A coating thickness uniformity model for physical vapour deposition systems: overview

E L S E V I E R Surface and Coatings Technology 71 (1995) 16-29

A coating thickness uniformity model for physical vapour deposition systems: overview

K.S. Fancey Research Centre in Surface Engineering, Department of Engineering Design and Manufacture, University of Hull, Hull HU6 7RX, UK

Received 25 January 1994; accepted in final form 12 April 1994

Abstract

A coating thickness uniformity model, for physical vapour deposition (PVD) in low-pressure gas, is described. The model is derived from consideration of the proportions of non-thermalised and thermalised vapour fluxes arriving at the front and back surfaces of thin fiat substrates. Here, front and back refer to surfaces facing towards and away from the vapour source respectively, and it is shown that R = coth(s/21), where R is the front-to-back coating thickness ratio, s is the source-to-substrate distance, and l is associated with the mean free path for vapour thermalisation. Experimental work, which has been performed to test the validity of the model under various deposition conditions, is reviewed and updated. The results demonstrate that the model can be applied to PVD by thermal evaporation (using resistive or electron beam heating), and to plasma-based systems which employ magnetron sputtering or cathodic arc evaporation sources, or which operate under ion plating conditions. Data from the model can be used for predictive purposes or to provide information on phenomena such as vapour particle thermalisation and virtual source effects.

Keywords: Coatings; Thickness; Uniformity; Vapour; Thermalization

1. Introduction

Coating thickness uniformity can be an important factor when selecting or optimising a deposition process for a particular application. For physical vapour deposition (PVD) techniques, frequent use is made of rules derived from the cosine law for idealised vapour sources [1] . In practice, however, their applicability can be restricted since (a) real vapour sources operating at practical emission rates rarely exhibit ideal behaviour and (b) many PVD systems operate under 'soft' vacuum conditions, where scattering of vapour particles by the ambient gas between source and substrate significantly reduces the probability of linear trajectories assumed by the cosine law. Nevertheless, the interest in modelling radial coating thickness uniformity has led to, for example, empirical modifications and computer-aided methods based on cosine law emission characteristics for various PVD systems [2 -5 ] .

The presence of a low-pressure gas is often essential to the operation of many PVD systems, particularly when plasma-assisted PVD, such as ion plating, is utilised E6]. An inert gas (usually argon) may be used with or without the presence of plasma to cause scattering of the vapour, thereby allowing substrate surfaces remote from the vapour source to become coated. Thus accept-

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able coating thickness uniformity can be achieved on all component surfaces by utilising the effect, either on its own, or to augment the benefits obtained from substrate movement and manipulation methods during deposition. Although this scattering phenomenon, which is strongly dependent on source-to-substrate distance, has been exploited for many years [7] , attempts to model the behaviour seem to have received less attention in the literature than radial thickness uniformity.

The objectives of this paper are to review and con- solidate some recent work on a simple model, which establishes a relationship between the influence of gas- scattering effects on coating thickness uniformity and source-to-substrate distance. Although information from this model has been published elsewhere, significant findings have been confined to conference proceedings; moreover, this paper provides the opportunity to reinter- pret some of the earlier results or inferences, which may have led to erroneous conclusions, and to update others in the light of new information.

2. Model development

The general approach to modelling coating thickness distributions in PVD tends to rely significantly on the

https://www.researchgate.net/publication/256368674_Film_thickness_distribution_in_magnetron_sputtering?el=1_x_8&enrichId=rgreq-58adf07c-4e90-4ac4-8776-39e1912f9a3d&enrichSource=Y292ZXJQYWdlOzIyMzQ4NjY5MztBUzoyNzM4OTg1ODMzNTk0OTFAMTQ0MjMxMzkxOTQ2Mg==

K.S. Fancey / Surface and Coatings Technology 71 (1995) 16 29 17

use of computer-aided techniques [3-5,8-12]. Although computer-based models can yield results which compare well with experimental data, they are frequently limited to specific situations and some may require long compu- tation times. As an alternative to considering the behaviour of individual vapour particles (an approach often favoured by computer modellers), the situation could be viewed macroscopically to produce a simple relationship between process control parameters and thickness uniformity. An early attempt at this approach was to develop a general empirical relationship, which related thickness uniformity to gas pressure, source-to-substrate distance and substrate area [13]. The relationship was subsequently found to have a limited range of applicability [14,15] however, and a more appropriate model 1-15-17] has been proposed using the following analysis.

Fig. 1 shows the basic principles behind the model. The geometry of the vapour source and substrates allows us to limit consideration of the vapour flux motions to upwards and downwards directions only. The thin substrates are small compared with deposition chamber dimensions, so that they can be assumed to have no influence on vapour movement. The vapour can be considered to have two components, these being non- thermalised and thermalised fluxes. The former arises from the fact that even for materials vaporised by direct

PROPORTION OF NON-THERMALISED

FLUX

e x p ( - s / l )

PROPORTION OF THERMALISED

FLUX

1 - e x p ( - s / l )

' I

1 '

1 • ~"~ . COATED v ~ ~ , : : ~ SUBSTRATE

VAPOUR SOURCE

Fig. 1. Schematic showing the basic principles of the coating thickness uniformity model.

heating, such as resistive or electron beam (EB) evaporation, the energy carried by the vapour as it leaves the source could be 5-10 times greater than that of the ambient scattering medium. Titanium, for example, has a melting temperature close to 2000 K and, if evaporated into a gas at room temperature (290 K), the vapour will leave the source with a seven-fold increase in initial energy over that of the scattering medium. Should plasma conditions be present, the ionised gas species in the plasma would not be expected to have a significant influence on the overall gas temperature, since their temperatures will typically be 500 K [ 18]; also, even in PVD plasmas which have been enhanced (e.g. by using RF biasing or thermionic support), the degree of ionisation for gas species is unlikely to exceed 10 - 4 in magnitude, based on electrostatic probe data [19,20]. With or without plasma, however, heat transfer effects from the vapour source would increase the gas temperature, although this may only be significant (in relation to successful operation of the model) for gas in close vicinity to the source.

