Film thickness measurement by absolute methods received 1 July 1970; accepted 3 July 1970

C Greaves BSc, PhD, Alnst, Lanchester Polytechnic, Eastlands, Rugby, Warwicks

Absolute methods for measuring the thickness of thin films are considered and a performance survey is given for a selection of commercial instruments.

1. Introduction strate with a suitable step formed by masking during deposition. The treatment of thin film monitoring techniques previously A vertical tracking force as low as 1 mg is often used to reduce given by the author’ is extended in the present article toabsolute the possibility of damage to the surface of the deposit. In prac- methods for measuring film thickness. As pointed out in the tice, however, the surface is usually marked by the stylus which previous article many monitoring techniques require pre- can cut into the material, particularly if it is a soft material. calibration against a suitable absolute method. A selection of This can lead to inaccuracies and, therefore, it is often desirable such methods is reviewed in this present article with particular that an even coating should be deposited over the whole area of emphasis being placed on those methods where measuring the specimen after the step has been formed, so that the effect instruments are commercially available. Absolute methods are should be self cancelling across the step. usually carried out on the bench rather than in situ in a vacuum The vertical movement of the stylus, as it traverses the speci- system and often require more skill in operation than the moni- men, is magnified by a pivoted arm which carries the stylus and toring techniques used during the production of thin films. is detected and converted into an electrical signal by a solid

Some of the monitoring measurements previously described state transducer or an electromechanical system. The resulting can be performed on the bench and in this sense can be regarded electrical signal is amplified and displayed on a meter or prefer- as absolute methods provided a satisfactory correlation factor ably a pen recorder chart in terms of the vertical movements of between thickness and the actual measured physical property is the stylus. Step height measurements can be readily obtained known. Two suitable methods are the modulated beam photo- from the distance between the mean lines corresponding to the meter and microbalance techniques. The modulated beam film surface and substrate surface as shown in Figure 1. photometer can be operated just as readily on the bench to measure optical reflectance or transmittance which, if required, can be converted to thickness. However, this conversion is only possible over a rather limited range and calibration against a truly absolute method is really required. Provided that the mass of the substrate is known, microbalance techniques may be Film surface used to measure the surface density of a deposit quite accur-

-- A

ately. The range of suitable microbalances is even wider than those available for monitoring since null balance techniques are no longer essential as they are in monitoring applications. How- ever, better reliability may be obtained if null balance tech- niques are used since the weighing operation can then be carried out in a vacuum enclosure thereby reducing inter- ference from draughts, errors due to contaminants and other unwanted effects.

Step height 10 nm

1 -- - 2. Stylus Method Substrate The method is an extension of well established surface profile surface

measurement techniques and has been described by Wright?. The thickness of a film of any material is measured by traver- sing a small radius blunt diamond stylus across a test groove formed in the material or over the edge of a step from the deposit to the substrate. The thickness is recorded as the Figure 1. Typical trace for stylus method on X 1000 000 range. difference in levels between film surface and substrate surface.

It is desirable that the substrate should be smooth compared The instrument is not absolute in the strictest sense since for with the thickness of the deposit. To ensure this, measurements the best reliability it should be calibrated from time to time are often made on a sample deposited on an optically flat sub- using a set of calibrated grooves. The calibration grooves them-

Vacuum/volume 20/number 10. Pergamon Press LtdlPrinted in Great Britain 437

C Greases: Film thickness measurement by absolute methods

selves require initial calibration by, for esample, an inter- ference method.

PhotographIc plate

3. Interferometer Methods An interferometer technique was first used to measure film thickness by Wiener3 in 1887. Similar techniques’-” arc now well established in many applications other than film thickness measurement, for example surface topography measurements and hardness measurements. The advantage of such methods is that they give an absolute metrical thickness rather than an optical thickness or a thickness derived from some other property.

3.1 Multiple beam interferometry using fringes of equal thickness. The method is suitable for any film material. A film is deposited onto a glass substrate, preferably an optical flat; if half of the substrate is masked the deposited film will form a step. A fairly thick layer of opaque material, such as 80 nm or more of silver, must be deposited over the film and substrate, as shown in Figure 2, in order to increase the reflectivity of the film to pro- duce high definition reflection fringes and to ensure that any phase change occurring in reflected light from each side of the step should be the same.

