FULL DIAGNOSTICS OF AN INDUCTIVE PLASMA SECTION OF AN ION THRUSTER MODEL Текст научной статьи по специальности «Физика»

ФИЗИКО-МАТЕМАТИЧЕСКИЕ НАУКИ

УДК621.315.592

Daliev Kh.S.

doctor of physical and mathematical Sciences (DSc), Dean of the faculty ofphysics, National University of Uzbekistan named after Mirzo Ulugbek

Daliev Sh. Kh.

doctor of philosophy (PhD) in physics and mathematics, senior researcher, laboratory of physics semiconductors and microelectronics, National University of Uzbekistan named after Mirzo Ulugbek

Atamuratov A.E.

candidate of physical and mathematical Sciences, associate Professor,

head of the Department of Physics, Urgench State University Erugliev U.K. junior researcher

Department " Physics of semiconductors and polymers» National University of Uzbekistan named after Mirzo Ulugbek, faculty of physics, Republic of Uzbekistan, Tashkent

Далиев Хожакбар Султанович

доктор физико-математических наук (DSc), декан физического факультета, Национальный университет Узбекистана имени Мирзо Улугбека

Далиев Шахрух Хожакбарович доктор философии (PhD) по физико-математическим наукам, старший научный сотрудник лаборатории физики полупроводников и микроэлектроники, Национальный университет Узбекистана имени Мирзо Улугбека Атамуратов Атабек Эгамбердиевич кандидат физико-математических наук, доцент, заведующий кафедрой «Физика», Ургенчский государственный университет

Эруглиев Уктам Комилович младший научный сотрудник кафедра «Физика полупроводников и полимеров» Национальный университет Узбекистана имени Мирзо Улугбека, физический факультет, Республика Узбекистан, г. Ташкент

A STUDY OF THE INFLUENCE OF HIGH-ENERGY BRAKE y-RADIATION OF A BETATRON AND y-RAYS 60Co ON THE PARAMETERS OF MOS TRANSISTORS

ИССЛЕДОВАНИЕ ВЛИЯНИЯ ВЫСОКОЭНЕРГЕТИЧЕСКОГО ТОРМОЗНОГО y-ИЗЛУЧЕНИЯ БЕТАТРОНА И y-КВАНТОВ 60Со НА ПАРАМЕТРЫ МОП-ТРАНЗИСТОРОВ

Summary. By measuring the current-voltage characteristics investigated influence of high-energy brake y-radiation of a betatron and y-rays 60Co on the parameters of MOS transistors. It is shown that the magnitude of the energy transfer of radiation F under irradiation with 60Co-quanta in comparison with the action of high-energy brake y-radiation is two times less, and the displacement of the current-voltage characteristics is significantly more. It is established that at 60Co irradiation with y-quanta, the density of surface states ANss in the whole studied energy range is 35-40% higher than the values of ANss after high-energy brake y-radiation.

Key words: MOS transistor, irradiation, current-voltage characteristics, energy transfer radiation.

Аннотация. С помощью измерения вольт-амперных характеристик исследовано влияние высокоэнергетического тормозного y-излучения бетатрона и y-квантов 60Со на параметры МОП-транзисторов. Показано, что величина переноса энергии излучения F при облучении y-квантами 60Со по сравнению с воздействием высокоэнергетического тормозного y-излучения в два раза меньше, а смещение вольт-амперных характеристик при этом существенно больше. Установлено, что при облучении y-квантами 60Co значение плотности поверхностных состояний ANSS во всем исследованном диапазоне энергии на 35-40% больше значений ANSS после высокоэнергетического тормозного y-излучения.

Ключевые слова: МОП-транзистор, облучение, вольт-амперная характеристика, перенос энергии излучения.

Постановка проблемы. Исследование влияния различных внешних факторов (температуры, электрического поля, радиации и легирования различными примесями) на физические явления, происходящие в кремниевых многослойных структурах типа металл-диэлектрик-полупроводник является одной из актуальных задач современной микроэлектроники. Изучение процессов образования дефектов и изменения электрических свойств системы Si-SiO2 при внешних воздействиях вызывает интерес широкого круга исследователей. Этот интерес обусловлен, во-первых, выяснением механизма образования электрически активных дефектов в объеме полупроводника, в диэлектрике и на границе раздела Si-SiO2. Во-вторых, выяснением возможностей и пределов применения таких воздействий в технологии полупроводниковых приборов. Несмотря на то, что имеются довольно полные экспериментальные данные по влиянию облучения, температуры и других воздействий на функционирование МДП-приборов, остается еще много неясного в физическом происхождении и природе различных типов зарядов в системе Si-SiO2.

Анализ последних исследований и публикаций. Известно, что количество и параметры радиационных повреждений в многослойных структурах сильно зависят от условий и от вида облучения. В настоящее время имеется достаточно работ, посвященных исследованию влияния у - квантов

10*

10*

ю3

104

60Со на свойства МНОП-структур [1-5]. В работе [2] было исследовано воздействие высокоэнергетического тормозного (ВЭТ) у-излучения на характеристики кремниевых МНОП-структур. Но до настоящего времени почти нет работ, посвященных изучению влияния ВЭТ у-излучения на параметры МНОП-структур и сравнительного анализа с воздействием у - квантов 60Со.

Формулирование целей статьи. Целью данной работы являлось изучение выходных и передаточных вольт-амперных характеристик (ВАХ), порогового напряжения МОП-транзисторов, типа КП 304 А, облученных у-квантами 60Со и ВЭТ у-из-лучением.

Изложение основного материала. Облучение МОП-транзисторов производилось потоком у-квантов 60Со с мощностью экспозиционной дозы в месте расположения образца 390 Р/с, что соответствовало плотности потока энергии квантов 0.12 Вт/см2. Диапазон переносов энергии излучения в наших исследованиях составлял (1^10)-104 Дж/см2.

