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`January 31, 2014
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`Certification
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`Park IP Translations
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`This is to certify that the attached translation is, to the best
`of my knowledge and belief, a true and accurate translation from
`Russian into English of the Encyclopedia of Low-Temperature
`Plasma, Introductory Volume III.
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`_______________________________________
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`Abraham I. Holczer
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`Project Manager
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`Park Case # WCPHD_1401_001
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`15 W. 37th Street 8th Floor  New York, N.Y. 10018
`Phone: 212-581-8870  Fax: 212-581-5577
`
`GILLETTE 1104
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`

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`ENCYCLOPEDIC SERIES
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`ENCYCLOPEDIA OF
`LOW-TEMPERATURE
`PLASMA
`
`
`Introductory Volume
`III
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`Under the editorship of
`V. E. FORTOV,
`Member of the Academy of Sciences
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`MOSCOW
`“NAYKA”
`MAIK “NAUKA/INTERPERIODICA”
`2000
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`Page 2 of 23
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`7
`
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`CONTENT
`
`Section VI
`
`INTERACTION OF LOW-TEMPERATURE PLASMA WITH CONDENSED
`MATTER, GAS AND ELECTROMAGNETIC FIELD
`
`INTRODUCTION
`
`VI. 1. INTERACTION OF PLASMA WITH CONDENSED MATTER
`
`VI.1.1. Basic concepts and effects of the interaction of plasma with the condensed matter
`1. Introduction (7). 2. Basic properties of SB (solid bodies) and their surfaces when interacting with LTP
`(low-temperature plasma) (7). 3. Parameters of particles and radiation streams arriving from plasma on the surface
`of condensed matter (8). 4. Classification of emission phenomena at the vacuum-SB boundary (9). 5. Basic
`processes defining a mass transfer between plasma and surface (10). 6. Processes defining energy balance
`interacting with SB plasma (11). 7. Emission from the surface of photons (11). 8. Erosion and transformation of a
`surface due to plasma action (12). 9. Unstable surface-plasma interactions. Influence of magnetic field (12).
`
`13
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`VI.1.2. Structure of solid bodies
`1. Interatomic bonds (13). 2. Structure of crystals (18). 3. Electronic structure of SB (21). 4. Oscillations in SB and
`quasi-particles (29). 5. Faults of crystalline structure. Amorphous bodies (36).
`
`42
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`VI.1.3. Properties of solid bodies
`1. Mechanical and thermal-physical properties of SB (42). 2. Electrical, magnetic and optical properties of SB
`(45).
`
`57
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`VI.1.4. Properties of solid bodies boundary. Contact phenomena
`1. Introduction. Concept of surface (57). 2. Structure and potential relief of SB boundary (57). 3. Work function
`and electron affinity (61). 4. Contact phenomena. Contact potential difference (64). 5. Surface thermodynamics
`(66).
`
`66
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`VI.1.5. Electron emission from a solid body surface
`1. Classification of emission types (66). 2. Thermionic emission (67). 3. Photoelectric emission (71). 4. Field
`electron emission (74). 5. Burst electron emission (78). 6. Hot electron emission (78). 7. Exoemission (81).
`
`84
`
`
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`VI.1.6. Emission of electrons at interaction of particles with a surface
`1. Secondary electronic emission (84). 2. Potential ion-electron emission (90). 3. Kinetic ion-electronic emission
`(91).
`
`92
`
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`VI.1.7. Interaction with the surface of thermal atoms and ions
`1. Accommodation (92). 2. Adsorption (phenomenology of processes) (93). 3. Physical phenomena at adsorption
`(the modeling description) (95). 4. Surface ionization. Evaporation of natural atoms (98).
