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Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 357–372

Contents lists available at ScienceDirect

Journal of Electron Spectroscopy andRelated Phenomena

journa l homepage: www.e lsev ier .com/ locate /e lspec

econdary electron emission and fundamentals of charging mechanisms in XPS

acques Cazaux ∗

epartment of Physics, Faculty of Sciences, University of Reims, Moulin de la Housse, BP 1039, 51687 Reims Cedex 2, France

r t i c l e i n f o

rticle history:vailable online 24 March 2009

ACS:: 79.60. Bm1.80.Cb1.82.−d7.85.−m&Tt

a b s t r a c t

Fundamentals of charging mechanisms in XPS are investigated with special attention to the X-ray-induced secondary electron emission (SEE) yield from insulators, ıX(h�), that is, first, responsible ofcharging and of differential charging. In the defocused mode, the SEE emission is compensated bythree different types of effects: inner trapping effect in the positively charged layer; internal effectsoccurring at the specimen/substrate interface; external effects resulting from emitted secondaryelectrons retuning back to the specimen. A detailed investigation of these mechanisms leads to ananalytical expression for time evolution of the surface potential as a function of irradiation time, VS = f(t),via incident flux and characteristics of samples. In particular, it is shown that internal effects lead to three

eywords:urface analysisPS

nsulating materials-ray-induced secondary electron emissionhotoelectron X-ray microscopy

different regimes for VS = f(t) depending upon the thickness of the specimen while, in the focused mode,external effects are a function of the lateral dimension of the sample and of its surrounding. Numericalapplications permit to obtain order of magnitude in laboratory XPS as well as in spectro-microscopydeveloped from the use of synchrotron X-ray sources. Various practical details concerning for instancethe influence of heterogeneities of the specimen either in thickness or in composition as well as thechange of incident angle in angle resolved XPS or the change of incident photon energy have been

deduced.

. Introduction

In XPS, charging effects are identified by the peak shift and peakroadening of photoelectrons and Auger lines as a direct conse-uence of the surface potential change over the projected slit of thenalyzer on the investigated insulating samples. In the past, con-iderable attention has been paid to these effects [1–5] and thisttention continues nowadays as it may easily be observed fromome present contributions to this special issue (and to anotherne devoted to charging in electron spectroscopies) as well as fromecently published papers in this field [6–11]. Most of these papersre devoted to practical solutions to overcome the correlated spu-ious effects or to extract useful information from the investigatedample but only a few papers are looking in detail at the fundamen-al role of secondary electron emission (SEE) and of the inducedompensation mechanisms. The main goal of present paper is anttempt to fill this gap.

Via the positive charges left by electron emission into the vac-

um, secondary electron emission is first responsible of chargingechanisms. But this emission also leads to self regulation effects

ia the progressive establishment of a surface potential function,S(x, y, t) which stops, in turn, a part of the SEE but it also mod-

∗ Tel.: +33 326042137.E-mail address: jacques.cazaux@orange.fr.

368-2048/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.elspec.2009.03.007

© 2009 Elsevier B.V. All rights reserved.

ifies the trajectories of the emitted secondary electrons, externaleffect, while crossed injection of charges at the sample/substratemay occur as internal effects. Then, to understand charging mech-anisms in XPS, it is useful to consider, first, some aspects of thephysics of X-ray-induced SEE of insulators under non-chargingconditions (Section 2) in order to analyze, next, a simplified evo-lution of charging for a uniform surface potential such as thatobtained in a defocused mode on a homogeneous specimen ina parallel geometry (Section 3). Even for such a simplified situa-tion, this evolution is complicated by the occurrence of internalcompensation effects detailed in Section 4 and by the influenceof SE electron trajectories into the vacuum and returning or notback to the specimen (Section 5). The sum of these internal andexternal compensation effects permits to suggest a time evolutionof charging as a function of specimen and experimental condi-tions (Section 5). The more complicated investigation of situationsresulting from angle resolved XPS or of focused mode or of theuse of an additional electron irradiation are considered in Section6. Mostly based on fundamental arguments, this article concernsany type of instrument based either on the use of laboratory X-ray sources or on the use of synchrotron sources. The goal of

present contribution is to provide a continuity to a previous arti-cle of present author on the same subject [1] with, here, a deeperattention to physics of secondary electron emission and a clarifica-tion of a few obscure or sometimes incorrect points contained in[1].

