Localization of absorption losses in oxide single-layer films

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Localization of absorption losses in oxide single-layer films

E. Welsch, H.G. Walther, H.J. Kühn

To cite this version:

E. Welsch, H.G. Walther, H.J. Kühn. Localization of absorption losses in oxide single-layer films.

Journal de Physique, 1987, 48 (3), pp.419-424. �10.1051/jphys:01987004803041900�. �jpa-00210456�

Localization of absorption losses in oxide single-layer ^films

E. Welsch, ^{H. G.} Walther and H. J. Kühn

Sektion Physik, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, ⁶⁹⁰⁰ Jena, G.D.R.

(Requ le 13 novembre 1985, revise le 8 septembre 1986, accepte le 3 octobre 1986)

Résumé. ²⁰¹⁴ Les mesures d’absorption réalisées par la méthode de l’absorption photoacoustique dans des films

TiO2, Ta2O5, ^et ZrO2 ^en forme de coin à 03BB ⁼ 488 nm, 515 nm et 647 nm permettent ^de séparer l’absorption ^{due au}

volume de celle due à l’interface. Pour les films de TiO2 ^et Ta2O5 l’absorption due à l’interface film-substrat est

supérieure ^à l’absorption due à l’interface air-film, tandis que pour les films évaporés ^de ZrO2 les ^deux contributions sont comparables. ^De plus ^on donne les résultats préliminaires ^{de la} dépendance ^en fonction de la longueur ^{d’onde de}

ces films.

Abstract. ²⁰¹⁴ Absorption measurements performed by ^{means of} photoacoustic absorption (PAA)-technique ⁱⁿ wedge-shaped TiO2’ Ta2O5, ^and ZrO2 single-layer ^{films at 03BB = 488 nm, 515 nm, and 647 nm} permit ^a separate determination of bulk and interface absorption, respectively. ^For TiO2 ^and Ta2O5 ^films investigated ^{the film-}

substrate interface absorption Afs ^{dominates over} the air-film interface absorption Aaf, whereas for evaporated ZrO2

films both the interface contributions ^are nearly ^{the same. In} addition, preliminary results concerned with the

wavelength dependence ^{of the} absorption of the films investigated ^are presented.

Classification

Physics ^Abstracts

68.20 ^- 68.45 ^- 68.48 ^- 78.65 ^- 42.78H

1. Introduction.

To characterize thin films it is _necessary to separate ^the different components ^of

optical absorption

^{within the}

layer investigated [1].

^{In order to}

explain

^the

physical origin

^of

absorption

itself such

spatial

localization measurements must be

performed necessarily assuming

a

homogeneous absorptivity along

the film thickness and an

integration

^over the lateral

inhomogenities

ⁱⁿ

the interfaces.

We started from an

investigation

of the thickness

dependence

ⁱⁿ

single-layer

^films. By

varying

^the

optical

thickness the

averaged

^bulk

absorption

coefficient

a is yielded.

^The

extrapolated

^{zero thickness}

absorp-

tion represents ^{the sum} of contributions of air-film

(aaf)

^and

film-substrate (afS)

^interface

absorption,

and

generally,

^{does not allow to}

distinguish

^between

these different sources of

absorption.

^In

preceding

papers ^we described an extension of these

absorption

measurements of

multilayer

^films

[2],

^{and a method}

which enabled us to suppress the contribution of interface

absorption

^{of a}

single-layer

^{film and, accord-}

ingly,

^to determine the

genuine

^bulk

absorption directly [3].

^For

single-layer

^films

deposited

^onto

glass-substrat-

es, however, ^{a more}

complete

^{set of} measurements is

required

^{in the case} that these three

quantities

^{are to be}

separated. Following

^a method first

suggested

^{and lined}

out by Temple

[4]

^the

absorption

^of

wedge-shaped single-layer

films is measured by

making

^{use of the}

characteristic

changes

^{of the} relative power

density

^at

the air-film and film-substrate interface

for À 14

^and

A/2 optical

thickness,

respectively.

The aim of this paper is ^{to measure} the

absorption

^of

wedge-shaped T’02, Ta2o5,

^and

Zr02 single-layer

^films

deposited

onto BK-7 disk

shaped

substrates

by

^{means of a}

photoacoustic

gas

cell-microphone (PAA)-technique [5].