`
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`vi
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`VI.1.8. Introduction, reflection and stimulated
`1. Introduction (117). 2. Basic dependences of
`
`desorption of particles sputtering ratio (117). 3. Characteristics of sputtered
`100
`particles (119). 4. Experimental methods of sputtering
`1. Introduction (100). 2. Potentials of particles pair
`studying (120). 5. Theoretical models of sputtering
`interaction with medium atoms (100). 3. Atomic
`(121). 6. Non-traditional mechanisms of sputtering
`particles slowdown (101). 4. Atomic particles paths in a
`(125).
`substance (101). 5. Reflection of particles (103). 6.
`
`Desorption under the influence of various plasma
`VI.1.11. Modification of solid bodies surface under
`components (108).
`ion and plasma action 126
`
`1. Introduction (126). 2. Development and leveling of
`VI.1.9. Trapping of gas ions and their emission 109
`surface relief due to the non-uniformity of sputtering
`1. Introduction (109). 2. Experimental observation
`of its various sections (126). 3. Relief development as
`(109). 3. Physical processes at the ionic introduction of
`the consequence of radiation-stimulated processes in
`gas (112). 4. Models for the description of ionic
`SB volume (129).
`introduction of gas (114). 5. Numerical programs (116).
`
`VI.1.10. Sputtering
`
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` 117
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`VI.2. PLASMA WITH THE CONDENSED PHASE
`VI.2.1. Near-surface laser plasma 138
`5. Application of photoresonance plasma (157).
`1. Introduction (138). 2. Target heating by laser
`
`irradiation (139). 3. Generation of NSLP (near-surface
`VI.2.3. Dusty plasma 160
`laser plasma) in DM (diffusion mode) in vapor-gas
`1. Introduction (160). 2. Generation and charging of
`mixtures (143). 4. Generation of plasmas in
`dust particles in plasma (161). 3. Interaction of dust
`hydrodynamic mode with the presence of an erosive jet
`particles with external fields and between themselves
`(146). 5. Conclusions (149).
`(164). 4. Non-ideality of dusty plasma and phase
`
`transitions (166). 5. Waves in dusty plasma without
`VI.2.2. Photoresonance plasma 149
`magnetic field (169). 6. Diagnostics of dust particles in
`1. Introduction (149). 2. Methods for PRP
`plasma (172). 7. Experimental studies of highly
`(photoresonance plasma) obtaining and researching
`non-ideal dusty plasma and dust crystal (177).
`(150). 3. Elementary processes in photoresonance
`plasma (152). 4. Kinetics of photoresonance plasma
`generation and decay (155).
`VI.3. PHENOMENA AT THE PLASMA-GAS BOUNDARY
`Introduction 182
`impulse waves in channels (197).
`VI.3.1. Ionization impulse waves 183
`VI.3.3. Plasma sheath originating due to spacecraft
`1. Origination and structure of impulse waves in gases
`motion in atmosphere 199
`(183). 2. Initiation of Maxwellian distribution (184). 3.
`1. Parameters of plasma in impulse-heated layer
`Excitation of rotational degree of freedom (186). 4.
`around streamlined body (199). 2. Advancing
`Kinetics of vibrational relaxation (187). 5. Kinetics and
`photoionization of air in front of head IW front (202).
`mechanisms of molecular dissociation per IW (impulse
`3. Jet structure of liquid-propellant engine exhaust
`wave) (188). 6. Mechanisms of ionization of gases per
`products (203). 4. Nonequilibrium recombination of
`impulse waves (191).
`free electrons in supersonic jet of exhaust products
`
`(204).
`VI.3.2. Role of irradiation transportation in forming and
`
`distributing of strong ionization impulse waves 194
`VI.3.4. Recombination process at the plasma-gas
`1. Role of irradiation transportation in forming of strong
`boundary line 206
`ionization impulse waves (194). 2. Distribution of
`1. Introduction (206). 2. Model equations of plasma
`parameters in precursor zone of strong ionization
`channel originating (206). 3. Basic elementary
`impulse wave (196). 3. Influence of irradiation
`processes (207). 4. Characteristics of plasma channel
`transportation on distribution of strong ionization
`(211).
`
`
`VII
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`
`.
