CC BY
61
G.G. Bondarenko et al.
Modeling of an Impact of Thin Insulating Film on the Electrode Surface on Discharge Ignition in Mercury Illuminating Lamps at Low Ambient Temperatures
G.G. Bondarenko1, M.R. Fisher2, V.I. Kristya2, P. Zukowski3
1National Research University Higher School of Economics,
Myasnitskaya str., 20, Moscow 101000, Russia
2Bauman Moscow State Technical University, Kaluga Branch,
Bazhenov str., 2, Kaluga 248000, Russia
3Lublin University of Technology,
Nadbystrzycka str., 38A, Lublin 20-618, Poland
Received 17.12.2018
Accepted for publication 28.02.2019
Abstract
The mixture of argon and mercury vapor with temperature-dependent composition is used as the background gas in different types of gas discharge illuminating lamps. The aim of this work was to develop a model of the low-current discharge in an argon-mercury mixture at presence of a thin insulating film on the cathode and to investigate the influence of film on the discharge ignition voltage at low ambient temperatures.
When discharge modeling, we used the obtained earlier expression which describes dependence of the mixture ionization coefficient on temperature. When there was a thin insulating film on the cathode the model took into account that positive charges are accumulated on its surface during the discharge. They generate an electric field in the film sufficient for the field emission of electrons from the metal substrate of the electrode into the insulator and some of them can overcome the potential barrier at the film outer boundary and go out in the discharge volume improving emission characteristics of the cathode.
Calculations showed that at a temperature decrease the electric field strengthes in the discharge gap and the voltage in it are increased due to reduction of the saturated mercury vapor density in the mixture followed by the decrease of its ionization coefficient. Existence of a thin insulating film on the cathode surface results in an increase of the cathode effective secondary electron emission yield which compensates the reduction of the mixture ionization coefficient value.
The results of discharge characteristics modeling demonstrate that in case of the cathode with an insulating film the discharge ignition becomes possible at a lower inter-electrode voltage. This ensures outdoor mercury lamp turning on at a reduced supply voltage and increases its reliability under low ambient temperatures.
Keywords: mercury illuminating lamp, low-current gas discharge, insulating film on cathode, field electron emission, discharge ignition voltage.
DOI: 10.21122/2220-9506-2019-10-1-7-13
Адрес для переписки:
В.И. Кристя
Московский государственный технический университет имени Н.Э. Баумана, Калужский филиал, ул. Баженова, 2, г. Калуга 248000, Россия e-mail: kristya@bmstu-kaluga.ru
Address for correspondence:
V.I. Kristya
Bauman Moscow State Technical University, Kaluga Branch, Bazhenov str., 2, Kaluga 248000, Russia e-mail: kristya@bmstu-kaluga.ru
Для цитирования:
G.G. Bondarenko, M.R. Fisher, V.I. Kristya, P. Zukovski.
Modeling of an Impact of Thin Insulating Film on the Electrode
Surface on Discharge Ignition in Mercury Illuminating Lamps
at Low Ambient Temperatures.
Приборы и методы измерений.
2019. - Т. 10, № 1. - С. 7-13.
DOI: 10.21122/2220-9506-2019-10-1-7-13
For citation:
G.G. Bondarenko, M.R. Fisher, V.I. Kristya, P. Zukovski.
Modeling of an Impact of Thin Insulating Film on the Electrode
Surface on Discharge Ignition in Mercury Illuminating Lamps
at Low Ambient Temperatures.
Devices and Methods of Measurements.
2019, vol. 10, no. 1, pp. 7-13.
DOI: 10.21122/2220-9506-2019-10-1-7-13
УДК 537.525:621.327.53
Моделирование влияния тонкой диэлектрической пленки на поверхности электрода на зажигание разряда в ртутных осветительных лампах при низких температурах окружающей среды
Г.Г. Бондаренко1, М.Р. Фишер2, В.И. Кристя2, П. Жуковский3
'Национальный исследовательский университет «Высшая школа экономики», ул. Мясницкая, 20, г. Москва 101000, Россия
Московский государственный технический университет имени Н.Э. Баумана, Калужский филиал,
ул. Баженова, 2, г. Калуга 248000, Россия 3Люблинский технологический университет, ул. Надбыстрицкая 38A, г. Люблин 20-618, Польша Поступила 17.12.2018 Принята к печати 28.02.2019
Смесь аргона и паров ртути с зависящим от температуры составом используется в качестве рабочего газа в различных типах газоразрядных осветительных ламп. Целью данной работы являлось построение модели слаботочного разряда в смеси аргон-ртуть при наличии на катоде тонкой диэлектрической пленки, а также определение ее влияния на напряжение зажигания разряда при низкой температуре окружающей среды.