The non-thermalised flux is assumed to have no downward component of motion and its relative proportion decreases exponentially with source-to-substrate distance. As the non-thermalised flux decays with distance, the proportion that is thermalised increases. This reduces the front-to-back coating thickness ratio ('front' representing substrate faces pointing towards the source), as the thermalised flux, being in thermal equilibrium with the ambient gas, is assumed to have no preferential direction. Hence the thermalised flux has upward and downward components of equal magnitude. Expressing these arguments mathematically:

The amount of non-thermalised vapour moving upwards

= C e - sj' ( 1 )

where s is the source-to-substrate distance, l is a mean free path associated with thermalisation and ~ is a function of s to account for the progressive dilution of the vapour flux; thus for an ideal point source, for example, ~O would be expected to follow an inverse square law with s.

The amount of vapour completely thermalised

= ~ ( 1 - e ~/;)

.'. Thermalised vapour moving upwards -

(2)

~O(1-e -ss)

2 (3)

.'. Total vapour moving upwards = Eq. ( 1 ) + Eq. (3)

~(1 + e-s/l) - (4)

2

.'.Total vapour moving downwards = Eq. ( 2 ) - Eq. (3)


18 KS. Fancey / Surface and Coatings Technology 71 (1995) 16~9

~,(1 - e - s/t) - ( 5 )

2

Assuming that the front-to-back coating thickness ratio R depends only on vapour arrival rates, then dividing Eq. (4) by Eq. (5) gives

R = ~ _ e- s/~ - coth (6)

Eq. (6) may be transposed, so that

s I = (7)

- In [ ( R - 1 ) / (R + 1 )]

The model can therefore be verified from experiment by considering Eq. (7). Since s and R can be obtained from experimental data, plotting s versus -ln[(R-1)/(R+I)] will yield a linear relationship of gradient l, if the model is valid.

The basic requirement would be to test the validity of the model under gas evaporation conditions (i.e. evaporation into argon gas with no plasma). Nevertheless, its applicability to ion plating and deposition with plasma- based vapour sources (i.e. sputtering and evaporative arc) also needs consideration because of the industrial significance [6]. Ion plating involves the deposition of vapour onto substrates in a low-pressure abnormal glow discharge (usually of argon); the substrates are negatively biased with respect to the plasma in which they are immersed, so that (positively) ionised gas and vapour species can energetically bombard the growing coating by accelerating across the (thin) cathode sheath which surrounds each substrate. The effect of this energetic bombardment is to produce dense, well-adhered coatings at low substrate temperatures. Similarly, magnetron sputtering and evaporative arc vapour sources can emit particles which have significantly higher energies than those obtained from thermal evaporation sources. Although the model does not account for influences that higher energy deposition may have on coating uniformity, any effects can be expected to be made less significant by consideration of R rather than actual coating thicknesses.

3. E x p e r i m e n t a l

To perform the validity tests, four PVD coating units were utilised (designated Rigs A-D); Table 1 gives further details. The gas pressures used during deposition were in the range 4-10 mTorr. The general layout for PVD with an EB vapour source (Rigs A-C) is shown in Fig. 2(a). All EB vapour sources comprised a differenti- ally pumped 225 ° bent beam, impinging onto a melt held in a water-cooled copper crucible. Thin flat substrates (usually four) were mounted horizontally around

a vertical supporting rod positioned centrally above the source, the main concern being that adjacent substrates or supporting structures would have no significant influence on the arriving vapour flux. For gas evaporation in Rig A, no bias was applied to the substrates except for sputter-cleaning purposes prior to deposition. RF ion plating in Rigs A and B was achieved with a capacitively coupled power supply connected between the substrate feedthrough and the grounded deposition chamber. The relatively small area of the substrate assembly made itself cathodic with respect to the chamber walls; the resulting d.c. offset voltage dropped across the cathode sheath caused the substrates to be subjected to ion bombardment from the plasma. A low-frequency (380 kHz) RF supply was used in Rig A, which avoided the need for an impedance matching network, whereas Rig B utilised a more conventional 13.56 MHz supply. The thermionic emitter assembly, shown in Fig. 2(a), was only used under d.c. reactive ion plating conditions (Rig C). The emitter enhances the glow discharge, ena- bling higher substrate current densities to be obtained at lower bias voltages and gas pressures, which in turn provides significant improvements in coating properties when compared with simple d.c. diode ion plating [6,21].