`Here u is concentration of diffusing gas, у – concentration in defects, w – concentration of
`defects themselves, φ – ion slowing profile, S – drain in defects, r – effective radius of defect, N
`– SB atomic density, ξ – the number of possible locations in interstitial sites around a defect.
`In the case of diffusion in multilayered structure diffusion in each stratum is considered,
`concentrations at boundary lines are related through solvability. An external source is usually
`taken from independent calculations. Internal drain in defects consists of two members:
`diffusion inflow in defects and thermally or radiationally activated outflow out of them. The
`same member in a diffusion equation also describes the velocity of accumulation of particles in
`defects-traps. Usually some types of defects with various binding energies and concentrations
`are considered, but the above given drain fixed for one type of defects. In boundary conditions
`the balance of diffusion flow and desorption flow is registered. It is supposed that between
`concentrations on SB surface and beneath it the local balance is set, i.e. if the coefficient of
`proportionality of these concentrations is taken correctly, desorption velocity is proportional to
`the quadrate of volume concentration near to a surface. The coefficient of proportionality
`known as an effective recombination coefficient is either calculated analytically, or measured
`experimentally. Except the second order desorption in boundary conditions the thermal and
`radiationally activated desorption as well as desorption of the first order can be entered.
`Computer programs allowed to describe considerable quantity of various experiments on
`the ionic introduction of gas (VI. 1.308 VI. 1.309). An inevitable problem in this case is a
`considerable quantity of parameters which frequently unknown before the experiment and are
`viewed as adjustable ones. Therefore,
`
`cm
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`cm
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`Pic. VI. 1.308. Thermodesorption spectrum D, introduced under ion bombardment in W at 473 К; points – experiment; lines –
`calculation at various velocities of defects occurrence during ion implantation
`Pic. VI .309. Re-emission of deuterium during ion irradiation; points - experiment, lines - calculation at various values of peak
`concentration of defects yield at irradiation
`
`for more or less accurate selection of parameters the concurrent description of several
`experiments is done. In this case arbitrariness of parameters selection is strongly restricted.
`These parameters, defined from the experiment, are then possible to use for predicting the
`behavior of ion-implanted gas under other conditions.
`To summarize one should note that a considerable quantity of empirical information on
`implantation of ions in SB is collected by now. In elementary modeling situations the
`experimental regularities are rather clear and they can often be well described mathematically.
`However, the physical pattern of phenomenon often appears essentially more complex than
`beliefs available at present. There are many facts which cannot be explained, and there are a lot
`of factors which can hardly be predicted. Therefore, practical predictions of behavior of ion
`implanted gas for specific technical applications need proper attention.
`1. McCracken G.M. The Behaviour of Surfaces under Ion Bombardment. Reports on
`Progress in Physics. 1975. V.38. P.241-327. 2. Ozawa K„ Fukushima K., Ebisawa K. Data
`Compilation for Radiation Effects on Hydrogen Recycle in Fusion Reactor Materials. Preprint
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`JAERI-M 84-089, 138 p. 3. Yamaguchi S., Ozawa K„ Nakai Y., Sugizaki Y. Data on Trapping
`and Reemission of Energetic Hydrogen Isotopes and Helium in Materials. Preprint JAERI-M
`84-093, 59 p. 4. Radiation hardness of materials. Issues of helium and hydrogen in reactor
`materials. Abstract, Coll. book / Edited by A.V. Shalnov and B.A. Kalin. — M.: ICSTI, 1986.
`114 p. 5. Pisarev А.А., Chernikov V.N. Interaction of hydrogen with radioactive defects in
`metals / In book: Interaction of hydrogen with metals. — М.: Nayka, 1987. P.233-264. 6.
`Wilson K.L.. Hydrogen and Helium Trapping. Nuclear Fusion, 1984. Special Issue, p.28-42.