Выходные ВАХ МОП-транзисторов типа КП 304А исследовались в диапазоне напряжений сток-исток, включающем линейный участок и область насыщения. Изменение линейных участков ВАХ образцов, облученных ВЭТ у-излучением при переносе энергии F=130Дж/см2 и образцов, облученных у-квантами 60Со при переносе энергии F=63.5 Дж/см2 представлено на рис. 1.

Vй

№ 10» ]0* Ю1 Iff

Рис.1. Линейная область выходной ВАХ МОП-транзисторов:

1-контрольные образцы; 2- облучение ВЭТ у-излучением с переносом энергии излучения 130 Дж/см2; 3- облучение у-квантами 60Со с переносом энергии излучения 63,5 Дж/см2.

Хотя величина переноса энергии излучения при облучении у-квантами 60Со почти в два раза меньше, смещение ВАХ при этом существенно больше, чем при воздействии ВЭТ у-излучения. Влияние ВЭТ у-излучения на пороговое напряжение МОП-транзистора исследовалось в диапазоне переносов энергии излучения (10^6)103 Дж/см2. Измерение пороговых напряжений образцов до и

после облучения производилось при VBS=0 и Vds=90 мВ. В исследованном диапазоне переносов энергии излучения наблюдается монотонное смещение этой зависимости в сторону больших значений VGS и изменения ее крутизны с увеличением переноса энергии излучения. Соответственно этому, VMG с увеличением переноса F монотонно увеличивается в сторону больших отрицательных значений (рис. 2, кривая 1). Отметим, что при облучении у-квантами 60Со при практически одинаковых переносах энергии излучения увеличение VMG значительно больше (кривая 2), чем при воздействии ВЭТ- излучения (кривая 1).

Lü1 m3 ioJ io<

Рис.2. Зависимость порогового напряжения МОП-транзисторов от

переноса энергии излучения для образцов, облученных

высокоэнергетическим тормозным у-излуче-нием (1) и

у-квантами от 60Со (2)

Результаты измерений относительного изменения эффективной канальной подвижности при облучении у-квантами 60Со и ВЭТ у-излучением показали, что с увеличением переноса энергии излучения эффективная подвижность в инверсионном канале монотонно уменьшается, это связано с уменьшением передаточной характеристики МОП-транзистора. Зависимость эффективной канальной подвижности от переноса энергии излучения при облучении у-квантами 60Со также отличается от такой зависимости при облучении ВЭТ у-излучением. При облучении у- квантами 60Сo с сравнительно меньшей величиной F по сравнению с ВЭТ-излучением наблюдается большее изменение цэфф. Результаты измерений показали, что передаточная подпороговая ВАХ образца, облученного у- квантами 60Сo с переносом энергии F = 4.109 Дж/см2 имеет большее смещение и изменение крутизны по отношению к контрольному образцу, чем образец, облученный тормозным спектром с F = 7.5.109 Дж/см2. Рассчитанные по этим ВАХ энергетические спектры поверхностных состояний (ПС) показывают, что при сравнительно меньшем значении переноса энергии F при облучении у-квантами 60Сo значение плотности поверхностных состояний ДNss во всем исследованном диапазоне энергии на 35-40% больше значений ДNss после ВЭТ у-излуче-ния.

Выводы из данного исследования. Таким образом, из сравнительного анализа измерений вольт-амперных характеристик МОП-транзисторов

типа КП 304А, подвергнутых воздействию высокоэнергетического тормозного у-излучения бетатрона и у-квантов 60Со можно сделать вывод, что величина переноса энергии излучения F при облучении у-квантами 60Со по сравнению с воздействием ВЭТ у-излучения в два раза меньше, а смещение ВАХ при этом существенно больше. Установлено, что при облучении у-квантами 60Co значение плотности поверхностных состояний ANSS во всем исследованном диапазоне энергии на 35-40% больше значений ANSS после ВЭТ у-излучения.

Список литературы:

1. Александров О.В. Влияние смещения на поведение МОП-структур при ионизирующем облучении. ФТП, 2015, т.49, в.6, С.793-799.

2. Далиев Х.С. Воздействие высокоэнергетического тормозного у излучения на характеристики кремниевых МНОП структур. ДАН РУз, 2009, в. 5, С.36-39.

3.Попов В.Д. Два этапа поверхностного де-фектообразования в МОП структуре при низко интенсивном воздействии gamma-излучения. ФТП, 2016, т. 50, В.3, С.354-359.

4. Федоренко Я.Г., Отавина Л.А., Леденева Е.В., Свердлова А.М. Влияние радиационного воздействия на характеристики МДП структур с окислами редкоземельных элементов. ФТП, 1997, том 31, № 7, С.885-888.

5. Khlifi Y. Kassmi K., Aziz A. Ionizing Radiation Effect on the Electrical Properties of Metal/Oxide/Semiconductor Structures . M.J. Condensed Matter. 2005, Vol.6 (1). Р. 20-26.

V.A. Riaby,1 V.P. Savinov,2P.E. Masherov,1 and V.G. Yakunin2

1Research Institute of Applied Mechanics and Electrodynamics (RIAME) of the Moscow Aviation Institute

(National Research University), 5 Leningrad Rd., Moscow 125080, Russia 2Moscow State University (MSU) named after M.V. Lomonosov, Physical Dept., Moscow 119991, Russia

FULL DIAGNOSTICS OF AN INDUCTIVE PLASMA SECTION OF AN ION THRUSTER MODEL

(Review of the book under the same title, Riga: LAMBERT Academic Publishing, 2018, 102 pp.)

