radiation, and Fig. 3 the radiation energy. The found dependence of the radiation energy on the pressure of saturated HgX2 vapor agrees well with experimental data [6]. The proposed kinetic model difers from the previous ones in that it involves the HgX(XҫB) transitions arising owing to the collisions between HgX molecules and electrons. The rate constants for these transitions were determined theoretically, with no ad- 420 justable parameters. In order to elucidate the role of reactions 4 and 5, we calculated the intensity of radiation emitted by a lamp in the case �� = 0. The results of these calculations are shown in Figs. 2, c and 3 by dashed curves. The ҥgures testify that both the peak radiation power and the radiation energy of a lamp decrease by approximately a factor of four at �� = 0. Of no less importance is the fact that, along with quantitative changes, qualitative ones are also observed. Namely, the dependence of the excilamp radiation power on the HgX2 pressure ceases to be non-monotonic, which contradicts experimental data. Hence, the population of the HgX(B) state owing to collisions between plasma electrons and HgX(X) molecules substantially enhances the excilamp radiation intensity. Reactions 4 and 5 must be taken into account in the kinetic models of working medium of excimer light sources. Reaction 4 allows one to predict some unexpected features of radiation emission by excilamps on the HgX(B—X) transitions. For example, in the recent experiment [13], two sequential current pulses with a time interval of an order of 100 ns were passed through a working medium of an excilamp on HgBr(BҫX) transitions. The amplitudes of current pulses were approximately equal, but the peak power in the second radiation pulse exceeded that in the ҥrst pulse by more than twice. Qualitatively, this effect can be explained by the fact that, before the second current pulse, a signiҥcant amount of HgBr(X) molecules were stored in the working medium during the ҥrst emission pulse. As a result of their collisions with electrons, these molecules were transferred into the excited state, so that the intensity of excilamp radiation increased by more than 100%. ISSN 2071-0194. Ukr. J. Phys. 2015. Vol. 60, No. 5 Emission Kinetics of a HgBr Discharge Excilamp 6. Conclusions The main result of this research consists in the development of the kinetic model for the radiation emission of a mercury halide excimer lamp. An important element of the model is the coeicient of electron losses introduced for the ҥrst time. This coeicient takes into account the attachment of gas-discharge electrons to electronegative halidecontaining molecules. It was shown that this process directly afects the eiciency of an excimer light source. A method to calculate the coeicient of electron losses analytically is proposed, which simpliҥes the evaluation of the excimer light source eiciency. The proposed kinetic model is used to explain the dependence of the radiation intensity of an excilamp based on the HgBr(B → X) transitions on the partial pressure of HgBr2 molecules. An importance of collisions between electrons and excimer molecules giving rise to the electron transitions between the HgBr(X) and HgBr(B) states is elucidated for the ҥrst time. The results of calculations are quoted for the mixture of HgBr2 with Ne. However, this model can also be used to calculate and optimize the parameters of an excimer light source, in which other bufer gases and other excimer molecules, in particular, HgCl and HgI, are used. The authors are grateful to O.M. Malinin for the experimental data and to M.G. Zubrilin for the discussion of the results obtained. 1. E.W. McDaniel and W.L. Nighan, Gas Lasers (Academic Press, New York, 1982). 2. B.M. Smirnov, Sov. Phys. Usp. 26, 31 (1983). 3. M.I. Lomaev, V.S. Skakun, E.A. Sosnin, V.F. Tarasenko, D.V. Shitts, and M.V. Erofeev, Phys. Usp. 46, 193 (2003). 4. M.I. Lomaev, E.A. Sosnin, and V.F. Tarasenko, Progr. Quant. Electron. 36, 51 (2012). 5. U. Kogelschatz, J. Opt. Technol. 79, 484 (2012). 6. A.N. Malinin, Dr. Sci. thesis (Uzhgorod Gos. Univ., 1998) (in Russian). 7. A.N. Malinin, N.N. Guı̆van, L.L. Shimon, A.V. Polyak, N.G. Zubrilin, and A.I. Shchedrin, Opt. Spectrosc. 91, 864 (2001). 8. A.A. Malinina and A.A. Malinin, Opt. Spectrosc. 105, 32 (2008). ISSN 2071-0194. Ukr. J. Phys. 2015. Vol. 60, No. 5 9. A.A. Malinina, N.N. Guivan, and A.K. Shuaibov, J. Appl. Spectrosc. 76, 711 (2009). 10. A.A. Malinina, N.N. Guivan, L.L. Shimon, and A.K. Shuaibov, Plasma Phys. Rep. 36, 803 (2010). 11. M.M. Guivan, A.A. Malinina, and A. Brablec, J. Phys. D 44, 224012 (2011). 12. A.A. Malinina, A.N. Malinin, and A.K. Shuaibov, Quant. Electron. 43, 757 (2013). 13. A.A. Malinina and A.N. Malinin, Plasma Phys. Rep. 39, 1035 (2013). 14. V. Kushawaha and M. Mahmood, J Appl. Phys. 62, 2173 (1987). 15. A.N. Malinin, Laser Phys. 7, 1168 (1997). 16. A. Mandl, J.H. Parks, and C. Roxio, J. Chem. Phys. 72, 504 (1980). 17. V.A. Kochelap and S.I. Pekar, Theory of Spontaneous and Stimulated Chemoluminescence of Gases (Naukova Dumka, Kyiv, 1986) (in Russian). 18. K.P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979). 19. V.V. Datsyuk, I.A. Izmailov, and V.A. Kochelap, Ukr. Fiz. Zh. 38, 242 (1993). 20. Physical and Chemical Processes in Gas Dynamics. A Computerized Handbook. Vol. 1: Dynamics of Physical and Chemical Processes in Gas and Plasma, edited by G.G. Chernyi and S.A. Losev (Moscow State Univ. Publ. House, Moscow, 1995) (in Russian). 21. W.L. Nighan, J.J. Hinchen, and W.J. Wigand, J. Chem. Phys. 77, 3442 (1982). 22. Properties of Inorganic Compounds. A Handbook, edited by A.I. Eҥmov, L.P. Belorukova, I.V. Vasilkova, V.P. Chechev (Khimiya, Moscow, 1983) (in Russian). Received 17.10.14. Translated from Ukrainian by O.I. Voitenko В.В. Дацюк, I.О. Измайлов, В.В. Наумов КIНЕТИКА ВИПРОМIНЮВАННЯ ГАЗОРОЗРЯДНОЇ HgBr ЕКСИЛАМПИ Резюме Запропоновано кiнетичну модель робочого середовища газорозрядної ексилампи на переходi BҫX ексимерних молекул бромiду ртутi HgBr. Модель пояснює немонотонну залежнiсть iнтенсивностi випромiнювання ексилампи вiд парцiального тиску молекул дiбромiду ртутi прилипанням електронiв до цих молекул. Встановлено, що в зiткненнях з високоенергетичними електронами молекули HgBr(X) переходять у збуджений стан HgBr(В), завдяки чому характеристики ексилампи покращуються. 421