some aspects of simultaneous evaporation techniques

OPTICA ACTA, 1985, VOL. 32, NO. 5, 557-572

Some aspects of simultaneous evaporation techniques

D. N. W. CHINNERY

National Physical Research Laboratory, CSIR,P.O. Box 395, Pretoria 0001, Republic of South Africa

(Received 16 August 1984; revision received 18 March 1985)

Abstract. In spite of pioneering work by early investigators on the develop-ment of co-evaporation techniques, this potentially useful method of produc-ing intermediate refractive indices is not widely used for making optical thinfilms, probably because of the additional experimental difficulties. This paperdeals with the problem of the spatial variation of the thickness and refractiveindex of co-evaporated layers on rotating and stationary substrates, for whichmathematical expressions are given. The experimental results are broadly inkeeping with the theoretical predictions. The experimental set-up, and theproblems of water adsorption and index measurement are briefly mentioned.

1. Introduction

The desirability of an experimental procedure for producing optical thin filmswith prescribed refractive index values, intermediate between those of existingcoating materials, was first mentioned more than a quarter of a century ago [1].Since then non-available or 'non-technological' refractive indices have been usedin a wide variety of design techniques for multilayer systems [2-7], the latest ofwhich [8] was published in 1982. The concept of a continuously variable indexhas been exploited to the fullest in computer synthesis procedures [9-13].

All such design methods suffer from a common problem, namely a solutionobtained by means of variable indices will nearly always be degraded ultimatelyby having to approximate the ideal index values to the nearest available practicalvalues of existing coating materials.

The equivalent layer concept [14] offers a way out of this difficulty, but oftenat the expense of simplicity in design. Co-evaporation provides an alternativeanswer but with the inherent disadvantage of greater experimental complexity.This disadvantage is probably one of the main reasons why the co-evaporation ofoptical thin films is still a relatively rarely used method compared with the enor-mous volume of optical coatings that are made by evaporation from singlesources. By co-evaporation we mean here the evaporation of two materials fromtwo different sources simultaneously and not, in the sense used by some authors,the evaporation of a pre-mixed compound from a single source.

The potentialities of co-evaporated homogeneous films for optical purposeshave been explored in a limited number of experimental studies [15-24]. Withequipment for the automatic and semi-automatic control of evaporation ratesbeing made more readily available from commercial sources, it is to be expectedthat co-evaporation will receive increased attention in the future as a method forthe production of optical coatings.

D. N. W. Chinnery

The major experimental parameters that determine the refractive index of aco-evaporated layer are obviously the rates of evaporation of the componentmaterials. It is clear that the end result will also be affected by other factors thatcommonly play a role during any evaporation, such as the residual gas pressure,the temperature of the substrate, the rate of condensation of the film, substratecleaning procedures and the internal geometry of the coating plant.

In the study and application of the design methods metioned above, controlledvariation of the refractive index in the third decimal place is often desirable. Anysecondary parameters that are liable to affect the index during coating shouldtherefore be assessed beforehand if possible, so that they can either be eliminatedor at least be taken into account. The following is an investigation of the thicknessdistribution and the closely related refractive index distribution of a layer madeby simultaneously evaporating two materials in the coating plant described in § 3.

2. Distribution equations

The thickness distribution of a coating on a substrate under a variety of condi-tions has been investigated both theoretically and experimentally by variousauthors. Aspects such as the type of source, e.g. either a point source or a directedsurface source [25, 26]; the geometry of the internal components in the bell-jar,e.g. the position of the substrate on the rotary cage and the offset of the sourcewith respect to the axis of rotation [25-27]; and whether the top plate of therotary workholder is domed or flat [28], have been dealt with in considerabledetail. In certain applications, such as narrow-band filters, a uniform thicknessdistribution over the substrate is very important. Rotating substrates, planetarydrives and rotating shutters are therefore commonly used to achieve maximumuniformity [25, 27, 29-31].