By ^these measurements a separate determination of the bulk and interface

absorption, respectively,

^is

attained.

Preliminary

^{results on the}

wavelength ^depen-

dence of the bulk

absorption

coefficient

a f

^{and the}

specific

^interface

absorption

aaf

and afs

^of

Ta205

^{art k} 488, 515, ^{and 647 nm are included.}

2. Preparation ^{of the} coatings.

The

Ta205

^and

Ti02

^{films were formed}

by

^reactive

sputtering

^from

dc-magnetron sputtering

^{sources. A}

source with 50 mm diameter Ta-target ^was used for the

deposition

^of

Ta205

^films

(samples

^{I and}

II).

^These

films were

deposited

^{in a 60 % Ar and 40}

% 02 atmosphere

^{at 0.7 Pa total} gas pressure, using ^{110 W}

applied

power.

Previously, sample

^{II was} coated with a non-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01987004803041900

420

stoichiometrie

Ta2o,, layer

^{of a few nanometer thick-}

ness. This

layer

^was

deposited

^{at the same} total gas pressure, but reduced to 25 % oxygen ^content. The

applied

power ^was 140 W. In all cases the target- substrate

separation

^{was 60 nm.}

The

Tio2

^film

(sample III)

^{was formed} by

sputtering

from a PPS 4 source

[9]

^{with 160 mm} target ^diameter.

Here the gas pressure ^{was 0.4} Pa, ^the oxygen ^content 25 % and the

applied

power 200 ^W.

The formation of

wedge-shaped

^{films was attained}

by help

^{of a} thin aluminium

plate

^{which was mounted at a}

distance of 10 mm from the substrate surface so that

one half of its area was covered. Because of the

angle

distribution of

sputtered

^{atoms close to} the substrate the

deposition

^{rate is a} function of the distance from the

edge

^{of the}

plate.

^{Thus, an area is}

yielded,

^{where over a}

distance of about 6 mm the

deposition

^rate

changes continuously

^{from 0 to} 60 nm/min for

Ta2o5

^{and from 0}

to 6 nm/min for

Ti02, respectively.

The

Zr02 layers

^are

prepared by

electron beam

evaporation using ZrO27tablets

^as

starting

^material.

The substrate temperature ^{was 520 K.} After film

depos-

ition - no

aging

process ^was

performed.

The refractive indices of the films at a

wavelength

^of

515 nm are estimated by transmission measurements to

be about 2.10, 2.40, ^{and 2.05 for}

Ta2o5, Tio2,

^and

Zro2, respectively.

3. Measuring ^method and calculation of bulk and interface absorption from the measured data.

To

investigate

^the

absorption

^of

single-layer

^films

deposited

^onto

glass-substrates

^{we have to}

distinguish

between four

regions

^where

optical absorption originates :

the air-film interface

(af),

the bulk of the film

(f),

the film-substrate interface

(fs),

and the bulk of the substrate

(s).

Hence, the measured total

absorp-

tion A of the

sample investigated

consists of an air-film

as well as a film-substrate interface term and bulk

absorption

of the film as well as of the substrate

[4] :

where aaf

and

^{represent the}

specific absorption

^{at the}

air-film and film-substrate interface defined as the ratio of power absorbed ^at the interface to

light

^{power at the} interface,

a f and as

^{are the}

spatially averaged

^{film and}

substrate

absorption

coefficients,

respectively,

^and

df

^and

ds

^{are the}

geometrical

thicknesses of the

single- layer

film and the substrate,

respectively.

Finally,

pa f and Pfs denote the relative

light

power densities at the film interfaces. As a first approximation,

we define

assuming ^an arithmetically

averaged

refractive index at the interface between the two different optical ^media

where I Tij I’

^{is the} time average of the square of the electric field

strength

^{at the interface} ij. pf and p, ^are defined as

spatially averaged

^{over film and substrate} volume,

respectively.

where I Ef Iand I Ea I

^{are the} time averages of the square of the electric field ^at the bulk of the film and external to the

sample, respectively.

^The calculation of electric field distribution was

performed using standing

wave electric field

equations

within the film. In the measurement, the

sample

^was

slightly

^{tilted to avoid}

interference effects between the two substrate inter- faces due to the

long

^coherence

length

^{of laser}

radiation. Thus,

multiple

reflections in the substrate must not be taken into account.

