The temperature of a substrate, while the covering is drawing on it’s surface, страница 27

Finding the position of the conditional anode. If the magnetic trap is effective enough, i.e. electron circulate in it until the whole energy received from the electric field, will not be used on maintenance and formation of plasma, one electron can makeWe/W₀ ions where We - the energy received by electron from the electric field, and  Wo - the total energy spending on one act of ionization. To a first approximation it is possible to count We=eUp, whereUp – the discharge voltage. SizeWo includes energy of ionizationeφ_i (φ_i - potential of ionization of working gas) and the energy spent for resonant and not resonant excitation (it is possible to not take into account the energy spent for elastic impacts, because at low pressure the probability of elastic impacts is very small) [20]. Calculation of  Wo is difficult, and one usually use experimental data. For argon W0 = 4,8·10^-18 Joule/ion (30 eV/ion) [39].

Thus, having defined the number of ionizing collisions which electron can make, and taking into account, that electron moves away from the cathode on distance, approximate equal to larmor radius at each collision in plasma, with use of formulas (8.3) and (8.7), we can calculate distance between the cathode and conditional anode in magnetron sputtering system for the discharge in argon [25, 26]:

.                                               (8.10)

The formula (8.10) does not take into account change of larmor  radius of electron owing to heterogeneity of the magnetic field and change of its energy at drift in plasma. It can be used only for the approximate evaluation of position of the conditional anode in the discharge with primary anode potential drop. In case of the discharge with primary cathode potential drop position of the conditional anode is defined by expression [25, 26]

,                                (8.11)

where N=W_e/W_o – number of ionizing collisions which electron can make with atoms of working gas.

For the account of heterogeneity of a magnetic field it is necessary to take for calculation average value of the induction in the field of plasma (usually 0,6 … 0,7 maximal values at a sprayed surface) or to settle the invoice distribution of field lines of the induction of the magnetic field above the cathode - target surface [44]. In that specific case when electron moves on a cycloid in homogeneous electric and magnetic fields taking into account the expression (8.5) [25, 26, 39]

                                       (8.12)

Real anode of magnetron sputtering system should settle down from the center of the dispersion zone on distance, not smaller than _Хо, otherwise it will grasp electrons, capable to ionize gas, from the magnetic trap, and efficiency of working gas ionization will decrease. At a peripheral arrangement of the anode in flat magnetron sputtering system it should be placed outside the area of entrance and an exit of field lines of the magnetic field.

8.1.3 Localization of plasma of discharge

One of features of magnetron sputtering systems is localization of plasma of the abnormal glow discharge at the spraying surface of the target, plasma has the form close to toroidal, and a degree of its ionization is maximal in the central part above the zone of dispersion. The reason of localization of plasma relative to the average line of the zone of dispersion is explained by heterogeneity of magnetic and electric fields.

First of all, localization of plasma occurs owing to magnetic focussing of electrons in the magnetic field, field lines of which have the form of an arch. This phenomenon can be considered by the example of electrons which initial speeds are directed on a normal to the surface of target. As shown at figure 8.2,a i, electrons, emitted from edges of the dispersion zone, move along the field line of the magnetic field to the middle of the dispersion zone under action of component speedv _// while movement in the direction is limited by a strong transverse magnetic field. Concentration of electrons above the average part of the dispersion zone results in increasing of intensity of ionizing collisions and, hence, to growth of plasma density in this area. As a result of it, the density of an ionic current along the dispersion zone is non-uniform. It is stronger in the center and weaker at borders.