`© А.A. Pisarev
`
`VI.1.10. Sputtering
`1. Introduction. The cathode sputtering, now known as sputtering, is material damage due
`to accelerated ions or atoms which occurs in the form of atoms or more rarely in the form of
`nuclear clusters or molecules. The basic characteristics of sputtering is the coefficient of
`sputtering Y, defined as the relation of the number of sputtered atoms of a target to the number
`of bombarding ions (atoms). The coefficient of sputtering depends on the type of ions (its
`atomic number Zi and mass Мi), energy Ɛ and the incident angle of θ ions as well as on material
`itself and target temperature.
`Angular distribution Y (θ, φ) and energy distribution of sputtered atoms are also important
`characteristics of sputtering.
`2. Basic dependences of sputtering coefficient. For normally falling ions (θ = 0) the
`general character of dependence of sputtering coefficient Y from energy of ions Ɛ, atomic
`numbers Zi, Za and masses Мi, Ма of ions and target atoms, as well as from binding energy U of
`surface atoms is well conveyed by the simple empirical formula (Pic. VI. 1.310):
`
` (10.1)
`where Ɛ and U are expressed in eV, and Y – in at./ion. The peak values of sputtering coefficient
`is reached at energies Ɛ = Ɛm = 50ZiZa eV. For light ions (Н, D, Не) Ɛm is 0.5-10 keV, and Y(Ɛm)
`≈10-3 – 10-2 at./ion. For heavy ions the maximum Ɛm is shifted to the side of high energies, and
`Y (Ɛm) reaches values of ≥ 10 at./ion. At higher energies Ɛm >> 50ZiZa eV) the formulae gives
`the following dependence Y ~ 1/Ɛ, but experimental dependencies Y(Ɛ) better coincide with
`more precise theory, according to which Y ~ In (Ɛ)/Ɛ. At low energies Ɛ < 50ZiZa eV Y,
`according to (10.1), ramps with the increase of energy Ɛ. This fact is proved experimentally fro
`heavy ions at energies 100 eV ≤ Ɛ ≤ 500 eV, and for light ions at less energy interval. At lower
`energies the dependence Y(Ɛ) is nonlinear and can be approximated by another empirical
`formulae:
`
`
`Energy Ɛtr is called threshold energy of sputtering. The transition from the dependence defined
`by formulae (10.2) to the dependence (10.1) occurs at Ɛ≈20Ɛtr. Sometimes it is considered that
`the is no absolute threshold of sputtering, though Ɛtr makes sense as parameter being included
`in formulae (10.2), which approximates
`
`(10.2)
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`Page 6 of 23
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`at./ion
`
`
`Pic. VI. 1.310. Dependence of sputtering coefficient in stainless steel on energy of ions for different ions; curves - calculation
`under the formula (10.1), points - experiment
`
`experimental data up to the values Y ≈ 10-5 at./ion fairly good. As such minor sputtering can be
`neglected it is almost possible to use the concept of sputtering threshold Ɛtr. The sputtering
`threshold depends on energy of sputtering and on the relation of masses Mi/Ma. Empirical
`relation
`
`(10.3)
`
`at
`
`at
`
`
`conveys Ɛtr (U) and Ɛtr (Mi/Ma) dependencies in a satisfactory way and allows to estimate the
`value of sputtering threshold accurate to factor 2.
`The dependence of sputtering coefficient on the target material is demonstrated, firstly, in
`the dependence of mass and atomic number of target atoms, and secondly, in the dependence of
`binding energy U which is usually considered to be equal to the energy of sublimation
`correlated to one atom. As the energy of sublimation has periodic character of dependence
`from Za, so the dependence Y(Za) also has the periodic character. At this, the minimum U(Za)
`corresponds with the maximum Y(Za) (Pic. VI, 1.311). The minimum values of sputtering
`coefficient have targets consisting from atoms with incomplete shells: C, Ti, V; then Zr, Mo
`and Nb, then Ta and W. Such precious metals as Сu, Ag and Аu have maximum sputtering
`coefficients.
