Method of collecting pure vibrational absorption spectra of amorphousthin ®lms

Tong Lia, Jerzy Kanickia,*, Carol Mohlerb

aCenter for Display Technology and Manufacturing, Department of Electrical Engineering and Computer Science, The University of Michigan, 2360 Bonisteel

Blvd., Ann Arbor, MI 48105, USAbDow Chemical Company, Midland, MI 48641, USA

Received 5 June 1998; received in revised form 14 February 1999; accepted 15 February 1999

Abstract

We have presented a practical method to collect vibrational absorption spectra of hydrogenated amorphous thin ®lms free of interference

fringes and free of absorption deviation induced by interfacial re¯ection. The experimental setup description and theoretical explanation

given in this paper have provided adequate information for spectrum collection. Based on the same setup, we have also demonstrated that a

vibrational absorption spectrum free of shape distortion can be obtained by using a regular light source. Through the comparison between

proposed and conventional methods, we have shown that a pure vibrational absorption spectrum is the most reliable spectrum for absolute

thin ®lm microstructure assessment, while a shape-undistorted spectrum is reliable for relative thin ®lm microstructure assessment. q 1999

Elsevier Science S.A. All rights reserved.

Keywords: Fourier transform infrared spectroscopy; Optical properties; Silicon; Silicon nitride

1. Introduction

Microstructure of thin solid ®lms is normally character-

ized by its vibrational absorption spectrum obtained by

Fourier transform infrared spectroscopy (FTIR) [1]. Various

structural parameters such as bond absorption strength coef-

®cients, or oscillation proportional constants, stoichiometry,

hydrogen content (H-content), etc., are derived from

conventional spectra, which are widely used in material

quality assessment [2,3]. However, the conventional vibra-

tional absorption spectra collected at normal beam inci-

dence contain interference fringes [4,5]. So, many

different measures have to be taken to eliminate the

fringe-caused deviation from the as-measured spectra.

Among a variety of measures, three methods appear to be

the most popular. The ®rst method involves subtracting a

mathematically generated fringe pattern from the measured

spectrum [6]. The second utilizes a wedged double-side

polished silicon (Si) wafer as the substrate [2]. The third

is to deposit a very thin layer ( , 1000 AÊ ) so that the fringe

spacing is large enough that the baseline looks like a straight

line [3]. Although these measures do reduce the interference

induced deviation to some extent, they have very limited

capability to completely eliminate the fringes from the spec-

trum. For example, since fringe patterns can never be

perfectly matched due to the difference between theoretical

and measured patterns [7,8], the subtraction of the interfer-

ence fringes from the absorption spectrum can hardly yield a

reliable result. Thus, a practical and reliable measurement

method is very much desired if a quantitative determination

of the ®lm microstructure is needed.

In fact, method to avoid the interference deviation has

been developed for quite a while in spectroscopy in general

[9]. However, similar method has not been adopted in this

speci®c area somehow. This paper describes the method of

collecting a vibrational absorption spectrum free of inter-

ference fringes. In particular, by utilizing Brewster's law

[10] we can eliminate the re¯ection from a certain interface

at certain light incident orientation. Comparison with a

conventionally recorded spectrum indicates that the

proposed method is the only existing method that allows

the collection of a pure vibrational absorption spectrum

without interference fringes induced absorption deviation.

2. Experimental

The hydrogenated amorphous silicon (a-Si:H) and hydro-

Thin Solid Films 349 (1999) 283±288

0040-6090/99/$ - see front matter q 1999 Elsevier Science S.A. All rights reserved.

PII: S0040-6090(99)00193-5

genated amorphous silicon nitride (a-SiNx:H) thin-®lms

were deposited on double-side polished crystalline Si wafers

in a plasma-enhanced chemical vapor deposition (PECVD)

system using standard RF excitation with the power of 25

and 100 W, respectively. During the process, the Si

substrate temperature was set at 2508C, process chamber

pressure was kept at 0.43 Torr, and gas ¯ow rates were 50

sccm (silane) for a-Si:H, 18 (silane) and 200 sccm (ammo-

nia) for a-SiNx:H. The ®lms' thickness was measured using

a Dektak surface pro®ler after step etching. It should be

pointed out that the a-Si:H thin ®lm used in this study was

intentionally prepared with a high concentration of SiH2

bonds to illustrate the difference between baseline corrected

and fringe-free spectra.