Reference plote- I I Portiolly tronsporent-I\\ coating

Step

Opoque coating -

Film

Substrote

Figure 2. End view of wedge shaped air gap system.

The step film is used to form the bottom of a wedge and the top is formed by a similar substrate with a partially transparent coating of about 80 per cent reflectivity as shown in Figures 2 and 3. The reflection coating on the reference plate is provided to enhance the definition of the fringes. The substrates are fixed so that lines of equal air gap thickness run along the substrates parallel to the common edge and at right angles to the film step; effectively two wedges are formed side by side.

Reference plate Reference plate Poftlolly transparent Poftlolly transparent cootlng cootlng

1 1 Substrote Figure 3. Side view of wedge shaped air gap system.

Monochromatic light is used to illuminate the wedge arrange- ment perpendicularly and the reflected light is viewed with a low power microscope as shown in Figure 4. For reflected light an interference pattern of straight dark fringes on a mono-

433

Beam\ Splitter

Low power mlcroscope

Monochromatic

Collimator

Wedge shaped air gap

Figure 4. Optical arrangcmcnt for multiple beam interferometry using fringes of equal thickness in the reflection mode.

chromatic background is set up as shown in Figure 5. The pattern indicates points of equal air gap thickness with a dis- placement at the step in the film and by suitable analysis will reveal the film thickness at the step.

For normal incidence, from conventional interference con- siderations, it can be shown that the difference in air gap between two adjacent fringes is 1/2. The height of the step (i.e. film thickness) can be obtained from the displacement of a fringe at the step in terms of a fraction of fringe spacing and thus give the film thickness in terms of units of A/2. In practice

Substrate

.

Film

/

/*I 2

Figure 5. Part of a typical fringe pattern of the step between substrate and film using fringes of equal thickness and monochromatic light.

C Greases: Film thickness measurement by absolute methods

a common technique is to photograph the fringe pattern and carry out the analysis on the photographic plate.

This technique is limited to films of thickness greater than about 3 nm by the physical character of the films rather than by optical limitations. Tolansky” has stated that, from a resolution point of view, the displacement in fringes \\;hich arc on oppo- site sides of a dividing line, as in Figure 5. can be judged to i/5th of a fringe and for highly defined fringes this corresponds to approximately 0.5 nm. The restriction to 3 nm is mainly due to the phenomenon of “bedding-in”“*” caused by the granular nature of very thin lilms. If a film is thicker than i/Z (i.e. approximately 300 nm for sodium light), then the step will show an overlap of orders which may lead to confusion. However, in practice it is possible to overcome this difficulty. It is almost certain that any mask used to form the step \vill not be perfectly straight and sharp but will impart a certain recognizable pattern on the fringes which can, with skill, bc used to identify the relevant order of displaced fringes.

Thickness measurements can be satisfactorily achieved using general purpose interference equipment but the amount of specialist skill required can be reduced by using the specially designed multiple beam interferometers which are commercially available for the purpose.

The equal thickness fringe patterns required in this tech- nique may be set up at the step in the film by methods other than the formation of a wedge shaped air gap. For example, a modification of the classical Michelson interferometer arrange- ment may be used in which the specimen takes the place of the usual movable mirror in the standard Michelson instrument, but in which the required relative movement is obtained by moving the entire interferometer with respect to the stationary specimen. Another method uses a double quartz prism and polarized light to form lines of equal path difference by com- paring the specimen surface at two positions. A possible advan- tage of these two methods is that no separate reference plate is required and the need for a physical contact between such a plate and the specimen is avoided thus reducing the risk of accidental damage to the film surface.

3.2 Multiple beam interferometry using fringes of equal chro- matic order. This is again a method which is suitable for any film material. It is often preferred to the method using fringes of equal thickness since flatness of the substrate is no longer critical and it is possible to use direct readings from the drum of a constant deviation spectrometer when obtaining the thick- ness. It has the disadvantage that considerably more skill is required in interpreting the fringe pattern since white light is used to illuminate the film.

The sample may be prepared, in a similar way to that des- cribed in Section 3. I, to form a step with a highly reflective coat- ing covering the whole substrate or an alternative method, used successfully by Scott et al”, of scraping a groove out of the film down to the substrate level may be employed. In either case a localized fringe system is set up between the specimen and a partially transparent reference plate by illuminating normally with white light and viewing with a spectrometer as shown in Figure 6. The interference plates may be adjusted until a small area of nearly constant thickness becomes visible, when a pattern of dark fringes on a continuous background with a displacement at the step is obtained (Figure 7).

