Quantitative infrared spectroscopy of thin solid and liquid films under attenuated total reflection conditions

VIBRATIONAL SPECTROSCOPY ELSEVIER

Vibrational Spectroscopy 8 (1995) 121-133

Quantitative infrared spectroscopy of thin solid and liquid films under attenuated total reflection conditions Peter Grosse *, Volkmar Offermann L Physikalisches lnstitut der Rheinisch-WestJfilischen Technischen Hochschule Aachen, D-52056 Aachen, Germany Received 21 July 1994

Abstract

Infrared (IR) spectroscopy of thin films demands optical arrangements, in which the electric field of the IR radiation interacts as much as possible with the film. Powerful tools to solve this problem are methods like illumination with polarised light at oblique incidence, internal reflection and attenuated total reflection (ATR). These methods have various advantages which will be explained and illustrated on various examples: thin oxide layers on insulators and metals, excitation of surface polaritons in oxide films on Si, restricted penetration depth to avoid an echo from the back of the sample. We have further shown by some unconventional applications of ATR experiments the particular facilities to characterise layered systems. In competition with other analytical methods characterising thin films and surfaces, IR ATR spectroscopy is a fast, non-destructive, and unpretending method of large reliability. The discussed examples of applications may confirm this statement. Keywords: Infrared spectrometry; Attenuated total reflection; Internal reflection; Dielectric function; Simulated spectra; Thin films

1. Introduction

The characterisation of solid and liquid samples by infrared (IR) spectrometry is based on investigating structures in the spectra due to phonon or impurity vibrations and structures due to free carders as electrons or holes in semiconductors. The characteristic parameters to be determined are in most cases the resonance frequencies and oscillator strengths related to the stoichiometry of the sample. In metals, semimetals, and semiconductors the desired parameters are the plasma frequency and the collision rate related to the concentration and the mobility of the electrons or holes. All these microscopic excitations contribute by susceptibility terms to the macroscopic property of matter * Corresponding author. 0924-2031/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved

SSD10924- 2031 ( 94 ) 0 0 0 6 8 - 9

dielectric function (DF). Therefore the aim of spectrometry is the determination of the DF e(to). Since in non-magnetic materials the DF is related to the complex refractive index, the DF may be determined from experimental data of the phase velocity and the decay of the electromagnetic wave obtained from transmittance and reflectance data. In some cases an immediate, intuitive interpretation of measured spectra is possible looking only for the chemical composition of the specimen. This is valid e.g. in the fingerprint region of the vibrational modes of organic molecules for conventional spectroscopic methods as transmittance or reflectance data. The reason is that these absorption lines are very narrow and weak. This is already discussed in [ 1 ]. There it has been shown that a more detailed, careful interpretation is necessary as well when materials with wide, strong absorption bands

P. Grosse, V. Offermann / Vibrational Spectroscopy 8 (1995) 121-133

122

®

®

©

ments the peculiar facilities to characterise layered systems.

2. D i e l e c t r i c f u n c t i o n a n d s i m u l a t e d s p e c t r a Fig. 1. ATR configurations: (a) internal reflection usable for spectroscopy on films or layered samples, suitable for studies of the Berreman effect; (b) conventionalinternal reflection usable for spectroscopy on a semiinfinite medium; (c) Otto geometry, suitable for the excitation of surface polaritons (SEW).

are considered as when more sophisticated spectroscopic methods are applied as e.g. photo acoustic spectroscopy (PAS), diffuse reflectance (DRIFT), or attenuated total reflectance (ATR). Here we discuss the situation of oblique incidence and ATR, since these methods are powerful tools in spectroscopy of thin solid or liquid films, because IR spectroscopy of thin films demands optical arrangements, in which the electric field of the IR radiation interacts as much as possible with the matter of the film. In the ATR configuration the sample is mounted behind the totally reflecting plane of an ATR prism (cf. Fig. 1). Then the sample will be excited by the electric field of propagating or evanescent waves, penetrating in the space behind the prism. At frequencies near the vibronic resonances, the sample will absorb the radiation, which leads to a decay of the reflection signal. This method has various advantages: - stronger interaction of light in the film, due to a longer path and due to an enhancement of the electric field; - more information, since data are available for s- and p-polarisation, and additional structures in the spectra occur (Berreman effect, surface polaritons); - scanning depth is variable, thus depth profiles may be analysed. A straightforward interpretation of these spectra is not possible in general. A very successful method to interpret them is a simulation of the spectra based on a model DF and on Maxwell's equations. The desired parameters of the DF are obtained by an optimum fit. Here the method and its advantages will be explained and illustrated on various examples. In addition we show by some unusual applications of ATR experi-

The frequency-dependent, complex DF e(o~)is the general material property representing the response of matter to an electric field. From this function one can calculate the complex refractive index n + iK = ~/e, the quantity organising the propagation of electromagnetic waves and their reflection at interfaces. 1 As an ansatz for the DF we use the expression e(¢o) = e' + i d ' = 1 + ~Xj(oJ)