`at./ion
`
`
`Pic. VI. 1.311. Dependence of sputtering coefficient from atomic number of sputtered element at irradiating with ions of
`helium at energy value of 400 eV
`
`At high doses of irradiation the periodic dependence Y from Zi is also observed. The
`maximum sputtering is caused by ions of rare gases. The periodic dependence Y from Zi is
`explained by changing of chemical composition of the surface layer of a target and implanting
`of bombarding ions and lowering the binding energy of surface atoms.
`In case of sputtering of alloys or compounds consisting of different atoms, it is possible to
`use as a first approximation averages (Za) and (Ma) in formulas for Y, the binding energy is
`considered to be equal to the energy of automatization. But, generally speaking, values of U
`can be different for complex compounds. Besides, complex targets, for example steels, can
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`consist of different phases. The predominant sputtering of light components is detected
`experimentally. Combining of subsurface layer of one component leads to the diffusion of this
`component from the depth of a target.
`For crystalline targets physics is much richer. When the compounds of А3В5 (e.g. InSb,
`
`GaAs) are sputtered the difference in angular distribution of components A and B being
`sputtered is detected (Pic. VI. 1.312). Besides, in the process of sputtering there the
`reorganization (reconstruction) of a surface occurs, which is, in turn, different for the facets of
`component A and B. Relative sputtering coefficients for components A and B per different
`facets of a monocrystal (for example InSb) and for a polycrystal are different.
`
`and
`
`
`
`
`degrees
`Pic. VI. 1.312. Angular distribution in plane (110) of Sb and In atoms, sputtered from facet (111) of InSb monocrystal
`
`Sputtered coefficient Y at 0 < θ ≤ 70° increases as θ increases approximately as
`
`
`where v changes due to the energy and type of ion in the interval of 1 < v < 2 (Pic. VI. 1.313). At
`θ≈ 70 - 80° Y(θ) it reaches maximum and then decreases with increasing of θ, which is caused
`by the reflection of ions from the surface glancing incidence provided. The relation Ymax/Y(0)
`becomes greater if the energy of ion is greater and mass is less.
`
`keV
`
`at./ion
`
`degrees
`degrees
`
`Pic. VI. 1.313. Sputtering coefficient of nickel as functional relation of incidence angle of ions of Н+, D+ and Не+ with energies
`of 1, 4 and 8 keV
`Pic. VI. 1.314. Sputtering coefficient dependence of Cu monocrystal, facet (100), from the incidence angle of ions Аr+ with
`energy of 27 keV; points - experiment, curve – calculation per the transparency theory
`
`In the case of a monocrystal the dependence Y(θ) is not monotonous: on the curve Y(θ)
`minimums are observed when ion beam is oriented along close-packed directions (Pic.
`VI.1.314). Then the ions which entered the crystal between nuclear lines move without intense
`collisions with the atoms of a target and without causing a sputtering.
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`At temperature being less than T1 coefficient Y is not actually dependent on the
`temperature, and at Т ≈ T1 starts to grow rapidly concurrently with the growth of temperature
`(Pic. VI.1.315). Sometimes temperature T1 is defined per the empirical relation T1 = 0.7 Тm,
`where Tm is melting temperature, though in some cases, e.g. for stannum, T1 > Tm. The other
`empirical relation is T1 = U/40k (k is Boltzmann constant). Temperature T1 depends on the
`type, energy and density of ion flow in a slight way.
`The change of target temperature can lead to the change of its phase composition that in
`turn influences the process of sputtering. For example, the ionic irradiation of semiconductors
`at temperature being below some critical Та (depending on the type of ion) leads to
`amorphization semiconductor surfaces.
`
`
`Pic. VI.1.315. Sputtering coefficient of cuprum being bombarded by the ions of Аr+ with the energy of 400 eV, from the
`temperature: 1 — electrolytic copper, 2 — rolled copper, 3 — cuprum monocrystal, facet (101)
`
`At the temperature is higher than Ta, the dependence Y from on the angle of incidence of ions is
`observed being characteristic for a monocrystal, and at Т < Та this dependence has monotonous
`character, as for the unstructured target (Pic. VI.1.316). This transition is carried out in the
`sufficiently narrow range of temperatures.