Performing

^a

photoacoustic absorption

measurement we obtain a

measuring signal

^caused

by optical absorp-

tion. This

signal

^{is a}

complex

^{function of a} combination of

optical,

thermal and

geometrical

parameters ^{of the}

sample.

Considering

^a

photoacoustic

^gas

cell-microphon

^set

up the pressure

signal p

^measured

provides

information about the

optical absorption. Applying

^{the Rosen-}

cwaig-Gersho-theory [6]

^and

taking

^{into account inter-}

ference of

optical

^{as well as thermal waves we obtain}

the

complex

^values ac-pressure

amplitude

p

[5]

cp is a

complex

^valued

frequency-dependent

coefficient

describing

^the temperature-pressure conversion in the gas volume

with or =

( 1 + i ) ( 7r fl g ) 112-, g

^thermal

diffusivity, k

^thermal conductivity,

f

modulation

frequency and Jo

incident

light

power.

In the case of optical ^thin films the relations

af df

¹ crf

df .-c

^1, af uf ^and

as

^« Us ^are satisfied. Therefore, equation

(4)

^{reduces to}

Thus, ^for

optically

^and

thermally

^thin

layers

^{onto non}

absorbing

substrates the

photoacoustic signal

^is pro-

portional

^{to the}

optical absorption,

^{i. e.} proportional ^to

the sum of the interface and bulk

absorption

compo-

nents of a

single layer.

^To separate ^{the individual} a f, a fs and aa f we use

wedge-shaped sample layers.

Here, ⁱⁿ

dependence

^{of the}

light

^beam

position

^{on the}

layer

and, hence, of the actual film thickness, ^the

relative power densities ^at both interfaces and within the film volume are all

changing

^{in a} characteristic pattern,

ranging

^{from a} quarter-wave ^{to a halfwave}

optical

thickness, ^labeled by ^indices

(1)

^and

(2),

^re-

spectively. Measuring wedge-shaped

film up ^{to an}

optical

^{thickness at least of A, the rise in}

absorption

data

A (1)

or .L4 (2) versus the

optical

^thickness

permits

^a determination of a f f

The

specific

^interface

absorptions

asf

and a fs

^are

yielded

from

measuring

^data

extrapolated

^{to zero} thickness. By

rewriting equation (2)

^for quaterwave ^{as well as half-}

wave thickness we find

4. Experimental procedure and results.

First, ^{let us} consider the

experimental

conditions gener-

ally applied

^{for the}

photoacoustic absorption

^measure-

ments at a fixed

wavelength.

^The measurements were

performed

^{in an}

experimental

set-up

schematically

shown at

figure

^{1 and} described in detail elsewhere

[7].

The

optical absorption

^{was detected}

by

^a

photoacoustic

gas

cell-microphon

set-up

consisting

^{of cw} gas lasers ^as

light

^sources

(1), rotating

^{disk beam}

chopper (2),

^PAA

cell with

measuring

^condensor

microphone (3)

^and

lock-in

amplifier (4).

^A

sensitivity

of about o.1 V per ^W absorbed at 200 Hz was achieved connected with a

noise

equivalent

of power of about 0.5 tLW. ^{In this}

manner accurate measurements of both

amplitude

^and

phase angle

^{of weak}

signals

^{were carried out.}

Disk-shaped

^BK-7 substrates

deposited

^with

dc-sput-

tered

Ta2o5

^or

Tio2

^and

evaporated Zro2 wedge- shaped single layer

^films,

respectively

^{were used as}

samples.

In

figure

^{2 the}

signal voltage

per incident laser power

Uma./,,, is ^presented

^{versus the}

chopper frequency

^{f for}

a

gauge-absorber,

^a

Ta205

^{thin film on BK-7}

(sample I)

and a bare BK-7 substrate. The calibration was per-

Fig. 1. ^- Scheme of the experimental set-up.

formed

by using

^a thin aluminium coated

glass-sub-

strate of known

absorption. According

^{to the case of}

optical absorption originating

^from

thermally

^{thin sam-}

ples

^{we observe a}

f -1-dependence

of the measured

signal.

^The

signal peak

^{close to 1 kHz is due to the}

resonance behavior of the

photoacoustic

^{cell. In order}

to prove the

suitability

of the method we

manipulated

the ratio of film-substrate to air-film

specific

^interface

absorption (aflafs)

^{in an}

purposed-directed

^manner.