При моделировании разряда мы использовали полученное ранее выражение, описывающее зависимость ионизационного коэффициента рассматриваемой смеси от температуры. В случае наличия на катоде тонкой диэлектрической пленки в модели учитывали, что в разряде на ее поверхности накапливаются положительные заряды. Они создают в пленке электрическое поле, достаточное для возникновения полевой эмиссии электронов из металлической подложки электрода в диэлектрик, часть из которых может преодолевать потенциальный барьер на внешней границе пленки и выходить в разрядный объем, улучшая эмиссионные характеристики катода.
Расчеты показали, что при снижении температуры происходит увеличение напряженности электрического поля в разрядном промежутке и напряжения на нем, обусловленное уменьшением концентрации насыщенных паров ртути в смеси, а следовательно, и ее ионизационного коэффициента. Наличие же тонкой диэлектрической пленки на поверхности катода может приводить, вследствие существования полевой эмиссии электронов в пленку, к увеличению эффективного коэффициента электронной эмиссии катода, компенсирующему снижение величины ионизационного коэффициента.
Представленные результаты моделирования характеристик разряда демонстрируют, что в случае катода с диэлектрической пленкой становится возможным возникновение разряда при более низком межэлектродном напряжении. Это обеспечивает зажигание лампы наружного освещения при меньшем напряжении питающей сети и повышает ее надежность в условиях низких температур.
Ключевые слова: ртутная осветительная лампа, слаботочный газовый разряд, диэлектрическая пленка на катоде, полевая электронная эмиссия, напряжение зажигания разряда.
БОТ: 10.21122/2220-9506-2019-10-1-7-13
Адрес для переписки: Address for correspondence:
В.И. Кристя V.I. Kristya
Московский государственный технический университет Bauman Moscow State Technical University, Kaluga Branch,
имени Н.Э. Баумана, Калужский филиал, Bazhenov str., 2, Kaluga 248000, Russia
ул. Баженова, 2, г. Калуга 248000, Россия e-mail: kristya@bmstu-kaluga.ru
e-mail: kristya@bmstu-kaluga.ru
Для цитирования: For citation:
G.G. Bondarenko, M.R. Fisher, V.I. Kristya, P. Zukovski. G.G. Bondarenko, M.R. Fisher, V.I. Kristya, P. Zukovski.
Modeling of an Impact of Thin Insulating Film on the Electrode Modeling of an Impact of Thin Insulating Film on the Electrode
Surface on Discharge Ignition in Mercury Illuminating Lamps Surface on Discharge Ignition in Mercury Illuminating Lamps
at Low Ambient Temperatures. at Low Ambient Temperatures.
Приборы и методы измерений. Devices and Methods of Measurements.
2019. - Т. 10, № 1. - С. 7-13. 2019, vol. 10, no. 1, pp. 7-13.
DOI: 10.21122/2220-9506-2019-10-1-7-13 DOI: 10.21122/2220-9506-2019-10-1-7-13
Introduction
Arc illuminating lamps are nowadays a widespread type of gas discharge devices in which a mixture of argon with fixed density and mercury vapor with the density depending on temperature is often used as the background gas [1-5]. After the lamp turning on the low-current discharge is initiated in it which then transits into the glow and arc modes [6].
A lamp important characteristic is the discharge ignition voltage which equals to the minimum potential difference between the electrodes at which the gas breakdown occurs in the inter-electrode gap. Its reduction results in decrease of the lamp energy consumption and also in increase of its reliability and service time [7]. Value of the ignition voltage is determined by the processes of electron emission from the lamp cathode and ionization of the background gas in the discharge volume. In an argon-mercury mixture, along with the direct ionization of atoms by electrons, also ionization of mercury atoms in collisions with excited argon ones (the Penning reaction) can considerably contribute [4, 8, 9]. This leads to an increase of the ignition voltage of outdoor lamps under a reduction of the ambient temperature due to a decrease of the mercury vapor content in the mixture. As a result, the supply voltage can become insufficient for mixture ignition.
