photoelectron signal simulation from textured samples covered by a thin film

*Corresponding author. Tel.: #359-2-7144680; fax: #359-2-9753201.

E-mail addresses: [email protected] (K. Vutova), [email protected] (G. Mladenov), [email protected] (T. Tanaka),[email protected] (K. Kawabata).

Vacuum 62 (2001) 297}302

Photoelectron signal simulation from textured samples coveredby a thin "lm

K. Vutova��*, G. Mladenov�, T. Tanaka�, K. Kawabata�

�Laboratory of Electron Beam Technologies, Institute of Electronics, Bulgarian Academy of Sciences, 72 Tzarigradsko shosse,1784 Soxa, Bulgaria

�Department of Electronics, Hiroshima Institute of Technology, Miyake 2-1-1, Sacki-ku, Hiroshima 731-5193, Japan

Received 27 June 2000; received in revised form 3 January 2001

Abstract

In this paper we propose a mathematical model for calculating the XPS intensity distribution from textured samplesurfaces covered with a thin "lm. The surface roughness is approximated using triangular prisms. Analytical expressionsfor calculation of the angular photoelectron intensity distribution are given. The obtained results allow an understandingof the relation between the escape depths of emitted photoelectrons and the angular XPS intensity distribution. Theresults show that the X-ray photoelectron signals vary signi"cantly with a change in surface overlayer thickness andprism slope angle �. The maximum of the XPS intensity distribution does not correspond to the maximum escape depthof emitted photoelectrons. The ejected photoelectron ejection angle characterizes the maximum location depth of theinvestigated component or chemical bond. This model is useful when evaluating the surface roughness and the "lmthickness. � 2001 Elsevier Science Ltd. All rights reserved.

Keywords: X-ray photoelectron spectra (XPS); XPS angular intensity distribution; Textured sample surface; Thin "lm; Photoelectronshadowing e!ect; Mathematical model

1. Introduction

Angle-dependent X-ray photoelectron spectro-scopy is an advantageous, non-destructive methodfor the surface composition characterization ofsamples covered by thin "lms or chemically treatedsamples. Analysis of the material under the top

layer is needed in many cases. The use of XPS andits application as a quantitative analytical methodis often hindered by surface roughness. The e!ect ofsurface roughness is often neglected and XPS stud-ies are based on the assumption of perfectly #atsurfaces. In the papers [1}12], the importance ofthe e!ect of roughness has been shown and itsin#uence on the relation between the escape depthof the emitted photoelectrons, that reach the ac-ceptance aperture of the detector, their ejectionangle and the angular XPS intensity distribution.With these data one can receive more informationabout the depth distribution of the investigatedcomponent or chemical bond.

0042-207X/01/$ - see front matter � 2001 Elsevier Science Ltd. All rights reserved.PII: S 0 0 4 2 - 2 0 7 X ( 0 1 ) 0 0 1 5 5 - 5

Fig. 1. Geometrical conditions and labelling of the prismsurface sample.

In this paper, we continue the mathematicalsimulation of angle-resolved X-ray photoelectronsignals from textured surfaces [10}12]. The case oftextured samples covered by a thin "lm is studied.A model for calculating XPS angular intensity dis-tributions of the ejected photoelectrons from thecovered sample material is proposed. The ejectedphotoelectrons that are stopped by the adjacentroughnesses are taken into account (they do notadd to the calculated spectra), that is the photo-electron shadowing e!ect. The results show that theX-ray photoelectron signals depend signi"cantlyon this shadowing e!ect in the cases of high anglevalues (near to �/2). The following assumptionsare used in our simulation: (i) the value of thesurface "lm thickness is less than 3!5� (� is theescape depth of emitted photoelectrons [13]),(ii) the surface roughness is approximated usingmany repeating simple geometrical shapes, (iii) thesubstrate is covered with a single uniform surfacelayer, (iv) the ejected photoelectrons have straight-line trajectories and (v) the elastic energy losses areneglected. We also neglect e!ects due to X-rayrefraction, re#ection and X-ray shadowing.

2. Mathematical model

2.1. Photoelectron intensity in the case of asingle prism

Our model uses triangular prisms to approxim-ate the sample's textured surface topology. Similarmodels were used to approximate the surfaceroughness in the case of a thick sample of uniformmaterial composition [1,11,12]. We denote with� the prism slope angle, representing the roughness* Fig. 1. The line l, determined by the angle � (withrespect to the surface normal) in an arbitrarycross-section perpendicular to the prism base, char-acterizes the direction of the photoelectron ejection.The prism shapes have the following properties: allprisms are identical (with equal base and height)and their side edges are parallel to the tilt axis. Thedi$culty of this model when using an arbitraryangle between the prisms' rib direction and that ofthe detector is overcome by turning the sample onthe z-axis which coincides with the sample normal.