(1)

In this expression each susceptibility term X~belongs to one absorption line j, caused by electronic or vibrational excitations. As mainly vibrational transitions are considered here, we summarise the electronic contributions to a valence electron background Xw, which is a real, constant parameter, if the actual frequency is much smaller than the frequencies of the electronic resonances. The vibronic excitations are approximated in our model DF by oscillator terms as ,~(¢.o)

EVE+

g~e¢ ~" gPoj-- o92 - io90~

(2)

where Ooj is the resonance frequency of the jth oscillator, ~ = e Z N / E o m is the oscillator strength and O~ = Fis the line width. The very reliable quantities in IR spectrometry are the resonance position g2o necessary to identify the chemical component, and O z proportional to the concentration N of the responsible oscillators. This ansatz fits the IR spectra of nearly all substances. In case of conducting materials as semiconductors one X term must be added with/20 = 0 to represent the free charge carriers. All simulations in this paper are based on a DF type of Eq. 2. To simulate the spectra besides the DF the optical arrangement of the specimen in the illuminator must be considered. This will be taken into account by solving Maxwell's equations (boundary conditions, Fresnel's formula, see e.g. [2] ) for the individual geometry. 1 This is vafid only for "non-magnetic" materials. In magnetic materials [/.,(to) v~1 ] holds n + ir = V~e. The reflection is then dependent on the relative admittance y = ~ .

P. Grosse, V. Offermann / Vibrational Spectroscopy 8 (1995) 121-133 TO I

20

"

I

"

LO

I

vacuum may be neglected, and only absorption has to be taken into account. Let the plane of incidence be the x - z plane and the interface between the two media be the x - y plane. For s-polarisation the E field has only the component Ey = Eo independent of 0, whilst for ppolarisation the E field will be distributed between an x and a z component

I

_2

10

S

-10 I

•

30

I

•

I

i

I

I

.

7

E = (EoCOSO,O,EosinO)

6

9

4 3

E

10

E

A= ....

I

'

J

i

,

(3)

For a very thin film we obtain from Maxwell's equations the absorption [2] :

5

z-

20

800

123

0

900 1000 1100 1200 1300 1400 wavenumbar t0/2xc [on "I]

Fig. 2, Model subs~aac_e (parameters fit the oscillator at 1075 cm -1 of fused silica). Di¢]eqtric function e(to) and energy-loss function Ira{ - l / e ( t o ) } are exhibited. The symbol TO labels the pole of the DF, LO labels the zero.

To discuss the influence of various optical arrangements on the structure in the related spectra we use a model substance; one oscillator (12o=1075 cm -1, Op=867 cm -1, /2~=20 cm -1) in a background evE--2.4. This l~rameter set fits a n S i O 4 vibration mode of fused silica. The DF is shown in Fig. 2. It must be emphasized that there exists a frequency interval in which Re{e} is negative. That is not observed for most oscillators of organic molecules in the fingerprint region, since the bands are too weak!

3. Very thin films and the Berreman effect

As we discussed in the introduction, experiments at oblique incidence are recommended in spectroscopy of very thin films. They yield a higher sensitivity and more pronounced structures in the spectra. At an angle of incidence 0 > 0 we have to consider two contributions to the structures in the spectra: - the direction of the electric field i.e. the case of s- or p-polarisation, and - the value of 0. The effects of these two facts are intuitively clear when we discuss the situation of a very thin film. In this approximation the reflection at the interface film-

to leg[2+ IEyl2+ IEzl2 d lm{e(to) } • cn cos0 IEil 2

(4)

where n is the refractive index of the semi-infinite medium where the light E~ comes from. Very thin means here for dielectrics: thickness d << A, the wavelength in the film material, and for conductors: d << dp, the penetration depth. This approximation yields for the three important illuminating techniques in s- and ppolarisation the formulas given in Fig. 3 for the absorption 1 - T or 1 - R, respectively [ 3 ]. The approximate formulae can be understood as follows. 3.1. s-Polarisation In a transmittance experiment with a freestanding film the 0 dependence ~ 1/cos0 of the absorption is due to the prolonged path of the light in the film. No other 0 dependence exists, since the electric field E = Ey does not change with 0. Hence the absorption peak increases with increasing 0 (see Figs. 4 and 5). In the case of a very thin film on a metal substrate no absorption occurs. The electric field vanishes in our approximation, since it is shortened due to the high conductivity of the metal. Absorption may be observed only on thicker layers. This holds true as well in external reflectance measurements as in internal reflectance. 3.2. p-Polarisation Here the E vector is divided into a tangential component ,-- sin0 and a normal one ~ cos0 according to Eq. 3. According to Eq. 4, the absorption caused by the two components is proportional to the square of E, i.e. proportional to the square of cos and sin, respectively. The angular dependence ~ 1/cos0 related to the path length, which was already discussed for s-polarisation,

P. Grosse, V. Offermann / Vibrational Spectroscopy 8 (1995) 121-133

124

Transmission s po,

1-,,

p-po].

d

(5)

l COS

Co

1-Te= C°d" Im{e}cos0+Im~- 1~sin20] Co

~.

t. e J cosO)

(6)

External Reflection IRRAS s-pol. p-pol.

