ff3 fsf fc0 sc0 ls0 wsa">argon ion by diffusion and by electron collisions respec-
tively. If the diffusion term is much less than the colli-
sion term, then the following expression is obtained from
(11):

*
,Arcoll
coll
,
Ar
Ar Ar
e
e
kC
k


 (12)
Otherwise we have:

,Ar diff
diff
Ar
Ar
Ar Ar
ee
e
D
nknC


 , (13)
where the constants and are defined as the
ratio between the creation coefficient and the loss coeffi-
cient. At constant pressure they are assumed do not de-
pend on discharge power.
coll
+
Cdiff
C
Using (4) the emitted intensity of the Ar ion is

*Ar ato
*
Ar Ar
ij e
IKnC
m
, (14)
if argon ion excited from the argon neutral (see (8)).
When argon ion excited from the ion ground state and
minor diffusion (see (9) and (12)), the intensity can be
written:
Copyright © 2012 SciRes. JMP
N. P. POLUEKTOV ET AL.
1500


**
*
ion coll
ion coll
+* +
Ar ArAr
Ar
e
e
ion
I
KKn
KnC C

 
C
 

 
(15)
If argon ion excited from the ion ground state and do-
minant diffusion (see (13)) we have:


**
+*
ion diff
ion coll
*+
Ar ArAr
Ar
e
ee
ion
I
KKn
KnC nC

 
 

 
C
(16)
It is seen from the previous expressions, that the emis-
sion intensity is related to the electronic density, which is
about linearly proportional to the magnetron power.
The intensities of argon ions are proportional to about
square of the magnetron power as it follows from Figure
9. This implies that the main losses for argon ions are by
diffusion at 20 cm according to expression (16).
Similar equations can be obtained for copper atom and
ion lines. The copper atom density in the ground state at
the steady state is given by:

Cu
Cu ,Cu
Ar
Cu D
ee
nk
, (17)
where γCu is the sputtering coefficient and ,Cue is the
destructive rate by ionization in the following reaction:
k
Cu Cue
 ee
e
(18)
If copper excited states are supposed to be created
mainly by the electron impact on the copper ground state
*
Cu Cue , (19)
Then the line intensity can be expressed versus elec-
tron density as:

 
2
Cu Cu
*diff
Cu ,CuCu ,Cu
Ar Ar
Cu ee
eDD
ee ee
nn
ICu nnk nk



 

(20)
Here we used Equations (13) and (17). If diffusion
term Cu
D
is much less than collision term ,
,Cuee
nk
Cu ,Cu
D
ee
nk
(21)
we obtain:

*
Cu e
I
n
(22)
Figure 10 shows that emission intensity of copper
atoms increases linearly with a slope 1. Thus, the pro-
posed kinetic scheme with the expressions (13) and (17)
explains the observed behavior of Cu line intensities,
indicating that copper atoms were lost due to the ioniza-
tion by electron collisions at a distance of 20 cm from
magnetron.
Another argument in favor of this conclusion is the
results of experiments on the absorption of resonance
lines of copper. Figure 11 shows the absorption coeffi-
cient A of the resonance Cu line 324.7 nm, obtained at a
Figure 11. Absorption coefficient A of the Cu spectral line
324.7 nm as function of magnetron power.
distance of 20 cm vs magnetron power. 1
L
PP
L
I
I
AI
 ,
where IL is the light intensity of the lamp with hollow
cathode, IP is intensity of Cu atoms in plasma, when
lamp off and IL+P is the intensity, measured with lamp
and plasma on. When current of electromagnet Iel =
1.25 A plasma density at this distance is low (see Fig-
ure 4) and ionization of Cu atoms also small. Density of
sputtered Cu atoms increases with growing power and
coefficient A grows. When Iel = 0.6 A plasma density
downstream the magnetron is great and increases with
magnetron power. The ionization of Cu atoms grows also,
density of Cu atoms decreases and coefficient A falls.
Recall that value of the sputtered Cu atoms inside of the
cathode is about the same in both cases. These measure-
ments confirm our conclusion that the ionization of Cu
atoms is dominant loss term at a distance of 20 cm from
magnetron. Detailed description of these measurements
is beyond scope of this article.
For the emission intensity of the copper ion we con-
sider two-step mechanism:
*
Cu Cue

e
, (23)
where Cu+ is produced by reaction:
Cu Cuee
e
 (24)
Then
*
Cu Cu
e
In
(25)
The copper ion density in the ground state is given by
analogy to (11):

