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Mathematics in Industry Information Service Eprints Archive

1993 European Study Group with Industry
Micro-Droplet Formation in High Current
Vacuum Electroplating
(proposed by Multi-Arc (U.K.) Ltd.)
CJB, J\VD, RS, JC, GvVD
February 16, 1994
1 Introduction
A technique used to coat metal surfaces with Titanium Nitride is to vaporise a Titanium
cathode by using a high temperature electric discharge or arc. If the cathode and the
metal target are placed in an evacuated chamber containing a low pressure of Nitrogen
gas, then the Titanium vapour becomes ionised and, if the target is at a negative potential
with respect to the cathode, the ions will move toward it and react with Nitrogen at the
surface to produce a thin layer of Titanium Nitride. The resulting geometry is illustrated
below
c """"OD£
-ItV
- 2,00 ~
'ONS
-to + •
..
+ -+-
1
A major disadvantage to this process is that as well as Titanium vapour, the arc also
produces micro-droplets of Titanium liquid. These droplets have a size of up to 20jlm
in diameter and move at speeds upwards of lOOms-I. When they strike the target the
resulting surface coating becomes uneven. Attempts to avoid this problem by changing
the location of the target with respect to the cathode, result in reduced efficiency for the
process.
The objectives of the study group were as follows
• to identify the underlying mechanisms leading to droplet formation,
• to clarify ways in which the size and number of droplets could be reduced
• to understand how the efficiency of the process depends upon the shape and position
of the cathode.
2 Formation of pits by an electric arc
The electric arc in the coating process is initially formed by placing an earthed wire
in contact with the cathode. The arc formed by this procedure vaporises some of the
Titanium of the cathode forming a cloud close to the cathode. The arc is subsequently
maintained by a flow of high energy positive ions from the cloud to the cathode. The
effect of the bombardment of the ions is to heat up the cathode. This not only melts
and vaporises the cathode but releases electrons from the cathode surface. The electrons
ionise the Titanium vapour and the process continues. During arcing there are currents
of about 50A due to the electrons emitted from the cathode and about 5A due to the ions
leaving the cloud surface, eventually reaching the target which they coat with Titanium.
The bombardment of the cathode by the energetic Titanium ions results -in the for-
mation of pits on the cathode surface which are the source of both the Titanium vapour
and the Titanium droplets. Typically a pit will grow and when it reaches a critical size
will stop growing and a new pit will form at another point on the cathode.
Experiments indicate that a typical pit size is around 10Ilm and a typical time for pit
formation is around Sans. We tried to do some experiments to see how the pit size was
related to arc current but were unable to make the required measurements. Some of the
literature indicates that pit size is proportional to the arc current. We indicate below the
processes involved in the pit formation.
o
e
Prr
• Experimental. measurements of pits indicate that they look like splashes - Le. they
look as though a molten pool of metal has been suddenly struck by a large object,
causing droplets to "splash out" at an angle of about 20 deg with respect to the
cathode. A typical such pit is indicated below. It seems unlikely that such a
pattern would be the result of steady ion bombardment.
Figure Scanning electron photomicrograph of
Arc crater
• Further experiments indicate that the pit size is increased if an Aluminium cathode
is used rather than a Titanium one and that it is reduced if Nitrogen is introduced
into the chamber. The location of the pits can be partially controlled by the appli-
cation of an external magnetic field but otherwise the location of the arc (and the
current "active" pit) tends to move erratically over the electrode.
Our study of the formation of the pits attempted to explain these observations.
3
3 Processes involved in the growth of a pit
The mechanisms involved in the formation of a pit can be summarised by the following
figure
VAPouR c,&.ou 1)
+ -- - J-:
+ le. t
J. - Je- ••• of -
sov
Here the ion cloud is at an (observed) potential of about 50v with respect to the
cathode. From this cloud there is an ion current density of i. bombarding the cathode
which releases an electron current density of i; The pit is of size a and temperature T.
The energy input to the pit is a combination of the energy of the bombarding ions
and the ohmic heating effect of the electron current.
This energy is lost through conduction, melting the Titanium, vaporising the Titanium
and in ejecting the micro-droplets.
It is possible to compare the magnitude of these effects by using known properties of
the materials.
Energy in
4
• Measured electron current = 50A
• Electron current density for a pit of radius 10J,L = a
. 50 OllA -2Je = ( 5)2 = 1.6 x 1 m.