In all of the above, the investigations have been confined to normal single-source evaporations. As far as is known the corresponding problem for co-evaporation has not received any attention in the literature, although a ring source[25] could perhaps be regarded as a special case of multi-source co-evaporation.In the case of a two-component co-evaporation there is an additional aspect thatneeds to be considered, namely the possible effect on the compositional distribu-tion resulting from the simultaneous non-uniform distributions of the twomaterials.

The following is a simple theoretical and experimental investigation to assessthe importance of such an effect in a co-evaporation process. A detailed mathe-matical derivation of the formulae set out below has been given elsewhere [32], soonly a very brief explanation will be given here, using the following notation(where the subscripts I and 2 refer to the electron beam and thermal sources,respectively):

fl, f2 Evaporation rates in hertz per second.G,, G2 Corresponding proportionality factors.hi, h2 Vertical distances from plane of substrate to sources (see figure 1).k, k2 Condensation coefficients of the materials under co-evaporation

conditions.ml, m2 Total masses of material emitted per unit time.R1, R2 Horizontal distances of sources from centre of rotation (see

figure 1).

558

Simultaneous evaporation techniques

POINT ON SUBSTRATE

2

SOURCE 1

Figure 1. Internal arrangement of sources with respect to substrate (see the text).

t Thickness of coating at a point P on the substrate (see figure 1).q Radial distance of point P (see figure 1).

PIl, P2 Bulk densities of the evaporants.p Density of the co-evaporated mixture.

D = (h2 + q2 + R2 - 2qR 1)3 12(hl2 + q2 + R2 + 2qR1) 31 2.

E = (h2 + q2 + R22 _ 2qR2)312(h2 + q2 + R2 + 2qR2)

31 2.

2.1. Thickness distribution-rotating substrate

It is considered reasonable to assume that under co-evaporation conditions thematerials from the two sources will combine additively at the substrate. It isfurthermore assumed that both sources have evaporation characteristics thatapproximate those of a directed surface source [25,29]. For the experimentalsituation under consideration the substrate will be regarded as being parallel tothe sources.

It is also convenient to work with the relative thickness t/to, where tm is themean thickness at a radius q (weighted with respect to the angle of rotation) andto is the thickness at q = 0, as this eliminates the unknown density of the co-evaporated mixture. However, it is not possible to eliminate the total masses mland m2 emitted by the sources, which must therefore be determined experimen-tally. The only experimental parameters to which they can be related are theevaporation rates fl and f2 (in Hz s-l) of the materials as measured by the crystalmonitors. If it is tentatively assumed that

ml = Gl fl and m2 = G2 f 2 , (1)

where the proportionality factors G1 and G2 depend on parameters such as thedensity, the internal lay-out of the vacuum chamber, the calibration of the crys-

559

D. N. W. Chinnery

tals and the characteristics of the sources, then the relative thickness of a co-evaporated mixture on a rotating workholder is given by

t_ G, f (h2 + R2)2(h2 + R2) 2 klhl2(hl2 + q2 + R 2)

t - kh2(h2 + R2) 2Glflj + k2h2(h2 + R12) 2G2 f2 D1 ~~ ~2 2 2 1

G2f 2(h2 + R2) 2(h2 + R2) 2 k2 h2(h 2 + q2 + R 2) (2)kxh2(h + R2) 2 Glfl + k2 h 2(h2 + R2)2 G2f 2 E(2)

If only one source is present, then we may put (say) f2 = 0 in equation (2)which then reduces to the normal relative thickness distribution of a singledirected surface source [29]. In a similar fashion, at the centre of rotation whereq = 0, equation (2) becomes tmlt o = 1.

2.2. Refractive index distribution-rotating substrate

It is clear that, in general, the thickness distributions of the two materials willnot be identical and that a compositional variation in the radial direction of aco-evaporated layer can thus be expected, resulting in a similar variation of re-fractive index.