-d

(7)

R, = 0 1-Re=a°gd'Im~-l~sin20-

1-

-metal

(8)

I. ~ J cos8

co

Internal Reflection ATR s-pol.

1 - R, = 0

p-pol.

1-Rp=4n3~°d co

(9)

I

I

netal

I m ~ - I l sin20 "

(10)

LT J c-~sO

Fig. 3. Absorption by a very thin film. Approximation formulae after [3].

is valid for both components. Therefore the absorption due to Ex is ~ cos20/cos0 = cos0, a decrease in absorption at large 0. The contribution of E z is ,,, sin20/cos0, an absorption increasing with 0, cf. Fig. 4. Whereas in thin films the tangential field is responsible for absorption bands at frequencies of the maxima of Ira{e}, the normal component of the field causes absorption bands at frequencies of the zeroes of the DF, or more correct at the maxima of the energy-loss function I m { - 1/8} =d'/l el 2. This is the so-called Berreman effect (see [1,4,5]), observable only at p-polarisation. To explain this polarization dependence we consider the situation near the interface of a thin film f deposited 5

•

1

"

I

"

I

4 .... ~=.o ='°

"

I

"

I

"

I

"

I

"

"1

'

/

on a substrate s. The power of the dissipated energy is given in general by Maxwell's equations by Pdiss=

tOEo~"

[E(z) 12/2

In case of s-polarisation the electric field has only the tangential component Ey, independent on the angle of incidence 0. So one gets

Pdi~ = WEod'lEyl z/2

(12)

At p-polarisation the electric field of the incident wave can be decomposed near the interface in a tangential and a normal component. The magnetic field, however, has only a tangential component Hy independent on the angle of incidence 0. Therefore at ppolarisation we substitute the two components of the E field by the magnetic field in Pdiss, Eq. 11. According to Maxwell's equation one obtains

ckz

tangential: Ex =-zoHy;

2

(11)

tOE

k.

normal: E z = -C-zoHy 0),5"

1,

0

(13) 10 20 30 40 50 60 70 80 90

angle of incidence 0 [degree]

Fig. 4. Geometricweightingfactorsof the absorptionby various E fieldcomponents,see also Fig. 3.

Pdt~s

toEo67[les- sin201 sin 20-1 _ leslz + l--~:12J~IHyl2/2

with Zo = ((~o/tZo), the vacuum impedance.

(14)

P. Grosse, V. Offermann/

VibrationalSpectroscopy8 (1995) 121-133

125

.g

. . . . ,if/

O

transmission ATR IRRAS

e-

70 °

10

Fig. 5. Simulated absorption of a film of the model substance as in Fig. 2 for s-polarisation.The icon matrix explains the configurationof illumination. For transmittance experiments of a suspended film in vacuum Eq. 14 yields with es = 1 sin20

Pdiss--tOEo,~f[cos O ,,~f,'---~]Zo'Hy[2/2 __

rt

2

.at_

2

(15)

corresponding to the absorption Eq. 6. For the film on a metal back we use the approximation Iesl >> 1 valid for metals in the IR. In this case the first term in Eq. 14 can be neglected, because the tangential E field is shortened, and only the term for the normal E field remains tt

Pdiss =

2

f

" ) - -1

0.)•o• f s i n 0 I m ~ - - ~ f / ~ l H y l

2

/2

(16)

Eq. 16 corresponds to the absorption in Eq. 8. Obviously the absorption near the LO frequency is enhanced

by a factor 4 compared to the transmittance experiment. The formulae shown in Fig. 3, however, are only approximations for very thin films. The exact solutions of Maxwell's equations for various optical arrangements and film thicknesses up to 10 nm are plotted in Figs. 5 and 6. These results are simulations assuming the model substance as in Fig. 2. The peak at the frequency of the zero of the DF is labelled by D-LOin the figures, the peak at the maximum of the DF is labelled by/'Zro. Both Eqs. 15 and 16 lead to absorption structures proportional to the energy-loss function caused by the normal component of the E field. In Fig. 2 the dielectric function of the model substance is compared with the energy-loss function. The heights of the maxima, responsible for the absorption structure in the spectra,

126

P. Grosse, V. Offermann / Vibrational Spectroscopy 8 (1995) 121-133

I-rill

ATR

transmission IRRAS

15 0

I

I

I

700

10

Fig. 6. Simulated absorption of a film of the model substance as in Fig. 2 for p-polarisation. The icon matrix explains the configuration of illumination.