Abstract

Radio frequency low pressure inductive xenon plasma was generated in a gas-discharge section of an ion thruster model. Its full diagnostics consisted of integral and local measurements. Integral diagnostics of a gasdischarge section included measurements of general parameters of the discharge device and its feeding line that determined overall physical-technical image of the facility (Patented). Local diagnostics determined spatial plasma parameter distributions using cylindrical Langmuir probes of two kinds: the straight probe-1 that operated in the middle cross-section of discharge space and the L-shaped probe-2 moving along the discharge and revolving around its axis, both of them provided by conventional bare probe protective shields. In the same cross-section with the probe-1 operated radially movable plane by-wall probe simulator also measuring radial distributions of plasma parameters. Probe-1 data were initially considered to be objective and reliable and they were published in two articles. Subsequent analysis of its results including electron energy distribution function (EEDF) showed its noticeable deviations from the Maxwellian function in dependence on the shield-1 length. The reason for them was disclosed because the probe-2 could repeat probe-1 measurements in the common special position lsh1=0 and lsh2^0 where the probe-2 was exposed to its shield influence. In this position probe-2 lowered all plasma parameters. Comparison of both probes' data identified the principled relationship between measurement errors and EEDF distortions caused by bare probe shields. This dependence was used to correct the initial probe-1 measurements eliminating its shield's influence. Physical analysis of probe errors based on previous authors' works showed that they were caused by a short-circuited double-probe effect in the bare metal shields. As the result, three new probe application directions were proposed: a) elimination of bare probe protective shield's influence on measurement results (Patent Application); b) measurements of the probe sheath thicknesses and the mean ion mass using cylindrical probes in Maxwellian plasmas (Patented); c) evaluation of ion current density to a wall under floating potential using plane by-wall probe simulator (Patent Application).

Key words: gas-discharge plasma, ICP discharge, antenna coil, ferrite core, Langmuir probe, Maxwellian plasma, Bohm effect, Boltzmann law, "3/2 power" law.

INTRODUCTION

The present work is dedicated to the studies of radio frequency (RF) inductively coupled plasma (ICP) generated in a gas discharge input section of an RF ion thruster model. A planar antenna coil enhanced by ferrite core was used in this section to generate xenon plasma at pressure p = 2 mTorr and at the driving frequency f = 2 MHz. Full plasma diagnostics consisted of two parts: a) detailed integral diagnostics arranged according to the author's patented method and b) local plasma diagnostics using two cylindrical Langmuir probes and one radially movable plane by-wall probe simulator for plasma parameter measurements.

Probe diagnostics arranged in the present work stimulated the development of three novel Langmuir probe application directions: 1) elimination of bare

probe protective shield's influence on measurement results; 2) measurement of the probe sheath thicknesses and the mean ion mass using cylindrical probes operating in Maxwellian plasmas in which the Bohm effect, the "3/2 power" and the Boltzmann laws are valid; 3) evaluation of ion current density to an ion extracting grate (IEG) of an ion thruster model, and particularly to the internal ion extracting IEG electrode that operates under floating potential, using the radially movable plane by-wall probe simulator at the ceramic rod's butt. These diagnostics directions are described in the present work.

1. Experimental setup

The drawing of the RF ion thruster model studied in the present work is presented in Fig. 1.

5 6 7 8 9 10 11 12 13 %

Fig. 1. Drawing of the RIT model 1—vacuum chamber, 2—to VGPS-12 probe station, 3—movable vacuum fitting UT1/16", 4—the straight Langmuir probe-1, 5—temperature-sensitive gauge, 6—quartz window (5 mm thick), 7—antenna coil, 8—ferrite core, 9—cooling air output, 10—to discharge feeding line, 11—the L-shaped probe-2, 12—reference probes, 13—8 equally spaced xenon feeding 0.4 mm holes, 14—"one-touch" input union for cooling air, 15—xenon feeding circular collector, 16—input xenon feeding flange, 17—plane by-wall simulator, 18—flange for ion extracting grate (IEG) installation, 19—meshwork having IEG gas-dynamic resistance, 20—tungsten filament of the opened halogenous lamp (to start ICP discharge)

It contains a vacuum chamber 1, quartz window 6, and planar antenna coil 7 with ferrite core 8 connected to the electric feeding line that consisted of a transformer matching network (MN) and RF generator (RFG). The upper half of the vacuum chamber 1 (about 1 liter in volume) was used as a discharge section of the thruster model, where the ultimate oil less vacuum reached p ~ 10-6 Torr. The plasma pressure p = 2 mTorr at the xenon flow rate q = 2 sccm was provided by a meshwork 19, that was used here instead of the thruster's IEG simulating its gas-dynamic resistance. Inductive xenon plasma of this model was very pure (99.9999%) and was generated at the driving frequency off = 2 MHz.

In Fig. 1 three Langmuir probes used for local plasma diagnostics can be seen: two cylindrical probes, one of them the straight probe-1 (4 in Fig. 1) that radially moved at a distance of z = 33 mm from the internal surface of the quartz window 6, and another, L-shaped one 11 inserted into the vacuum chamber through its bottom, moving along the discharge and revolving around its axis, and in the same with probe-1 cross-section plane probe 17 installed at the ceramic rod's butt . The dimensions of both cylindrical probe tips, 0.15 mm in diameter and 10 mm in length with a probe holder

1.6 mm in diameter, were selected in a separate experiment [1] to arrange negligible local plasma distortions. Note that beside probe tips, their probe holders were represented by reference probes 12 in the form of 10mm pieces of their shields, 1.6 mm in diameter. These reference probes had to be connected to the VGPS-12 probe station, together with the measuring probes to eliminate RF distortions of their Volt-Ampere characteristics (VACs).

In Fig. 1 a special point A with lsh1 = 0 at 13 mm from the chamber wall is shown. It is the very important measurement probe position for the present work. In this point the shield of the probe-1 (4 in Fig. 1) was absent and the probe-2 (11 in Fig. 1) operated here with rather long shield-2 and could repeat probe-1 measurements for the sake of their result comparison to determine the influence of shield-2 on its probe measurements.

The rest elements of the experimental facility can be examined considering Fig. 1.

1. Integral diagnostics of an ICP gas-discharge device

Integral diagnostics consisted of a priori measurements of antenna coil parameters in free space and within the assembled discharge unit subsequently

measuring antenna coil currents without discharge and with ICP discharge in the plasma section of the model. As the result the detailed physical-technical image of the facility was obtained including RF power loss in all different elements of the discharge feeding line and the efficiency of RF power transfer from RFG to plasma 7gp. All these parameters were determined at the exact RFG-discharge matching.