422

Fig. ^{2. -} PAA-signal ^{of a} gauge sample, ^a wedge-shaped Ta2o5 saniple ^of optical thickness nd ⁼ k /4 ^and A/2, ^{and a}

BK-7 substrate at A ⁼ 647 nm.

Aiming

^{at this a BK-7 substrate was coated with a thin}

nonstoichiometric

(and

^therefore

absorbing) Ta2o,, layer

^and then overcoated with a

wedge-shaped Ta205 single-layer

^{film up to a}

optical

^thickness

nd -- 2 A

(sample II).

^The

absorption ATaZox of

^this

sublayer

^{should be chosen to be in the} order of the interface

absorption Afs,

^and

sublayer

^{thickness was}

small

compared

^with

A/4,

^{too. A} bare reference BK-7 substrate was coated

directly

^{with a}

wedge-shaped Ta205 single-layer

^film

(sample 1). (Sample

^{I and}

sample

^{II were formed in one}

run).

The PAA-measure- ment was carried out in À

/4

steps.

Obviously,

^{as shown}

by figure

3, ^{for the}

samples

^{I and II the measured}

absorption

^A increases with

increasing optical

^thick-

ness.

Using equation (8)

^the

averaged

^bulk

absorption

coefficient

a f

^was calculated.

Replacing a and taking

into consideration the relative

light

power densities from

equations (9a)

^and

(9b)

^we obtain the

specific

interface

absorption

aaf

and afs

and, therefore, ^{the film} and interface

absorption Af (calculated

for halfwave

layer). Aaf

^and

Afs. A

summary of the above described

Fig. ^{3. - Measured} absorption A (1 ) (triangles) and A (2) (circles) ^{of a} wedge-shaped Ta205 single layer ^with (full symbols) and without (open symbols) ^{a thin} absorbing Ta2o., sublayer. ^Data calculated from the photoacoustic signal

at A ⁼ 515 nm and f ^{= 200 Hz.}

quantities

^is

given

^{in table I.}

(Note

^{that the} aaf,

Aaf

^can

be calculated

only

^{less accurate than the other}

ones).

As evident from our results the

specific

^film-sub-

strate

absorption

a fs and, ^{therefore the}

absorption Afs

of the

samples

^{I and II differs}

remarkably,

^{i.e. the non-}

stoichiometric

Ta20., underlayer

^{causes a}

significant

,increase of the film-substrate

absorption

^{in the}

sample

^II.

Thus, the difference between the interface

absorption

of the

samples

^{I and II,}

A fs II - Af I) ) , ^represents

the

Ta20x sublayer absorption ATa2ox

measured sepa-

rately

^{in a}

satisfactory approach

^i.e.

holds.

Consequently,

^we may conclude on the suit-

ability of the PAA-technique

^for,

firstly,

^the

separation

of bulk

absorption

^{within a}

single-layer

^{film and,}

secondly,

^{for the} separate measurement of air-film and film-substrate interface

absorption.

^In

figure

^{4 the}

Fig. ^{4. - Measured} absorption a ( 1 ) (triangles) ^{and A (2)} (circles) ^{of a} wedge-shaped Tio2 single layer ^{at 647 nm} (open symbols) ^{and of a} Zro2 ^{one at 515 nm} (full symbols).

measured

absorption A

^is

presented

^{for a}

wedge- shaped Ti02 single-layer

^film

(sample III).

^{For this}

sample

^an

optical

thickness of

only

up ^to nd %:. A was

chosen

(in

^{contrast to}

samples

^{I and}

II),

^therefore,

because of a insufficient number of data

points

^we

failed to determine a

possibly existing

small bulk

absorption

coefficient

a f,

T’02- The calculated interface parameters ^{and interface}

absorption

^{are shown in}

table I.

In the same

figure

^{the measured}

absorption

^{A is also}

presented

^{for a}

wedge-shaped Zro2 single-layer

^film

(sample IV)

up ^{to an}

optical

thickness nd --

3/2 A.