are given in simple cases approximately by Max{~f"} = ~p/D-ro/2~ and Max{energy-loss function}=/~/OLO/2~2VE. Although near OLO the imaginary part of DF is very small, a strong absorption line is observed due to the enhancement of the normal electric field. This is shown in detail in Fig. 7 for the configuration 10-nm film on a Ge prism, p-polarisation at 0= 15 °. A metallic backing of the film leads to a further field enhancement, in particular when the incident light comes from a prism with a high refractive index (Fig. 6). This leads to another factor n 3, i.e. for a Ge prism the sensitivity is amplified by a factor 64 (n = 4). The conventional absorption of the vibronic resonance at vanishes for very thin films on a metallic substrate, as explained above.

In all cases the absorption due to the normal electric field shows a maximum blue-shift, compared to the frequency of the conventional vibronic resonance. Two absorption bands may be observed, both caused only by one vibronic mode. The Berreman effect is a macroscopic phenomenon of electrodynamics and not a microscopic problem of molecular dynamics! In case of weak and narrow bands often the two absorption peaks are not separated enough to be resolved. This is the case for many vibronic absorption lines of organic molecules in the fingerprint region! The Berreman effect, however, becomes relevant in spectroscopic characterisation of thin films of e.g. oxides, nitrides, silicides, and compound semiconductors, i.e. substances being very important in thin film technology and microelectronics.

P. Grosse, V. Offermann / Vibrational Spectroscopy 8 (1995) 121-133 40

I

'

|

•

I

',

:

',

:

',

I

method is also called internal reflection [6] (cf. Figs. 1 and 3). In practice this will be achieved by a wave propagating inside a prism or a semicylinder. Depending on 0 the electromagnetic field penetrates into the medium outside the prism as a propagating wave if 0 < 0tota 1 o r as an evanescent wave, if 0 > 0tota 1 (cf. Fig. 8). At frequencies near the vibrational lines the excitation of the sample results in absorbtion of the radiation, which leads to a decay of the reflection signal. The reason for the total reflection, as explained in Fig. 8, is the fact, that the periodicity of the electromagnetic field in time (o9) and space (ktang=kx,y, the component of the wave vector k in the interface) must be the same at both sides of the interface. On the other hand for the total length kj in mediumj holds, according to the wave equation

30

_ 2o 10 o 4

oO[

:

',

:

~- 6ooi

~

127

400

1~ 2o0 (g °

•"- 0.03

o92 Ej~- = k~j~- k~tang"1-k~norm

~" 0.02 o

(17)

o.ol

_~ 0.00 900

1000

1100

1200

1300

1400

The incident wave, propagating in the medium e 1 (prism), has a component

wavenumber =/2xc [crn"I]

Fig. 7. Berreman effect in an SiO2 film (d = 10 nm) on the Ge prism, p-polarisation, 0 = 15°. The maximum absorption at Oro is due to the large Im{ ~}, an enhancement of the tangential electric field hardly takes place. The blue shifted absorption maximum at/2LO is caused by a strong enhancement of the normal field (field enhancement ca. 28), whereas lm{8} is very small.

4. Internal reflection Consider now a thick film or even a semi-infinite medium covering the reflecting surface outside of the ATR prism (cf. Fig. lb). An electromagnetic wave incident onto the plane surface will be reflected inside the prism, depending on the angle 0. Therefore the

O92

~a,g = ~ sin2 0 = e l - j s i n 20

(18)

Outside the prism, in the adjacent medium 2, the component k~ng must be the same as in medium 1 (eq.(18) ) due to the continuity condition. Thus we get from Eqs. 17 and 18 for the component knormin medium 2:

(.02 k~norm ~-- o°2-~ --

(.02

O92

~1 c-~2 i n 2 0 = ~ - ( e 2 - e l s i n 2 0 )

(19)

In case el,2 are real, then the sign of ~ o ~ decides on the character of the wave field in medium 2, see Fig. 8:

n=2

n=l

O~total

O:Ototal

O~)tot=l

Fig. 8. Continuity in spatial periodicity at an interface between medium I with n = 2 (prism) and medium 2 with n : 1 (vacuum). At a given frequency the wavelengths in the two media are ;tl and A2.For 0 > 0tota~the tangential periodicity cannot be continued. In medium 2 no propagating wave can be excited.