This diagnostics was conducted at the very beginning of the subsequent experiment because it provided the base for the precise local diagnostics. It was elaborated, realized and applied to a couple of ICP devices [2-6]. It included measurements of up to 29 parameters that were called as control indicators resulting in registration of RF power losses in all discharge feeding line elements, in all facility design parts and in the ICP discharge. They determined overall physical-technical image of the experimental RIT model that characterized the quality of its design, selection of the MN engineering circuit and their practical realization.

Here we present only separate results of integral diagnostics that will be usefull below. After determination of active resistances of all elements of the discharge feeding line, antenna coil currents I0 and I were very precisely measured by the Rogovsky coil, RF current monitor Pearson 2878, without discharge (I0) and with ICP discharge (I): for Pm = 30-250 W these currents varied in the ranges In = 3.8-10.3 A, / = 2.1-3.7

A. Exact RFG-discharge matching, that corresponded to maximal incident RFG power Pm, equal to half of the full RFG power Pg/2, made discharge feeding line to be active where voltages on different reactive elements were mutually compensated and any line properties could be determined using Ohm's law. In this situation there was no danger for the RFG in the absence of its interaction with reflected RF power. In all subsequent experiments with local plasma diagnostics RFG was always exactly matched with its load. According to transformer model of the ICP discharge [7] equivalent discharge resistance was in series connected with the antenna coil resistance resulting in the RF power transfer efficiency according to the formula ^gp=1 -(I/I0)2. In the present experiment this parameter varied in the range ^GP^m) = 0.63^0.88 that shows rather high energy efficiency of this model that resulted from 1) planar geometry of its antenna coil corresponding to convenient aspect ratio of the model's gas-discharge space thickness and its diameter and from 2) use of coil's ferrite core that uplifted mutual coil-discharge inductance and RF power transfer into the discharge lowering RF power loss in the antenna coil.

This direction of diagnostics allowed for detailed determination of RF power balance for the experimental device. Its example for the incident RFG power Pm=150 W is shown in Fig. 2.

Fig. 2 RF power balance of the model's plasma section for Pin=150 W

It confirms rather high energy efficiency of this model. To obtain additional information on plasma properties, integral diagnostics was undertaken for twice xenon plasma pressure, p = 4 mTorr. It was found that at this pressure equivalent resistance of the discharge plasma increased by about two times that meant that at the parameters of the present device xenon plasma conductivity went down with increasing pressure. It is well known that such character of conductivity isobar behavior corresponds to temperatures in the area to the left of temperature zone where these isobars cross each other and where xenon plasma ionization degree is not more than 1% [8].

Note that presented here integral diagnostics technique has been protected by the patent [2], therefore this technical decision has exceeded world level and this conclusion is confirmed on the state level.

3. Local diagnostics of the thruster model's plasma section using cylindrical

Langmuir probes having bare protective shields

Local measurements of plasma parameters were necessary for effective thruster model designing. They were arranged using the advanced automated probe station VGPS-12 [9]. Initial measurements of plasma parameter radial distributions were conducted in the middle cross-section of the gas-discharge space using the straight probe-1. These accurate measurements were repeated several times in every probe position. Their results were considered as rather precise and objective and were published in the articles [5, 6]. The probe-2 repeated probe-1 measurements in the middle cross-section of the gas-discharge space and then determined longitudinal plasma parameter distributions that were necessary for thruster model designing. In the present work probe-2 data were analyzed only for the special position A (Fig. 1) where probe-1 shield was absent and the probe-2 was exposed to full influence of its shield.

Subsequent detailed analysis of electron energy distribution function (EEDF) behavior in the form of quantitative evaluations of their distortions using our

method [5, 6] resulted in very interesting information. According to this method measured electron saturation current densities jes should be compared with the theoretical Maxwellian jasM in the form of the ratios jas/jasM. The last theoretical parameter is the electron saturation's current density for the ideal isotropic collision-less Maxwellian plasmas, calculated using the measured plasma parameters, electron concentration ne, and electron temperature Te:

jasM = (l/4)ene(8kTJmne)m

where e is the elementary electron charge, k is the Boltzmann constant, and me is the electron mass. To our opinion this comparison shows real EEDF deviations

from the Maxwellian functions, i.e. closeness of real plasmas to Maxwellian substances.

Denoting these ratios as Rm = (j as/ / as m), we determined the radial distributions RM(r) for the main probe-1 (4 in Fig. 1) that moved at radial positions, r = 0-60 mm when its shield-length varied in the range lsh = 560 mm. Note that in the special position A only an 8-mm piece of the reference probe remained in contact with the plasma; the rest its elements, 2 mm piece of the reference probe and initial part of its shield, were hidden in the movable vacuum fitting 3 (Fig. 1).

The results of this action in the form of RM(r) radial dependences for different levels of the incident RFG power are presented in Fig. 3.

0.87

0,85

0,80

i

0,75 0,70

P =200 Wfi

*rToo 1 50

3

50//

1 1

0.87

0 15 30 45 60

r, mm

Fig. 3 Radial RM1 distributions for the probe-1 at different incident RFG powers Pi,

It can be seen that at r = 0 Rm values varied in rather wide range and towards r = 60 mm position they linearly converged and rose to the single peripheral point Rm ~ 0.87. This figure characterizes closeness of xenon plasma to the Maxwellian substance in the special point A. This position is not very far from the chamber wall, perhaps in the depth of the discharge space plasma was closer to the Maxwellian substance. Fig. 3 proved that EEDF deviations from the Maxwell function linearly depended on the length of the bare

probe protective shield-1. At the special position A where the probe-1 operated without its shield-1, the probe-2 operating under the influence of its non-zero shield-2 repeated plasma diagnostics that showed that shield-2 lowered all plasma parameters. At different levels of RFG power probe-2 data corresponded to different values of Rm2. This fact helped to present the comparison of both probes' measurements in the form of ratios (X2/X1) depending of on Rm2 for x = Te, ne, Vs, and jes that are shown in the left part of Fig. 4.

