photoelectron signal simulation from textured samples with modified surface composition

SURFACE AND INTERFACE ANALYSISSurf. Interface Anal. 2002; 34: 597–600Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/sia.1368

Photoelectron signal simulation from textured sampleswith modified surface composition

K. Vutova,1∗ G. Mladenov,1 T. Tanaka2 and K. Kawabata2

1 Laboratory of Electron Beam Technologies, Institute of Electronics, Bulgarian Academy of Sciences, 72 Tzarigradsko shosse, 1784 Sofia, Bulgaria2 Department of Electronics, Hiroshima Institute of Technology, Hiroshima, Japan

Received 16 July 2001; Revised 7 November 2001; Accepted 27 December 2001

In this paper we propose a mathematical model for calculating XPS intensity distributions from multi-component textured samples with a step-like distribution approximating the depth compositional profiles.The surface roughness is approximated using triangular prisms. Analytical expressions for calculation ofangular photoelectron intensity distributions are given. The results obtained concern textured sampleswhere the height of the surface roughness structures are 3–5 times greater than the ejection depth. Thevalues of the altered layer thickness and the values of the emitted photoelectron’s ejection depth are of thesame order. This model is appropriate when studying the changes of compositional depth profiles in therange of the photoelectron ejection depth. Copyright 2002 John Wiley & Sons, Ltd.

KEYWORDS: x-ray photoelectron spectroscopy (XPS); XPS angular intensity distribution; textured sample surface;compositional depth profile; mathematical model

INTRODUCTION

X-ray photoelectron spectroscopy analysis is an inter-pretable, informative and essentially non-destructive tech-nique for surface quantitative investigations. The observedsurface elemental composition can be affected by a number offactors: preferential sputtering; bombardment-induced mod-ification; surface segregation during crystallization of meltedalloys; oxidation, diffusion or surface modification duringchemical treatment. The surface layer elemental compositionof multi-component samples often differs from that in thebulk because of segregation phenomena. The XPS signalsobtained in the listed cases are defined by the depth profileof the component concentrations near the sample surface.An important case is when the layer thickness values of themodified composition and the values of the photoelectronejection depth are of the same order. Another feature ofmany samples is that the investigated surface is not flat.Various methods have been proposed to solve the prob-lem concerning extraction of information on the in-depthconcentration profile by XPS angular-resolved spectra1 aswell as by XPS intensity simulation in the case of texturedsamples.2 – 4

In this paper, we continue the mathematical simulationof angle-resolved XPS signals from textured surfaces.3,4 Thecase of textured multi-component samples with modifiedsurface composition is studied. A model for calculating the

ŁCorrespondence to: K. Vutova, Laboratory of Electron BeamTechnologies, Institute of Electronics, Bulgarian Academy ofSciences, 72 Tzarigradsko shosse, 1784 Sofia, Bulgaria.E-mail: [email protected]/grant sponsor: Science for Peace NATO program;Contract/grant number: SfP 973718.Contract/grant sponsor: Hiroshima Institute of Technology.

XPS angular intensity distribution by taking into accountthe photoelectron shadowing effect is proposed. The resultsobtained are for textured samples where the height ofthe surface roughness structures is 3–5 times greater thanthe ejection depth. The altered layer thickness values andthe photoelectron ejection depth values are of the sameorder.

MATHEMATICAL MODEL

Photoelectron intensity in the case of flat samplesThe XPS signal from a multi-component sample is propor-tional to the photoelectron flux emitted from a layer ¾5 Athick beneath the surface5

Ii,fl�� D k∫ 1

0ni�z� exp

(� z

�i cos �

)dz �1�

where Ii,fl is the intensity of the photoelectron flux at a take-off angle � (between the normal of the sample surface andthe analyser axis) due to the ith component of the sample,ni�z� is the atomic density of the ith component at a depth z,�i is the photoelectron ejection depth6 and k is a normalizingproportionality coefficient (k includes the energy-dependenttransmission function of the analyser, the photoemissioncross-section, etc.).

The following considerations are based on the assump-tion that the concentration–depth profile is a step-likefunction. The atomic concentration of the component is inde-pendent of z within the altered layer of thickness d and so ithas constant values when z � d (at the surface altered layer)and when z > d (in the bulk). Let ni�0� and ni�1� be thecomponent concentrations at the sample surface and in the

Copyright 2002 John Wiley & Sons, Ltd.