The refractive index ®lm was deduced from IR spectrum

by observing a straight baseline at Brewster angle using p-

polarized light (see subsequent sections). Likewise, the Si

wafer's refractive index was deduced by observing maxi-

mum gain using Bio-Rad FTS-40 Fourier transform infrared

spectrometer at Brewster angle with p-polarized light,

because a complete energy transmission can be realized at

this point. The absorption coef®cients of the absorption

peaks were measured at Brewster angle condition (see

subsequent section for details), and the extinction coef®-

cients were calculated from

k � a

4pv�1�

[8,11] where a is the absorption coef®cient and v is the

wavenumber. The measured refractive indices of Si

substrate and ®lms (a-SiNx:H and a-Si:H), and absorption

as well as extinction coef®cients of the ®lms are tabulated in

Tables 1 and 2 for a-SiNx:H and a-Si:H, respectively.

The IR spectra were recorded at room temperature using a

Bio-Rad FTS-40 Fourier transform infrared spectrometer

and analyzed using Bio-Rad Win-IR software. The spectra

having a spectral resolution of 8 cm21 were the average of

64 scans. The aperture of the probe beam was set at 2 cm21

and detector gain ampli®cation was set at unity. A Pike

ZnSe Wire Grid linear polarizer was used to produce a p-

polarized probe beam and a Harrick Brewster's angle

sample holder was used to adjust the beam's incident

angle. An unit assembly was made in our laboratory to

accommodate polarizer and sample holder, in which the

polarizer is positioned at the central spot of the probe

beam, and can be easily slid in or out according to the

experimental requirements.

3. Method of collecting a pure vibrational absorptionspectrum

3.1. Theoretical fundamentals

3.1.1. The Brewster angle

When a beam of light passes through a thin ®lm with the

thickness comparable to the light wavelength, a pattern of

interference fringes can normally be observed due to

constructive and destructive interference of the re¯ected

and transmitted light components from various interfaces

[10]. These fringes are the superposition between fringes

of p- (electrical ®eld vibrating within the plane parallel to

the incident plane) and s-polarized (electrical ®eld vibrating

perpendicular to incident plane) light beams, since an unpo-

larized light beam can be viewed as a sum of a p- and s-

polarized waves. The re¯ectances of p- (Rp) and s- (Rs)

polarized waves at the interfaces strongly depend on the

T. Li et al. / Thin Solid Films 349 (1999) 283±288284

Table 1

Measured refractive indices, extinction coef®cients, and optical absorption coef®cients for various modes of a-SiNx:H, and refractive indices of Si substrate at

corresponding wavenumber

v (cm21) 800 Si-N(as)a 1200 N-H(b) 1547 N-H2(b) 2160 Si-H(s) 3346 N-H(s)

ns 3.84 3.86 3.87 3.89 4.01

nf 1.91 1.90 1.89 1.88 1.82

kf 0.868 0.171 1:642 £ 1022 7:033 £ 1023 3:667 £ 1022

a (cm21) 8.724 £ 103 2:574 £ 103 3:193 £ 102 1:909 £ 102 1:542 £ 103

a The bracketed scripts of as, s, and b stand for asymmetric stretching, stretching, and bending modes, respectively. For Si-N(as) and N-H(b) modes, the

optical absorption coef®cient is calculated from the conventional measurement using Newton recursion method. The ®lm thickness is about 1000 AÊ .

Table 2

Measured refractive indices, extinction coef®cients, and optical absorption coef®cients for various modes of a-Si:H, and refractive indices of Si substrate at

corresponding wavenumber

v (cm21) 630 Si-H(r) etc. 845 (Si-H2)n(b)a 880 Si-H2(b) 2000 Si-H(s) 2090 Si-H2(s)

ns 3.83 3.84 3.84 3.89 3.89

nf 3.27 3.28 3.28 3.31 3.31

kf 0.15865 5:605 £ 1023 1:481 £ 1022 1:354 £ 1022 1:54 £ 1022

a (cm21) 1:256 £ 103 59.52 1:6378 £ 102 3:403 £ 102 4:0459 £ 102

a The bracketed scripts of s and b stand for stretching and bending modes, respectively. The ®lm thickness is about 9000 AÊ .

beam's incident angle and the refractive indices of the

media [10]. Of which, Rp initially decreases with the

increase of incident angle, and after it reaches minimum,

the re¯ectance starts to increase with the incident angle

rapidly [12]. The incident angle, which yields the minimum

(vanished) re¯ectance, is called Brewster angle. This angle

is determined by the indices forming the interface, and can

be expressed by [10,13]

tanuB � nr

ni

�2�

where nr and ni are the refractive indices of the refracted and

incident media, respectively.