Perhaps the simplest way to obtain film thickness from this fringe pattern is that originally described by Scott et all” in

Beam, Splitter

l--v--l Spectrometer

White light source

Parallel sided

Adiustina screw

Figure 6. Optical arrangement for multiple beam interferometry using fringes of equal chromatic order in the reflection mode.

which an accurately calibrated constant deviation spectrometer is used to measure the wavelength and wavelength displacement of particular lines in the pattern. From conventional inter- ference considerations, for normal incidence and for reflected light, the interference equation is

16, d.=2y+n

where 1~ is the order, A is a particular wavelength, y is the air gap thickness and 8 is the phase change on reflection at the sur- face. This assumes that there is no phase change due to passage of the light through the partially transparent coating of the reference plate; an assumption which is justifiable if the reflec- tivity of this coating is greater than 80 per cent. At the step in the film there is a displacement of a particular fringe and assum- ing that the phase change is the same on both sides of the step by differentiation of (1).

and since ~nA,=(rrz+l)l~ (3) eliminating 111 gives

a, da h’=m2 . z

(4)

where the displacement dy corresponds to the film thickness, &,, is the displacement of the fringe corresponding to r3, and d, is the wavelength of the adjacent fringe, as shown in Figure7.

439

C &eaves: Film thickness measurement by absolute methods

m

k I -- di --

m+l

m+2

Order Wovelength

Substrate Film

/

Figure 7. Part of a typical fringe pattern at the step between substrate and film using fringes of equal chromatic order and white light.

Thus by reading i. ,, I2 and CL?,, from the drum of the spectro-

meter the film thickness may be obtained. Figure 7 is much

simplified and in practice a much more complex pattern occurs, with suitable skill many combinations of adjacent wavelengths may be used to determine the film thickness.

Since fringes of equal chromatic order can be made narrower than the Fizeau fringes used in the method described in Section 3.1, much greater accuracy can be obtained and the method is ideally suited for use with extremely thin films.

4. Ellipsometer Methods It has been well known for many years” that ellipsometry offers a precise method for studying and measuring the thickness and refractive index of thin reflecting films deposited on to a suit- able substrate. Ellipsometer methods have not been as exten- sively used as inteference methods but can prove to be extremely sensitive. The high degree of skill required, particularly in the cumbersome process of converting experimental readings to thickness and refractive index values, has probably been the main contributor to this lack of popularity. Ellipsometer methods utilize measurements of angles, phase differences and amplitude ratios.

When plane polarized light is reflected from a thin reflecting film the state of polarization of the light is altered, usually becoming elliptically polarized. The magnitude of these polarization changes is dependent on the thickness of the film and its refractive index. Thus a study of the state of polarization can reveal both the thickness and refractive index of the film. The quantities tan y, the ratio of the reflected amplitudes for light polarized parallel to and perpendicularly to the plane of incidence, and A, the relative phase difference between them, can be measured directly’* and used to calculate film thickness. Alternatively w and A may be obtained from measurements of the orientation of the major axis of the elliptically polarized light to the plane of incidence, and 11 the ellipticity. The full significance and relationship of these quantities has been ex- plained in a review by Bennett and Bennett13.

Experimental apparatus required for ellipsometry is fairly standard consisting essentially of a spectrometer table on which the specimen is mounted, a light source, polarizer, com- pensator, analyzer and detector. Accuracy depends to a large extent on the rate of change of light intensity with angular

440

rotation of the compensator or analyzer near to the extinction

positions. An mstrument which can be used to accurately determine s and ;I has been developed by the British Scientific

Instrument Research Association. The instrument, shown in Figure 8. incorporates a magneto-optical detection system to

* Light source

// d7 ii Collimator

,’ /

\ Quarter wove plate

Photo -multiplier

Figure 8. Optical system of photoelectric ellipsometer developed by BSIRA.