However, when a thin insulating film exists on the cathode surface, positive charges are accumulated on it during the discharge. They generate an electric field in the insulator sufficient for the field emission of electrons from the electrode metal substrate into the film [10, 11]. The emitted electrons are accelerated by the field in the film conduction band and a fraction of them can overcome the potential barrier at the film outer surface and go out into the discharge volume increasing the emission characteristics of the electrode. Therefore a method of reduction of the discharge ignition voltage consists in formation of an insulating layer with thickness 101-102 nm on the lamp metal electrodes surfaces.
Influence of field electron emission from the metal substrate into the insulating film on the cathode emission properties and the discharge ignition voltage was investigated in [12]. It was shown there that this influence was determined completely by the film emission efficiency 5f equal to the fraction of electrons emitted from the substrate, which goes out of the film into the discharge. But only fixed 5f magnitudes of about 0.1 were used in [12] whereas
in real lamps its value depends on the film thickness and the electric field strength in it, determined by the discharge conditions [13, 14].
In this work a model of the low-current discharge in an argon-mercury mixture under the presence of a thin insulating film formed at the cathode is developed. An analytical expression for the film emission efficiency 5f obtained in [14] is used. Dependence of 5f on the background gas temperature in the low-current discharge in argon-mercury mixture is calculated. It is shown that existence of an insulating film can result in a considerable reduction of the discharge ignition voltage at low temperatures.
Model of the low-current discharge
Let the voltage sufficient for arising of the low-current gas discharge to be applied to the discharge gap (length d) between the flat metal cathode covered with a thin insulating film (thickness Hf) and the metal anode (see Figure 1). The discharge current density j is determined by the equation of the discharge circuit:
Ud + Uf + RSj = Uo, (1)
where Ud = Edd and Uf = Ef Hf are the voltage drops in the discharge gap and in the insulating film, respectively, Ed and Ef are the electric field strength values in them, S is the electrode surface area occupied by the discharge, U0 is the external applied voltage, R is the ballast resistor which value is large enough to ensure a small value of j at which the discharge is low-current one [15].
Cathode Anode
. Ef E
Insulating film
0 uf Hr d + H, f ud J z
- R U„o-1 1-
Figure 1 - Schematic of the discharge geometry
Under the current flow in the discharge, bombardment of the cathode by ions proceeds and positive charges are accumulated on the film surface, which generate strong electric field in the film. When its strength Ef reaches value of ~ 108 V m-1 the field electron emission from the cathode metal
substrate into the film starts with the macroscopic current density determined by the Fowler-Nordheim equation [14, 16]:
( . , W »/ \l/2 A
jf (Ef )= +2
as fE'
t2 (о )(m -Xd )
exp
bv (yo )(m7m)
Ef
"(фm -Xd )'
3/2
,(2)
where v2 (y0 ) = 1- y0 + (l/3)y02ln y0;
t2 (yo) = 1 + (1/9) yo2 (1 - ln yo); yo = c^Ef/(m - xd);
a = 1.54110-6 AeVV-2; b = 6.831 109 V-m^-eV-32; c = 3.795 10 5 eVm1/2 V1/2; © is the metal substrate
' T m
work function; x d is the film material electronic affinity; m and m* are magnitudes of the electron mass in vacuum and in insulator, respectively. Here Ef = pUf /sfHf [17]; p is the electric field enhancement factor on the relief elements of the metal-insulator boundary; sf is the fraction of the boundary surface near the relief tops from which the field emission of electrons goes on due to the electric field enhancement on them; Sf is the high-frequency permittivity of the film material.