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58 J. Cazaux / Journal of Electron Spectroscopy

. X-ray-induced secondary electron emission fromnsulators, ıX

.1. X-ray-induced SEE yield from insulators: experiments andodel

In comparison to the proliferation of papers [11] devoted tolectron-induced secondary electron emission, ı, a rather few num-er of papers have been devoted to the X-ray induced secondarylectron emission, ıX (number of emitted secondary electrons perncident photon). In this last field, the most important contributionso emission of electrons using X-ray excitation in the 0.1–10 keVhoton range are that of Henke and coworkers [12–15] with the

nvestigation of various semiconductors and insulators [13] and alsoolid xenon [15] as well as gold for applications as photo-convertersn fast X-ray cameras and as X-ray detectors [14]. Fig. 1 shows theorresponding experimental results for the best metal to be useds photon-electron converter, Au, the best conventional insulator,sI, and the best unconventional insulator, solid Xe.

The explanation of the general shape of the reported experi-ental curves, ıX(h�), may be easily deduced from the mechanisms

nvolved in the generation of secondary electrons. Well-known inPS, these mechanisms are a consequence of the main interaction ofn incident photon of energy h� in the 0.1–50 keV range: the photo-lectric effect. Besides the X-ray absorption, the photoelectric effecteads to the creation of single photoelectrons and of Auger elec-rons. A small fraction of these two energetic (primary) electrons

ay directly escape into the vacuum but most of them, generatedt depths far larger than the photoelectron attenuation depth, �,

xperience multiple elastic and inelastic interactions before escap-ng into the vacuum in a way similar to that of incident electronsn the electron-induced SEE, ı. During their transport, they create aarge number of electron-hole pairs (low energy SEs) in their slow-ng down. The ratio of the primary (elastic and inelastic photo- and

ig. 1. Experimental X-ray-induced SEE yield, ıX = f(h�) of Au, CsI and condensed Xe,nspired from [15].

lated Phenomena 178–179 (2010) 357–372

Auger electrons) to the total is less than 1% for most of the insula-tors, whereas it may reach 10% for metals (see Fig. 12 of Ref. [14]).Then, ıX results from the generation, transport and escape of lowenergy electrons and it represents the major contribution to thetotal electron emission from insulators irradiated with X-rays andthen the major contribution to charging.

Based on the similarities of SE interactions and because theabsorption of X-ray, �, is nearly a constant in the surface layerfrom which the emitted SE are originating, a semi-empirical expres-sion for ıX = f(h�), has been inspired from the constant loss modelfrequently used for the electron induced SEE, ı = f(E◦) [11]. In thesurface region, the average number of SEs, dnse, generated betweenz and z + dz by one incident photon of energy h� is then given by[16]:

dnse ∼ E(z)dz

Ese= �dz

(h�

Ese

)(1)

In Eq. (1), E(z) dz is the mean photon energy lost between z andz + dz; � is the linear absorption coefficient of the investigated mate-rial for the X-ray photon energy being operated and Ese is the meanenergy required to produce a SE able to escape into the vacuum andhaving then a kinetic energy Ek in the vacuum above the vacuumlevel.

Next using the same exponential attenuation function for thetransport of the secondary electrons (attenuation length, s; maxi-mum SE escape depth r = 3s) and the same parameter A for the SEescape probability (as those used for expressing ı in the constantloss model), the integral of Eq. (1) gives

ıX = A(

hvEse

)(�s)

[1 − exp

(− 1

�s

)](2)

The present form of ıX is then closely similar to the yield deducedfrom the Constant Loss Model for ı by substituting �−1 by R (therange of incident electron in e-induced SEE yield) and h� by E◦

(incident beam energy):

ı = A(

E◦

Ese

)(s

R

)[1 − exp

(−R

s

)](3)

In fact, the term into [1 − exp (−1/�s)] in Eq. (2) is often equals tounity and the same type of calculation leads to ıX(i◦) = ıX(0◦)/cos i◦

for an incident angle i◦ far from the grazing incidence: a result easilydeduced from the increase of the path length of X-rays through theuseful layer of thickness s/cos i◦.