In addition to deposition with an EB vapour source, Rig A was used for performing gas evaporation with a resistively heated tungsten wire basket suspended 7 cm above the chamber base; the layout was otherwise similar to Fig. 2(a). The study of model performance with magnetron sputtering and arc evaporation sources was performed on Rig D. This was facilitated by employing a single multifunctional source [22], comprising a rectangular d.c. planar magnetron with a titanium cathode, mounted on one of the chamber sidewalls (Fig. 2(b)). This could be operated as a conventional balanced magnetron sputtering source or as an unbalanced magnetron by removing the inner magnets, the latter case causing a significant proportion of the plasma ion flux to reach the substrates [23]. Furthermore, the magnetron could be modified to operate as a cathodic arc evaporation source, the magnetic fields restricting cathode spot motion to the sputtering erosion track shown in Fig. 2(b). For all three operation modes, the substrates were mounted in front of the magnetron in a 'stepladder' pattern on a grounded supporting assembly.

After deposition, coating thicknesses were measured at the centre of each sample face by the ball crater technique [24,25]. For each sample face, at least four craters were made and usually four thickness readings were taken from each crater scar, from which the mean and standard error were calculated. Coating thicknesses were in the submicron to tens of micron range. In some cases, with relatively thick coatings, the residual stresses developed during deposition resulted in the production of inferior craters; here, scanning electron microscope fractography was alternatively employed.

K.S. Fancey / Surjace and Coatings Technology 71 (1995) 16 29 19

Table 1 Details of the PVD equipment used to investigate the validity of the coating thickness uniformity model

Rig Deposition technique Source Vapour source material dimensions

Deposition Range of chamber source-to- dimensions substrate

distances used

D

Gas evaporation with EB gun source Ti, Al, p y s z a

380 kHz RF ion plating with EB gun source Ti

Gas evaporation with resistively heated source AI (tungsten wire basket)

13.56 MHz RF ion plating with EB gun source PYSZ

D.c. thermionically enhanced reactive ion plating Ti with EB gun source; plasma gas comprised Ar with 10% N 2 to produce '[iN coatings

Multifunctional vapour source to provide Ti cathodic arc evaporation, balanced and unbalanced magnetron sputtering

Crucible internal diameter = 4.8 cm Crucible internal diameter - 4.8 cm Basket approx 1 cm diameter, 1 cm deep

Crucible internal diameter = 6.5 cm

Crucible internal diameter = 6.0 cm

40z40x40cm 5 35cm cube 40x40×40cm 5 20cm cube 40 × 40 × 40cm 10.5 25.5 cm cube

'D' shaped in plan 15 45 cm view, 60 cm minimum width, 70 cm high

70x70x70cm 24.5 52cm cube

Rectangular 60 × 70 crn base, magnetron target, 50 cm high 38 x 10 cm

10 32.5 cm

a PYSZ = partially yttria stabilised zirconia

4. Results and discussion

4.1. Gas evaporation

Fig. 3 shows plots of the model in accordance with Eq. (7), for EB gas evaporat ion of t i tanium in Rig A at three argon gas pressures. The relationships appear to be linear, indicating model validity. The solid lines represent linear regression (least squares) fits to the data, using the assumption that errors in s insignificant compared with errors resulting from R (this assumption had been over looked in previously published results from the model; however, the effect on linear regression data is minimal). It is interesting to note f rom Fig. 3 that the extrapolated plots show small positive intercepts on the y-axis. These may be at tr ibuted to systematic error or to a phenomenon not accounted for in the model, such as substrates impeding the vapour flow or variations in coat ing microstructural density which, under certain conditions, might influence some R values. Nevertheless, the intercepts have been generally observed with all deposit ion runs utilising thermal evaporat ion, and they are thought to represent the height of the 'virtual source' above the melt pool [16,17]. The virtual source may be a dense vapour cloud, as suggested by Smith [26] , from which the vapour appears to originate.

The results in Fig. 3 also show that the gradient I decreases as the argon gas pressure is increased, supporting the not ion that l is a measure of thermalisat ion distance. Further evidence of this is demonst ra ted in Fig. 4, which indicates that I is inversely propor t iona l to the gas pressure; in addition, extrapolat ing the plot gives a prediction for I which is comparable to deposit ion

chamber dimensions for evaporat ion without the presence of argon gas. If t i tanium is evaporated into an ideal vacuum, and the vapour is assumed to consist only of free atoms, I might be expected to be infinite. The apparent ly finite value for 1 at zero argon pressure may, however, be at tr ibuted to effects such as residual gas in the chamber (e.g. desorbed gases) and, with particular reference to the virtual source region, the mutual scattering of vapour particles. Furthermore, close inspection of the data suggests that the relationship in Fig. 4 is subli- near; a curve could be drawn through the data points to the origin of axes. Clearly, with such limited data, the curvature may be due to experimental error. Nevertheless, the observat ion that I decreases at a slightly slower rate than the gas pressure increases could be due to real effects. For example, radiant heat from the vapour source would be expected to lead to localised gas rarefaction, whose influence on l might not be straightforward as gas pressure is increased. Other phenomena, such as the possibility that at least some of the metal vapour comprises a tomic clusters, might also have a role; these clusters are believed to be formed by homogeneous nucleation [27,28]. Larger clusters would be expected to exist at higher gas pressures and, a l though they might radiate heat (unlike free atoms), their presence could increase l (in compar ison with smaller clusters and free atoms), if energy losses through collisions are considered [15,27].