Symmetrical shapes with respect to z-axis as cones,cone-shaped rings and hemispheres have been alsoused in our papers [10,11] which are free of thisdi$culty.In the case of a single prism ABCA

�B�C

�, the

generated photoelectron intensity I�(�) is given by:

I�(�)"I

�(�)#I

�(�). The terms of this equation

present the XPS intensity distributions from theprism walls BB

�CC

�and AA

�CC

�, respectively

(Fig. 1):

I�(�)"�

�

�

I�exp�!

z

� cos(�!�)�dz

"I�� cos(�!�) exp�!

d

� cos(�!�)�, (1)

I�(�)"�

�

�

I�exp�!

z

� cos(�#�)�dz

"I�� cos(�#�) exp�!

d

� cos(�#�)�, (2)

where I�is a constant, which depends on X-ray

intensity, density of the atoms and photoionizationcross-section; d is the surface "lm thickness and � isthe escape depth of emitted photoelectrons [13].Note that the angle � di!ers by �/2 from the

photoelectron ejection angle usually used in papersgiving experimental results (it is measured withrespect to the sample surface). The angle � charac-terizes the position of the detector relative to thesample.

2.2. Photoelectron intensity in the case oftextured overlayer sample

When the sample surface consists of many re-peating simple geometrical structures (triangular

298 K. Vutova et al. / Vacuum 62 (2001) 297}302

prisms), the XPS intensity can be calculated asa sum of the signals from two types of side walls(BB

�CC

�and AA

�CC

�), taking into account the

shadowing e!ect of the ejected photoelectrons fromthe adjacent prisms.It is necessary to separate the ejected photo-

electrons that reach the acceptance aperture ofthe detector from those that are stopped by theadjacent roughness features. We divide the prismwalls into n segments (with identical areas) by linescoinciding with the prism edges. If the ejectedphotoelectron ejection angle � is less than the valueof the critical angle �

��( j is the segment number),

then it reaches the detector with a probability of 1.If �*�

��, then this probability is zero. The value

of ��

is determined by tg ��

"a�/b

�, where a

�is

the distance between the j-segment and the planeperpendicular to the base of the adjacent prism andb�is the distance between the j-segment and the top

edge of the same prism, along the perpendicular tothe prism base. Hence, the total photoelectron sig-nal I

��(�) from the corresponding prism wall

(BB�CC

�) can be represented as a sum of n signals

(generated from the above-mentioned n segments):

I��

(�)"I�(�)n

��

k��

(�), (3)

where the coe$cient k��

(�) [11] characterizes theshadowing e!ect of the ejected photoelectrons fromthe adjacent prism: k

��(�)"1 when �(�

��,

and k��

(�)"0 when �*��

. Hence,��

��k��

(�)"n when �(�/2!�; and I�(�) is

calculated from Eq. (1).In a similar way, the signal I

��(�) generated from

the prism wall AA�CC

�is

I��

(�)"I�(�)n

��

k��

(�), (4)

where the values of the shadowing coe$cientk��

(�) [11] are k��

(�)"1 when �(�/2!�;and k

��(�)"0 when �*�/2!�; I

�(�) is cal-

culated from Eq. (2).Thus, taking into account the photoelectron

shadowing e!ect, the total XPS intensity I(�) fora given value of �, can be presented as a sum ofthese two components from Eqs. (3) and (4)

I(�)"I��

(�)#I��

(�). (5)

3. Results and discussion

In the case of #at overlayer samples the nor-malized XPS intensity distributions are similar toa cosine law. But the results in the case of texturedoverlayer samples are di!erent. Fig. 2 shows cal-culated angular distribution of XPS intensity I(�),using the triangular-prisms model at �"153 (theprism slope angle) for di!erent values of the "lmthickness d. Our calculations are for hydrogenatedamorphous silicon (a-Si : H), deposited on texturedtransparent conductive SnO

�/glass substrate for

fabrication of p}i}n photovoltaic cells. The Sn��

spectra are used for studying the di!usion of Sn inp-layers. The experimentally obtained value of � is23.3As [14]. The curves in Fig. 2 represent the totalangular XPS intensity distribution (from the totalsample surface) and the components of this signalfrom the two types of side walls. One can see thephotoelectron shadowing e!ect in#uence on thesecomponents and their relative contribution to thetotal XPS signal. Curves 1 correspond to the com-ponent I

��(�) (the signal from the wall BB

�CC

�),

whereas curves 2 describe the component I��

(�)(the signal from the wall AA

�CC

�). One can see

a slope change on curve 1 and on the total curve inFig. 2(a and b) at �"�/2!�"753 due to thein#uence of the photoelectron shadowing e!ect.This curve slope change is negligible for thick layers(Fig. 2 (c) and (d)) because of the low values of theXPS intensity.The curves in Fig. 3 are obtained for the value of

the prism slope angle �"303. Fig. 3 (a)}(d) corres-ponds to the values of the "lm thickness d as in thecase of Fig. 2 (a)}(d). The slope change on curve1 and on the total curve of XPS distribution isat �"�/2!�"603. The maximum of curves1 (they represent the XPS signal from the wallBB

�CC

�) correspond to the case �"�"303.