P. Grosse, V. Offermann / Vibrational Spectroscopy 8 (1995) 121-133

128

silicon dioxide I

I

I

5. Surface polariton waves

I

~'~3

In the previous chapter we have discussed the phase velocity Cph= w/kta,g of the electric excitation near the interface of a higher refractive medium 1 and a medium 2. When this phase velocity is larger than the phase velocity c/n2 of the propagating waves in medium 2, then we found that only exponentially damped tails penetrate in the medium 2. We therefore now ask in general if waves can exist, pinned to the interface between two media 1 and 2, with an amplitude decreasing exponentially on both sides of the interface. It can be shown that those waves are possible, however, in case of p-polarisation only [ 7]. 2 They are called surface polaritons or surface electromagnetic waves (SEW). For the magnetic field of such a transversely decaying wave we use the following ansatz:

N "0

•

0

-1

-2 4

•

I

'

I

J

0 1 )osition z [~m]

2

I

'

I

'

I

'

I

'

I

'

I

•

I

,

I

,

I

,

I

,

19 1D r" 0

~o

,

I

10 20 30 40 50 60 70 80 90 angle of incidence e [degree]

Fig. 9. Penetration depth versus angle of incidence outside an ATR device (lower part). Exponentialdecayof the fieldin an SiO2sample (z>0), mountedon a Ge ATR prism at 2000 cm-1, 0=25 ° (upper part). The modulationfor z < 0 is the interference pattern due to the superposition of the incident and the reflected waves inside the Ge prism. If (82 - el sin20) > 0, then k, ormis real, i.e. the wave outside the prism in medium 2 is a propagating one. If ( 8 2 - 81 sinE0) < 0, then k.om~ is imaginary, and total reflection occurs. Only tails of the electromagnetic field penetrate into medium 2. The characteristic critical angle 0tota I follows from the condition 8z - 8,sin20total = 0, i.e. sin0to,al = n2/nl

(20)

We describe the decay of the fields above the critical angle by a penetration depth dp given by C

(21)

dp --/_01/82 -- 81sin20 The penetration depth decreases from dp=o~ to dp = c~ [~/( ~2 - ~1 ) ] when 0 increases from 0totalto 90 °. In Fig. 9 we have shown the situation of a sample mounted on a Ge prism. In the ATR prism (z < 0) the field is periodically modulated. That is the interference pattern due to the superposition of the incident and reflected waves. Outside the prism ( z > 0) the field decays exponentially in the Si02 sample.

//j =/-/jy exp ( - kS'z) exp i( k;c - ~ot)

(22)

a wave propagating in the x direction with a maximum H field in the interface at z = 0. The corresponding tangential E field Ej~ and the normal field Ejz are given by Eq. 13. Since in the interface z-- 0 the tangential E field is continuous, i.e. Elx = E2, leading to the condition kl__z= k2z 81 82

(23)

Moreover the components of the wave vectors must obey the wave equation, Eq. 17. From these two conditions one obtains the dispersion relation for surface polaritons:

0)2 8182 0")2 ~ ~ - - C2 < + 82' ~Z C2 8, + 82

(24)

For simplicity, we discuss only real DF's 81,2. An exponential decay of a wave in both z directions according to Eq. 22 requires 8a + 82 < 0. Propagation in x direction requires a real k~, andthus 8182 d 0 , i.e. the sign of the two DF's must be opposite. In case of an interface of a medium 2 and vacuum (81 = 1) Eq. 24 has the form 2 In magnetic materials (/x ~ 1) those modes are also possible in s-polarisation.

P. Grosse, V. Offermann / Vibrational Spectroscopy 8 (1995) 121-133 '

0

'

• I • I ' I ' I • I • I ' I ' I

1,

-1

~,

,

n¢ -2

,, . . . . . . . . IIi

i I ,

I

I

I

1"

,

10 20 30 40 50 60 70 80 90

O.a

'

angle of incidencee Idegree]

!°+I, 1 0.4

~ 0.~' 1000

1100

1200

1300

wavenumber ~/2xc [cm"~]

Fig. 10. Dependence of the spectral position of surface polaritons on the angle of incidence in an Si ATR attachment. Simulations based on the model shown in Fig. 2. The air-gap in the Otto geometry has a thickness d ~ 1 p~m.

c 2 1 + ez

to2 klZ2

1

c 2 1 + ~'2

to2 k2zZ

~

frequencies, related to dispersion Re{62(to)}. When the surface polaritons are excited, the ATR reflectance shows an absorption band. These bands can be observed at frequencies approximately lying in the interval D-ro < to < OLO. The external excitation of surface polaritons in the sample by the ATR tails takes place across an air gap between the back of the prism and the sample (Otto geometry [ 8 ] ), see Fig. 1. The thickness of the gap is of the order of the penetration depth, Eq. 21. Thus, on the one hand, the tails of the wave in the ATR prism are strong enough to excite the surface mode. On the other hand, the field of the surface mode couples only very weakly in the prism. All details discussed here for an interface between a dielectric medium 2 and vacuum are analogously also valid for a second dielectric medium 1 instead of vacuum. The assumption of real DF's was made only to discuss the meaning of the various formulae. In the simulations discussed later in all cases complex DF's have been taken into account, using the same formulae.