The effect of using different source materials for EB evapora t ion in argon gas at 10 mTorr can be seen in Fig. 5. Note the different gradients for each material; factors which are most likely to influence l here are source temperature (which determines the initial energy

20 K.S. Fancey / Surface and Coatings Technology 71 (1995) 16-29

DC/RF BIAS OR EARTH t

SUBSTRATES AND %

S U P P O R T I N G ~ I ASSEMBLY

vr--Ar GAS

PLAN

EB GUN THERMIONIC SOURCE EMITTER

EROSION r R A C K ~

• ~ " - - M A G N E T R O N SOURCE

(b)

Fig. 2. Experimental layouts used for testing model validity: (a) gas evaporation and ion plating with an EB vapour source (Rigs AC); (b) PVD with a magnetron source which can operate in cathodic arc evaporation, or balanced/unbalanced sputtering modes (Rig D).

of vapour particles) and the mass of the vapour particles compared with argon atoms (which influences scattering angle and other collision-related phenomena). Thus aluminium, for example, with small atomic mass and low melting temperature, might be expected to give a relatively small value for l.

Fig. 6 indicates how evaporation rate can affect coating thickness uniformity. Here, an approximate doubling in evaporation rate for the EB evaporation of aluminium seems to have significantly increased the virtual source height but has had little effect on I. Clearly, the higher

virtual source is explained by the vapour cloud above the real source becoming larger at the higher rate. The large error bars on the upper plot in Fig. 6 are due to the x-axis log function expanding the measurement errors in R as the latter approaches unity.

In Section 2, a major assumption in the development of the model was that the substrates are small in comparison with deposition chamber dimensions. It is interesting to speculate as to whether there is a minimum substrate size for successful operation of the model. The data in Fig. 7 provide some information in this regard;

K. S, Fancey / Surface and Coatings Technology 71 (1995) 16 29 21

20 5.1 mTorr . . . . . . ' / " c o r r o o e f f • 0.9942 / /

s ,-15.01om / 7 / (cm) \ , n t o o t . . o 3 , om / /

l O . O m , orr

/ / / c o r r c o e f f • 0.9992 / / \ / I • 9 .68 cm

I / / / ~ intcpt-+1.61 cm 10 / / , , ~ / ,~ ' ; = 7.6 mTorr

/ / t , , , / corr coeff • 0.9964 / / / , / l -11.50 cm . / / / ,°to°t • .134 om

4*~ I :::::" i : : ' " 8 4 2 1 .4 R

0 / iI I I i i ,

0 0 . 5 1 1 .5 2

- in [ ( R - 1 ) / ( R * I ) ]

Fig. 3. Model results for EB evaporation of titanium in Rig A at different argon gas pressures onto copper substrates, 3 × 3 × 0.1 cm; evaporation rates were 0.14 0.19 g rain 1. Error bars represent standard errors; data points from [16,17].

0.1

1-1

( c m -1)

0 . 0 5 °.

c o r r c o e f f • 0.9984 I (when PAr" O) • 35.16 cm

l x PAr ( f rom g r a d i e n t ) - 132.4 mTorr.cm

0 i - - J 0 5 PAr (mTor r) 10

Fig. 4. Plot of gradient data from Fig. 3, demonstrating inverse proportionality between / and argon pressure.

EB gas evaporation of titanium has been performed on substrates of different widths, d. The results for d = 2 cm and 3 cm are similar (within the limits of experimental error), yet the values for R when d = 9 mm are comparatively low, yielding a negative intercept value on the y- axis. Although the evaporation rate was slightly lower for the latter case (by about 20%), this would not be expected to give a negative intercept. The negative value might imply that there was no virtual source or that the source was emitting from a lower level, caused by depletion or 'burrowing' effects. Since the former is unlikely and subsequent inspection of the melt revealed no evidence of the latter, the effect may be an indication

of the model breaking down when substrates with very small dimensions are used. A possible explanation is that the model is less appropriate when a substrate dimension becomes comparable to the mean free path (2) between collisions by vapour particles. From the calculations of Westwood 1-29], 2 for a vapour atom in 10 mTorr of argon gas at (assumed) room temperature is about 6 ram. Heat from the vapour source and the possible presence of atomic clusters would obviously influence this value; nevertheless, 2 would be expected to be comparable to d = 9 mm. Under these conditions, the probability of non-thermalised vapour particles (which are assumed to move only in an upward direction)


20

S

(cm)

10

0

z , , c o . , ^ . 7 - - ' / " ' / " ' corr coeff 0 . 9 9 9 8 ~ / / / I - 11.51 cm "~,, / / / intcpt =.2.07 cm , =/~.__~___~ , / , / ~ A L U M I N I U M

_ _ / / ~ ~ c orr co ell = 0 . 9 9 8 3 , n t c p t ! " 8.18.÷1.84cm cm

8 4 2 1.4 I I

0 1 3

1.2 R I

2 -In [(R-1)/(R+I)]

Fig. 5. Model results for EB evaporation (Rig A) in argon gas at 10 mTorr of different evaporant materials onto copper substrates, 3 x 3 x 0.1 cm; evaporation rates were 0.026 g min- 1 (zirconia), 0.050 g min- 1 (aluminium) and 0.143 g min- 1 (titanium). Data points from [ 17].