Value of Ef can be found from the condition of equality of the macroscopic current density jf of the field electron emission from the cathode substrate into the film and the discharge current density j, i. e. from equation:
jf (Ef ) = j. (3)
Electrons emitted into the film are accelerated by the electric field and decelerated in collisions with phonons [13, 14]. When they reach the film outer boundary a fraction Sf of them goes out of the film into the discharge increasing the cathode effective secondary electron emission yield yeJ^ which equals to the average number of electrons emitted from the surface per an incident ion. Value of the film emission efficiency is determined by an expression [14]:
5 f = 1 - exp
H
m
e J n=0
1+-
exp
~-dу
(4)
d У
where H0 = Hf - Ht; £en = eEfHf - ефm - n Ae;
■heEfl2V2m (фm-Xd)t(Уо);
e d = I
Ht is the tunneling length of an electron with the initial energy about the Fermi energy sF ofthe cathode metal substrate; As is the energy lost by an electron in each collision with a phonon in the insulator; Xe is the average electron path length between collisions
with phonons in the direction perpendicular to the cathode surface; h = h/2n, h is the Planck constant; e is the electron charge magnitude.
In the gas discharge, a substantial fraction of electrons emitted from the cathode surface returns to it due to scattering by the background gas atoms and only their fraction fes goes into the discharge volume. Therefore the real film emission efficiency in the discharge equals to Sf = f Sf [15]:
fe es f
feS = 1/(1 + V/4We ),
where v is the average velocity of electrons emitted from the cathode; we is the electron drift velocity in the gas.
As a result the cathode effective secondary electron emission yield is determined by expression [14]:
Y eff =(( Y г + 5 fe ))-5 fe ),
(5)
where y. is the cathode ion-electron emission yield.
The condition of low-current discharge self-sustaining in the inter-electrode gap is [6]:
a(Ed )d = ln (1 +1/ y eff),
(6)
where a(Ed) is the ionization coefficient of the background gas equal to the average number of ionizations of its atoms by an electron per a unit length.
For the argon-mercury mixture a(Ed) value in wide ranges of variation of temperature T and the electric field strength Ed it is determined by expression [18]:
a(Ed ) = A (N )n exp (-B (N n/Ed ), (7)
where A(N) = 0.18N3 + 5.84N2 + 54.45N + 209.20; B (N) = 0.08N3 + 2.50N2 + 22.28N + 90.40;
N = ln(nHg (T)/n) n = nAr + nHg (T);
nAr and nHg(T) are the argon and mercury vapor densities, respectively.
Equations (1)-(7) form a system for the low-current discharge characteristics in the argon-mercury mixture, including its ignition voltage Ut = Ud + Uf, when a thin insulating film covers the cathode, as well as under it absence (at Hf = 0 and Sf = 0).
Results of modeling
Calculations were performed for the discharge gap of length d = 210 3 m filled with the mixture of argon with density nAr = 6.57 1023 m3 corresponding to its pressure 2660 Pa at
temperature 20 °C and saturated mercury vapor, which density grows rapidly with temperature T as it is shown in Figure 2 [18]. The cathode was considered to be aluminum without an insulating film on the surface or with the insulating Al2O3 film of thickness H = 16 nm. The following parameter values were used [13, 14]: = 4 eV; X d = 2 eV; sf = 3; p = 3.8; m* = mg; As = CI. 125 eV; \ = 0.3 nm; s, = 103; y = 0.03. The ballast resistor
e ' f ' 11
ensured the discharge current density of about 10-5 Am-2, i. e. the discharge was low-current [15].
1(T4
10 7 I-1-'-1-
-30 -20 -10 0 10
T, °c
Figure 2 - Relative saturated mercury vapor content in the mixture as a function of temperature [18]
The calculated dependences of discharge characteristics on the mixture temperature are presented in Figures 3-5. It follows from them that in case of cathode without the film temperature reduction from + 10 °C to -20 °C (typical for northern countries in winter time), the electric field strength Ed value increases, whereas the discharge current density decreases. This results in discharge ignition voltage Ud increase by value of about 50 V which is in an agreement with experimental data [18]. At a temperature decrease below - 20 °C the discharge characteristics do not change, because the mercury content in the mixture becomes negligibly small and the discharge burns in practically pure argon.
