Dependence of Sputtering Coefficient on Energy and Incidence Angle of Bombarding Particles. Energy Spectrum and Average Energy of Sputtered Particles by the Example of a Tungsten Target

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Abstract

The work provides an overview of the functional dependencies (formulas) for describing the properties of atomic particles sputtered during ion bombardment of the surface of a solid body. The dependence of sputtering coefficients on the energy and angle of incidence of the bombarding particle is considered. The energy spectra and average energies of sputtered particles are presented. Using the example of a target made of tungsten and hydrogen isotopes as projectiles, formulas for calculating the quantities under consideration are proposed. These data are necessary to estimate the entry of sputtered tungsten atoms as an impurity into a hot plasma using transport codes. When the tungsten impurity concentration is more than critical, it is impossible to carry out a controlled thermonuclear reaction with the planned energy output in the ITER tokamak reactor. Sputtering coefficients also play an important role in modeling the entry of impurities into plasma installations as a result of the interaction of hydrogen fuel atoms with the materials of the divertor and the first wall.

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P. Yu. Babenko

Ioffe Institute

Author for correspondence.
Email: babenko@npd.ioffe.ru
Russian Federation, St. Petersburg

V. S. Mikhailov

Ioffe Institute

Email: babenko@npd.ioffe.ru
Russian Federation, St. Petersburg

A. P. Shergin

Ioffe Institute

Email: babenko@npd.ioffe.ru
Russian Federation, St. Petersburg

A. N. Zinoviev

Ioffe Institute

Email: babenko@npd.ioffe.ru
Russian Federation, St. Petersburg

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Supplementary files

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2. Fig. 1. Dependence of the sputtering coefficient on the energy of the bombarding particle. The dots are the experiment from [8]. The red solid line is Eckstein’s calculation for a planar surface barrier from [8]. The black thick solid line is our calculation for a spherical barrier. The black thick dashed line is our calculation for a planar barrier. The thin dashed line is the calculation using the Zygmund formula. The dotted line is the calculation using the Bogdansky formula. The dash-dotted-dashed line is the calculation using the Yamamura formula. The dash-dotted line is the calculation using the Falcone formula.

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3. Fig. 2. Dependence of the sputtering coefficient on the energy of the bombarding particle. Systems: H–W (a) and T–W (b). Our calculation for a spherical barrier is a solid bold line and for a planar barrier – a dashed bold line. Calculation of the Eckstein group is a solid thin red line. Calculation according to the Falcone formula is a dash-dotted line. Bogdansky’s formula is a line with open circles. Yamamura’s formula is open squares. Experimental data from [8] are dots.

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4. Fig. 3. Dependence of the sputtering yield on the angle of incidence of the beam on the target. The H–W system is considered. The energy of the incident particle E0 = 4 keV. The angle of incidence of the beam on the target θ is measured from the normal to the surface. Black solid circles are experimental data from [8]. The line with triangles is our calculation for a planar barrier. The solid red line is a simulation by the SDTrimSP program [8]. The line with empty squares is a calculation by the ACAT program. The dash-dotted line is the Yamamura formula [14]. Diamonds are calculations using the Zinoviev formula (10). The dashed line is the 1/cosθ dependence.

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5. Fig. 4. Dependence of the sputtering coefficient, normalized to the value at normal incidence, on the angle of incidence. H–W, D–W and T–W systems. The initial energy of the bombarding particles E0 = 1 keV. Lines are the calculation of the Eckstein group. Lines with symbols are our calculation. The case of a planar barrier is considered.

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6. Fig. 5. Energy spectrum of sputtered particles. Initial energy of argon atoms E0 = 5 keV. Beam incidence angle on the target θ = 45°. Points – experiment from [23]. Lines – calculation using Thompson (13) – (solid line) and Falcone (14) – (dashed line) formulas.

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7. Fig. 6. Energy spectra of sputtered particles calculated using our program. Case of a planar surface barrier. Results are given for different energies of the bombarding beam. a – H–W; b – D–W. Dots – our calculation. Lines – calculation using the Falcone formula (14).

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8. Fig. 7. Average energy of sputtered particles depending on the energy of the bombarding beam. Calculation by our program for a planar and spherical barrier. The following systems are considered: H–W, D–W and T–W. Figure from [9].

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9. Fig. 8. Average energy of sputtered particles as a function of the bombarding beam energy. Our calculation – symbols. Processing of Eckstein calculation data – lines. Systems: H–W, D–W and T–W. Planar surface barrier. Additionally, a comparison with the Falcone formula (16) is given – dashed line. The threshold energy values obtained with our program were used.

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10. Fig. 9. Average energy of sprayed particles depending on the ratio of the collision energy to the threshold energy. The dots are the results of our calculation. The lines are the calculation using formula (17).

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11. Fig.10. Dependence of the parameter γEth/Us on the mass ratio M2 /M1.

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12. Fig.11. Dependence of the parameter γEth/Us on the mass ratio M2 /M1.

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