This aspect can be investigated theoretically provided the mass concentrationsC1 and C2 of the component materials in the layer can be obtained. The followingapproximate expression for C1 (say) can be derived:

G1flklh 2(h 2 + q2 + R2)ECr - 2R2EGf 2 2 R2)D C, - I I - - __ I F, -, , ~~~~~~~~(3)

Gfkh(h + q2 + R)E + G2 f 2 kh2(h2 + q2 + R )D

from which the mass concentration of the other component is easily obtained as

C2 = 1 -C 1 . (4)

The radial distribution of the refractive index can thus be obtained by using thevalues of C1 and C2 in either the Lorentz-Lorenz or Drude mixture rules ofclassical optics.

2.3. Thickness distribution-stationary substrate

In the case of a stationary substrate it is assumed that its angular position ismeasured clockwise from source 1, say, and that is the constant angle betweenthe two sources (see figure 1) such that

¢2 = ¢/ -1 (5)

The relative thickness distribution of source 1 alone is given by

t_ (h + R6) 2

tol (h2 + q2 + R2 _ 2qR, cos 6)2 )

with a similar expression for source 2. For a co-evaporated layer we have

ml k l he m2 k2 h2

t (h2 + q2 + R 2- 2qR1 cos ¢,) 2 (h2 + q2 + R 2- 2qR2 cos 0b2)2

to ml k th 2i M2 k2 h (7)

(h2 + R2) 2 + (h2 + R2) 2

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2.4. Refractive index distribution-stationary substrate

An approximate expression for the mass concentration of, say, component I inthe co-evaporated mixture on a stationary substrate is given by the followingexpression: mkh

(h2 + q2 + R' - 2qR1 cos ,b) 2

C1 mlklh m2 k2 h2 (8)(h2 + q2 + R 2- 2qR1 cos ¢) 2 + (h2 + q2 + R2 - 2qR2 cos 2) 2

As in the case of the rotating substrate, the expressions for m1 and m2, given byequation (1), are also considered to apply to the case of a stationary substrate.

3. Brief description of equipment

The equipment in use at the National Physical Research Laboratory (NPRL),Pretoria, for the study of co-evaporation techniques is a standard Balzers ultra-high vacuum system (UTS 500) that is used mainly in the high vacuum range(10-4-10-3 Pa) because of the time factor required to achieve lower pressures.

The vacuum chamber is equipped with two evaporation sources: a simplethermal source and, roughly at right angles to it, a UHV compatible electronbeam gun. Three quartz crystal monitors control the coating process. Two ofthese act only as evaporation rate monitors via standard feedback control systemsto the sources. They are positioned about 250mm above the sources, and each isprovided with a small screen to prevent it from 'seeing' the source that it is notmonitoring. The third monitor is positioned centrally at the top of the vacuumchamber and is used for controlling the thickness of the co-evaporated layer.

The system is provided with three shutters, two of which are immediatelyabove the sources. These are hand-operated and simply cover the sources duringthe preheating and degassing phase. A third shutter, designed and built at theNPRL, is positioned on the rotary workholder so that it opens and closes imme-diately below the substrate. It is operated by means of a solenoid on the top plateof the workholder, that receives power from an electronic control via slip rings.The advantage of such a system is that the rotating substrate remains completelyprotected while the evaporation rates of the two materials are being adjusted andstabilized.

Of main importance to the present discussion is the geometrical layout of theinternal components of the vacuum chamber, since the dimensions will be used inthe calculations that follow.

With reference to figure 1 the following set of geometrical parameters apply tothe above coating plant:

Offset of e-beam source R1 = 95 mm.Mean substrate height above e-beam source hI = 440mm.Offset of thermal source R2 = 145 mm.Mean substrate height above thermal source h2 = 455 mm.