At Brewster angle the p-polarized light is fully trans-

mitted into the second medium without any re¯ection.

Thus, the vibrational absorption spectrum collected by

using p-polarized light at Brewster angle should display

no interference fringes. Based on the refractive indices of

a-Si:H and a-SiNx:H, the calculated Brewster angles for a-

Si:H and a-SiNx:H ®lms used in this work are 738 and 628,respectively, while the variations of Rp and Rs as functions

of the light incident angle can be found elsewhere [12].

3.1.2. Dispersion and extinction coef®cient consideration

It is well known that the refractive index is wavelength or

frequency dependent. Correspondingly, Brewster angle is

only de®ned for single wavenumber or spectral range in

which the variation of the refractive index is insigni®cant.

As indicated in Tables 1 and 2, the refractive indices of

different modes for both ®lms are different. Therefore,

strictly speaking, the interference-free spectrum should be

obtained at different incident angles according to the corre-

sponding index within absorption peak region. However, for

the ®lms used in this study, the variation of the refractive

index is not signi®cant within the observed spectral range,

and it becomes negligible when the index variation is

converted to the incident angle variation. A single Brewster

incident angle can result in a straight baseline within the

illustrated spectral range in the presence of the absorption

peaks. Therefore, for illustration purpose, only a single inci-

dent angle is used in this paper. In practice, however, the

usage of single or multiple incident angles should be based

on the observation of the straight baseline of the spectrum in

the observed spectral range.

For absorbing materials, the refractive index of the ®lm is

complex, which makes the analysis of the re¯ection, espe-

cially at oblique incidence, very complicated. The extinc-

tion coef®cients at various absorption peaks will change the

interference pattern (intensity and period) at the peak more

or less according to the value of the extinction coef®cient

[11]. For most modes of both ®lms, these extinction coef®-

cients are small, and will not cause signi®cant fringe pattern

deviation from that of non-absorbing baseline. However, for

prominent peaks such as 880 cm21 of a-SiNx:H and 630

cm21 of a-Si:H, the extinction coef®cients are nontrivial

and will cause signi®cant fringe pattern deviation from

that of the baseline at incident angles other than Brewster.

Fortunately, when the incident angle approaches Brewster

angle, this deviation becomes insigni®cant, which is indi-

cated by the fact that at Brewster angle all absorption peaks

have minimum intensities (see subsequent sections). That is,

when the baseline of the absorption spectral range becomes

straight, the absorption peak has a minimum peak intensity

indicating that the interfacial re¯ection is minimized. The

details of the extinction coef®cient impact on the absorption

peak intensity, especially at normal incidence, are beyond

the scope of this paper and can be found elsewhere [8,14].

For the simplicity, the extinction coef®cients are ignored in

the calculation. Instead, the effective indices obtained from

the IR spectrum are used, and hereafter labeled as refractive

index.

As shown in Tables 1 and 2, the refractive index of Si

wafer also varies with the wavenumber, although the varia-

tion is not signi®cant in the observed spectral range. This

variation will cause the absorption intensities deviate differ-

ently at different absorption peaks at normal incident, since

the magnitude of the re¯ection at the ®lm-substrate interface

varies at different wavenumbers due to index non-unifor-

mity. However, at Brewster angle, this variation does not

affect the absorption spectrum, because the multiple re¯ec-

tion is eliminated at the ®rst interface. Hence, again, for the

simplicity, only a unique refractive index of the substrate is

used in the subsequent illustration.