(25)

c 2 1 + ~z

Here e2 must be negative and in particular - ~ < e2 < - 1 to obtain a real kx. For the phase velocity of those surface waves holds to/kx < c. Hence a surface wave cannot be excited by the ordinary electromagnetic wave propagating with the vacuum velocity c. There is a possibility, however, to stimulate the surface waves by the decaying tails at the back of an ATR prism (Fig. 8), because the tails propagate corresponding to a wave vector kx, Eqs. 18 and 25: 2

1.2

('02"

2

~~x=npriSmc2al0n

0)2

~2

C2 1 + 6 2

(26)

6. E x a m p l e s

After the discussion of the basic phenomena observable in optical experiments at oblique incidence and internal reflection, we want to show examples of measured spectra. 6.1. B e r r e m a n effect

As explained above for p-polarisation in thin films an absorption band will be observed at the frequency 0.6 0.5

i.e. via an ATR prism a surface polariton can be excited, depending on the refractive index of the prism and on 0, at a frequency to for which the DF e2(to) obeys: (27)

nprismSin2 0 ~2(to)

129

1 --

2 " nprismSln

2

0

This is shown in Fig. 10 where the real part of the DF of the model oscillator (Fig. 2) in the spectral region near the TO resonance is plotted. Illuminating the sample via an Si prism at 0 = 35 or 25 °, respectively, leads to the excitation of surface polaritons at different

Ta20 s

.....

12; 0.3

0.1 0.0

'

0

'

!

1000

'

~

2000

3000

4000

wavenumber m/2xc [cm "~]

Fig. 11. Internal reflection spectra of an oxidised Ta layer. Experiments in p-polarisation and simulated spectra. Configuration: Ge cylinder prism, 3 nm Ta/Os, opaque Ta layer on a glass substrate, 0 = 60 and 70 °.

P. Grosse, V. Offermann / Vibrational Spectroscopy 8 (1995) 121-133

130

of the zero of the DF (LO resonance). This absorption is enhanced when the film is deposited on a metal substrate (cf. Fig. 7). In Fig. 11 reflectance spectra [9] are shown of a 3-nm tantalum oxide film, as grown on a sputtered Ta layer. The absorption is caused by optical phonons characteristic of the stoichiometry Ta2Os. A further advantage was achieved by mounting the sample on a Ge ATR prism to amplify the absorption structure (see Fig. 7). Thus it is possible to characterise also very thin oxide films by internal reflection technique. The second example is the characterisation of a depletion layer on a GaAs sample. In semiconductors negative charges of monopolar or dipolar layers on the surface repel the conduction electrons into the bulk and an electron-free depletion layer remains (cf. Fig. 12). These layers lead to an absorption due to the Berreman effect. In Fig. 13 the external reflectance spectrum of an opaque, conducting n-GaAs sample is shown for nearly perpendicular incidence ( 0 = 7°). The spectral structures in the reflectance are the two plasmon-phonon edges near 260 and 400 cm-1, characteristic of heavily doped polar semiconductors (e.g. [10]). These two edges are near the zeros of the DF of doped semiconductors. The second spectrum in Fig. 13 shows the internal reflectance of the same specimen, measured at 0 = 70°, p-polarisation. Now another absorption peak is observed at the frequency of the zero (LO resonance) of insulating GaAs. This is the Berreman absorption of the dielectric, insulating depletion layer on the highly

conduction - - -', ,.-: ...............

. . . . . . . . .

'~

0

~

Fermi

band

tO

u

0.8

0.a 0.4

0.3

7* p-pol.

reflection

external : I

0.0

ATR

0.8

:

',

m I

:

i

I

'

'

I

70* p-pol.

(13 ¢J

o.a

LO

u

'~

o.4 0.2 0.0

0

'

I00

'

~o

" ~"

wavenumber

'

3OO

40o

5OO

[cm-l]

Fig. 13. Reflectance of an opaque n-GaAs sample. Upper part: external reflection at 0 = 7 ° for p-polarisation. Lower part: internal reflection, the sample was mounted on a Ge ATR semicylinder, 0 = 70 °, p-polarisation. The absorption peak labelled by LO is caused by the Berreman effect of the optical phonon in a depletion layer on the GaAs sample. Solid line: experiments; broken lines: simulations.

conducting GaAs bulk sample. A quantitative interpretation of the spectrum yields a thickness of the depletion layer of 15 nm [11].

ene.r~y

donator

states

valence

band

nbulk

positionz

Fig. 12. Surfaces of semiconductors are often charged negatively due to surface states or adsorbates. These charges repel the free conduction electrons into the bulk and an insulating depletion layer remains (schematic).