obtain a higher sensitivity and accuracy. A Nicol prism ensures that the incident light is plane polarized before it is reflected from the specimen when it becomes elliptically polarized. A quarter-wave plate compensator in a particular orientation with reference to the axis of the elliptically polarized light restores the light to its plane polarized form. A Faraday cell modulates the plane of polarization of the light about a mean position and the light then passes to the analyzer, a second Nicol prism. At the extinction position balanced amounts of light pass through the analyzer to be detected by the photo- multiplier. The output from the photomultiplier is combined vectorially with the modulation signal on an oscilloscope pro- ducing Lissajous figures which provides an accurate detection method. This procedure allows x and y to be determined from the orientations of the compensator and analyzer at extinction

Table 1. Com

parison of

film

thickness m

easurement

methods

Method

Classification Principle

Comm

ents

Comm

ercial instrum

ent

Manufacturer

Type Approxim

ate operating range

Comm

ents

Stylus m

ethod Direct

measurem

ent of

height Suitable

for m

etallic, Rank

Precision Industries

Ltd, Talystep

I I nm

to

10jrm

of step

from

lilm

to substrate

scmiconducting

or Rank

Taylor Hobson,

(8 ranges)

by traversing

a stylus

across diclcctric

lilms.

For Lcicester,

England it.

Vertical m

ovcmcnt

is cxtrcm

cly thin

lilms

converted by

a transducer deposit

should bc

on an

G V

Planar Ltd.

Surface Profile

5 nm

to 5 jirn

system

to give

electrical optically

flat substrate

Windmill

Road. M

onitor SPM

IO (3

ranges) signal

proportional to

the Sunbury-on-Tham

cs, thtckncss

Middlescu,

England

Multiple

beam

An equal

thickness fringe

Suitable for

metallic.

Varian Vacuum

Division.

A-scope 3nm

to2jtm

Simple

to operate

since tntcrfcrom

ctry ustng

system

is set

up using

mono-

scmiconducting

or 61 I

tlansen W

ay, Palo

Alto, interferom

eter specially

designed for

thin frinacs

of equal

chromatic

light. The

diclcctric lilm

s. if

totally California

94303, USA

film

measurem

ent. Fringe

thickness dtsplaccm

cnt bctwccn

the two

covcrcd by

a thick

pattern set

up using

wedge fringe

patterns al

the step

rcllcctivc him

. Prcfcrablc

shaped air

gap bctwcen

botwccn the

tilm

and to

“SC optic;llly

Rat spccim

cn and

similar

plate substm

tc gives

the step

subsrrntc acting

as a

reference height

in term

s of

the wavclcngth

of the

light Gacrtner

Scicntilic Corp.

M307 3

nm

to 3 jrm

M

odifcd Michelson

Inter- I201

Wrightwood

Ave. M

icro fcrom

cter. Specim

en replaces

Chicago, III

60614. USA

intcrfcromctcr

movable

mirror,

it rem

ains stationary

while entire

j” intcrferom

ctcr is

moved

0 AZ

Fringe pattern

set up

by xi

C Rcichcrt

Optischc W

crke AG,

McF

Microscope

IO

nm

to a

few ,,rn

Wicn

XVII, E

and polarization

creating lines

of equal

path Hcrnalscr

Haupstr 219,

Interferometer

difference using

a double

22 Austria

attachment

quartz prism

and

polarized 3

5 light

to exam

ine the

specimen.

2 Rofcrcnce

plate not

rcquircd

Ill

2 Intcrferom

etry using

An equal

chromatic

order Suitable

for m

etallic. Rank

Precision Industries

Ltd, Thin

film

measuring

3 nm

IO

a few

I’m

Manufacture

of N 130

now frinacs

of equal

frtngc system

is

set up

using scm

iconducting and

Analytical Division.

Interfcrencc discontinued.

Fringe pattern

5 chrom

atic order

\\ hitc light.

The displaccm

cnt diclcctric

lilms

if totally

Hilgcr 61 W

atts, M

icroscope N

130 set

up using

parallel sided

air

E of

the fringes

at the

s~cp covcrcd

by a

thick 31

Camden Road,

and W

avclcngth gap

bctwccn specim

en and

?i bcf\\ccn

the lilm

and

the rcllccting

lilm.