3.2. Experimental setup and operation

The experimental setup used in this work is illustrated

schematically in Fig. 1. As shown, an unpolarized beam

from light source impinges on a linear polarizer with its

polarizing axis within the plane of the paper and orthogonal

to the light beam. Then the transmitted p-polarized beam

incidents on the sample with an oblique angle of uB as

illustrated in the ®gure. The ®lm absorption spectrum is

taken in two steps: ®rst, a background scan of a bare Si

wafer is recorded; and then, a sample scan of the thin ®lm

on Si wafer is taken. After normalization by the background

scan, the sample's absorption spectrum is presented. There-

fore, it is important that the background and sample scans

are made at the same incident angle (uB), since any incon-

sistency between background and sample scans will cause

improper normalization of the ®nal spectrum. Speci®cally,

T. Li et al. / Thin Solid Films 349 (1999) 283±288 285

Fig. 1. The p-polarized probe beam passing through the stack of the thin

®lm and substrate at Brewster angle incidence.

substrates set at different light incident angles have different

effective thicknesses, which will result in a spectrum

containing the information of both the ®lm and the substrate

instead of ®lm's only.

When the Brewster condition of the ®rst interface is satis-

®ed, for p-polarized wave, the interference fringes can be

avoided, since the transmitted light reaching the detector

contains no re¯ected light component. This situation is

well described schematically in Fig. 1 (left side). A p-polar-

ized light beam strikes the ®rst interface (air±®lm) and fully

transmits into the ®lm. Part of this transmitted light beam is,

then, re¯ected by the second interface (®lm±substrate). This

re¯ected light beam again is fully transmitted at the ®rst

interface (®lm±air) into the air, and no partial re¯ection

exists in this direction. Since the Brewster angle in the air

and the resulting refracted angle in the ®lm are complemen-

tary (uB 1 ur � 908) [10], the re¯ected angle within the ®lm

is also at Brewster condition1. It might be argued that if the

Brewster condition of the second interface (from ®lm to

substrate) is satis®ed, fringe-free spectrum can also be

realized. This is true mathematically, however, theoretical

analysis shows that the second Brewster condition can

hardly be met, because the external light incident angle

with respect to the second interface is normally not large

enough to reach the Brewster condition at the ®lm-substrate

interface. Furthermore, even if the ®lm refractive index is so

small (other than a-Si:H and a-SiNx:H) that the second

Brewster condition can be realized, most of the light energy

will be lost due to high re¯ection at the ®rst interface at a

very large external incident angle [12]. The spectrum

collected with this little probe energy will be very noisy,

and can hardly be reliable. Hence, the ®rst Brewster angle is

the only option in practice.

It should be noted that so far only the re¯ection within the

thin ®lm has been analyzed and no re¯ection within

substrate was considered. Since the thickness of the

substrate is usually very large in comparison with the ®lm

thickness, and is out of the spatial coherent range, it will not

cause any interference fringes in the vibrational absorption

spectrum. Therefore, the fringe's analysis was always made

with the assumption that thickness of the substrate is in®-

nite, and this assumption ®ts well with the experimental

results.

4. Results

4.1. Comparison between fringe-free and conventional

spectra

Figs. 2a and b compare the fringe-free and conventional

(with fringes) vibrational absorption spectra of a-Si:H and a-

SiNx:H thin ®lms, respectively. The distortion induced by

the interference fringes is clearly illustrated by the compar-

ison between the distorted and pure absorption spectra. In

the conventional spectrum, taking a-Si:H for example, for

the peak located at around 2000 cm21, the left shoulder of

the peak is ampli®ed while the right shoulder of the peak is

diminished. Likewise, the left and right side of the peak

located at around 630 cm21 are enhanced differently, and

the amplitude of the peak is intensi®ed signi®cantly while

the peak's position is slightly shifted towards lower wave-

number. In addition, the larger absorption peaks, in conven-

tional spectra, have a larger absolute peak intensity

enhancement. The illustrated conventional absorption spec-

trum of a-SiNx:H has a similar distortion effect. But, it

should be noted that in Fig. 2b the peak at 1040 cm21 emer-

ging from the shoulder of the asymmetric peak located at

880 cm21, and the amplitude enhancement of the peak

located at 1215 cm21 are longitudinal-like optical resonance

(LO) effect of Si-N bond. Meanwhile the signi®cantly

T. Li et al. / Thin Solid Films 349 (1999) 283±288286

1

{ tanuB � tan�908 2 ur� � 1

tanur

� nr

ni;

[ tanur � nr

ni

� tanu0B ) Brewster condition:

Fig. 2. Comparison between conventional and fringe-free vibrational

absorption spectra for (a) a-Si:H and (b) a-SiNx:H thin ®lms, respectively;

where dashed curves represent the conventional and solid curves represent

the fringe-free spectra. The fringe-free spectra were recorded with p-polar-

ized light incidence at 738 for a-Si:H and 628 for a-SiNx:H, respectively.