40

S

(cm)

20

0.105 g/mln corr coeff • 0 . 9 9 7 4 ~ ~ • I = 8.85 cm intcpt • ÷6.69 cm

. ~ ~ ' " 0105 glrnin "" 4 / / corr coeff • 0.9983

o." " ' " j

.-'" 4 2 L I I

0 1

1 • 8.18 cm intcpt • ÷1.84 cm

1.4 1.2 1.1 1.05 R I I t i I I I

2 3 4 -In [(R-1)/(R+I)I

Fig. 6. Model results for EB evaporation (Rig A) in argon gas at 10 mTorr of aluminium at different evaporation rates; 3 x 3 x 0.1 cm copper substrates were used for the 0.05 g min -1 run and 7.5 x 2.6 × 0.1 cm glass substrates were used for the 0.105 g min -1 run. Data points from [17].

striking the front faces of substrates may be reduced, since the angle from which the particle approaches must become more critical. For thermalised particles, this effect has less significance because they are assumed to have equal probability of striking front or back faces; hence the values for R must be reduced.

4.2. Ion plating

A direct comparison between gas evaporation and RF ion plating in Rig A can be seen in Fig. 8. The ion-

plated case shows a small but significant improvement in uniformity, despite the slightly lower gas pressure used. This is probably caused by increased coating densification and sputter removal effects during ion plating, which may be expected to reduce R when compared with gas evaporation. Clearly, true thermalisation distances are less appropriately represented by l under ion-plating conditions.

When the influence of energetic bombardment during ion plating becomes very severe, interpretation of parameters derived from the model may be less reliable. An

K.S. Faneey / Surface and Coatings Technology 71 (1995) 16-29 23

2O

S

(cm)

1OF

0 ' "

d- 2.0 cm ~ ~ / ¢ corr coef f • 0 . 9 8 3 6 \ / / / /

1" 10.67 cm N / / / / 8UBSTRATE intcpt • +0.92 cm " ~ " / / /

(0.1 ¢m thlok) / / " / j . \7,- 3 . 0 o °

' d / / / " / corr coe f f - 0.9992 / / ~ t - 968 cm / S n=°c°

/ / , -o.9cm . / ~ " _ / corr coeff -0 .9999

~..././ ..4~" ! • 9.98 cm i / oo //,." ...'" intcpt • -0,61 cm

4 2 1.4

0 .5 1 1.5 2

- In [ (R-1) / (R+I ) ]

R

Fig. 7. Model results for EB evaporation (Rig A) in argon gas at 10 mTorr of titanium onto copper substrates of different widths; evaporation rates were 0.113 g rain -1 (d=0.9 cm), 0.140 g min -1 (d=2.0 cm) and 0.143 g min -1 (d=3.0 cm). Data points from [17].

2O

S

(em)

10

0

GAS EVAPORATED (PAr" 10.0 m T o r r ) ~ ~ / / / = ~ / o: r9.C6~. : f : 0.9992 / /

intcpt - +1.61 cm / /

~ ~ RF_IO N pLATED (PAr" 9.5 t/1Torr) / / corr c o e f / ~ , 8,88 ;m 0.9968

intCpt • ÷1.66 cm

/ /

8 4 2 1.4 1.2 R I I I _ _ [ I I I - - 1

0 1 2 3 -In [(R-1)/(R+I)]

Fig. 8. Model results for EB evaporation (Rig A) in argon gas of titanium onto 3 x 3 x 0.1 cm copper substrates to study the influence of RF biasing; evaporation rates were 0.130 g min-1 (ion plating) and 0.143 g rain-1 (gas evaporation). Data points from [ 16,17 ].

example of this is shown in Fig. 9. Here, zirconia was RF ion plated in Rig B. When compared with the zirconia data in Fig. 5, the result for l is some three times greater than the value anticipated for gas evaporation at a similar pressure; also there is a large negative intercept, which is difficult to explain in terms of vapour source characteristics. With an RF (diode) discharge, the influence of energetic bombardment tends to be greater where the presence of incident coating vapour is less. Thus denser coatings are achieved on substrate surfaces more remote from the vapour source, i.e. at larger

source-to-substrate distances and on the back faces of substrates. It is believed that these effects have made R relatively larger, particularly at distances further from the source; this in turn would increase the gradient and contribute towards the negative intercept observed in Fig. 9 [30].

Fig. 10 shows the results from two runs in which titanium nitride coatings were produced by d.c. reactive ion plating with a thermionic emitter (Rig C). With this type of layout, the intensity of energetic bombardment can be adjusted to match the availability of incident


50

S

(cm)

25

cor r c o e f f • 0 .9853

I • 63 .86 crn

in tcpt • -30 .44 crn

. ' 1

10 5 3 2 R 0 I I I I I iI I r I I

0 0.4 0.8 1.2 -In [(R-1)/(R*I)]

Fig. 9. Model results for EB evaporation (Rig B) of zirconia in argon at 4.5 mTorr under RF ion plating conditions onto 4 × 4 x 0.12 cm stainless steel substrates; evaporation rate was 0.565 g min -1. Data points from [30].

60

S

(cm)

4O

20

NEW MELT co r r coe f f • 0 . 9 9 7 2 - ~ 1- 25.79 cm ~ ~ y in tcpt • *2 .86 cm . / 7 , ~

/~ , / / ' ~ ~ OLD- MELT co r r c o e f f • 0 .9937 I • 14.49 cm

, , , , , ,-~- in tcp t • ÷8.86 cm

, - ,Y ....::.."