4. Measurement of refractive index

The refractive indices were measured by Abeles' method [33], using a Wattshigh precision goniometer with a beamsplitter attachment that enabled accuratezero readings to be made. This, together with certain additional precautions that

561

D. N. W. Chinnery

will not be elaborated on here, ensured that the refractive index could be mea-sured with a good repeatability to the third decimal place. The index values areexpressed as the mean of five measurements, plus or minus half the range.Although the mean does not necessarily lie at the midpoint of the range, this is aconvenient way of assessing the validity of comparisons between index determi-nations that were carried out at different times. The coatings were stored contin-uously at 22 °C and at a relative humidity of between 40 and 45 per cent. Theindex measurements were carried out under the same conditions.

The films for the index determinations were evaporated on to either SchottK 50 or SF 15 glass substrates that were 50mm long by 20mm wide. A suitablesubstrate holder enabled half of the surface to be coated in the lengthwise direc-tion with a sharp demarcation line between the uncoated area and the 10 mm widecoating; this facilitated the observation of the Brewster angle.

5. Comparison of theoretical and experimental results

Four possible mixtures that are potentially useful from a practical point ofview have been considered in this study. These are the combinations of MgF 2

with the oxides A12 03 , ZrO 2 , Ta2 O5 and TiO2 .In the absence of experimental data concerning the behaviour of materials

under co-evaporation conditions it was necessary to make the following assump-tions regarding some of the parameters in the equations: (1) the nominal bulkvalues were used for the densities of the materials; (2) the condensation coeffi-cients k and k2 were considered to be equal, but not necessarily equal to unity.

An experimental method was used to obtain values for the factors G1 and G2

which arise from equation (1). These factors, which can be termed source masscoefficients for convenience, represent the total masses evaporated from thesources per unit time at a given rate. Direct weighing of the source plus materialbefore and after evaporation, together with measurement of the correspondingtime interval, therefore provide a means of approximating G1 and G2 -

In the case of the thermal source this could be done simply by removing thetantalum boat from the electrodes. For the electron-beam source a suitable stan-dard crucible liner was used, which could be lifted out very easily.

The measurements were carried out for both sources separately at an indi-cated evaporation rate of 10Hzs - . The time was taken from the moment therate meters showed a mass change to the moment when they returned to zero.The evaporation time was made relatively long (about 10 min) to reduce theerrors caused by the instability of the evaporation rates at the beginning and endof the evaporation.

The experimental values obtained are set out in table 1. In the case of MgF2

three evaporations were done. Source mass coefficients of 00255, 00257 and00254 were obtained, the variation between which indicates reasonable consis-tency; the value given in table is the mean of these three values. It is concludedthat, although other errors may arise in this method, the procedure provides atleast a good first approximation to G1 and G2 -

The refractive indices that were used in the calculations are measured valuesthat were obtained from single source evaporations in the plant. (It should benoted that reactive evaporation techniques were not used for any of the coatingsin this investigation.) They were measured after a few days exposure to air to

562


Table 1. Experimental parameters used for calculation of thickness and refractive indexdistributions.

Measured Nominal Source mass coefficientrefractive index bulk density, p (g min-1 per

Material (2 = 580nm) (gcm -3 ) 10 Hzs - 1)

MgF 2 1391 + 00004 31 2.55 x 10-2A12 03 1'584 + 0.0005 4-0 339 x 10-2ZrO2 1-899 + 00023 5'6 415 x 10-2Ta2O 5 2-015 + 0.0011 8-3 257 x 10-2TiO2 2'180 + 0.0010 42 2-97 x 10-2

allow for the major ageing effect to take place, which has been shown to occurwithin very short periods [34, 35]. All the relevant material parameters are sum-marized in table 1. In the case of a stationary substrate one further parameter isrequired, namely the angle between the sources. This was measured to be approx-imately 105 ° .

5.1. Theoretical thickness distribution-rotating substrate

The theoretical relative thickness distributions were calculated from equation(2) for the following three combinations of evaporation rates (in Hz s -1):

f = 10, f 2 = 40;

f = 10, f 2 = 10;

A = 40, f 2 = 10.The former and the latter represent useful experimental limits that were com-monly used in this investigation. The above results are shown in graphic form infigure 2 for only one material combination, MgF 2 + A12 03 , as there is a greatdeal of similarity with the other mixtures. The relative thickness distributions ofeach source acting singly have been included for comparison.