Inserts show the simulated baseline variation as function of ®lm's thickness,

which is indicated by various values. The baseline periods indicated in the

inserts represent spectral range of 500±3000 cm21 for a-Si:H and 500±4000

cm21 for a-SiNx:H.

reduced asymmetric peak located at 880 cm21 is a trans-

verse-like optical resonance mode (TO) of Si-N bond [15±

17]. These enhanced and reduced peak intensities are due to

the sensitivity of the longitudinal components of infrared-

active vibrations to long-range electric forces. Those

features can be easily distinguished from the interference

effect. In fact, the optical densities of longitudinal- and

transverse-like modes are always directly and inversely

proportional to the light incident angle, respectively

[15,16], while the peak shape changes induced by the inter-

ference fringes do not have a constant relation with the light

incident angle.

Apparently, the baseline of the conventional vibrational

absorption spectrum is just a pattern of the interference

fringe. As indicated in the inserts, the baseline pattern is

determined by the parameters such as ®lm thickness and

refractive index at normal light incidence. In particular,

®lm's thickness and refractive index determine the optical

path which is re¯ected by the fringe period (or spacing); and

®lm's refractive index determines the magnitude of inter-

face re¯ection, which in turn dictates the fringe amplitude.

The baseline in the case of a-Si:H (9000 AÊ ) spectrum (from

400 to 3000 cm21) is about one period of interference

fringes, while that of a-SiNx:H (1000 AÊ ) spectrum (from

400 to 4000 cm21) is less than a quarter of one period as

indicated in the inserts of Figs. 2a and b, respectively. For a

given material, the refractive index has a consistent value in

a certain spectral range and fringe has a nearly constant

amplitude, but the period varies with the ®lm thickness as

depicted graphically in the inserts. For the same kind of

®lms with different thickness, the absorption peaks could

sit at different locations of the fringe (i.e. peak or valley

of the interference fringe) according to the thickness of

the ®lm, which will result in quite different ®nal peak

shapes. Furthermore, for the most cases, the absorption

peaks of the conventional spectrum still have different

shapes (other than ideal) even after the baseline correction.

As expected, with a p-polarized light incidence at uB, a

spectrum with a straight and horizontal baseline (solid spec-

trum) can be obtained due to a minimized fringe amplitude

resulting from a vanished re¯ection at the air-®lm interface.

Moreover, for the fringe-free spectra, the absorption peak

shapes are all consistent for the same kind of ®lms with

different thicknesses, which indicates that peak shape is

thickness or fringe pattern independent. It is also noted

that all fringe-free absorption peaks have smaller intensities

than those in conventional spectrum, which is the result of

the elimination of the multiple re¯ection induced absorption

enhancement [14]. As matter of fact, at oblique incidence,

the optical path has been increased by a factor of 1=cosur,

and the absorption intensity should be increased correspond-

ingly. The fact that the absorption intensities at normal inci-

dence are larger than those at the Brewster angle incidence

is the indication that the absorption enhancement induced

by the increase of the optical path is insigni®cant comparing

to that induced by the interfacial multiple re¯ection.