1,0

0,8

CN

H

0,6

Probe-1

Probe-2 data J--- B f

e r 0 s ,'V

V'' Jes ■ ■ r = 60 mm 1

0,6

0,7

R

0,8

0.87

0,9

m

Fig. 4 Dependencies ofplasma parameter reductions vs. RM for probe-2 and probe-1

It can be seen that shield-2 rather slightly lowered Te (by about 10%) but the rest probe data went down more deeply. Here the results of probe-1 measurements at the special position A are shown as the point (X2/X1) = 1 at Rm1 = 0.87 which means that at this measured by probe-1 minimal EEDF deviation from the Maxwell function (/es1//esM1) = 0.87 both probes with the same probe tips and without protective shield influences would result in the same plasma parameters with (X2/X1) = 1. That is why this universal probe-1 point was used to linearly approximate it with all four groups of probe-2 data resulting in physically universal functions (x2/x:)(Rm) that characterized bare shield influence on different parameter probe measurements in the xenon plasma of the present thruster model.

These dependencies were used to determine the influence of the bare shield-1 on the plasma parameters beside the probe-1 and rectify errors of the initial measurements. This task was solved excluding the intermediate variable Rm that was done using analytical expressions for the straight lines of Figs. 3 and 4. In Fig. 3, we have:

Pin = 50 W: RM1(r)=3-10-3r + 0.69 (1) Pm = 100 W: RM1(r)=1.283-10-3r + 0.793(2) Pm = 150 W: RM1(r)=1.1-10-3r + 0.804 (3) Pm = 200 W: Rm1 (r)=0.933 • 10-3r + 0.814(4)

In Fig. 4, we have:

(Te2/Te1) = 0.3919RM + 0.659 (5)

(ne2/ne1) = 0.7838Rm + 0.3181 (6)

(Vs2/Vs1) = 1.0811Rm + 0.0594 7)

(/es2//es1) = 1.5405Rm - 0.3402 (8)

To determine radial distributions for Te measurement corrections, equations (1)-(4) were inserted into equation (5) which resulted in the following expressions:

Pin = 50 W: (Te2/Te1) = 1.1757-10-3r + 0.9294 (9) Pin = 100 W: (Te2/Te1) = 0.5028-10-3r + 0.9698(10) Pin = 150 W: (Te2/Te1) = 0.4311-10-3r + 0.9741(11) Pin = 200 W: (Te2/Te1) = 0.3658-10-3r + 0.978(12)

They are graphically presented in Fig. 5.

Fig 5 Radial distributions of the Te correction ratios for Pin = 50-200 W

Inserting equations (2)-(4) into linear expressions (9)-(12), similar measurement correction functions were obtained for the three remaining plasma parameters, ne, Vs, and jes. Finally, all the measurement points of the radial distributions Te(r), ne(r), Vs(r), andjes(r) [5, 6] were divided by the corresponding correction ratios similar to Fig. 5 and the corrected radial distributions for all four plasma parameters were presented in [10].

Measured EEDF distortions depending on the length of the straight probe's bare shield attracted our attention to the authors' previous works where the behavior of large-scale conducting bodies in contact with plasmas was studied. In [11] a bare probe protective shield was considered as such a body and it was shown qualitatively that it behaved like a short-circuited double-macro-probe that initiated short-circuited current flowing in the shield and in plasma lowering all its parameters. Now it became clear that this physical phenomenon functioned in the present experiment and its

influence on plasma parameters was determined here quantitatively.

According to our opinion this method of local plasma diagnostics reducing measurement errors for Langmuir probes with bare protective shields is novel exceeding global level. That is why the patent application [12] for this technical decision was filed to the Russian Patent Bureau.

4. Measurement of the cylindrical probe's sheath thicknesses and the mean ion mass

It is well known that in the isotropic collision-less plasmas with the Maxwelian EEDF three physical relationships are valid: the Bohm effect, the Boltzmann law for electron flow in retarding electrical potential field and the "3/2 power" law in the form of the Child-Lang-muir-Boguslavsky (CLB) equation. In this case it seems possible to determine two interesting physical parameters - probe sheath thicknesses and ion mass Mi. In [13, 14] this task was solved for cylindrical probes

with bare protective shields that were used to measure uncorrected xenon plasma parameters at the RFG power range Pin = 50^200 W [5, 6].

In the present work this solution was refined using described above corrected xenon plasma parameters. First of all they were used to check up EEDF distortions in all volume of the gas-discharge space. It was found that for Pin = 50 W the bulk of xenon plasma corresponded to the Maxwell function with the error more than -20 % and for Pin = 100-200 W this error was rather less: about -13%. That is why corrected plasma parameters for Pin = 100-200 W were used to additionally refine [14] results. Initially corrected ion current densities jif to a probe under floating potential Vf were calculated using Boltzmann formula ¡ii=jci=jcf.'

with corrected plasma parameters including AVf = Vs -Vf. These data are expressed by the Bohm formula for a cylindrical probe [13]

jif=KBCyiene(2eTe/Mi)1

(13)

where KBCyi = xCBCyi is combined Bohm coefficient (x = R/a, R is probe sheath radius, a is probe radius, Cecyi is the Bohm coefficient that should be experimentally confirmed) and Mi is ion mass. This for-muia aiiowed for caicuiations of the corrected combined Bohm coefficients KBCyicon- for the special experiment with the known xenon ion mass Mi = 2.18-10-25 kg that are presented in Fig. 6 by empty cir-cies.