6.2. Internal reflection The internal reflection method has three characteristic advantages compared to conventional reflectance or transmittance experiments: field amplification related to a higher sensitivity, variable scanning depth depending on 0, and only one surface of the sample being investigated [6]. Now three examples are discussed making use of various penetration depths dp, according to Eq. 21. The first example is a very classical one: in Fig. 14 vibrational spectra of a silicone oil are presented. One spectrum has been measured in ATR configuration. Then the DF of the silicone oil was determined from the experimental data by a fitting procedure (cf. Fig.

P. Grosse, V. Offermann / Vibrational Spectroscopy 8 (1995) 121-133 1.0

.

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1000

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1600

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600

.

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1500

.

.

.

Fig. 15. DF of the silicone oil, fitted to the experimental ATR spectrum of Fig. 14.

2000

wavenumber o/2~c [cm -1]

Fig. 14. Below: measured and simulated ATR spectrum of a silicone oil (ATR attachment: KRS6 semicylinder). The simulation is based on an optimum fit of the DF (see Fig. 15). The deviation of the fit from the measured data is hardly resolved. Above: simulated transmittance spectrum, calculated with the fitted DF. The bands are saturated, hence a quantitative analysis of a transmittance experiment would not be possible.

15). 3 Finally the transmission spectrum of a cuvette filled with the silicone oil was simulated. The transmittance shows a saturation of the strong bands, thus a quantitative interpretation would be impossible. In the ATR experiment a very small penetration depth dp was chosen by adjusting a suitable large 0. Since the thickness of the active layer, contributing to structures in the spectrum, was of the order dp = 0.5/zm, the absorption bands are not saturated here. In the second example a thin layer of porous Si (porosity ca. 80%) on an opaque Si wafer is considered. These samples are of interest for optoelectronic devices. The specimens are prepared by an electrochemical etching procedure [12]. The ATR spectra in Fig. 16 are obtained at 0= 7 ° and 75 °. At 7 ° no total reflection occurs since the critical angle is 41 °. Therefore dp is infinite, i.e. the light will be partially reflected at the surface air-porous Si and at the interface porous Si-Si. The interference of the echoes leads to FabryPerot fringes in the W-spectrum. From periodicity and amplitude of the fringes, the refractive index and thick-

ness of the porous layer can be determined [ 13 ]. In our case the thickness is 17/zm. Then 0 is increased up to 75 ° and the corresponding dp decreases down to ca. 1 /zm. That is smaller than the thickness of the porous layer and the Fabry-Perot fringes disappear, since no echo from the internal interface arises. The spectrum now clearly reveals absorption lines due to adsorbates on the porous silicon. For these experiments an illuminator is recommended which allows to change the angle of incidence without new alignment and without opening of the spectrometer [ 14]. The third example is a simulation of experimental data not shown in this paper [ 15]. It demonstrates the enhancement of spectral structures obtained for powder samples, when the experiments are carried out by internal reflection, and the powder is immersed in a liquid, highly refracting matrix. In Fig. 17 the absorbances of a FeOOH powder sample (Goethit) are compared in i

tO

~8

i

i

75°

T

"

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~

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~ 0.8 '~

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3 The fit was an iterative procedure. Starting with an oscillator model (Eq. 2) this first approximation was improved by changing the imaginary part of the fittet DF and calculating the real part according to the Kramers-Kronig relation.

i

u/2wc (cm-11

Fig. 16. ATR spectrum of 17 porous silicon on a Si wafer. At 0 = 7 ° the penetration depth is much larger than the thickness of the porous layer, Fabry-Perot fringes are observed. At 0 = 75 ° the light penetrates just about 1 p,m in the layer, no interference fringes result.

132

P. Grosse, V. Offermann / Vibrational Spectroscopy 8 (1995) 121-133 1.0

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1500

[cm-1]

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2000

Fig. 17. Simulated ATR spectrum of FeOOH powder immersed in paraffin oil: 3-~m film of powder in oil (volume fraction 10%) spolarisation, 0=45 °, parallelepiped KRS5, 10 internal reflections. Solid line: matrix paraffin oil; dotted line: matrix vacuum. The small dips near 1500 cm -1 are caused by the incompletely compensated absorption of the oil.

case the powder is immersed in vacuum or paraffin oil. 4 For the simulation an ATR attachment was considered of a KRS5 parallelepiped, 45 °, leading to 10 internal reflections. The thickness of the powder sample was assumed to be 10/xm and the volume fraction of the powder 10%. The mixing of powder and matrix was taken into account by calculating an effective DF according to the M. Garnett formula [ 16]. The simulation shows the advantage of a highly refracting matrix to obtain stronger structures in the spectrum, related to a higher sensitivity. The advantage of the ATR configuration is the simple preparation: the specimen is a mixture of FeOOH and paraffin oil deposited on the active surface of an ATR prism. Further in ATR spectroscopy the preparation of samples of liquids and pastes is very simple by wetting the ATR attachment by the material under consideration. And if the penetration depth is smaller than the thickness of the sample, no information about the state of the back or of the thickness is necessary for a quantitative interpretation of the measured data.