8.5
« 6.5 -
S
^' 4-5 "
o
0.5 -1-■-1-
-30 -20 -10 0 10
T, °c
Figure 3 - The discharge current density as a function of temperature for the cathode with insulating film (solid line) and without the film (dashed line)
0.08
0.06 0.04
0.02-'-1-1-
-30 -20 -10 0 10
T, °C
Figure 4 - The cathode effective secondary electron emission yield as a function of temperature. Designations are the same as in Figure 3
250
i >-
225 -
>
■ 200 -175 -
150-1-1-1-
-30 -20 -10 0 10
T, °C
Figure 5 - The discharge ignition voltage as a function of temperature. Designations are the same as in Figure 3. Points are experimental data [19] for the cathode without the film
Under the presence of an insulating film on the cathode a contribution to its effective secondary electron emission yield Yeff along with the ion-electron emission makes the field electron emission from the metal substrate into the insulating film.
Therefore, value of y * exceeds its value for the
'eff
cathode without the film considerably. Hence, fulfillment of the discharge sustaining condition (6) becomes possible at a reduced value of the ionization coefficient of the background gas, i. e. at lower electric field strength in it and, consequently, at lower voltage Ut between the electrodes. It can be seen in Figure 5 that the decrease of Ut due to the field electron emission from the cathode substrate is of about 20 V at low temperatures which facilitates the discharge ignition in the arc illuminating lamp under such conditions.
Conclusion
A model of low-current discharge in the argon-mercury mixture when a thin insulating film exists on the cathode surface is developed in the paper. It takes into account the ion-electron emission from
the cathode surface, and the field electron emission from the cathode metal substrate into the film, caused by the strong electric field generated in the cathode during the discharge. Using this model dependences of the discharge characteristics on the mixture temperature are calculated.
It is shown that because the saturated mercury vapor density decreases with temperature rapidly, a reductionofthe mixture ionizationcoefficientalso takes place. Therefore, the electric field strength in the discharge gap and the voltage drop across it are increased which can prevent the discharge ignition in the lamp at low ambient temperatures. When the cathode surface is covered with a thin insulating film the field electron emission from the cathode metal substrate increases the cathode effective secondary electron emission yield. As a result, the discharge ignition becomes possible at lower value of the ionization coefficient of the background gas and, consequently, at a lower voltage drop between the electrodes. This ensures the discharge ignition under smaller supply voltage values and increases reliability of mercury lamp operation at low ambient temperatures(typical for the northern countries in winter time) and under instability of the supply network voltage.
Acknowledgments
This work was performed in frameworks ofthe program «Organization of Scientific Researches» of the Russian Federation Ministry of Science and Higher Education in Bauman Moscow State Technical University (project 3.8408.2017/6.7) and was supported financially by the Russian Foundation for Basic Researches and the Kaluga Region Government (project 18-42-400001).
Support from the Basic Research Program of National Research University «Higher School of Economics» is gratefully acknowledged.
Благодарности
Работа выполнена в рамках реализации государственного задания «Организация проведения научных исследований» Минобрна-уки РФ в МГТУ имени Н.Э. Баумана (проект 3.8408.2017/6.7) при финансовой поддержке РФФИ и правительства Калужской области (проект 18-42-400001), а также в рамках Программы фундаментальных исследований НИУ ВШЭ.
References
1. Flesch P. Light and light sources: High-intensity discharge lamps. Berlin, Springer, 2006, p. 344.
2. Zissis G., Kitsinelis S. State of art on the science and technology of electrical light sources: from the past to the future. J. Phys. D: Appl. Phys., 2009, vol. 42, no. 17, pp. 173001.
DOI: 10.1088/0022-3727/42/17/173001
3. Schwieger J., Baumann B., Wolff M., Man-ders F., Suijker J. Backcoupling of acoustic streaming on the temperature field inside high-intensity discharge lamps. J. Phys.: Conf. Series, 2015, vol. 655, pp. 012045. DOI: 10.1088/1742-6596/655/1/012045
4. Langer R., Garner R., Paul I., Horn S., Ti-decks R. Cold starting of fluorescent lamps - part I: a description of the transient regime. Eur. Phys. J. Appl. Phys., 2016, vol. 76, no. 1, pp. 10802.
DOI: 10.1051/epjap/2016160277
5. Bondarenko G.G., Kristya V.I., Savichkin D.O., Zukovski P. Simulation of cathode surface sputtering by ions and fast atoms in Townsend discharge in argon-mercury mixture with temperature-dependent composition. Devices and Methods of Measurements, 2018, vol. 9, no. 3, pp. 227-233.