1r X 10-
• Ion current density
• Power of ion bombardment per unit area
where U is the "cathode drop" potential of about 50v. Thus
• Power of ohmic heating per unit volume
where s = 150 X 10-8 is the conductivity of Titanium. Thus
Wo ~ 3.75 x 1016wm-3.
We note that vVo x a ~ W B. This indicates that the effects of ohmic heating and of ionic
bombardment are comparable.
Energy out
• The timescale to heat a volume a3 of Titanium with density d = 4500kgm-3 and
heat capacity c = 500 to its melting point of Tm = 1 600K is
This figure agrees with the experimentally observed value for the time of pit forma-
tion.
• The timescale to melt a volume a3 of Titanium with latent heat of melting Am is
t-. = Amdaj(woa + WB) ~ IOns. which is again about right.
• The timescale to vapourise a volume a3 of Titanium liquid with latent heat of
vapourisation Av = 9 X 106 is
This is rather longer than the time for the existence of the pits. We conclude that
during pit formation only part of the molten Titanium will be vapourised and that
the ramainder must be ejected as micro-droplets.
5
(We also note that the timesca.le for heat loss by conduction, given a conductivity k = 20
IS
tc = dca2 / k ~ 1OOOns :» 50n.
Thus heat loss by thermal conduction may be neglected.)
4 Electron Emission
During the ion bombardment, electrons are emitted from the surface of the cathode and
it turns out that understanding this process gives a vital clue into the mechanisms behind
the formation of the micro-droplets.
The emision of the electrons is (according to literature) governed by three processes,
thermionic emission, quantum mechanical tunnelling and (appropriately) a mysterious
process called "Nottingham heating". Of these, only thermionic emision is significant. In
this process the electron current density je is proportional to temperature T so that
A graph of this function is given below
•Jt
~ ~~ ~~T
Essentially the thermionic emission process acts like a switch in that je is quite·in-
significant if T < 5000K and takes the, measured, valve of 1.611Am-2 when
T = 7600K
which is significantly greater than the melting point of Titanium at 3 300K. We conclude
that to reach this high temperature the molten Titanium in the pit must be superheated.
This superheating may be caused by the high pressure P of the ion bombardment
given by
P = ji (2~m) = 2.21 X 107Pa
where m = 7.68 x 10-26 Kg is the ion mass, e the electron charge.
(We note that the impulse I due to this pressure is I = Pa2tp where tp is the pits
formation time. If this impulse is transferred to the Kinetic energy of a microdroplet
travelling at speed v then
This gives an, approximately correct, value for the droplet velocity.)
6
5 A possible mechanism for micro-droplet formation
Existing models for pit creation postulate a "steady state" in which the electron-eI?ision
is just sufficient to ionise the cloud of Titanium vapour to produce more ions and thus
more electrons. In these models it is postulated that the pit grows until it is so large that
the total current 7ra2i, is greater than the available current from the power supply.
We find this unsatisfactory for two reasons, most significantly the photographs of the
pit resemble those of a sudden explosion and secondly the extreme sensitivity of i, to
the cathode temperature would seem to rule out any "slowly evolving" process.
An alternative mechanism was proposed to overcome these objection, starting from
the presumed existence of an ion-cloud and no "active" pits.
1. The ion cloud would drift over the cathode (perhaps under the action of a magnetic
field) until it encountered an imperfection at which the electric field was higher than
elsewhere.
2. Positive ions would move to wards the cathode under the action of the field. These
ions would bombard the cathode melting it and raising its temperature.
3. At a critical temperature the electron current emision from the cathode would rise
rapidly (here the thermionic emission is acting like a switch). The electrons quickly
move into the ion cloud causing significant new ionisation.
4. As a consequence of this ionisation there is a huge new pulse of ions bombarding the
cathode. This pulse drives out the melt causing the "splash" like picture observed.
Following the expulsion of the melt the remaining cooler cathode cannot maintain the
electron emision and the process stops.
A further modification to this picture, proposed by JRO, arises if we postulate a fixed
ion density in the cloud. Whilst the ions bombard the cathode the high ion pressure
prevents the metal from vaporising. However, if the pressure due to the ions drops (ei-
ther because their number or their velocity decreases), then the (superheated) melt will
explode. The speed of sound in molten Titanium is of the correct order of magnitude for
this to be a feasible process. In fact it is not necessary to invoke a supersonic flow for
this; vapourisation within the body of the melt will cause a large volume change that will
eject molten metal. This picture seems quite plausible in view of the simple arguments
below.