4 2 1.4 1.2 1.1 R = I = = I = I L I

0 1 2 3 4 -In [(R-1)/(R*I)]

Fig. 10. Model results for EB evaporation (Rig C) under thermionically supported d.c. ion plating conditions to produce titanium nitride coatings onto 5 x 5 × 0.15 cm titanium substrates; gas pressure was 5 mTorr, evaporation rate was 0.60g min -1. The plots show how changes in the titanium melt can influence coating thickness uniformity. Data points from [31,32].

coating vapour at substrate surfaces throughout the deposition volume [21], resulting in coatings that can have near-uniform density. Hence model results are likely to have more validity here than for the RF case in Fig. 9, as demonstrated by the positive intercepts and realistic values for l in Fig. 10. The two plots in Fig. 10 are, nevertheless, dissimilar, even though they differed only in terms of the condition of the titanium source material used. The 'old' melt had previously been used for 25 runs and periodically replenished with new mate-

rial, whereas the 'new' melt was in unused condition. Although both runs were otherwise identical, the new melt required almost twice the EB gun power to maintain the same evaporation rate provided by the old melt. The molten pool region of the old melt was observed to be smaller and indented, the electron beam almost 'burrowing' into the melt during deposition. This would have resulted in a higher vapour emission rate per unit area of source, giving a denser vapour cloud above the old melt and raising the virtual source height as shown in

K.S. Fancey / Surface and Coatings Technology 71 (1995) 16 29 25

Fig. 10. The smaller molten pool is thought to be caused by partial contamination of the melt by nitrogen; the Ti-N compounds formed can be expected to have higher melting temperatures than pure titanium, thereby con- fining the molten region to that which contains only pure metal [31].

Fig. 10 also indicates that the value of l for the old melt is similar to the result obtained (at the same gas pressure) for the evaporation of titanium (i.e. 15 cm) in Fig. 3, using the smaller EB gun source of Rig A. For the new melt, however, l is longer. This may be caused by the higher EB gun power needed to evaporate the new melt, resulting in greater heat losses, which in turn increases gas rarefaction and lengthens the mean free path between collisions [31].

Further investigations with Rig C revealed that the plasma potential could be raised sufficiently to allow the successful deposition of titanium nitride onto earthed substrates. This change in biasing conditions also influenced the model parameters, the most significant effect being an observed increase in the height of the virtual source as the plasma polential was raised. This may have been caused by changes in the shape of the vapour cloud, arising from increased bombardment of the melt pool by low-energy electrons from the plasma. These electrons would be expected to influence source heating and vapour ionisation [32].

With the abundance of publications on ion plating, the use of data from other published sources would be a stringent test of model performance. Unfortunately, the availability of usable published data seems to be restricted to information from the deposition of metallic coatings by d.c. diode ion plating at different argon gas pressures, where only one substrate is coated in each run. With such data, 1 can only be determined from Eq. (7) by assuming that virtual source effects were negligible. The results, plotted in the same form as Fig. 4, are shown in Fig. 11; despite the uncertainties involved when using such data, the plots are approximately linear. Although data from [33] show some curvature, the regression lines predict finite values for l at zero argon pressure, as observed in Fig. 4.

4.3. D!fferent vapour sources

Fig. 12 demonstrates model validity for gas evaporation of aluminium using the resistively heated vapour source in Rig A. The dotted lines represent data from Fig. 6, for direct comparison with EB evaporation. The value of 1 from the resistive source is very close to values for the EB data, implying that the different source characteristics had little effect on phenomena which would influence vapour particle collisions. When comparing evaporation rates, the virtual source height for the resistive source is relatively low. This is probably caused by differences in coverage and shape of the

vapour clouds over the two types of source; the tungsten basket used for resistive evaporation approximates to a point emitter, so that the vapour cloud may surround the entire source, making its effective centre closer to the position of the real source. This is in contrast to the EB source which is surface mounted in the base of the deposition chamber [ 31 ].

Results from investigations with the magnetron sputtering/cathodic arc source (Rig D) are plotted in Fig. 13. Data from the balanced and unbalanced sputtering modes are so similar that, for clarity, only experimental points from the former are shown. The results demonstrate model validity only for the outermost substrates, the sample closest to the source having better coating uniformity (smaller R) than predicted. Since the pattern is consistent for all three source modes, the effect might be attributed to the influence of source geometry; the comparatively small substrates enable the magnetron source to be considered as two offset line emitters at close range, which may, for example, increase the probability of non-thermalised flux depositing on the back face of the substrate closest to the source, thereby reducing R [31]. Furthermore, the effects of energetic particles emitted by the three source modes require consideration. For example, neutral sputtering gas atoms, reflected from a sputtering target, can have initial energies exceeding that of the sputtered atoms [36,37], possibly of the order of 100eV [36]: the energies of vapour ions emitted from an arc evaporation source are in the range 10-150eV [38,39] and the proportion of vapour which is ionised could be more than 80% [40]. As sputtering thresholds are typically in the order of 20 eV [18], material depositing on the front face of the closest substrate would be the most susceptible to sputter removal by these energetic species (in addition to increased coating densification), causing a relative reduc- tion in R.