598 K. Vutova et al.

bulk, respectively. Then, using Eqn (1), we can obtain

Ii,fl�� D k∫ d

0ni�0� exp

(� z

�i cos �

)dz C k

∫ 1

dni�1�

ð exp(

� z�i cos �

)dz D k�ini�0� cos �

ð{

1 C[

ni�1�

ni�0�� 1

]exp

(� d

�i cos �

)}�2�

Photoelectron intensity in the case of texturedsamplesOur model uses triangular prisms to approximate thesample’s textured surface topology.2 – 4 We denote the prismslope angle by ˛ (representing the roughness) (Fig. 1). Thetake-off angle � is defined as the angle between the normalof the prism base and the analyser axis. In the case of a singleprism, the generated photoelectron intensity Ii,s�� due tothe ith component of the sample composition is given byIi,s�� D Ii,s,1�� C Ii,s,2��, where Ii,s,j�� D Ii,s,j,1�� C Ii,s,j,2��(j D 1, 2). The terms of this equation present the XPS intensitydistributions from the two prism walls—Eqns (3) and (5) arethe signals from the right-side prism walls BB1CC1, whereasEqns (4) and (6) present the signals from the left-side prismwalls AA1CC1 (Fig. 1), respectively

Ii,s,1,1�� D k∫ d

0ni�0� exp

[� z

�i cos�� ˛�

]dz D k�ini�0�

ð cos�� ˛�

{1 � exp

[� d

�i cos�� ˛�

]}�3�

Ii,s,1,2�� D k∫ d

0ni�0� exp

[� z

�i cos�� C ˛�

]dz D k�ini�0�

ð cos�� C ˛�

{1 � exp

[� d

�i cos�� C ˛�

]}�4�

Ii,s,2,1�� D k∫ 1

dni�1� exp

[� z

�i cos�� ˛�

]dz

D k�ini�1� cos�� ˛� exp[� d

�i cos�� ˛�

]�5�

Ii,s,2,2�� D k∫ 1

dni�1� exp

[� z

�i cos�� C ˛�

]dz

D k�ini�1� cos�� C ˛� exp[� d

�i cos�� C ˛�

]�6�

Equations (3) and (4) present the XPS intensity distributionsfrom the altered surface layer. The XPS signals from the bulkare described by Eqns (5) and (6).

When the sample surface consists of many repeatingtriangular prisms, the XPS intensity can be calculated as thesum of the signals from the two types of side walls, takinginto account the shadowing effect of ejected photoelectrons

A B

C

C1

α αθ l

Figure 1. Geometric conditions and labelling of the prismsurface sample.

from the adjacent prisms.3,4 It is necessary to separate theejected photoelectrons that reach the acceptance apertureof the detector from those that are stopped by the adjacentroughnesses (the photoelectron shadowing effect). We dividethe prism walls into n segments (with identical areas)by lines coinciding with the prism edges and we alsouse the values of the critical angle �cr,m : tg�cr,m D am/bm,where am is the distance between the m segment and theplane perpendicular to the base of the adjacent prism, andbm is the distance between the m segment and the topedge of the same prism, along the perpendicular to theprism base. Then the total photoelectron signal Ii,sh,j,q��from the corresponding prism wall can be representedas the sum of n signals (generated from the above-mentioned n segments): Ii,sh,j,q�� D [Ii,s,j,q��]/nn

mD1kq,sh,m��(j, q D 1, 2), where Ii,s,j,q�� is calculated from Eqns (3)–(6)and the coefficient kq,sh,m�� characterizes the shadowingeffect of the ejected photoelectrons from the adjacent prism:k1,sh,m�� D 1 when � < �cr,m; k1,sh,m�� D 0 when � � �cr,m.k2,sh,m�� D 1 when � < ��/2� � ˛; and k2,sh,m�� D 0 when� � ��/2� � ˛.

Taking into account the above-mentioned shadowingeffect, the total XPS intensity Ii�� at a given value of˛ can be presented as the sum of these components:Ii�� D Ii,sh,1,1�� C Ii,sh,1,2�� C Ii,sh,2,1�� C Ii,sh,2,2��.