2.2. Comments on ıX(h�)

An advantage of Eq. (2) is to explain the general shape of experi-mental ıX(h�) curves and in particular of their absorption jumpsrelated to its h� × �(h�) dependence. Via the role of � it alsoexplains why high Z materials such as Au, CsI or Xe are the bestcandidates for photon-electron converters. Another important con-sequence of Eq. (2) is the possibility to deduce the evolution ofıX(h�) in a large photon energy range from only its knowledge,ıX(h�◦), at one photon energy, h�◦ [16]:

ıX (hv)ıX (hv◦)

= hv × �(hv)hv◦ × �(hv◦)

(4)

With the help of tabulated values for linear absorption coeffi-cient �(h�) [17,18] (or results of theoretical calculations for X-rayabsorption cross-sections [19]), this approach permits, for a givensample, to extend to any photon energy the results obtained from

only the use of one radiation such as Al K� [13].

Again for a given sample, another consequence of the close cor-relation between ı and ıX is the possibility to deduce the evolutionof ıX(h�) from the best fit of ı(E◦) experiments or calculations rel-ative to this sample. This operation consists of inserting into Eq.

J. Cazaux / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 357–372 359

Fig. 2. Calculated X-ray-induced SEE yield, ıX = f(h�) using parameters deduced fromelectron induced experiments, ı = f(E◦). (a) MgO where the influence of crystallinesaD

(soTw

Fig. 3. Calculated X-ray-induced SEE yield, ıX = f(h�) using parameters deduced fromelectron induced experiments, ı = f(E◦). (a) BeO [24]; (b) NaCl [16]. In (a), the influ-ence of escape probability, A, on the yield is illustrated with a full line correspondingto a bare surface and a dashed line corresponding to a Cs rich surface. (b) gives an

tate is shown with two varieties of MgO, a single crystal (J and Mc Kay, upper curve)nd a polycrystalline specimen (U and al.n lower curve) [24]. (b) Condensed H2, HD,2 and T2 (from [25]).

2) parameters values, A, Ese and s, derived from ı(E◦). Examples of

uch a procedure are given in Figs. 2 and 3 when applied to a varietyf inorganic insulators and to some condensed gases (see below).he same procedure may also be transposed to some polymers forhich ı(E◦) data are available [20]. The reverse process consisting

example of the combined influence of the change of ‘s’ with temperature (dashedand dotted lines: G 77 and G 593 K) and of the change of A, cleaved and non cleavedsurfaces (continuous line: H 293 K).

in deducting ı(E◦) curves from ıX(h�) experiments is also possibleas illustrated in Fig. 3 of Ref. [16] for the CsI specimen of Fig. 1.

An experimental evidence of the close correspondence betweenelectron-induced and X-ray induced SEE is given by the iden-

tity (within experimental errors) of the shape (peak position andwidth-at-half-maximum) of the spectral distribution of the emitted(electron-induced and X-ray-induced) secondary electrons, ∂ı/∂Ekand ∂ıX/∂Ek, obtained on a given insulator. Relative to KCl crystals,

360 J. Cazaux / Journal of Electron Spectroscopy and Re

Ft[

Fotfirb

aoi

gsstbmiorpsmabgtosotFsatwbe

14

ig. 4. Spectral distribution of the SE electrons issued from a KCl using electron exci-ation experiments, ∂ı/∂Ek,(symbols) [21] and X-ray excitation, ∂ıX/∂Ek (full lines)13]. Calculated curves derived from Eq. (5) are also given (dashed lines).