Evidently,

the measured

absorption

^A increases with respect ^{to the}

increasing optical

thickness, and, ^there- fore, ^{a bulk}

absorption

coefficient

a-f,

zro

may be

calculated, ^{see table I.} Furthermore, ^{both interfaces} contribute to the overall

absorption

^to almost the same extent. Next, ^we

investigated

^the

wavelength depen-

dence of the bulk and interface

absorption a f’

aaf, ^and a fs of

Ta2o5 using sample

^{I. The} measurement was

carried out with an Ar-Kr ion laser at k ⁼ 488, 515, and 647 nm. The calculated parameters

af’

aaf, and afs5

respectively,

^{are shown in}

figure

^5.

Fig. ^{5. -} Calculated bulk absorption coefficient af, specific

interface absorption Qaf ( 0 ) ^and a, ( E (sample I) ^at

A = 488, 515, ^{and 647 nm.}

5. Discussion.

Considering

the localized

absorption quantities

pre- sented in table I we may draw the

following

conclusions for the

single-layer

^films

investigated :

1. A

change

ⁱⁿ

’specific

^interface

absorption

afs caused

by

^a

purpose-directed

^{manner is} detectable

by

means of

PAA-technique.

^{From this an influence of}

such processes ^as surface sputter

etching,

^substrate

cleaning,

^and

polishing

^on the interface

absorption

should be detectable.

2.

Taking

^{into account} the increase of the film ^bulk

absorption

^{of the}

wedge-shaped, sputtered samples

^I...

III with the thickness the

specific

film-substrate inter- face

absorption

a fs exceeds

significantly

^both

specific

air-film

absorption

aaf and the ^film bulk

absorption,

^i.e.

holds at A = 515 nm. Hence,

improving

^the

optical quality

^of the film-substrate interface it should be

possible

^to diminish the over-all

absorption

^{of a}

single- layer

^{film as a}

key

^to

improving

^the

performance

^of

optical

^{thin films. For the}

wedge-shaped evaporated sample

^IV

Afs -- Aaf -- Af holds.

3. When

comparing

the above results for

Ta2o5

^with

the data

given by Demiryont et

^al.

[8]

^{carried out with}

transmission measurements any

comparison

^{must be}

done more

restrictively

^because of the low _accuracy of the transmission

measuring

^method. Therefore, ^the

absorption

^index

kTa 2 0

calculated in

[8]

^{is more than}

one order of

magnitude higher

^than the value deter- mined by ^us.

424

Table I. ^-

Measured absorption ATa20X’ calculated material parameters af,

aaf,

and afs,

and the portions

offilm

^and

interface

absorption of the

samples

investigated at ^{À. = 515 nm}

(samples

I, II, IV) ^{and À = 647 nm}

(sample

Ill), respectively.

4. From

figure

^{5 for}

Ta 2 0 5 af,

:> Qaf also holds for the

wavelengths investigated.

Moreover, ^their

wavelength dependence

^{is not}

monotonely decreasing

^for

increasing

A as observed for

genuine

^bulk

absorption according

^to

Urbach’s rule. A reason for these

findings

could be the presence of contaminations ^at the film interfaces. It should be

emphasized

^{that the above} measurements are

of

preliminary

^character

only.

^Further

investigations

have to be performed ^to confirm and to

complete

^these

results.

Acknowledgments.

The authors are

grateful

^{to F.} Coriand and M. Rack for their technical assistance ^{in careful} measurements.

References

[1] BENNETT, ^J. M., Thin Solid Films 123 (1985) ^27.

[2] WALTHER, ^H. G., WELSCH, E., ^J. Opfermann, ^Thin

Solid Films 142 (1986) ^27.

[3] CORIAND, F., SCHAFER, D., WALTHER, ^H. G., WELSCH, E., WOLF, R., ^{Thin Solid Films 130} (1985) ^29-35.

[4] TEMPLE, ^P. A., Opt. Engineering ²³ (1984) ^325.

[5] ^{WALTHER, H.} G., WELSCH, E., Scientific Instrumenta- tion (Warsaw), in press.

[6] ROSENCWAIG, A., GERSHO, A., ^J. Appl. Phys. ⁴⁷ (1976) ^64.

[7] WALTHER, ^H. G., Exp. ^Techn. Physik ³² (1984) ^531.

[8] DEMIRYONT, H., SITES, ^J. R., GELB, K., Appl. Opt.

24 (1985) ^490.

[9] SCHILLER, S., HEISIG, U., GOEDICKE, K., ^{Thin Solid} Films 40 (1977) ^327.