4.2. Comparison between fringe-free and virtual fringe-free

spectra

A straight and horizontal baseline in the vibrational

absorption spectrum can also be realized by an unpolarized

light beam when the angle of the incident light is greater

than uB. As mentioned above, an unpolarized light beam can

be viewed as the sum of a p- and s-polarized waves. For a

given ®lm, when ui , uB, with the increase of incident

angle, the fringes caused by p- and s-polarized components

show a decreasing and an increasing amplitudes, respec-

tively, due to corresponding natures of interfacial re¯ec-

tances [12]. Meanwhile their fringe's period and curvature

direction remain the same. When ui . uB, with the increase

of the incident angle, the fringe amplitudes of both p- and s-

polarized components increase, again, due to the natures of

corresponding interfacial re¯ectances. However, the phase

or curvature direction of the p-polarized fringes is ¯ipped,

T. Li et al. / Thin Solid Films 349 (1999) 283±288 287

Fig. 3. Comparison between `virtue' fringe-free and pure vibrational

absorption spectra for (a) a-Si:H and (b) a-SiNx:H thin ®lms, respectively;

where dashed curves represent the `virtue' fringe-free spectra and solid

curves represent the pure spectra. The `virtue' fringe-free spectra were

collected with unpolarized light at 768 for a-Si:H and 688 for a-SiNx:H,

respectively. The inserts illustrate the ideal baseline summation between

p- and s-polarized components, where spectrum periods represent the spec-

tral range of 500±3000 cm21 for a-Si:H and 500±4000 cm21 for a-SiNx:H,

respectively.

while that of the s-polarized fringes remains the same. (It

should be noted that p- and s-polarized fringes always have

the same fringe period at any incident angle because of the

same optical path they experienced.) Consequently, the

summation of two fringe patterns with the same period

but opposite curvature directions will yield a pattern with

a reduced amplitude. This averaging effect could result in a

zero amplitude at a speci®c external incident angle (u v),

which is illustrated in the inserts of Figs. 3a and b for a

large and a small interference fringe period, respectively.

The spectrum collected at this speci®c angle can be labeled

as `virtual' fringe-free vibrational spectrum, since it still

contains multiple re¯ection caused deviation although it

looks as if it were a fringe-free spectrum due to the presence

of straight and horizontal baseline.

The virtual absorption spectra recorded with an unpolar-

ized light at 768 and 688 are shown in Figs. 3a and b for a-

Si:H and a-SiNx:H, respectively, in comparison with the

spectra recorded at uB with a p-polarized beam. For a-

Si:H thin ®lm, an incident angle of 768 is needed for the

p- and s-spectra to balance each other and to yield a straight

and horizontal baseline. Likewise, for a-SiNx:H thin ®lm,

the incident angle of 688 is needed for the observation of this

fringe-cancellation. Apparently, the `virtual' fringe-free

spectra are de®nitely closer to ideal spectra than the conven-

tional spectra are in terms of absorption peak shapes.

However, as illustrated in Fig. 3, the peak intensities in

the `virtual' spectra are enhanced with respect to those

observed in the ideal fringe-free spectra. In fact, the multiple

re¯ection still partially bounces the probe light within the

®lm although the fringe pattern is gone due to the cancella-

tion between p- and s-polarized patterns. The effective opti-

cal path in this case appears to be longer than its real value,

and hence, a larger absorption is observed.

It is well known that the ®lms with different stoichiome-

tries, H-contents, and doping levels will exhibit different

refractive indices, and hence, different interfacial re¯ec-

tances. Therefore, in `virtual' fringe-free spectra, the same

absorption peaks (spectral location) of different ®lms will

exhibit different peak densities. On the other hand, in real

fringe-free spectra, bond densities are well de®ned, since the

interfacial re¯ectance is removed from the spectra. Based on

an appropriate optical path normalization, an absolute

assessment of the ®lm's microstructure can be realized.

5. Conclusion

We have presented a practical method to collect the pure

vibrational absorption spectra free of the interference

fringes and the interfacial re¯ections for hydrogenated

amorphous solid thin ®lms. This method is based on the

principle that at Brewster incident angle the p-polarized

light beam experiences no re¯ection at the interface of air

and ®lm. We have also shown that an absorption spectrum

with undistorted features (shapes) can also be obtained by

using an unpolarized beam at angles greater than Brewster

angle. However, the peak intensities are enhanced in this

kind of spectrum due to existence of the interfacial multiple

re¯ection. Comparison between the conventional and the

fringe-free absorption spectra indicate that, based on the

proposed method, a very reliable absolute and relative mate-

rial's microstructure characterization can be realized.

Acknowledgements

This work was supported by AFOSR/ARPA through

Multi-disciplinary University Research Initiative (MURI)

under the contract number F49020-95-1-0524, and by the

Center for Display Technology and Manufacturing at the

University of Michigan.

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