ig. 4 shows a comparison between this spectral distribution asbtained from electron excitation experiments (symbols) [21] andhat obtained from X-ray excitation experiments [13]. On the samegure, the dashed curves, with � = 0.5 eV and � = 1 eV, representesults of calculations based on the following expression suggestedy Henke et al. [13]:

∂ı

∂Ek= FEk

(Ek + �)3(5)

In Eq. (5), F is a normalization factor to fit the maximum to unitynd � is the electron affinity of the insulator of interest. One maybserve that the agreement between the two types of experiment

s excellent even if their agreement with calculations is rather poor.In fact the big problem to deduce the evolution of ıX(h�) of a

iven sample from the use published data, ı = f(E◦), or results ofophisticated calculations is that the chemical composition of thisample is not sufficient to determine its yields. This fact is illus-rated with the poor level of agreement, rarely better than 25%,etween various published yield results, ı = f(E◦), for a commonetals (such as aluminum or copper) for which there are a dozen

ndependent sets of data available [22,23]. These deviations are notnly due to inherent uncertainties of experiments but they alsoesult from the physics involved in the SEE yield. In a three-steprocess (SE generation, transport and escape), the generation is thetep only dependent from the intrinsic properties (chemical for-ulae) of the investigated material but SE transport and escape

re very sensitive to extrinsic parameters. SE transport is governedy interactions of a-few-eV electrons with impurities, dislocations,rain boundaries and, for insulators with atomic vibrations whilehe escape probability A is extremely sensitive to any slight changef electron affinity, �, that is in turn very sensitive to surface compo-ition, structure and environment and also crystalline orientationf the surface. Via the influence of crystalline state on SE attenua-ion length in ı(E◦), its expected influence on ıX(h�), is illustrated inig. 2a for two varieties of MgO, a single crystal and a polycrystallinepecimen for which the s value has been estimated to s ∼ 12–14 nm

nd to s ∼ 3.6 nm, respectively [24]. The influence of atomic vibra-ions on ‘s’ and then on ı(E◦) and on ıX(h�) is illustrated in Fig. 2bith its change from s ∼ 4 nm to s ∼ 7 nm when going from H2 to T2

ecause of the difference in the zero point vibrations [25]. The influ-nce of electron affinity, �, on escape probability A and then on ı(E◦)

lated Phenomena 178–179 (2010) 357–372

and on ıX(h�) is illustrated in Fig. 3a for BeO with the change of A/Ese

from ∼22 keV−1 for bare surfaces to ∼34 keV−1 for ceasited surfaces[24]. Inspired from [16], the combined influence of the change of svia temperature change and of A, cleaved and non cleaved surfaces,

are illustrated in Fig. 3b for some NaCl single crystals.

2.3. Practical consequences

Despite the difference in the yield, ıX(h�), of different insulatingsamples having a common chemical composition, the most strikingresults shown in Figs. 1–3 is the very large difference between ultralight or light insulators and heavy insulators as a consequence offactor � in Eq. (2). For a given irradiation such as Al K�, the yieldincreases four decades from ıX ∼ 10−3 for condensed hydrogen upto ∼20 for condensed Xe and it passes by a few 10−2 for BeO and bythe unity for Au. Between the extreme and very specific situations ofH2 and Xe, one may expect yield values lower for polymers such aspolyethylene than for glasses or metallic oxides such as ZnO, MnO,etc. Then for a given incident flux of photons, a less positive chargingis expected for light polymers than for heavier insulating samples.On the contrary, the use of a gold grid mesh on an insulating sub-strate is more efficient than the use of a Cu or C mesh for providingSE electrons to compensate the positive charging resulting fromnormal SEE emission from the sample.

For a given insulator, it is sometimes possible to minimize charg-ing by a suitable choice of the incident irradiation but keepingunchanged the number of incident photons. For instance, in theXPS investigation of catalysts on MgO substrates, the use of Mg K�

line would be better than the use Al K� line because ıX is at aboutthree times larger for Al K� as a consequence of the Mg K absorptionjump (see Fig. 2a) while the photoelectron line intensities decreasewith their photo-ionization cross-sections.