We can now make some qualitative predictions from the above model
• If an Aluminium cathode is used then i; has the same dependence upon temperature
but Aluminium has a lower melting point. As a consequence, more Aluminium will
7
melt until the critical temperature when electrons are released. Thus the size of the
pits in Aluminium will be greater .
• If Nitrogen is introduced into the chamber then (it is believed) the critical temper-
ature at which electrons are released is lowered. As a consequence the pits have less
time to grow and their size is smaller.
Both of these predictions agree with experiment.
• Following the critical temperature at which electrons are emitted the melt will heat
up by ohmic heating so that
dT ex: J.2 ex: T4e-B/T
dt e
where B = 90 OOOK. Although this equation would appear to provide the possibility
of finite-time blowup (T becoming infinite in a finite time) we must recall that other
factors such 'as the electric field are ommitted and that temperatures much above
7500 would lead to considerably higher currents than the apparatus can support. It
is the exponential, with the large value of B in this equation, rather than the fourth
power of T, that predicts a rapid acceleration in the growth of temperature. Thus
T (and hence je) will rise rapidly. This will cause the melt both to heat and to grow
(by conduction) although its size a and hence the temperature itself are limited by
the available current i.e.
where I is the available current from the supply.
The current can only stay within limits if the voltage between the cloud and the
metal surface drops. This, in turn, will reduce the pressure of ion bombardment
allowing the superheated melt to begin vapourising rapidly which, in turn, will drive
molten metal away from the cathode. The fact that a reduced ion bombardment
will still be taking place suggests that the ejected metal would be deflected sideways,
partly explaining the creation of the kinds of "splashes" that are observed.
The equation (*) indicates that the maximum pit size will depend upon I in some
manner. It would be useful to determine this dependence, but although attempts
were made at the study group, we were not able to make the relevant experimen-
tal measurements and there was not sufficient time to make reasonable theoretical
predictions.
8
6 The effect of the cathode geometry
If our model of an impulsive "splash" or of a deflected ejection of liquid producing the
micro-droplets is correct then, as the resulting droplets emerge at a "low angle" with
respect to the cathode, there may be ways to change the shape of the cathode so that
fewer droplets reach the target. One suggestion is that the cathodes could be concave i.e.
oo
\ , ,, , < , ,,,,-
There were two objections to this. Firstly that after a large number of pitting events
the local surface of the cathode would be so irregular that global changes would be
irrelevant. Secondly, that markedly reduced efficiencies of deposition on the target were
recorded for concave cathodes.
The latter effect is most interesting. Presumably the ion deposition on the target is due
to the macroscopic field distribution and using a concave cathode significantly effects this
(e.g. by lowering the field and causing more ions to come back to the cathode rather than
reaching the target). This would be an interesting area for future work! (See CJB work
9
Equipotentials for a flat cathode
200~----~~~-.-r.--,~-,~~~ __ ~~~~ __ ~~~
J 11 J ~ \ ~
cv 0
- 0
I
150
Cl)
o
cco
.~100
"0
.~
x<l::
50-1---
I ( I I I I I I ' , I ' I ' , I '
50 '\ 100 150
IN51J L..ATQ~
200 250 300 350
Radial distance
-
) , 4• 4' ~~ ,..
I -- -, - -, , 4 4' 4
~ I • I
~ ~ 4, ~~ ~ ~ ~ , ~ ~
-
~z
ov
400
on the space-charge equations.) Some preliminary field calculations in an axi-symmetric
geometry were made by RS and are included in this report.
7 Conclusions
We appear to have arrived at some reasonable descriptive models for the processes taking
place at the cathode. Estimates of time-scales, sizes and currents etc. all seem to be
consistent with observations, so that we may be reasonably confident that the models are
not wildly incorrect. However, we would recommend that the work be taken further in
the following ways:
• Determine the relationship between pit size and arc current
• Determine the relationship between arc current and droplet size
• Calculate the macroscopic field around the cathode in the presence of space-charge
and estimate the effect of cathode geometry on ion transport.
• Consider the effect of external magnetic fields.
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Micro-droplet formation in high current vacuum electroplating

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