,Cu
Cu ,Cu
Cu Cue
eD
ee
k
nnk




 

, (26)
Using condition (21) and Equations (17) and (26) it
can be deduce
Copyright © 2012 SciRes. JMP
N. P. POLUEKTOV ET AL. 1501








2
*
Cu ,Cu
2
Cu diff
Cu ,Cu
Cu ,Cu
32
Cu
,Cu ,Cu
Cu ,CuCu ,Cu
Cu
CuCu
Ar
Ar Ar
e
eD
ee
e
DD
eee
e
ee
DD
eeeee
e
n
In
nk
n
nk nk
nn
nk nknk k




 


 








e
(27)
The copper ion diffusion term Cu
D
is much more
than total destructive (including double ionization) term
,Cu
ee
nk
. So that

*
Cu e
2
I
n
(28)
Thus, from the intensity variation of Cu and Cu+ spec-
tral lines with magnetron power, it is deduced that the
dominant loss term are electron ionization for the copper
atoms and diffusion for the copper ions.
In our model we neglect the influence of metastable
states of Cu and Ar atoms. Our measurements of the ab-
sorption coefficient of the line Cu510.6 nm shown that
density of the metastable level 2D5/2 is of an order less
than density of the ground level. From the absorption
coefficient of Ar696.5 and Ar811.5 nm lines we calcu-
lated density of metastable Ar level s5 (Pashen notation).
The Ar metastable state density was found in the range of
1010 - 1011 cm3. Note that these data were obtained at a
distance of 20 cm from the target. Data on metastable Ar
atoms are in good agreement with the results obtained in
a high-density plasma discharges [16-18]. We also did
not account for Penning ionization of Cu and Ar atoms.
Due to these factors, the experimental intensities of Ar+,
Cu and Cu+ increase faster. However, these differences
are small, indicating that these processes make a small
contribution to ionization process.
The carried out experiments have shown, that magne-
tron hollow cathode discharge allows to receive at pres-
sure in some mTorr plasma density more than 1011 cm3
at a distance in tens cm. The high plasma density created
in the big volume, increases probability of ionization of
the sprayed atoms of a target. The stream of ions of the
target, controlled by an electric field near a substrate,
enables to deposit a highly conformal film on structures
of the complex form. The size, uniformity, a degree of
ionization of a stream of plasma can be supervised by the
appropriate choice of power, pressure, magnitude and
configuration of a magnetic field.
4. Conclusion
Langmuir probe and optical emission spectroscopy mea-
surements were used to study of plasma characteristics
and Cu ionization in HCM discharge. The pressure range
is 0.5 - 10 mTorr with 1 - 5 kW discharge power. Varia-
tion in the plasma parameters such as electron densities
and temperatures, electron energy distribution function,
plasma space and floating potentials as a function of the
position, pressure and power in the growth chamber were
measured in detail. The optical emission spectroscopy at
a distance of 20 cm from magnetron shows strong in-
crease of the intensity ratio from Cu+ ion and Cu neutral
lines with the power. These measurements indicated
large downstream ionization of sputtered copper atoms.
From the intensity variation of argon and copper atoms
and ions spectral lines with magnetron power, it is de-
duced that the main creation mechanism for argon and
copper ions is an electronic collision from the ground
state and the dominant loss terms are electron ionization
for copper atoms and diffusion for the ions.
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