More easily achieved with the use of a tunable X-ray sourcethe same strategy may be applied to differential charging whenthe photon energy crosses the absorption jump of one majorcomponent of the specimen. Nevertheless this strategy remainssometimes questionable when, for instance, Al K� radiation is usedfor the XPS investigation of catalysts on Al2O3 substrates becausesuch a use leads to a simultaneous decrease of charging and of thephotoelectron line intensities.

3. Homogeneous sample widely irradiated by a defocusedX-ray beam

3.1. Surface potential, VS

By definition, insulating materials are characterized by a verylarge DC resistivity, 1/� and the border between insulators and wideband gap semiconductors nearly corresponds to 1/� ≥ 1013 � m.Most of the insulating materials are also dielectrics and are charac-terized by their dielectric constant, ε = ε0εr where εr is the relativedielectric constant and ε0 is the dielectric constant of the vac-uum: 8.85 × 10−12 F/m. Via an exponential decay of the form exp.(−t/diel), the dielectric time constant, diel. = ε/� , is the measure ofthe residence time of a mobile charge locally set at a point insideof a given material [26]. The electrical situation of a thick homoge-neous insulator (thickness h larger than the maximum penetrationdepth of incident X-rays, h > >Rx), largely irradiated with a defo-cused X-ray beam presents some similarities to a plane capacitorwith a leak resistance, R (see Fig. 5a), and it is very useful to evaluateorders of magnitude for R. For an insulating specimen of thickness

h ∼ 1 mm and of a typical DC resistivity, 1/� , of ∼10 � m, a leakresistance R of ∼1019 � may be derived from Ohm’s law and thecorresponding evacuation current, Iev, is expected is of about 1 e/sfor a 100 �m × 100 �m irradiated area and for a surface potentialvalue, VS, of 1 V. Then, in the absence of radiation induced effects

J. Cazaux / Journal of Electron Spectroscopy and Re

Fig. 5. (a) Charge conservation (Eq. (10)) and approximate equivalence between awidely irradiated homogeneous insulator and a plane capacitor. Note that ISH (sam-ple holder current) is the sum of an evacuation current, Iev, and of an influencecgsi

(covS

�

doftt

�

t

�

o

n∼dwom

etε

urrent, Iinf, resultant from the time evolution of Qinf. The dashed and dotted rectan-les correspond to two different choices for the application of Eq. (10). (b) Influence ofubsurface heterogeneities on the surface potential function. The reference potentials that of the sample holder, S.H., set at ground.

leakage or migration of mobile ions), the very early initial electri-al situation is nearly that of a perfect plane capacitor before theccurrence of any compensation effect. During a short time inter-al, �t, the surface charge of this capacitor, �Q, results from theEE emission and it is given by

Q ∼ ˚◦Sq ıX �t (6)

In Eq. (6), q is 1.6 × 10−19 C; S is the irradiated area; �◦ is inci-ent photon flux and �◦S/cos i◦ is the number of incident photons/s.n area S. Then, with ıX(i◦) = ıX(0◦)/cos i◦, �Q is nearly independentrom angle i◦. The usual equation of a plane capacitor (with ε: dielec-ric constant = ε0εr and εr relative dielectric constant) relates �Q tohe corresponding increase of the surface potential, �VS:

Q = C �VS with C ∼ εS

h(7)

Then, �VS (measured with respect to the specimen holder seto ground) is given by

VS = ˚◦hq ıX �t

ε(8)

r∂VS

∂t= ˚◦h

qıX

ε0εr(9)

Again for a sample thickness, h, of ∼1 mm and εr = ε/ε0 ∼ 3.4, aumerical application of Eq. (9) leads to a potential increase, �VS, of0.1 V for (�Q/S) ∼ 3 × 10−9 C/m2 or <0.02 el./�m2 and this chargeensity corresponds to a photon density �◦ as low as <0.2 ph./�m2

hen the SEE yield is ıX ∼ 0.1. Eqs. (7)–(9) outline the importancef the sample thickness and the numerical values are two orders of

agnitude less for a sample thickness of 10 �m.