`
`In ferromagnetic solids near to a Curie point a spike-shaped jump of sputtering coefficient
`on the curve of temperature dependence of sputtering coefficient is observed (Pic VI.1.317)
`that is explained by the influence of spin-dependent corrections to the interaction of atoms
`which change the energy of sublimation and interaction potential of atoms.
`at./ion
`
`degrees
`
`Pic. VI. 1.316. Dependence of sputtering coefficient of silicium on the angle of incidence of ions of Аr+ (30 keV) on facet
`(111); rotation about an axis [112]; dark circles — crystalline surfaces (Т=600 °С), light — amorphous surface (Т = 200 °С)
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`Page 9 of 23
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`at./ion
`
`Per unit value
`
`
`
`eV
`
`
`
`
`Pic. VI.1.317. Dependence of sputtering coefficient of Ni facet (001) on the temperature at bombarding with ions of Аr+ (20
`keV)
`Pic. VI.1.318. Energy spectrum of sputtered atoms. Tantalic target is sputtered by cesium ions with the energy of 1200 (curve
`1) and 2150 eV (curve 2)
`
`3. Characteristics of sputtered particles. Power spectrum of the sputtered atoms dY/dƐ
`
`(pic.VI.1.318) possesses its maximum when Ɛ≈U. When energies Ɛ>UdY/dƐ~Ɛ-v, where v≈2,
`the high-energy spectrum tail as well as the average energy (Ɛ) of the sputtered atoms increases
`with the increase of the energy of ions Ɛ. The average energy (Ɛ) increases also with the
`increase of ion incident angle Ѳ and departure angle of the sputtered atoms v (Ѳ and v are
`calculated from the normal to surface). In the low-energy area of the spectrum (Ɛ<U), when the
`resolution is high, atoms with the Maxwellian distribution and temperature 0.1-1 eV are
`detected, but the general contribution of such particles to the sputtering is approximately 10 %
`with the exception of the heavy ions with energy about 1 keV and high temperatures of the
`target.
`
`In the mass-spectra of the sputtered particles clusters of two and more (up to 10) atoms are
`observed. However, the relative number of atoms sputtered by the clusters is not large (≤ 1%)
`and quickly decreases with the increase of number of atoms in the cluster. The number of atoms
`sputtered by the clusters increases with the increase of ionic mass. During sputtering with the
`small ions (H, D, He) the sputtering with clusters is practically absent. The number of sputtered
`clusters decreases with the increase of cluster energy, it decreases faster with the more atoms
`are present in cluster (pic. VI.1.319).
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`Pic. VI.1.319. The power spectrum of the sputtered atoms and charged clusters
`
`
`The bigger part of the sputtered atoms is neutral; the content of particles sputtered in the
`
`form of ions is usually less than 1 %. The exception is alkaline metals which are sputtered in
`the form of positive ions.
`
`
`Pic. VI.1.320. The angle distribution of sputtered atoms of tungsten bombarded by Kr+ ions (10 keV) reaching the surface at an
`angel Ѳ = 60°; solid-line curve – experiment, bar diagram – computer calculation
`
`
`The angle distribution of the sputtered atoms with normal ion incidence onto polycrystal is
`
`symmetric in relation to the normal when Ɛ > 1 keV, d2Y/dv2~ cos v for the high energies, while
`when Ɛ < 1 keV the atoms sputtered closer to the surface (with large v) are prevailing. When
`the ion incidence is angular (Ѳ ≠ 0) a peak is superposed on the distribution, symmetric in
`relation to the normal, in direction to which the primary displaced target atoms are displaced
`(pic. VI.1.320). When the incident angles are large this peak becomes prevailing. Though,
`when the energies are extremely high the angle distribution remains symmetric in relation to
`the normal even when the ion incidence is angular. In case of single crystal the angle
`
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`distribution of the sputtered particles is strongly non-isotropic: sputtered atoms are ejected
`mainly in directions of the close-packed atom lines of crystal (pic. VI.1.321), creating typical
`spots (spots of Wehner) in the picture of settlings of the sputtered substance.