Fig. 6 Corrected values of KBCylCorr, xCLBCorr, and xsFCorr at different levels of Pi,

The dependence of KBCyiCorr(Pm) was iineariy approximated by the dashed iine. The next step impiies determination of radii ratios x = R/a reiated to these KBCyi vaiues [13]. They can be obtained using joint so-iution of (13) and the CLB equation:

jif=(4eo/9)(2e/Mi)1/2(^Ff3/2/a2XCBL^L) (14)

0.5667xclb3-0.5847xclb2-0.5233xclb+0.537-

2.4564- 107^Vf3/2/KBCylCon-a2neTe1/2=0 (17)

It was solved for xclbcoit using experimental KBCylCorr points from Fig. 6 where these data are presented by crosses. Their linear approximation denoted by the xcLBCorr name corresponds to the function

where £0 = 8.8542-10-12 F/m is the dielectric permittivity of the vacuum and AL is the dimensionless Langmuir parameter depending on xcbl for a cylindrical probe [15]. Unification of (13) and (14) results in the equation

xclbal=(4£0/9) ^Vf3/2/KBCyla2eneTe1/2= 2.4564- 107^Vf3/2/KBCyla2neTe1/2 (15)

Here CLB index means correspondence of this equation to the CLB model of probe sheath that repels from it all electrons. The xclbAl=/(xclb) dependence was determined using A L values for the cylindrical probe [15]. Its quite precise approximation in the range xclb=1.1^3.3 resulted in the expression:

xclbAl = 0 .5667xclb3-0 .5 847xclb2-0 . 5233xclb+0 .537(16)

Unification of (15) and (16) gave the following cubic equation for xclb:

XCLBCorr = 2.9-0.0028Pin (18)

To correct these parameters according to the "Step-Front" probe sheath model that allows for electron penetration into the probe sheath, the corresponding data [16] for xclb = 1.4-3.6 were iineariy approximated by the expression

xsf=0,662xclb+0,433 (19)

Correction of the evaiuation dependence (18) was obtained by exciusion of intermediate variabie xclb inserting expression (18) into (19):

xsf=2,353 - 0.001854 Pm (20)

This dependence is presented in Fig. 6 by the dashed xsfcoit iine. It appeared over the dependence KBCyicorr(Pm). Therefore it became ciear that the Bohm coefficient CBCyi shouid be iess than unit because KBCyi = xCBCyi. The Bohm coefficient shouid be a universai

value to lower xsFcorr(An) dependence and to superpose it with the ^Bcyicorr(^in) function. In Fig. 6 it is shown by the dashed line 0.745xsfcoit that demonstrates normal level of this operation with the Bohm coefficient CBCylcorr = 0.745. Here the heavy dashed line represents 0.745xsf(^hi) function and the thin line is the result of ^Bcylcorr(^in) linear approximation and they seem to be rather close to each other.

Note that in [14] similar processing of the initial experimental data resulted in the Bohm coefficient CBcylcorr = 1.23, that was nearly twice higher than this parameter of the present work.

Now it is possible to finally formulate the practical, second stage of the new method of probe sheath thickness and mean ion mass measurement:

1) For plasma EEDF not far from the Maxwellian function expression (15) can be rewritten as:

xclb2 Al*3 .2972-101AVf>l2la2neTem (21)

2) Tabulated data [15] for Al determine the numerical dependence xclb2Al=/(xclb) in a way that with good precision was approximated by cubic polynomial for xclb=1.1^3.2:

xclb2 Al=4.1652xclb3 -14.784xclb2+18.605xclb -8.114(22)

combination of (21) and (22) resulted in the following cubic equation for xclb:

4.1652xclb3 -14.784xclb2+18.605xclb -8.1143.2972- 101^Vf3l2la2fteTe1l2=0 (23)

3) When eAVf<em - maximal plasma electron energy, the evaluated xclb data must be corrected using formula (19) to determine xsf giving real probe sheath thicknesses.

4) The corrected Bohm coefficient Cecylcorr=0.745 inserted into the Bohm formula (13) has allowed for ion mass determination with the expression

Mi~1.11e3XsF2ne2Te|/'if2

(24)

For a gas mixture propellant this parameter represents mean ion mass and for a propellant of definite nature it shows the degree of its purity or the level of its contamination by air inleakage into a vacuum chamber.

This method of probe diagnostics should be considered as a novel technical decision that exceeds global level because it is protected by the patent [17].

5. Evaluation of ion current density to an ion extracting electrode of an ion thruster

Knowledge of ion current density to the first IEG electrode of an ion source is very important for correct calculations and development of IEG accelerating cells and for determination of ion device's integral characteristics like an ion energy cost or efficiency of propel-lant consumption.

According to a well known standard method [15, 18], this task could be solved using close to reality IEG model with a set of plane by-wall probes fixed in the ion extracting electrode providing real plasma pressure. In the case of difficulties with probe insulations, IEG extracting electrode could be replaced by its dielectric imitator with a set of plane by-wall probes and with IEG perforations providing its normal gas-dynamic resistance. The preparation and actualization of such an experiment can take quite noticeable time and resources.

In the present work, it is proposed to solve this task without use of an ion extracting electrode or its dielectric imitator. Instead of them a relatively small piece of dielectric wall with a plane by-wall probe could be used being disposed on a radially movable probe holder. This simulator of a plane by-wall probe could provide steady-state influence of the wall on plasma in any radial position within model's discharge space so that its plasma properties could be determined by this plane Langmuir probe surrounded by dielectric surface.

This idea of a movable plane by-wall probe simulator was realized in the form of a ceramic rod's butt that served as the dielectric wall imitator supplied by a plane by-wall probe with its lead inserted into the rod's internal channel [19]. This rod had two channels, the second one necessary for the reference probe in the form of a bare metal sleeve. That is why both channels of the rod were filled with metal wires. The internal end of one wire served as a collecting surface of the plane probe fixed flash with the rod's butt. The second wire was brought out of the rod, bent back and was encircled by the reference probe. Beside the rod's butt a steady-state by-wall sheath was formed in plasma because its ceramic surface around the plane probe exceeded probe collecting surface by more than 10 times.