The change of h/εr by hi/εri, permits to apply the samequations to stratified specimens composed of layers of differenthicknesses, h1, h2, h3, having different relative dielectric constants;r1, εr2, εr3. Also when conductive but floating layers exist in the

lated Phenomena 178–179 (2010) 357–372 361

stratified specimen, the corresponding dielectric constant is infiniteand the effective insulating thickness is decreased in proportion. Apractical consequence of the above considerations is that the use ofinsulating adhesive tapes for sample mounting contributes to theinitial increase of the surface potential [27].

When the sample presents local change of thickness or compo-sition, the initial surface potential �V(x, y), is no longer uniformover the surface even when the local heterogeneities are below themaximum penetration depth of incident X-rays: Fig. 5b. This sim-ple fact has been utilized in Scanning Electron Microscopy (SEM)to image conductors and overlay marks even located underneathinsulating thin films that an e-beam cannot penetrate [28]. It hasalso been used in X-ray spectro-microscopy to image micro-patternin a semiconductor device with a depth resolution of 0.2 �m and alateral resolution of 0.5 �m [29]. Like in SEM, this initial situationis expected to change during irradiation via the homogenizationprocess resulting from the emitted SE going back to the specimen.

3.2. Charge conservation

The above assimilation to a plane capacitor is convenient toobtain orders of magnitude but it does not hold during irradiationbecause of the change of ıX with VS and because of the occurrence ofcompensation effects [1]. The time evolution is governed the chargeconservation relationship which may be written in the form:

∂Q

∂t= ˚◦SqıX − Icomp (10)

In Eq. (10), Q is positive; Icomp is the sum of all the compensationeffects described as an electric current Icomp and its sign is chosenpositive for outgoing electrons escaping from the irradiated area, S.Eq. (10) holds at any time from the early beginning of the irradiation,when Icomp = 0, up to the steady state, when ∂Q/∂t = 0.

The application of Eq. (10) implies a specific choice for thevolume where this equation is applied. In Fig. 5a this choice cor-responds to a volume limited by a dashed rectangle where Q+ isonly the charge of Eq. (6) inside the sample and then the internalevacuation current leaving this volume is Iev. When it is chosen toinclude the sample holder in this volume, dotted rectangle in Fig. 5a,the considered internal charge is the sum of Q+ and of a charge Qinf.,developed by influence on the sample holder while the sample cur-rent, ISH, results from the sum of Iev and of an influence current, Iinf.,associated to the change of Qinf. with time: Iinf. = ∂Qinf./∂t. This pointis underlined here to prevent the possible confusion between themeasurement of the specimen current and the evacuation current.

4. Compensation mechanisms from inside

4.1. Different thickness scales

Detailed below, the relative weight of quite all the inner com-pensation mechanisms are also sample thickness dependent andthree different thicknesses may be considered (Fig. 5a):

a) Thick samples of thickness h larger than the maximumpenetration depth of incident X-rays, RX, arbitrary defined asRX = 3 �−1 cos i◦. b) Samples of medium thickness, r < h < RX c) Thinsamples of thickness less than the maximum SE escape depth, r,arbitrary defined as r ∼ 3s.

For a thick sample, the above limits leads to three distinctregions: a positively charged surface layer of thickness r resultingfrom the holes left by SEE; an intermediated region where the inci-

dent X-ray beam generates a large number of electron/hole pairs butwhere most of electrons recombine rapidly with holes leaving thisregion approximately neutral from the electrostatic point of view;the deepest region, quite intrinsic, where the incident X-rays donot penetrate. Orders of magnitude for RX are photon energy and

362 J. Cazaux / Journal of Electron Spectroscopy and Re

Fn

mtrgeliai

the vacuum between the sample surface and the grounded pieces of

Fcg

ig. 6. Derived from tabulated values of absorption coefficients [18], orders of mag-itude for the maximum penetration depth of incident X-rays: RX ∼3/�.