6.3. Surface polaritons SEW The last example concerns absorption bands due to excitation of surface polaritons. The spectra of Fig. 18 are obtained on a 0.86/xm thick SiO2 layer deposited 4The plotted "absorbance" was calculated by the formula A = lOlg(Rpowd~r.~,at~ix/Rmauix).

Fig. 18. ATR spectrum of an 0.86-/,un SiO2 film on Si. Excitation of surface polaritons (SEW) at the air-oxide interface in the Otto geometry (Ge hemicylinder, air-gap 1.1 p,m).

on a Si substrate. This layered sample was measured in the Otto geometry, i.e. the oxidised surface of the sample was mounted parallel to the base plane of the ATR prism in a distance of 1.1 /xm. In p-polarisation the ATR spectrum shows absorption lines at positions depending on 0 according to Eq. 27. A consistent fit for the spectra obtained at various angles on the same specimen, based on one DF of SiO2, yields as a result a realistic DF, which is in particular of high accuracy in the spectral regime Re{~oxido} < - 1. The thickness of the air gap is also obtained by the fit. In case the available spectrometer is working up to high wavenumbers, the air gap can also be determined directly from measured Fabry-Perot fringes, observed below the critical angle with wavelengths smaller than the air gap. It must be emphasised once more, that absorption lines due to the excitation of surface polaritons are observable in the spectrum in between the absorption line of the TO resonance (s-polarisation) and the LO resonance (Berreman effect, p-polarisation) !

7. C o n c l u s i o n

The aim of the present paper was to discuss the advantages of peculiar spectroscopic methods as illumination at oblique incidence, internal reflection, and ATR, when the specimens to characterise are thin films. The topological and electromagnetic effects responsible for more pronounced structures in the spectra have been explained based on Maxwell's equations. The various situations have been demonstrated by simulated spectra, assuming a model substance similar to a vibrational mode of amorphous SIO2. It was shown, however, that the shape and position of characteristic absorption lines, observed by those

P. Grosse, V. Offermann / Vibrational Spectroscopy 8 (1995) 121-133

unconventional spectroscopic methods, differ in comparison to the lines obtained by conventional transmission spectroscopy. An example is the blue-shift of the absorption line due to the Berreman effect or due to surface polariton excitation. These problems become relevant in particular for substances whose DF shows strong, wide vibronic bands. Therefore we recommend to compare not immediately the absorbance in the spectra obtained by various methods, but to determine a property of matter, i.e. a susceptibility or a dielectric function, respectively. Such a material property then is the quantity appropriate to quantitative spectroscopy. Since the determination of the DF from spectral data is possible only in some cases by a straight-forward algorithm, we have recommended a fitting procedure. Examples of those fits are presented in the paper.

Acknowledgements The authors thank the members of our group of spectroscopists for stimulating discussions, assistance in the spectroscopic measurements and the development of suitable software, in particular W. TheiB, B. Heinz and M. Feuerbacher.

133

References [1] [2] [3] [4]

P. Grosse, Vib. Spectrosc., 1 (1990) 187. B. Harbecke, Appl. Phys. B, 39 (1986) 165. D.W. Berreman, Phys. Rev., 69 (1963) 2193. B. Harbecke, B. Heinz and P. Grosse, Appl. Phys. A, 38 (1985) 263. [5] P.Grosse, in U.R6ssler (Ed.), Advances in Solid State Physics, Vol.31, Vieweg, Braunschweig, 1991, p. 77. [6] N.J. Harrick, Internal Reflection Spectroscopy, Wiley, New York, 1967. [7] V.M. Agranovich and D.L. Mills (Eds.), Surface Polaritons, North-Holland, Amsterdam, 1982. [8] A. Otto, Z. Phys., 216 (1968) 398. [9] V. Offermann, P. Grosse, M. Feuerbacher and G. Dittmar, Verh. Dtsch. Phys. Ges. (VI), 29 (1994) 905. [ 10] P. Grosse, Freie Elektronen in Festk~rpern, Springer-Verlag, Berlin/Heidelberg/New York, 1979. [11] M. Feuerbacher, P. Grosse, V. Offermann and S. Hilbrich, Verh. Dtsch. Phys. Ges. (VI), 29 (1994) 1017. [ 12] A. Halimaoui, G. Bomchil and R. Herino, Microelectron. Eng., 8 (1988) 293. [13] M. Wernke, M. Amtzen, W. TheiB, V. Offermann, H. Miinder and M. Th6nissen, Verh. Dtsch. Phys. Ges. (VI), 29 (1994) 1029. [ 14] V. Offermann, P. Grosse, M. Feuerbacher and G. Dittmar, Vib. Spectrosc., submitted for publication. [ 15 ] U. Kiinzelmann, private communication. [16] M. Evenschor, P. Grosse and W. TheiB, Vib. Spectrosc., 1 (1990) 173.