`
`
`Pic. VI.1.321. Spots of Wehner obtained in the result of sputtering of copper single crystal (side (001)) with Ar+ ions falling at
`the incident angle 30° with the energies: 180 eV (a), 1 keV (б), 10 keV (в), 40 keV (г) and H+ ions with the energy 10 keV (д)
`
`4. Experimental methods of sputtering research. Research of sputtering is carried out by
`
`means of different methods: first, using the target which is examined before and after the
`sputtering, second, using the settlings of sputtered atoms on any screen, and, third, with help of
`direct registration of the sputtered particles.
`
`The research of target is done by means of the following methods:
`1) method of weighting; this is absolute and the most widespread method;
`2) method of calculation of electrical resistance of films and wires that get thinner in the
`sputtering process;
`3) by means of profile testing instrument which measures the ledge height between
`sputtered and non-sputtered (covered) part of the surface;
`4) method of marker from heavy ions which are inserted into the sufficient depth; it is
`possible to measure the marker depth with the help of reverse sputtering of the
`high-energy ions (Ɛ > 1 MeV); this depth decreases during sputtering.
`The inspection of amount of settlings of the sputtered substance needs calibration because
`it depends upon adherence of the sputtered substance, geometry and other conditions of the
`test. The sputtered substance settlings are researched by means of the following methods:
`1) photometrically, by the optical density;
`2) method of the radioactive isotopes;
`3) method of measuring of the resonance frequency of quartz crystal which the
`sputtered substance has settled out upon;
`4) method of measuring of the film thickness by means of reverse sputtering of the
`high-energy ions;
`5) by means of settlings evaporation and inspection of the evaporated atoms with
`spectroscopic methods;
`6) method of interference on the film.
`
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`The research of the sputtered particles is done by means of spectroscopic methods and
`with help of mass-spectrometer. In the first case the excited-state atoms are registered, in the
`second – the sputtered ones in the form of ions. In order to register neutral non-excited atoms
`they are stimulated or ionized with an electron beam or laser. All methods of directly sputtered
`particles research need calibration.
`The settlings distribution of sputtered substance provides information on the angle
`distribution of the sputtered particles. The impulse bombarding together with stroboscopic
`devices allow measuring of the power spectra by the travel time with the help of sputtered
`substance settlings. The power spectra can be measured with the electro-magnetic methods by
`bending of the charged particles as well as with spectroscopic methods by the Doppler drift.
`5. Theoretical models of sputtering. It is accepted to consider that the sputtering with SS
`ions happens in the result of the three main mechanisms: 1) in-line cascade of atom collisions,
`2) direct dislodging of target atoms with ions and 3) non-linear cascades or thermal peaks.
`5.1. Cascade model of sputtering. Cascade of atom collisions – is a sequence of collisions
`of moving atoms in which the displaced atoms of the following generations are generated and
`so on till the energy of moving particles reduces to the energy Ɛd needed for displacement of
`atom from its balanced position in the lattice. The cascade mechanism is the main one for the
`most of ions of medium energies and masses.
`The cascade theory of sputtering is based on kinetic equations for the sputtering functions
`of the moving ions and for the moving displaced ions. All collisions of ions with the crystal
`atoms and of atoms with other atoms are considered as binary and are calculated pursuant to the
`laws of classical mechanics with the interaction potential selected in the respective way. The
`theory is linear, in other words, it takes into account collision of moving particles only with the
`stable target atoms. Usually the system of kinetic equations is solved by means of the method
`of moments. This theory results in the following expression for the sputtering yield:
`
`
`FD(0, Ɛ, Ѳ) – density of energy generated during the elastic collisions near surface (when z = 0)
`in the cascade initiated by ion reaching the surface with energy Ɛ and angle of incidence Ѳ
`(function FD(0, Ɛ, Ѳ) is found in the result of solving of the kinetic equation); N – number of
`atoms in the unit of volume of target which is supposed to be structureless; C0 – constant in the
`differential section of T energy transfer, which for the atom model – rigid spheres, the most
`adequate for energies of colliding atoms, is less than 100 eV, has the formula
`
`
`Constant C0 is usually applies as equal to 3Ά2. The formula (10.4) has a simple physical sense.