Optically London

NWI,

England Spcctrom

cter D9003

reference plate

: substrate

gives the

step height

flat substrate

not ncccssary

3 in

terms

of line

wavclcngths

E in

the illum

rnuting light

ul 2 Ellipsom

etcr m

ethods The

state of

polarization of

Suitable for

metallic,

Measurem

ents are

generally

5

polarized light

rellcctcd from

sem

iconducting and

more

difficult to

perform

than the

film

gives inform

ation diclcctric

tilms.

The m

ethods above

r which

can bc

used to

obtain tcchniquc

is m

ade casicr

Gacrtncr Scientific

Corp. Lll8

I nm

to a few

jtrn Rotation

readings to

0.1’. thickness

and refractive

if the

lilm

is non-

I201 W

rightwood Ave.

Ellipsometer

Uses Nicol

prisms

E indcs

of the

film

I= absorbing.

If the

him

is Chicago.

Ill 60614,

USA LL

absorbing a m

ore Ll

l8G-f 1 nm

to

a few I’m

Greater

accuracy achieved

by . .

Ellipsomctcr

using Glan

Thompson

2 com

plex m

ethod is

rcquircd prism

s

5 G

Ll19 1 nm

to

a few

,*rn Rotation

readings to

0.01”. Ellipsom

eter Uses

Glan Thom

pson prism

s c,

C &eaves: Film thickness measurement by absolute methods

thus w and A can be calculated using the following expressions from the electromagnetic theory of light: cos 2 v=cos 2y cos 2s (3 and tan A=tan Zy/tan 2s. (6)

Drude” laid the theoretical foundations of ellipsometry in 1889 but used simplifying approximations which are only true if the film thickness is very much smaller than the wavelength of the incident light. A more exact treatment has been developed by Lucy” which gives an explicit formula when the film thick- ness is less than the light wavelength. For films of greater thickness the only approach open is to find, by graphical or arithmetical methods, the values of thickness and refractive index which fit the experimental observations. There are various analytical techniques available1s~17 but all are extremely com- plex and often require the use of a computer. A comprehensive coverage of experimental and theoretical techniques of ellipso- meter methods for studying surfaces and thin films has been given at a Symposium in 1964l*.

Va&kls has shown that the sensitivity of ellipsometer methods varies with film thickness and has indicated that an acceptable accuracy can still be achieved down to film thick- nesses of the order of 1 nm.

5. Comparison of methods The basic principles and ranges of the various methods are compared in Table I. Where applicable brief details of a selec- tion of commercial instruments are given.

References

3O Wiener. ll’ied.4r~~1. 31, ISS7. 629. ,’ S Tolansky, Alultipl~~ Beonr Il,r~,t:f~,~u,,rc/~~, cf Sut:frrc~~~,~ u~rd Films 194S, (o.Yford: Clorcv/dlJn Pwss). 5 S Tolansky. Sw:fhe t\li~~~otop~~~~rrrph~~, (I OhO), (Lo~~dwr: Lo~rgt~rowrr). o 0 S Heavens. Proc Phys SW. 64, 1951, 419. ’ A F Gunn and R A Scott, Ntrrrw, 158, 1946, 671. ” D G Avery, Nor,rw. 163, 1949, 916. !’ S Tolansky, ~\lrrlriple BCUIII Irrrerfirem~e Microscopy qf klerols, 1970, p 95. (Lo/rdo/r: .Actrd1wric PImY). *‘I G D Scott. T A McLauchlin and R S Scnnctt, J Appl P/t.vs. 21, 1950. 843. ” P Drude, H7ed Am. 36, 1589. 432. ” R E Hartman, J Opf Sot .Avr. 41. 1951. 244. “I H E Bennett and J M Bcnnclt. Ph.rsics o/Thin Filers, 4, (Ed G Hess mrd R E T/m, 1967. p I. (New York: AC&W;C Prc~s,s). I’ F Lucy, J C/w,,, Ph.w 16, 1948. 167. Ii A V&i&k, J Opr SW Am, 37. 1947, 979. I6 F L McCracklin. E Passoglia. R R Stromberg and H L Steinberg, J RPS Nnrl Bur Std. 67c\, 1963. 363. Ii D A Holmes, Appl Oprics. 6, 1967, 168. Iy E Passoglia, R R Stromberg and J Kruger (Editors), E//ipsontrfr.v itr /he ~~T~SIII’E~I~~II oJ’.wqk~s crud tbi~r~films. Nnr Brrr SIP Mis Pub1 No 256 1964.

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