This maximum is more pronounced in the case ofthick layers because of: (i) a decrease of the XPSintensity values and (ii) a considerable decreaseof the signal contribution from the wall AA

�CC

�(Fig. 3, curves 2) to the total XPS signal. Ford"5, 15, 30As the total curves are very similar, butthe total intensity curve for d"60As deviates con-siderably from them, especially in its maximumregion.

K. Vutova et al. / Vacuum 62 (2001) 297}302 299

Fig. 2. Normalized XPS intensity distribution vs. the angle � for �"153: (a) at d"5As , (b) at d"15As , (c) at d"30As , (d) at d"60As .Curve 1, I

��(�); curves 2, I

��(�); total curve, the total XPS intensity.


��(�); curves 2, I




��(�); curves 2, I


The calculated total XPS intensity and its twocomponents at �"603, for the same values of the"lm thickness d as for the case �"15 and 303, areshown in Fig. 4. The photoelectron shadowinge!ect determines: (i) the value of � correspondingto the maximum of I(�), as well as (ii) the partsof curves 1 (the signal from the wall BB

�CC

�)

and of the total curves for values of � higher thanthe value of � corresponding to the maximum ofI(�). This means that the photoelectrons participat-ing in the right part of the XPS intensity distribu-tion (at high values of �) do not traverse thelargest distances and the photoelectrons corres-pond to the maximum of I(�) do not traversethe shortest distances. The contribution of thecomponent I

��(�) to the total XPS intensity

decreases considerably when the values of dincrease. This fact can explain the considerabledeviation of the total XPS intensity curves at smallvalues of �.These results and curves correspond also to all

cases of textured samples covered with a "lm when

the parameter d/� has the following values:0.26, 0.78, 1.56 and 3.125.Limitations of space do not allow us to make

direct and detailed comparisons with the experi-mental results presented in Ref. [14], but the resultsshow qualitative agreement.

4. Conclusions

In our paper we describe a mathematical modelfor calculation of the angular XPS intensity dis-tribution from textured overlayer samples. Thismodel uses triangular prisms to approximate thesurface roughness. Analytical expressions forcalculation of angular photoelectron intensitydistribution are given, when using these geometri-cal shapes. The XPS signals from the textured sam-ples covered by a thin "lm di!er greatly froma cosine law. The results show that there is a char-acteristic slope change on the XPS intensity curvesat �"�/2!�. This change is more pronounced in

K. Vutova et al. / Vacuum 62 (2001) 297}302 301

the case of overlayers which are thin in comparisonwith �. When the value of � is more than 453 theangular XPS intensity maximum is not at �"03and it depends on the surface "lm thickness d. Theobtained results make it possible to understand therelation between the escape depths of emittedphotoelectrons, the ejected photoelectron's ejectionangle � and the angular XPS intensity distribution.

References

[1] Fadley CS, Baird RJ, Slekhaus W, Novakov T, BergstromSAL. J Electron Spectrosc Rel Phenom 1974;4:93}137.

[2] Bernardez LS, Ferron J, Goldberg EC, Bultrago RH. SurfSci 1984;139:541}8.

[3] Wu OKT, Peterson GG, LaRocca WJ, Butler EM. ApplSurf Sci 1982;11/12:118.

[4] Yan YL, Helfand MA, Clayton CR. Appl Surf Sci1989;37:395.

[5] Olive G. Surf Sci 1993;297:83.[6] Gunter PLJ, Niemantsverdriet JW. Appl Surf Sci

1995;89:69}76.[7] Gunter PLJ, Niemantsverdriet JW. J Vac Sci Technol

A 1995;13:1290.[8] Gunter PLJ, Glizeman OLJ, Niemantsverdriet JW.

Appl Surf Sci 1997;115:342}6.[9] Zalm PC. Surf Interf Anal 1998;26:352}8.[10] Mladenov GM, Vutova KG, Tanaka T, Kawabata K.

J Surf Anal 1999;5:82}5.[11] Vutova KG, Mladenov GM, Tanaka T, Kawabata K.

Math Comput Simulation 1999;49:275}83.[12] Vutova KG, Mladenov GM, Tanaka T, Kawabata K. Surf

Interf Anal 2000;30:552}6.[13] Penn DR. J Electron Spectr Rel Phenom 1976;9:29}40.[14] Kawabata K, Shiratsuki Y, Hayashi T, Yamada K,

Miyazaki S, Hirose M. Jpn J Appl Phys 1991;30:1231}4.


photoelectron signal simulation from textured samples covered by a thin film

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