In the present work a ceramic rod of 5 mm OD with two channels 1.5 mm in diameter was used. In these channels, copper wires of the same diameters were tightly fixed. One of them was used as a plane probe 1.5 mm in diameter at the rod's butt while another one was connected to the reference probe. The rest area of the rod's external surface was encircled by similar metal foil that served as a grounded screen fixed next to the reference probe with about 2 mm gap. The drawing of this plane by-wall probe simulator is shown in Fig. 7.

Fig. 7 The drawing of the plane wall probe simulator.

It can be seen that the collecting surface of the plane probe was non-uniformly surrounded by a ceramic surface because the probe was shifted from the center of the rod's butt by about 1 mm. Perhaps this fault can be avoided in the subsequent experiments.

Quantitative EEDF evaluations based on results of plane probe measurements of plasma parameters showed that in this case electron saturation current density ratios jes/jesM were lowered to about 0.5 which showed a substantive deviations of real EEDFs from the Maxwell function. Therefore plasma beside the surface of the ceramic rod's butt was a non-Maxwellian substance where Botzmann law was not valid that did not allow for ion current density evaluations using measured plasma parameters and the Boltzmann formula for a plane probe.

In this case ion current density to a wall under floating potential could be evaluated only using ion branches of the plane probe VACs extrapolating them to a floating probe potential. Usually, long probe ion branches look linear which determines the way of their extrapolation to this potential. Such VAC processing was recommended in [20] for semi-logarithmic and double-logarithmic VACs because this way of their ion branches' processing had some definite theoretic base. Following this recommendation, in the present work ion branches of semi-logarithmic VACs of the by-wall probe simulator were linearly extrapolated to a floating potential. Note that in the present experiment double-logarithmic VACs resulted in the same data because their extrapolation tangents were rather short. In [20] they were much longer reaching plasma space potential where ion saturation current densities jif obtained from VACs of both kinds differed rather noticeably.

Obtained in such a way radial distributions of ion current densities to a wall under floating potential for Pin = 100-250 W are presented in [19]. They were confirmed in subsequent experiments with ion beam with the error of about +30% [21].

According to the authors' knowledge this method of plane probe diagnostics also represents a novel technical decision that was filed as a patent application [22].

6. Discussion of measurement results

Integral diagnostics of ICP devices characterized their general physical-technical image that included their design and circuit engineering of ICP discharge feeding lines. Besides it showed possible ways to raise their energy efficiency and created the base for subsequent local plasma diagnostics that was very important for their effective arrangement.

The present work showed that bare probe shields disturbed plasma parameters proportionally to their lengths. To understand the reality of this situation, we analyzed probe-1 VACs to evaluate the Isc current in plasma around its shield and this process resulted in ISC ~ 0.02-0.03 A while the mean local current of the inductive discharge beside the probe-1 was about Ip ~ 0.2-0.3 A [10]. This comparison showed real possibilities for EEDF distortions in the present experiment.

This work can be very useful for all physicists engaged in plasma studies, especially for those dealing with RF plasmas, because Langmuir probe diagnostics is a very important and popular technique in plasma-

parameter measurements. The present results clarify that the best way to make objective probe measurements of RF plasma parameters is to use protective shields coated with dielectric layers to eliminate the short-circuited double-probe phenomenon mentioned in this work. In the case of probes with bare protective shields, it would be beneficial to follow the method proposed in the present work.

Measurements of probe sheath thicknesses can help to checkup correctness of probe theory used for probe measurements interpretation. As for mean ion mass determination, it characterizes the degree of pro-pellant purity or the quality of vacuum chamber tightness. So these additional plasma parameters contain rather useful information for any experiments. The proposed here additional applications of Langmuir probes can be considered as quite practical diagnostic technique because plasmas close to a Maxwellian substance are used in numerous technological or thruster devices.

The obtained here radial distributions of ion current density to a wall under floating potential can be considered as rather important information for preliminary calculations of geometry, forms and dimensions of accelerating IEG cells. The present experiment was carried out without IEG electrodes because here only physical parameters and the technical shape of the inductive device were studied. It showed that the present thruster model of a convenient design provided rather uniform plasma near the extraction IEG electrode with jff spread in the limits not wider than +20% and with rather high energy efficiency up to 0.88 which were the result of a plane antenna coil with ferrite core application. Comparison with probe diagnostics data [18] showed that these characteristics do not represent the upper limit of plasma uniformity but all the same they noticeably exceeded qualities of previously tested thruster models [23] so that the studied here apparatus can be considered as an effective prospect for such devices of new generation.

7. Conclusions

1. Integral diagnostics of ICP devices was done deeper and more effective in comparison with previous similar technique. Its protection by the patent [2] means that this technical decision exceeded global level.

2. Three novel methods of Langmuir probe diagnostics have been proposed, all of them having practical importance: a) reduction of measurement errors for probes having bare protective shields; b) measurements of probe sheath thicknesses and mean ion mass in Maxwellian plasmas; c) evaluation of ion current density to a wall under floating potential using movable plane by-wall probe simulator.

3. The proposed corrections of measurement results using probes with bare protective shields were realized in inductive xenon plasma of low pressure (2 mTorr) at Pm = 50-200 W using radially movable straight cylindrical probe.

4. In the special experiment with known xenon ion mass it was determined that for a cylindrical probe at Pin = 100-200 W the Bohm coefficient was equal to CBCyl=0.745.

5. Plasma beside the plane by-wall probe simulator turned out to be a non-Maxwellian substance where

ion current density to this probe under a floating potential could be evaluated only by linear extrapolations of ion branches of semi-logarithmic probe VAcs.

6. The obtained data on radial distributions of ion current density to the extraction electrode of the ion thruster model showed that this model of low aspect ratio with planar antenna coil with ferrite core can be considered as a promising prospect for thrusters of the next generation due to simplified and compact construction design of the model, its rather high energy efficiency, and reasonably uniform radial plasma distribution with possible future improvement.