Extrapolation of the linear regression lines back to the y-axis in Fig. 13 suggests that no virtual source effect was produced by any operating mode of the magnetron source; the small negative intercepts can be attributed to experimental errors. The result for 1 from the arc source data is more than twice the value obtained from the sputtering modes. Although the size and distribution characteristics of arc-evaporated particles may differ from sputtered material (e.g. macroparticles can be present in the former case [38,39]), a primary cause for the differences in l will be in the initial energies of the vaporised material. For material sputtered by low energy (100's eV) gas ions, the initial energy per sputtered atom is typically 2-20eV [29,36,37,41], which is generally less than the values cited earlier (10--150eV) for arc- evaporated material.

4.4. Vapour thermalisation

Further discussion is needed here on the thermalisation of vapour material. Firstly, it would be useful to


(C/m"ll)| IoLr r8 H i:fl~l N EoY ~3235] 0 / ~ / "

o.1 r- \ . / /

[ S °/

oo o i . . . . . .... ' - . - ,,., • / , " " " . 07' c o r r c o e - 0.9729

I'l'" O ~ 0 / ~ WAN ET AL [34 36]

L, ,,,'" c o r r c o e f f • 0.;712

0 t'"' , , 0 2 0 4 0 PAr (mTorr)

I

6O

Fig. 11. Model validity tests using published data from d.c. diode evaporative ion plating layouts. Resistively heated sources were used in [13] and [33], EB evaporation in [34,35].

3O

S

(cm)

2O

10

EB GUN SOURCE ~ / ~ / / / 0.05 g/rain / I • 8 . 1 8 c m / /

EB GUN SOURCE -~.,,~/// / 0.105 g/rain / / /i~/"~" I • 8 . 8 5 c m / / / ' ~ ' " - - R E S I S T I V E SOURCE

/ / . / 0.17 g / r a i n

/ / / ~ / c o r r c o e f f - 0 . 9 8 8 7

/ / t / I - 7.77 c m

/ ~ intcpt - +2.46 cm / .p"

/ .p" ,-2

i ,,/-

':':" ~ 4 2 1 •4 1.2 1• 1 1 •05 R 0 I I I I I I i I I I

0 1 2 3 4 -In [(R-1)/(R+I)]

Fig. 12. Model results for gas evaporation of aluminium (Rig A) with a resistively heated vapour source at 10 mTorr argon pressure onto 3.8 x 2.6 x 0.1 cm glass substrates. For comparison, dashed lines represent data from Fig. 6 using EB evaporation. Data points from [31].

compare I values obtained in this work with thermalisation mean free path data published elsewhere• A survey of the literature indicates that virtually all theoretically based models relating to vapour thermalisation distances are developed only for sputtering sources [29,36,37,42-47]• Usually, these models provide information on the average or total energy of sputtered flux either as a function of background gas pressure, distance from the source, or the pressure-distance product. Unfortunately, the values of I in Fig. 13 for the sputtering modes cannot be equated with thermalisation data published in this form, since l represents the distance at

which the proportion of thermalised flux has increased to 63% (i.e. 1 - e - l ) ; it does not directly represent changes in vapour energy (in this regard, earlier attempts at comparing 1 with data predicted from published models [16,17] are erroneous). The work of Motohiro and Taga [43], however, allows some comparison to be made. Data from their Monte Carlo model predicts that for 63% of the total flux arriving at a substrate to be thermalised, a distance of 23 cm would be required at 4 mTorr argon pressure. This is based on their consideration of silver- and silicon-sputtered fluxes, and they assume that the thermalised flux comprises atoms with

https://www.researchgate.net/publication/222117565_Monte_Carlo_simulation_of_the_particle_transport_process_in_sputter_deposition?el=1_x_8&enrichId=rgreq-58adf07c-4e90-4ac4-8776-39e1912f9a3d&enrichSource=Y292ZXJQYWdlOzIyMzQ4NjY5MztBUzoyNzM4OTg1ODMzNTk0OTFAMTQ0MjMxMzkxOTQ2Mg==


K.S. Fancey / Surface and Coatings Technology 71 (1995) 16-29 27

40

S

(cm)

20

ARC EVAPORATION corr coeff • 0.9959 1 • 51.15 c m ~ ~

/ a S

/ / -

/ / /"

// , ."8 4 t l " i 11

U N B A L A N C E D ~ MAGNETRON ~ SPUTTERING ~ , corr coeff - 0.9995 i / " ~ ! - 21.24 cm

~ - ~ -~- • DATA FROM -~ ~ BALANCED

• "" MAGNETRON ,," SPUTTERING

corr coeff • 0.9935 I - 18.65 cm

2 1.4 R O i I I I

0 0.5 1 1.5 2 -In [(R-1)/(R÷I)]

Fig. 13. Model results for the deposition of t i tanium onto 5 × 3 × 0.05 cm stainless steel substrates using the magnetron source in Rig D at 4 mTorr argon pressure. For each operating mode, the data point closest to the source has been excluded from linear regression analysis. To improve clarity, the regression line and error bars for the balanced magnetron sputtering mode have been omitted. Data points from [31 ].

energies of up to 0.2 eV. Although this upper energy limit for classifying a particle as thermalised might be considered to be high, the predicted distance compares well with the l values for sputtering (about 20 cm) in Fig. 13. Some comparison is also possible with a recent Monte Carlo model by Turner et al. [47]; their results predict a distance of 16-64 cm at 4 mTorr argon pressure for 63% of the flux to have energies of less than 1 eV, depending on whether light (carbon) or heavy (tungsten) sputtered atoms are considered. This predicted range would obviously be longer if the energy limit (1 eV) was reduced to a lower value, but the result might at least be expected to compare with 1 in magnitude.