RESULTS AND DISCUSSION

Calculated distributions of the XPS intensity in the caseof a flat sample at a typical value of �i D 20 A when thecomponent concentration values at the altered surface layerni�0� is half the component concentration values in the bulkni�1�, i.e. ni�0� : ni�1� D 1 : 2, are shown in Fig. 2. Thecurves are obtained for different values of the modified layerthickness d: curve 1, at d D 5 A; curve 2, at d D 15 A; curve3, at d D 30 A; curve 4, at d D 60 A. Figure 2(a) showsnormalized XPS intensities with respect to Ii,fl�0�. Curves1–4 are closer to each other and are similar to a cosinedistribution. Curve 4 is very similar to a cosine law becauseonly a few photoelectrons (of the total electron number) areemitted from a depth with a concentration that is differentfrom the altered surface layer concentration. In the caseof a thin layer (in comparison with �i) when d D 5 A,curve 1 deviates from a cosine law at high values of �,whereas for thick layers (when the photoelectron ejectiondepth is comparable to the layer thickness d) curves 2 and3 deviate from a cosine law at all values of �. Calculatedangular distributions of the XPS intensity Ii,fl�� (withoutnormalization) are shown in Fig. 2(b). The values of the XPSintensity decrease when the values of the modified surfacelayer thickness d increase. This result is opposite in the caseof a concentrated surface layer when ni�0� : ni�1� D 2 : 1. Thecalculated distributions for this condition and for the valuesof d in Fig. 2 are shown in Fig. 3.

The curves in Fig. 4 are obtained in the case of texturedsamples for prism slope angle ˛ D 60° and when ni�0� :ni�1� D 1 : 2. Curves 1–4 correspond to the values of thealtered surface layer thickness d as in the case of Fig. 2.Figure 4(a) shows calculated distributions of the normalized

Copyright 2002 John Wiley & Sons, Ltd. Surf. Interface Anal. 2002; 34: 597–600

XPS signal simulation from textured samples 599

0

0.2

0.4

0.6

0.8

1

0 15 30 45 60 75 90

No

rmal

ized

XP

S in

ten

sity

I i,f

l(θ)/

I i,fl(0

)

Curve 1Curve 2Curve 3Curve 4

0

5

10

15

20

25

30

35

40

0 15 30 45 60 75 90

XP

S in

ten

sity

I i,f

l(θ)

(arb

. un

its)


Take-off angle θ (degree) Take-off angle θ (degree)(a) (b)

Figure 2. The photoelectron intensity as a function of the take-off angle � in the case of a flat sample for different altered layerthicknesses when ni�0� : ni�1� D 1 : 2. (a) normalized XPS intensity; (b) XPS intensity without normalization.

00 15 30 45 60 75 90

5

10

15

20

25

30

35

40

45

Take-off angle θ (degree)

XP

S in

ten

sity

I i,f

l(θ)

(arb

. un

its)


Figure 3. The XPS intensity distribution vs. the take-off angle �

for ni�0� : ni�1� D 2 : 1 in the case of a flat sample.

XPS intensity Ii��/Ii�0�. Although one can see some similaritywith a cosine distribution [Fig. 4(a)], note that in the case of

textured surfaces the calculated XPS intensity is the sum ofthe signals from the two types of side walls and that thedecrease of the XPS intensity values at high values of � isdue to the shadowing effect. In this case the photoelectronswith low values of ejection depth make a contribution to thetotal XPS signal mainly when � is in the range 20–60° andtherefore the intensity curves deviate considerably from acosine law (at these values of �). The curves in Fig. 4(b)represent the XPS intensity without normalization. Thelocal maximum (the slope change) on curves 1 and 2 isat � D ��/2� � ˛ D 30° and is due to the fact that the totalXPS signal is the sum of the signals from the two types ofside walls.

Analogously, the data presented in Fig. 5 show that theslope change on the curves of the calculated XPS distributionsis at � D ��/2� � ˛ D 30°. These results are obtained whenni�0� : ni�1� D 2 : 1.