Acknowledgments

Authors wish to express their sincere gratitude to Prof. V. Godyak and his colleague B. Alexandrovich for their friendship and effective help in the arrangement of the present experiments.

Initial part of this work was supported by the RF Government's Grant No. 11.G34.31.0022, the RF President's Grant No. NSh-895.2014.8 and the Agreement Nos. 02.G25.31.0072 and 14.577.21.0101 and its concluding part was supported by the Ministry of Education and Science of the Russian Federation, Project No. 9.9055.2017IBP.

References

1. Masherov P.E., Influence of the first probe holder's relative size of the cylindrical Langmuir probe on the results of local plasma diagnostics, Vestnik Mos-kovskogo Aviatsionnogo Instituta, 2016, v. 23, No. 2, p. 42-49.

2. Riaby V.A., Godyak V.A., Obukhov V.A., Masherov P.E., Mogulkin A.I., Method of integral diagnostics of RF inductive gas-discharge device, Patent Holders: Authors, Russian Patent RU2601947, cl. H05H 1I46, filed on 26.03.2015.

3. Riaby V.A., Obukhov V.A., Masherov P.E., Mogulkin A.I., Balashov V.V., Integral diagnostics method characterizing gas discharge unit of an RF inductive ion thruster, Proc. 34th Intern. Electric Propulsion conf., Hyogo-Kobe, Japan, July 2015, rep. No. 450 (IEPc-2015-450), p. 1-9.

4. Riaby V.A., Obukhov V.A., Kirpichnikov A.P., Masherov P.E., Mogulkin A.I., Integral diagnostics method for a radio-frequency inductively coupled plasma discharge unit of an RF ion thruster, Russian Aeronautics, 2015, No. 4, p. 448-453.

5. Masherov P. E., Riaby V. A., Godyak V. A., Integral electrical characteristics and local plasma parameters of RF ion thruster, Rev. Sci. Instrum., 2016, v. 87, Paper No. 02B926.

6. Riaby V.A., Masherov P.E., Integral and local diagnostics of energy effective model of an RF ion beam source, Proc. of the Rus. Acad. of Sciencies. Power Engineering, 2016, No. 2, pp. 46-57.

7. Piejak R.B., Godyak V.A., Alexandrovich B.M., A simple analysis of an inductive RF discharge, Plasma Sources Sci. Techn., 1992, v. 1, p. 179-186.

8. Devoto R.S., Transport coefficients of partially ionized krypton and xenon, AIAA Journal, 1969, v. 7, No. 2, p. 199-204.

9. VGPS Probe System: www.plasmasen-sors.com.

10. Riaby V.A., Savinov V.P., Masherov P.E., Ya-kunin V.G., Elevating the precision of plasma probe diagnostics by elimination of bare probe protective shield's influence, J. of Chemistry: Edu. Res. & Practice, 2017, v. 1, No. 1, p. 1-5.

11. Masherov P.E., Obukhov V.A., Riaby V.A., Savinov V.P., Decrease of plasma perturbations caused by Langmuir probes, Proc. 21 Intern. Symp. on Plasma chemistry (cairns, Australia, Aug. 2013).- cairns: Austr. Nat. Univ., 2013, report 410 [www.ispc-confer-ence.orglispcproclispc21l IID410.pdf].

12. Riaby V.A., Masherov P.E., Savinov V.P., Ya-kunin V.G., A method of plasma diagnostics using Langmuir probes with bare protective shields and a device for its realization, Pat. Appl. No. 2017139277, filed on 13.11.2017.

13. Masherov P. E., Riaby V. A., Abgaryan V.K., Note: The expansion of possibilities for plasma probe diagnostics, Rev. Sci. Instrum., 2016, v. 87, Paper No. 056104.

14. Masherov P. E., Riaby V. A., Abgaryan V. K., Note: Refined possibilities for plasma probe diagnostics, Rev. Sci. Instrum., 2016, v. 87, Paper No. 086106.

15. Kozlov O. V., Electrical probe in plasma.-Moscow: Atomizdat, 1969, p. 20-21.

16. Piejak R. B., Godyak V. A., Garner R., Alexandrovich B. M., The hairpin resonator: A plasma density measuring technique revisited, J. Appl. Phys., 2004, v. 95, No. 7, p. 3785- 3791.

17. Riaby V. A., Masherov P. E., A method of local Maxwellian plasmas diagnostics using a single Langmuir probe, Patent Holder: Moscow Aviation Institute, Pat. Appl. No. 2016143184, filed on 03.11.2016. Positive decision taken on 20.11.2017.

18. Godyak V. A., Electrical and plasma parameters of IcP with high coupling efficiency, Plasma Sourses Sci. Technol., 2011, paper No. 025004 (7pp).

19. Masherov P., Riaby V., Abgaryan V., Evaluation of ion current density distribution on an extraction electrode of a radio frequency ion thruster, Plasma Sources Sci. Technol., 2017, v. 26, Paper No. 015004.

20. Nuhn B., Peter G., comparison of classical and numerical evaluation of Langmuir probe characteristics at low plasma densities. - Proc. XIII Int. conf. on Phenomena in Ionized Gases, contributed Papers (Berlin, Germany, 1977), 1977, v. 2, pp. 97-98.

21. Balashov V., cherkasova M., Kruglov K., Kudriavtsev A., Masherov P., Mogulkin A., Obukhov V., Riaby V., and Svotine V., Radio frequency source of a weakly expanding wedge-shaped xenon ion beam for contactless removal of large-sized space debris objects, Rev. Sci. Instrum., 2017, v. 88, Paper No. 083304.

22. Masherov P. E., Piskunkov A. F., Riaby V. A., A method of determination of ion current density to a wall in contact with plasmas and a device for its realization, Pat. Appl. No. 2016109229, filed on 15.03.2016.

23. Goebel D. M. and Katz I., Fundamentals of electric propulsion: ion and Hall thrusters. NASA: Wiley, USA, 2008.