DOI: 10.21122/2220-9506-2018-9-3-227-233
6. Lieberman M.A., Lichtenberg A.J. Principles of plasma discharges and materials processing. Hoboken, New Jersey, Wiley-Interscience, 2005, p. 756.
7. Hadrath S., Beck M., Garner R.C., Lieder G., Ehlbeck J. Determination of absolute Ba densities during dimming operation of fluorescent lamps by laser-induced fluorescence measurements. J. Phys. D: Appl. Phys., 2007, vol. 40, no. 1, pp. 163-167.
DOI: 10.1088/0022-3727/40/1/009
8. Brok W.J.M., Gendre M.F., van der Mullen J.J.A.M. Model study of DC ignition of fluorescent tubes. J. Phys. D: Appl. Phys., 2007, vol. 40, no. 1, pp. 156-162. DOI: 10.1088/0022-3727/40/1/008
9. Sobota A., van den Bos R.A.J.M., Kroesen G., Manders F. Transition between breakdown regimes in a temperature-dependent mixture of argon and mercury using 100 kHz excitation. J. Appl. Phys., 2013, vol. 113, no. 4, pp. 043308. DOI: 10.1063/1.4789598
10. Lee M.-B., Hahm S.-H., Lee J.-H., Song Y.-H. Emission behavior of nm-thick Al2O3 film-based planar cold cathodes for electronic cooling. Appl. Phys. Lett., 2005, vol. 86, no. 12, pp. 123511.
DOI: 10.1063/1.1894593
11. Stamenkovic S.N., Markovic V.Lj., Gocic S.R., Jovanovic A.P. Influence of different cathode surfaces on the breakdown time delay in neon DC glow discharge. Vacuum, 2013, vol. 89, pp. 62-66.
DOI: 10.1016/j.vacuum.2012.09.010
12. Bondarenko G.G., Fisher M.R., Kristya V.I. Modeling of the effect of temperature and field-induced electron emission from the cathode with a thin insulating film on the Townsend discharge ignition voltage in argon-mercury mixture. Vacuum, 2016, vol. 129, pp. 188-191. DOI: 10.1016/j.vacuum.2016.01.008
13. Suzuki M., Sagawa M., Kusunoki T., Nishimu-ra E., Ikeda M., Tsuji K. Enhancing electron-emission efficiency of MIM tunneling cathodes by reducing insulator trap density. IEEE Trans.: ED, 2012, vol. 59, no. 8, pp. 2256-2262.
DOI: 10.1109/TED.2012.2197625
14. Bondarenko G.G., Kristya V.I., Savichkin D.O. Modeling of the effect of field electron emission from the cathode with a thin insulating film on its emission efficiency in gas discharge plasma. Vacuum, 2018, vol. 149, pp. 114117. DOI: 10.1016/j.vacuum.2017.12.028
15. Arslanbekov R.R., Kolobov V.I. Two-dimensional simulations of the transition from Townsend to glow discharge and subnormal oscillations. J. Phys. D:
Appl. Phys, 2003, vol. 36, no. 23, pp. 2986-2994. DOI: 10.1088/0022-3727/36/23/020
16. Forbes R.G. Simple good approximations for the special elliptic functions in standard Fowler-Nordheim tunneling theory for a Schottky-Nordheim barrier. Appl. Phys. Lett., 2006, vol. 89, no. 11, pp. 113122.
DOI: 10.1063/1.2354582
17. Xu N.S., Chen J., Deng S.Z. Physical origin of nonlinearity in the Fowler-Nordheim plot of field-induced emission from amorphous diamond films: Thermionic emission to field emission. Appl. Phys. Lett., 2000, vol. 76, no. 17, pp. 2463. DOI: 10.1063/1.126377
18. Bondarenko G.G., Dubinina M.S., Fisher M.R., Kristya V.I. Calculation of the ionization coefficient in the Townsend discharge in the mixture of argon and mercury vapors with temperature-dependent composition. Russ. Phys. J., 2018, vol. 60, no. 12, pp. 2105-2110.
DOI: 10.1007/s11182-018-1332-7
19. Waymouth J.F. Electric discharge lamps. Cambridge, MIT Press, 1971, 352 p.
