The temperature of a substrate, while the covering is drawing on it’s surface, страница 35

dN – quantity of the atoms getting from dS' on dS in time dt.

cosφ=L/R, где R²=L²+r²+r'²-2·r·r'·cosψ', а y'=r'·cosψ', x'= r'·sinψ'.

dN=dГ·dS·dt | dΩ=dS·cosφ/R²,                                       (9.2)

where dГ – part of Г, created by dS'.

Then dГ·dS·dt= Г₀·f(φ)·dS'·dS·cosφ·dt /2π·R²,

as. dS'=r'dr'dx', then

dГ=Г₀·L/2π ∫ ∫ f(φ)· r'·dr'·dψ'/ (L²+r²+r'²-2·r·r'·cosψ')^3/2.

f(φ)=A·cosφ, then А∫sinφ·cosφdφ=A/2, so А=2. Then

∫ f(φ) sinφ·cosφdφ=1, а f(φ)=2cosφ.

Г(r)= Г₀·L²/π ∫ ∫ r'·dr'·dψ'/ (L²+r²+r'²-2·r·r'·cosψ')².                             (9.3)

As the radius of cathode Rc is several times less than distance between the cathode and substrate L, expression 1/(L²+r²+r'²-2·r·r'·cosψ')² can be presented as

1/(L²+r²+r'²-2·r·r'·cosψ')²=1/(L²+r²+r'²)²[1-2 r·r'·cosψ'/ L²+r²+r'²]^-2=[(1-x)^-2=1+2x+2·3x²/2+2·3·4x³/6+2·3·4·5x⁴/4!]=∑[(2k+1)/(L²+r²+r'²)^2+2k]∙[(2 r·r'·cosψ'/ L²+r²+r'²)^2k]≈ 1/(L²+r²+r'²)(1+12 r²·r'²·cos²ψ'/ (L²+r²+r'²)²).

Then the distribution function of the sprayed atoms on a surface of a substrate can be presented as

Г(r)≈2Г₀L²∫ (1+6 r²·r'² / (L²+r²+r'²)²)·(r'dr'/ (L²+r²+r'²)²).                              (9.4)

Г(r)=2Г₀L²[-(3L²r²+2r⁴+5r²R²+L⁴+2L²R²+R⁴)/2(L²+r²+R²)³+((2r²+L²)/2(/L²+r²)²)].

10. Creation of a technique of a heat mode of a substrate definition when drawing coverings in magnetron sputtering systems

In the previous sections of work the principle of action of magnetron sputtering systems, processes occuring on a cathode - target, in a discharge gap and on a surface of a substrate in magnetron sputtering systems has been considered. Also, influence of various parameters on processes of ionization of working gas, dispersion of a material of a cathode - target and sedimentation of a covering is estimated. In the given section all materials received in work will be shown in uniform system, and the algorithm of calculation of a thermal mode of a substrate when drawing coverings with help of MSS will be developed on the basis of the collected materials and the carried out analysis.

1) First step is definition of the conditional anode by the formula (8.12) resulted in the subitem 8.1.2 and after that definition of the discharge current by the technique, described in subitem 8.1.5.

2) The following step is definition of voltage spent on process of dispersion, using the received value for the discharge current and the given value of working pressure of the discharge;

P=U·I.                                                          (10.1)

3) Further we determine quantity of ions of working gas bombarding a surface of a cathode - target.

The charge of an ion can be presented as

Q_i=e·z,                                                         (10.2)

where Q_i – a charge of one ion of working gas;

е – an elementary charge;

z – a charge number (for one-ionized gas z=1).

As working gas in the discharge gap of magnetron sputtering system is one-ionized, then Q_i=e. The charge of ions of working gas bombarding a surface of a cathode - target will be equal

Q=e·N_i,                                     (10.3)

where N_i – quantity ions of working gas bombarding a surface.

The discharge current can be presented as expression

I=I_i+I_e,                                                         (10.4)

where I_i – ionic component of current;

Ie - electronic component of current..

I_i= Q/t,                                      (10.5)

where t – lead time of a current (in this case t=1s, because we find the value of a heat flow in unit of time, then I_i= Q).

On data, discribed in [25] I_e= k_ie I_i                                             (10.6)

Then, having substituted (1.3), (1.5) и (1.6) в (1.4) we shall obtain

I= I_e +e·N_i.                               (10.7)

Using expression (1.4) we can find quantity of ions of working gas bombarding a surface of a cathode - target