(na,)

z0

Io'-rI--w

I-W,..

0.96

0.92

0.88

0.84

nRA0 50 100

RADIAL DISTANCE (mm)150

Figure 2. Theoretical relative thickness distribution of MgF 2 + Al2 03 co-evaporated atvarious combinations of rates (in Hz s- l) on to a rotating substrate.

>-,~'. AO203 IO/MgF2 40

At203 l0'g. THERMALA2O 3 10/Mg F' IO~ '- ,,,.SOURCE- ,-OONLY

A12 03 40/MgF2 10

E-GUN ONLY .

I i I I I i i I I i I i I I

563

I

D. N. W. Chinnery

5.2. Theoretical index distribution-rotating substrate

The Lorentz-Lorenz mixture rule [36] has been found to apply to variousoptical thin films [18,22,37-39] and will therefore be used here in combinationwith equations (3) and (4) to obtain the theoretical refractive index distributions,corresponding to the above thickness distributions;

C1 n2 C2 n2

2 _-1 12 P2 2+n =C1 1 C2 1

2 +2p1 n2+2 P2 2 n2 + 2

where n is the refractive index of the mixture, and n1, n2 are the refractive indicesof the constituents. Selected values of the refractive index calculated in this wayare given in table 2.

Table 2. Selected theoretical refractive indices on a rotating substrate.

Radial Mixture and evaporation rate (in Hz s )distance

q MgF 2 10 MgF2 10 MgF 2 10 MgF 2 10 MgF 2 10(mm) A1203 10 ZrO2 10 Ta2 05 10 Ta2 05 20 TiO2 10

1570

120

1-49391493414925

162791626616243

1-55301-55181-5496

164721645716429

172721-72531 7217

The calculations were mostly restricted to equal evaporation rates (10 Hz s- 1)as investigation showed that the largest gradient could be expected under theseconditions in most cases. The Ta 2 0 5 + MgF 2 mixture later proved difficult tomeasure in practice as the index values were very close to the refractive index ofthe substrate. To avoid this problem the evaporation rate of the Ta2 0 5 wasincreased to 20 Hz s- 1. A column for this combination is therefore also includedin table 2.

From these theoretical results it would be concluded, except for perhaps theA12 03 + MgF 2 mixture, that the refractive index gradients would be measurableby Abeles' method. It would, however, be advantageous to have larger index gra-dients that could be measured with greater certainty. With this in mind, the pos-sibilities of a stationary substrate were investigated, as described below.

5.3. Theoretical thickness distribution-stationary substrate

In the case of the stationary substrate, the theoretical relative thicknesses werecalculated from equations (6) and (7) at three radial distances, 15, 70 and 120mm(which corresponded to three convenient experimental positions), and at variousangles with respect to source 1 (the electron beam gun). The distribution curvesfor the two sources acting separately are shown in figures 3 and 4. The thicknessdistributions arising from the combination of the sources are again very similarfor the various mixtures and only one, ZrO 2 + MgF2 , is therefore shown infigure 5 as a typical example.

564


0o

Figure 3. Theoretical

U)(I)LUz

I

I--LJLU

Figure 4. Theoretical

60 120 180 240 300 360ANGLE WITH RESPECT TO SOURCE (deg)

relative thickness distribution on a stationary substrate. Source only.

ANGLE WITH RESPECT TO SOURCE 1 (deg)relative thickness distribution on a stationary substrate. Source 2

only.

5.4. Theoretical refractive index distribution-stationary substrate

By superimposing figures 3 and 4 it can be readily seen that a suitable com-bination of radial and angular positions can be chosen in order to obtain largedifferences in the relative thicknesses of the materials deposited from the twosources.

