INVESTIGATION OF SHEATH AT ELECTRODE IN RADIO-FREQUENCY DISCHARGE

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INVESTIGATION OF SHEATH AT ELECTRODE IN RADIO-FREQUENCY DISCHARGE

V. Godyak, S.N. Ox.

To cite this version:

V. Godyak, S.N. Ox.. INVESTIGATION OF SHEATH AT ELECTRODE IN RADIO- FREQUENCY DISCHARGE. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-809-C7-810.

�10.1051/jphyscol:19797390�. �jpa-00219389�

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JOURNAL DE PHYSIQUE CoZZoque C7, suppldment au n07, Tome 40, JuiZZet 1979, page C7- 809

INVESTIGATION OF SHEATH AT ELECTRODE IN RADIO-FREQUENCY DISCHARGE

V.A. Godyak, S.N. Ox.

Moscow State University, Department of Physics, Moscow U.S.S.R.

To construct RP discharge theory joint accouating of electrodynamic properties of quasi-neutral plasma and space charge she- a t h a t electrode (EX66 ) is needed.letts consider the structure and electrodynamic properties of SCSE,which appear i n a s t a t i - onary symmetrical RE' discbarge between pla- ne nonemitting electrodes i n range of f r e - quencies/ I /:

we, 2 >7 2>

4;

( I ) ; ^LA)27zj h J ~ 7 8 v ( 2 ) where ^b ^e and ^{u c i}-electron and ion plasma frequencies; ic' -RF f i e l d frequency; \/

-

electron-atom c o l l i s i o n frequency; 2

-

ionization frequency; 3 Z -effective part of energy,lost by an electron a t collision.

Fig.1 shows a qualitative structure of SC

Fig.1

Plasma ions are supposed t o i n j e c t Fn SC SE with ion sound veloci2;y

&

^{( H S} -plasma boundary density) .As it follows from

( I ) ,ions are accelerated towards RF electrode by the time average component of SCSE field.At the same time electron den- s i t y p r o f i l e o s c i l l a t e s with the f i e l d frequency from ^{S m} t o RF electrode.The l a s t requirement i s f u l f i l e d when electron oscillation amplitude a t plasma boundary

as

exceeds considerably the Debye radius a t plasma bo~ndtiryf)eS .If the electron density i s step-like,then f o r mobile she-

a t h boundary we s h a l l have : 17, (s) = 0; [.;)

.

Let

'

^ss e t discharge current(disp1acement current i n ~ ~ 6 8 ) a s j(t) = ut = efi(yjgs Time average electron density i n ^XSE(h,)=

( together with stationary ion

$ace distribution determines the time average potential i n SCSE

-

q6(%)=(Y(r,4).~hen from equations of Poisson,ion mot;ion,RF current continuity and charge conservati- on f o r two SCSE / 1 / we s h a l l get a system of equations.This system links together time average SCSE characteristics with s e t parameters d = * _Ai and Lie =

-

vc _Ve⁽A;

-

ion mean f r e e path, v', -amplitude of sum- mary IU? voltage i n two SCSE, V, -electron temperature i n units of potential):

n; me).

where

7, =-S

_{v e} ;

1

^=&s: ^{9 i =}^n,^:(ye>

= x , ,

^z^{5 %} ⁼ ^y,^and^l,-instanta- neous values of reduced RF voltages i n two ^SCSE:

A

-characteristic dimension of quasi-neutral plasma.Point

%

=O corres

-

ponds t o plasma boundary and 3 = ^s^t t o RJ?

electrode.

T h i s system has been solved with com- puter f o r the large range of values ^&C =

5 -200 and oC =

lo4-

1 .Calculations sho- wed,that the l a s t member i n the second eq-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797390

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uation,linked with ionization i n SCSE,at

Sm<< A

,gives the negligible contributi- on t o the value

9;

.Time average SCSE %hi- ckness

- ^s,

,determining @SE capaci$ive impedance was fomd from

S;O)

₌

sy,

di ⁹

where 6 0 =

sph..

o So Fig.2' shows ion space distribution i n SCSE i n the case of uncollision sheath

( d =I

o - ~ ,

= I 0.' ) and also when there are several collisions ( oi =

, 'fi;

I ^-7)^.SO Fig.2 shows,that ion distribution inhomo- geneiky decreases while the number of col- l i s i o n s i n SCSE increases.The same is seen from Fig.3, where dependence

3 (S,)

a t dif f e- rent Uc is given.

Fig.2 Fig.3

According t o the calculations, -de- pendences of reduced S C S E thickness

80

(Fig.4) and reduced time average component of RF voltage i n SOSE L l o (Fig.5) may be approximated by following expressions with accuracy t o 1W :

k c

3 (4)

6 e = e ~ ~ C ' / r

_.~ ( s ) ;

u0= -

where parameter

e

weakly depends upon d and may be approximated exactly enough by expression: /. 8 t b (/+A)

t 5)

The r e s u l t s of calculations

4 '

^{are pre-}

sented a t Fig.6 .Approximation (5) is given by dotted 1ine.Experimental r e s u l t s / 2 /, obtained in RF discharge (mercuqy vapour) a t f repuency

$

= 40.8 YRz are given a t Fig.4 and Fig.6.

Fig.6

Letts note, that value

J0

,and theref ore the iZSE capacitive impedance,are determi- ned by amplitude of electron oscillations a t plasma boundarg

as

.Actually, displace- ment current i n SCSE i s equal t o conducti- on current i n plasma due t o the continuity of discharge current:

ve ^Uc

-

= *r5. - osoett i

then taking into accout (3) we get:

S o = 2e2as

A t high pressures ( o( >> I ) t h i s rela- tion, as follows from (5) ,takes the form:

2

^I^Us. T h i s r e s u l t coincides practical- Ly with r e s u l t s of / I / ,where y,- =I was assumed a priori.

References:

I * B . A . ~ o x ~ ~ K , @ M ~ u R ~ I - I A € ~ ~ M H , ~ J ~ I , I ~ ~ ~ . 2.~.A.Go~&,O.A.Popov,A.H.Hanna,Proc .XI11

Int.Conf.Phenom.Ioniz.Gases,p.347,Berlin, 7977.

Fig.4 Fig. 5

INVESTIGATION OF SHEATH AT ELECTRODE IN RADIO-FREQUENCY DISCHARGE

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