The curves in Fig. 6 are obtained for the prism angle˛ D 30°. The slope change on the XPS intensity curves is at� D ��/2� � ˛ D 60°. This result is due to the photoelectronshadowing effect influence on the components (from the

0

0.2

0.4

0.6

0.8

1

0 15 30 45 60 75 90


Curve 1

Curve 2

Curve 3

Curve 4

No

rmal

ized

in

ten

sity

I i(θ

)/I i(

0)

0 15 30 45 60 75 90


0

5

10

15

20

25

30

35

40

Curve 1

Curve 2

Curve 3

Curve 4

XP

S in

ten

sity

l i(θ

) (a

rb. u

nit

s)

(a) (b)

Figure 4. Calculated angular XPS intensity distribution vs. the take-off angle � in the case of a textured sample for ˛ D 60° (theprism slope angle) and ni�0� : ni�1� D 1 : 2: (a) normalized XPS intensity; (b) XPS intensity without normalization.


600 K. Vutova et al.

00 15 30 45 60 75 90

5

10

15

20

25

30

35

40

45


XP

S in

ten

sity

I i(θ

) (a

rb. u

nit

s) Curve 1

Curve 2

Curve 3

Curve 4


in the case of textured samples for prism angle ˛ D 60° whenni�0� : ni�1� D 2 : 1 and for different values of the modifiedlayer thickness d: curve 1, at d D 5 A; curve 2, at d D 15 A;curve 3, at d D 30 A; curve 4, at d D 60 A.

00 15 30 45 60 75 90

5

10

15

20

25

30

35


XP

S in

ten

sity

I i(θ

) (a

rb. u

nit

s) Curve 1

Curve 2

Curve 3

Curve 4


in the case of a textured sample at prism angle ˛ D 30° whenni�0� : ni�1� D 1 : 2 and for different altered layer thicknesses:curve 1, at d D 5 A; curve 2, at d D 15 A; curve 3, at d D 30 A;curve 4, at d D 60 A.

two types of side walls) of the XPS signal and theircontribution to the total XPS signal. This slope change is

more pronounced in the case of thin altered surface layers(curves 1 and 2).

CONCLUSIONS

In our paper we describe a mathematical model for thecalculation of angular XPS intensity distributions frommulti-component textured samples with modified surfacecomposition (a step-like distribution of compositional depthprofiles). This model uses triangular prisms to approximatethe surface roughness. Analytical expressions for the calcu-lation of XPS angular intensity distributions are given. Theresults show that the surface roughness influences greatly theXPS intensity distributions and they differ from a cosine law.An important influence of the surface roughness has beenpresented in Ref. 7, where the height of the surface roughnessstructures is less than that in our investigations. Obviously,both factors—the existence of a surface layer with modifiedcomposition and the existence of surface roughness—haveto be taken into account when one reconstructs the surfacedistribution of the investigated component using an XPSsignal. The shadowing effect and its influence on the XPSsignals is a special feature of the surface analysis in the caseof textured samples, therefore photoelectrons emitted fromthe most shallow sample part make the main contribution tothe XPS signal in the region of � D ��/2� � ˛. This fact differsfrom the case of flat samples, where the contribution of thesephotoelectrons is predominant at values of � near to �/2.

AcknowledgementsThe research was funded through Science for Peace NATO Program(SfP 973718 project) and the Hiroshima Institute of Technology,Hiroshima, Japan and National Council for Scientific Research atthe Ministry of Education and Science of Republic of Bulgaria undercontact No. MM-1004.

REFERENCES1. Yih RS, Rather BD. J. Electron Spectrosc. Relat. Phenom. 1987; 43:

61.2. Fadley CS, Baird RJ, Slekhaus W, Novakov T, Bergstrom SAL. J.

Electron Spectrosc. Relat. Phenom. 1974; 4: 93.3. Vutova K, Mladenov G, Tanaka T, Kawabata K. Surf. Interface

Anal. 2000; 30: 552.4. Vutova K, Mladenov G, Tanaka T, Kawabata K. Vacuum 2001; 62:

297.5. Tougaard S. J. Vac. Sci. Technol. A 1987; 5: 1275.6. Penn DR. J. Electron Spectrosc. Relat. Phenom. 1976; 9: 29.7. Hofmann S. Surf. Interface Anal. 2000; 30: 228.


photoelectron signal simulation from textured samples with modified surface composition

Documents