For example, at about 60 ° the thicknesses from both sources at a radial dis-tance of 15mm are roughly similar, whereas between about 100 and 160 ° the

1.15

1.05

0.95

0.85

U)

UJzI

LU

M

-LU

075

\ 'S.-~ x=7mmr- /

_ q%=120r 7/

, , , I I I L . I I .I , , I

13 A

565

I-LI

D. N. W. Chinnery

I.

1.15Or)C)

Z 1.05C'IT:E

I- 0.95W

0.85_JLwIEr'

0.75

0.650 60 120 180 240 300 360

ANGLE WITH RESPECT TO SOURCE (deg)Figure 5. Theoretical relative thickness distribution of MgF2 + ZrO 2 co-evaporated on

to a stationary substrate.

variation between the thicknesses is a maximum at radial distances of both 70 and120 mm. Correspondingly large refractive index variations could therefore also beexpected. This is confirmed by the example shown in figure 6 which was calcu-lated from equation (8).

5.5. Experimental results-rotating substrate

As the thickness and refractive index gradients arising from the co-evaporations are small it was necessary to select positions for the substrates that

1.8

6f 1.7',

z

i 1.7

ffWe

1.6.

N

- -

/

q,= 70mm /_ _ _

\aq= 120mp/, 14- - , I i I I I I i

2IO 180 Z40 300 360ANGLE WITH RESPECT TO SOURCE 1(deg)

Figure 6. Theoretical refractive index distribution of MgF2 + TiO2 co-evaporated on toa stationary substrate.

l~ W __ _ q = mm_

'- q=70mm i'

7 -N, \ a= 120mir ,."

l l l l l lol

K~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

. , I i I i i I I I I i I

.25

566

A-e. _

l _

11

\\


would provide the maximum theoretical differences in these values. At the sametime a practical limitation was imposed by the geometry of the vacuum chamberand, particularly, the shape of the upper shutter.

It was possible to position a substrate in a radial position near the centre sothat one end was at a radius q = 15 mm. As only about half of this substrate wasexposed to the sources, the other end could not be used for any measurement. Asecond substrate was also positioned radially so that its inner and outer ends wereat q = 70 and q = 120mm, respectively. The two substrates were not on the sameradius but had an angle of about 105° between them. The radius q = 120 mm ofthe outer edge of the substrate was the maximum that could be used without anyshielding effects occurring.

Water adsorption in the coatings was an additional problem to contend with.The effect of this on the refractive index immediately after removal from thevacuum chamber was observable within the 20-30min that it took to do a set of 5index measurements for one radial position. Considering the time delay betweenthe first and last set of readings it was therefore thought advisable to repeat thereadings at least once after a period of a few days when the indices were muchmore stable. In a number of cases a third set of readings was taken at a later stage.Examples of typical values are given in table 3. Compared with the theoreticalvalues in table 2 it can be seen that the ageing effect is roughly of the samemagnitude as the radial variation in the refractive index on a rotating substrate.

The Brewster angles of the coatings were measured by observation of, at most,a 10mm section at the end of the substrate. A suitable vertical shield attached tothe collimator prevented the remainder of the substrate from being visiblethrough the telescope.

After the final refractive indices were measured the substrate surface pluslayer were coated with aluminium so that the thickness of the layer could bemeasured on a Sloan Angstrometer. These measurements were also restricted to a10mm section at the end of the substrate. In each position three readings weretaken from which the mean thickness was calculated. It was found that the mostconsistent results could be obtained from this instrument by always keeping thefringe spacing between certain arbitrary limits.

Table 3. Experimentally measured refractive index values showing typical ageing of mix-tures co-evaporated on to a rotating substrate.