A second aspect of vapour thermalisation is to note the similarity between the I values for EB gas evaporation of titanium and those obtained from titanium sputtering. For ease of comparison, the product of 1 and argon pressure can be considered. The EB evaporation value from the gradient in Fig. 4 (132 mTorr cm) is probably inappropriate, since it does not include the effects of phenomena, discussed in Section 4.1, which relate to the projected finite value of l in the absence of argon gas. A more suitable result for EB evaporation might be the value based on the 5.1mTorr data in Fig. 3, which is 77mTorrcm. This compares closely with 74 85 mTorr cm from the sputtering runs, even though initial vapour energy in the EB evaporation case will be much lower, at less than 0.2 eV. The most probable explanation is that gas rarefaction (by extending the mean free path between collisions) would have a more significant influence on 1 from EB evaporation, as such sources are operated at substantially higher temperatures

than are sputtering sources. Another possibility is the influence of clusters. Although it is known that atomic clusters can be present in sputtered fluxes, their abundance is uncertain but they seem to exist mainly as dimers and trimers [41]. There is also uncertainty in the existence of atomic clusters in gas evaporation; nevertheless, if present, some may contain the order of 103 atoms [27]. These larger clusters might increase l, as mentioned in Section 4.1.

5. Summary

The overview of results presented in Section 4 demonstrates the applicability of the model to PVD systems. It can be used to provide information on phenomena, such as vapour particle thermalisation characteristics and virtual source effects, which might be difficult to ascertain by other methods. Nevertheless, the following limitations are highlighted: (a) there is evidence to sug- gest that the model will break down if substrate dimensions (other than the considered thickness) become comparable to the mean free path between collisions by vapour particles; (b) sputter removal effects and coating density variations between different substrate surfaces, resulting from the use of plasmas in PVD, may significantly influence the results obtained from the model; (c) vapour source geometry, other than one which approximates to a simple point or surface emitter, may affect model performance, particularly at close range.

Fig. 14 shows the model in graphical form, indicating how R approaches unity as source-to-substrate distance

10

R

40om\ 20 c m

'° I 5


0 0

Fig. 14. Graphical representation of the coating thickness

I I I I I

10 20 30 40 50 DISTANCE FROM REAL OR VIRTUAL SOURCE (cm)

uniformity model, R = coth(s/21), for various 1 values.

increases and l is decreased. Although R can never be unity (according to the model), it can be made very close to this value, though probably at the expense of some other coating property. Thus reducing R by using a larger source-to-substrate distance would decrease the coating deposition rate; making l smaller by increasing the gas pressure may have a detrimental effect on coating microstructure. Smaller values of l would be expected to represent thermal evaporation and sputter deposition processes, whereas larger values will probably be confined to higher energy vapour sources (such as arc evaporation), particularly at low gas pressures.

Provided that the assumptions in Section 2 and the limitations summarised above are not overlooked, the model may be applied to any PVD system where gas scattering of the vapour flux is significant. Although the model is restricted to thin flat substrates, Fig. 14 at least provides an indication of the effects of gas scattering, which in itself has potential uses in, for example, the scaling-up of industrial plant. To date, the model has only been tested with small substrates; however, at longer source-to-substrate distances, it is clear that large- area substrates would also be appropriate if they are small in relation to deposition chamber dimensions. Furthermore, the model has been extended to represent other situations, i.e. for non-horizontal substrates, thick substrates and for multiple vapour sources [15].

experimental data has demonstrated that the model has a wide range of applicability to PVD systems which utilise a low-pressure gas during coating deposition. Results and inferences drawn from the model have been reviewed, giving the following conclusions. (i) There is strong evidence to support the view that

thermal evaporation sources produce a dense vapour cloud close to the melt surface, which can behave as a virtual source. The virtual source characteristics depend on factors such as real source geometry and vapour emission rates.

(ii) The mean free path for vapour thermalisation, which is influenced by the initial energy of vapour particles and the frequency and kinetics of collisions with the background gas, may be significantly affected in PVD systems by gas rarefaction from vapour source heating and the size (and size distribution) of coating particles present in the vapour phase.

(iii) The model can be used as a diagnostic tool (e.g. to investigate the effects of vapour source contamination on run-to-run variability) or to provide some indication of probable coating thickness uniformity within a PVD system. Some caution must be exer- cised, however, when investigating systems which utilise plasma assistance or complex vapour source geometries.

6. Conclusions

A simple coating thickness uniformity model, which considers the role of vapour thermalisation in a background gas, has been presented. The application of

Acknowledgements

I am grateful to the Research Centre in Surface Engineering (RCSE) and the Department of Engineering Design and Manufacture (EDM) for their continuing

K.S. Fancey / Surface and Coat&gs Technology 71 (1995) 16-29 29

financial support. I would like to thank Professor A. Matthews (RCSE), Dr. A. Leyland (RCSE), Dr. P.A. Robinson (EDM) and Dr. G.A. Steigmann (Department of Applied Physics) for their help and useful comments. The work reported utilises data gathered on projects funded with support from the Science and Engineering Research Council.

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A coating thickness uniformity model for physical vapour deposition systems: overview