Values D and ρ are checked on experimental data. Results of comparison of experimental data with the formula (7.8) are shown on fig. 7.3, b and c. Curves 1 and 2 are theoretically calculated by Brown for two chosen values D and ρ. For comparison the values calculated by Jackson and Mott are resulted on the curve 1 fig. 7.3, a. However experimental points on this diagram coincide with a curve 2 received by division into 3 values, calculated by Jackson and Mott.
Fig. 7.3. Comparison of experimental and theoretical values of temperature dependence of the accommodation coefficient α.
On fig. 7.3, α the curve 1 represents the values calculated by Jackson and Mott for helium on tungsten. The curve 2 gives the values received by division of Jackson and Mott’s values on 3. Circles on a curve 2 represent experimental results. Curves 1 and 2 on fig. 7.3 are calculated by Brown [11] accordingly for accommodation of helium and neon on tungsten. These curves are received for two values of parameters D and р in expression (7.8). On fig. 7.3: 1-D=250 кал/моль, ρ = 0,70-108 sm - 1 2-D = 340 kal/mole, р=0,62·108 sm - 1. On fig. 7.3, in: 1-D = 640 кал/моль, р=0,82·108 sm - 1; 2-D = 800 kal/mole, р = 0,73·108 sm - 1. Circles represent the experimental values received by Silvernail [75].
The final explanation of temperature dependence of the accommodation coefficient can be expected from the quantitative theory based on more realistic assumptions, concerning the mechanism of interaction between adsorbed atom and a surface.
7) Conditions of the considered surface play the important role on influence of the accommodation coefficient, namely a degree of its physical, chemical and induced heterogeneity.
For example, Roberts [68] has shown, that in case of a rough surface of metal, which the atom of gas collides n time with, the measured accommodation coefficient αexp can be expressed by a ratio
αexp=1-(1-α)n, (7.10)
where α – the accommodation coefficient for ideally equal surface.
As a result, various variants of the accommodation coefficient calculation of factor have been considered. In our task the calculation of the accommodation coefficient for one-nuclear gas will be settled. Atoms take off the surface of a cathode - target with some energy, bombard a surface of a substrate transferring it a part of energy and settle on its surface, forming a covering, or leaving its surface with another energy. For definition of the accommodation coefficient we can use in this case the formula (7.1) or (7.2).
8 Methods of calculation of the discharge characteristics of magnetron sputtering systems
As it was stated above, complexity of definition of the discharge parameters in magnetron sputtering systems is caused by the burning of the abnormal glow discharge in the non-uniform crossed electric and magnetic fields. In the literature it was possible to find four various approaches to the decision of this problem. None of the methods is universal and suitable for authentic calculation of the discharge characteristics in an arbitrary case. Each method has disadvantages. For example, a number of assumptions is used. It simplifies calculation of characteristics, however it results to not taking into account some rather significant factors which influence on work of magnetron sputtering systems on the whole. At the same time every way of calculation has its advantages which are necessary to consider and take into account when choosing the method of definition of the discharge characteristics of magnetron sputtering systems.
8.1 The kinetic equations method
The first method of calculation of parameters of the discharge gap in magnetron sputtering systems is a method developed by B.S. Danilin [25, 26, 29, 38, 39]. Drift movements of the charged particles in the non-uniform crossed electric and magnetic fields are considered in work. Though for the full description of plasma it is not enough to consider drift movements of separate particles, it is possible to describe evidently some macroscopic properties of a plasma condition with their help.
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