Materialsand

evaporationrates in Time Refractive index(Hzs - l) (days) (A = 580nm)

MgF 2 10 0 1-471 + 00008+ 4 1474 0'0005

A1203 10 47 1.476 + 0-0005

MgF 2 10 0 1592 00005+ 2 1595 + 00004

ZrO2 10 43 1-596 + 00006

MgF 2 10 0 1-632 + 00004+ 3 1-635 +00006

Ta20 5 20 41 1635 + 0-0009

567

D. N. W. Chinnery

As the substrate could not be positioned at q = 0mm the theoretical andexperimental results can best be compared on the basis of a new relative thicknessdefined with respect to q = 15 mm, tm/tl5, which follows easily from the ratio ofthe relative thicknesses referred to q = 0, i.e.

tm t to

t15 to tl 5

By taking the actual measured thickness at q = 15 mm and calculating from itthe theoretical thicknesses at q = 70 and q = 120mm, the experimental and theo-retical results of various mixtures that were co-evaporated on to a rotating sub-strate can be compared graphically as shown in figure 7. In most cases the actualthicknesses show the expected trend, that is decreasing towards the outer edge ofthe workholder. There is a fair amount of spread in the experimental results,which is considered to arise partly from the difficulty of measuring small thick-ness differences with the Angstrometer. This problem has also been experiencedby other workers [40]. In the case of the refractive indices, direct comparisonbetween theory and experiment are more difficult to make as additional uncer-tainties, especially in the densities, enter into the calculations.

Typical refractive indices that were measured on the above coatings showed agreat deal of variation and poor correlation with the theoretical values, and aretherefore not given here. It was concluded that other inaccuracies that can arise,especially in the coating procedure, had an overriding effect that masked thesmall index gradients that were expected on a rotating substrate.

Larger index differences would obviously be more desirable. This was thusthe main motivation for investigating the use of stationary substrates whose posi-tions could be chosen so as to achieve large index differences that would be wellwithin the limitations of the Abel's method.

IOU

20

110

E I00oo

Y 90

zLIJZ 80.-,- 70

60

50

4n' 0 50 100 150iO

RADIAL POSITION (mm)

Figure 7. Comparison of theoretical and experimental thickness distributions of variousmixtures co-evaporated on to a rotating substrate.

) +

- - =.--- M = IT 2 05 20

MgF 2 IO/To2 05 20

MgF 2 /Ta20 5 20

) ~~~~~~~~~~x

)- _ ~ _ _ -_ __MgF 2 I0/A12 03 10

)... ., ,MgF 2 Lo/ZrO 2 10

MF 0/TaO0s IQ

568


5.6. Experimental results-stationary substrate

Four co-evaporations were carried out for this part of the experimental study,namely MgF2 with A12 03 , ZrO 2 , Ta 2 0 5 and TiO 2 . In order to compare thethickness measurements with theoretical values the procedure given here was fol-lowed.

(a) If T, 5 represents the actual thickness measured at q = 15mm (50°), thenusing the corresponding theoretical relative thicknesses, the thickness to atthe centre can be calculated from

to = T 15 /(relative thickness) 1 5

(b) Using this value of to, the theoretical thicknesses can be obtained from

t?0 = to x (relative thickness) 0,

and

tl 20 = to (relative thickness) 120 ,

where the relative thicknesses at the appropriate angles must be selected.

The theoretical and experimental thicknesses are compared graphically infigure 8. The agreement is similar to the corresponding results for a rotatingsubstrate.

Comparison of the refractive indices can best be done on the basis of thedifferences between the various values as shown in figure 9. The correlationbetween theory and experiment is as good as can be expected for an experiment ofthis nature where it is difficult to keep all the parameters constant. The resultsnevertheless agree with the expected trend.

150

140

E 130

0)[0Cen 120

IL)

1-0

90

80

70

60 80 100 120RADIAL DISTANCE(mm)

140

Figure 8. Comparison of theoretical and experimental thickness distributions of variousmixtures co-evaporated on to a stationary substrate.