`(NC0)-1 is a length of free path of cascade atoms and respectively the depth of layer which the
`energy can be transferred to the sputtered atoms onto the surface from. The energy contributed
`to the sputtering process during the cascade mechanism is equal to (NC0)-1 FD(0, Ɛ, Ѳ), and the
`number of atoms which receive the energy bigger than U in the cascade is equal to x FD(0, Ɛ, Ѳ)
`/ (NC0)U according to the formula of Kinchin-Pease. Taking into account only those atoms
`which have the energy Ɛ>U and impulses directed to the upper half-sphere, with the respective
`selection of constant x, we will receive the formula (10.4) for the number of the sputtered
`atoms.
`
`The power spectrum of the sputtered atoms in the cascade theory can be obtained if to
`insert into (10.4) U = Ɛ and differentiate using Ɛ. Then
`dY/dƐ ~ Ɛ-2,
`which is close to reality when Ɛ > U. Maximum on the curve dY/dƐ from Ɛ is obtained if to
`accept that the potential surface limit is not flat but has some curvature.
`
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`The cascade theory forecasts the isotropic angle distribution of the sputtered atoms for all
`
`angles of incidence of ions onto the target. The anisotropy becomes apparent when taking into
`account the mechanism of direct dislodging of target atoms by ions.
`
`The dependence of sputtering yield from the angle of incidence in the cascade theory has
`the expression
`
`Y ~ cos-v Ѳ,
`with v = 5/3 for Ma/Mi ≤ 1 or v ≈ 1 with Ma/Mi ≈ 1. In the modern interpretation the kinetic
`equations of the cascade theory are solved for the unrestricted circumference and such
`approach does not allow taking into account the ion reflection from the surface and
`consequently describing of dependence Y(Ѳ) with great Ѳ. Maximum on the curve Y(Ѳ) and
`decreasing of Y with increase of Ѳ when Ѳ is great is obtained with formula
`
`
`
`where RƐ(Ѳ) is factor of energy reflection from the surface.
`
`The cascade theory also allows reviewing the sputtering of polyatomic substances. In this
`case instead of one functional relation of sputtering FD(z, Ɛ, Ѳ) the functional relations FDk(z, Ɛ,
`Ѳ) of energy distribution which is released during elastic collisions of each k component are
`introduced. The system (k+1) of the kinetic equations is solved: k of equations for each
`component and one for the bombarding ion. The sputtering yield for each component is
`proportional to the functional relation FDk(0, Ɛ, Ѳ), representing the energy density in the
`present component. The main result of such approach is the primary sputtering of the lighter
`component. In the most cases this conclusion is confirmed experimentally. The cohesive
`energy which can be different for different atoms of polyatomic substances is also important
`for the selective sputtering. In the result of the primary sputtering depletion of the surface of
`one or several components may happen in the sputtering process. In case of increased
`temperature of target and in the result of radiation-enhanced diffusion the component diffusion
`in direction to the surface or from the surface is possible.
`
`The linear cascade theory explains satisfactory the bigger part of functional dependences
`of sputtering yield, but the theory allows calculation of numeric values of Y only with the
`accuracy to factor 2-3 even in those cases when the theory is applicable. This is explained by
`that the linear cascade theory does not take into account such important factors as:
`1) role of crystal structure of the most solid substances;
`2) complexity of the simple processes such as displacement from the lattice point and
`dislodging of atoms from the surface which are described si