I

-~ -___ - - - - -. -+MgF 2 10/TiO210

°o -- - -MqF 2 IO/ZrO2 10

0-MgF2 0/Ta20520

MgF2 I/Al2O3 I00

Wi

569

.--A

570 D. N. W. Chinnery

E 0.07 E~00 MnF -'0j 00 \ MgF2 10/TO205 20

II 0.05

0.04

NN

- Nx 0.0 I I

WQ0.02 ' xZ

0.01:7 I '" I. 1

Ud .Ub

Z 0.05LUJW 0.04-LbL 0.03

C 0.02 L MgF 10/At2 0310X ' ~1.. 0.01 -

0 i . .......

\X

\\ Mg F2 10 /Ti0210

0

'x\

N\: 0 ~ 0

'I I I\III I I I I ] I\ i

o0o

X MgF210/Zr0210N'N

,

N oiI I I I I

o Zo 40 60 80 oo 12z 0 20 40 60 80 100oo 120RADIAL DISTANCE(mm)

Figure 9. Comparison of theoretical and experimental refractive index distributions ofvarious mixtures co-evaporated on to a stationary substrate.

6. Discussion

Besides the inherent inaccuracies in the thickness and index measurements, anadditional problem is that these measurements are difficult to make at an exactpoint that corresponds to a well-defined theoretical value of the radius.

It is clear that better agreement between the experimental and theoretical ref-ractive indices requires more information on the actual values of the condensationcoefficients and the densities of the materials under co-evaporation conditions.More accurate index measurements should also lead to an improvement. A con-tributory factor may also be the fact that the co-evaporations were not carried outas reactive evaporations, as is commonly done in the case of the oxide materials,which could result in incomplete oxidation and possibly some inhomogeneity inthe mixtures. Although the evaporation rates from both sources were allowed tostabilize before the substrate was exposed to the evaporants, a brief scanningAuger microscopy (SAM) investigation of a MgF 2/AI2 03 layer on a Si substrateindicated that the composition of the layer can vary with depth because of theapparent diffusion of fluorine to the surface. Such inhomogeneities could alsoinfluence the results obtained by Abelks' method.

The ageing effect caused by water adsorption in the co-evaporated mixtures,which appears to have been totally ignored by previous investigators in this field,was similar to that observed in the component materials and is an indication of aporous structure that is typical of many single-material coatings. It was difficultto compensate adequately for this effect in the above experiments as facilities formeasuring the refractive index in vacuo were not available.

A shortcoming of the above theoretical approach is that the sources wereassumed to have the characteristics of a directed surface source. A further

5 ___


improvement could probably be.achieved by making use of the actual mass emis-sion characteristics of each source, which would have to be determined separa-tely.

It is considered that the experiment nevertheless demonstrated quite well thatthe thickness and refractive index of a co-evaporated layer vary with position.

It should be emphasized that the purpose of this investigation was not toachieve uniform thickness or refractive index distributions under co-evaporationconditions but to try to estimate the magnitude of the variations that can occur.

7. Conclusion

Depending on the layout of the internal components in a vacuum coatingplant, the different thickness distributions arising from two evaporation sourcesthat are run simultaneously with different evaporants will generally result in anon-uniform spatial distribution of the refractive index of the mixture coating.Such effects should be taken into account in the study of co-evaporated coatings,which frequently requires more detailed information about the refractive index.The above method provides a theoretical means of estimating the spatial variationin the thickness and refractive index of co-evaporated layers, that could beextended to cover the case of a curved workholder.

Acknowledgment

The author gratefully acknowledges discussions with Mr. D. F.Bezuidenhout, as well as the contributions of Messrs E. Theron, D. van Stadenand H. Klee to the construction of the beamsplitter attachment on the goniome-ter, and the assistance of Messrs A. Dierkse, W. van den Berg and L. Willner inthe construction of the shutter system, all of whom are from the Optical SciencesDivision of the NPRL. The author also wishes to thank Dr. C. M. Stander,formerly of the National Institute for Materials Research, for the SAM investiga-tion.

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some aspects of simultaneous evaporation techniques

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