aterial, Z, dependent. Derived from tabulated values of absorp-ion coefficients [18], Fig. 6 shows that RX is in the 1–100 micronange except, on one side, ultra-light materials and photon ener-ies above 1 keV and, on other side, heavy materials and photonnergies below 1 keV. The value of r is related to the SE attenuation

ength, s, that is situated between 5 and 10 nm for polycrystallinenorganic insulators [20,30] and for polymers [24] and, as indicatedbove, it is between 12 and 30 nm for single crystals of inorganicnsulators [20,30]. Noticeable exceptions are, on one side, the case

ig. 7. Top: Sketch of the V(z) potential function and of the Fz(z) component of the electrichange in direction of the open arrows. Bottom: corresponding change of the band structenerated SEs of kinetic energy less than �V(I) with respect to the vacuum level cannot es

lated Phenomena 178–179 (2010) 357–372

of condensed hydrogens where s ranges from ∼4 nm to 7 nm and, onother side, the case of condensed rare gases such as Xe where s mayreach a fraction of micron [15,31,32]. As expected, the s values areat least one order of magnitude larger than the attenuation lengthof photo and Auger electrons in the 1 keV-kinetic energy range.

4.2. Thick sample: inner trapping effect, sample holder andinfluence currents

Fig. 7 shows the electrostatic situation when thickness h is largerthan RX and when the sample surface is parallel to a groundedpiece into the vacuum such as the entrance slit of the spectrom-eter. In such a situation a more precise expression than Eq. (7) maybe obtained for the surface potential, VS, by solving a one dimen-sional Poisson equation. Such calculations have been performed fora two-layer model of electron irradiation (see Eq. (4) in [33]) and,here, the corresponding result may be simplified by setting Q− = 0(no negative charge) and Q+ = Q. In addition, Vh = Vg = 0 when neitherbias is applied to the specimen holder nor to any external electrode.The corresponding simplified result is

VS(1 + a) = Qh

Sε− Qs

2Sε(11)

In Eq. (11), parameter a is a = h/εrw and w is the distance into

the instrument: spectrometer or final window of the X-ray source.The same type of calculation also permits us to express the uni-form electric, Fe, established into the vacuum as well as the electricfield, Fi, established into the dielectric but outside the irradiated

field for a thick specimen. Note the inversion point I of Fz(z) and the correspondingure scheme when the vacuum level, VL, alignment is postulated. At around point I,cape into the vacuum. CB: conduction band; VB: valence band; �: electron affinity.

and Related Phenomena 178–179 (2010) 357–372 363

vt

F

F

aAttritia

fgfndtnlIecpFi

Q

oirmp(

I

Idpiuoamaio

4b

tgiw

J. Cazaux / Journal of Electron Spectroscopy

olume. These fields have only a one-dimensional component inhe z-direction given by

e ∼ −Vs

w(12)

i = Q

Sε+ Fe

εr(13)

These fields are all directed towards the positively charged layernd, inside it, the field changes direction at an inversion point I.t this inversion point the potential function V(z) is maximum and

he potential energy, qV(z), of electrons is minimum. Then, aroundhis point, some generated SEs of initial low kinetic energy withespect to the vacuum level cannot now escape into it: see q �V(I)n the bottom of Fig. 7. Via the correlated decrease of ıX, this innerrapping mechanism in the SE generation layer is a spontaneousnner self regulation effect leading to a less linear increase of �VSnd of �Q with time than that expected from Eqs. (8) and (10).

The field Fi in the intermediated region s < z < RX pushes a smallraction of electrons (resulting from number of electron/hole pairseneration) towards the positive layer and it also pushes a smallraction of the holes towards the rear electrode but the holes can-ot reach the specimen holder because of their very low mobilityue ‘polaron’ effect [34,35] and to their too large travel distanceso reach it. Then the intermediate region remains approximatelyeutral from the electrostatic point of view and, combined to a neg-

igible ohmic current, the result is a negligible evacuation current,ev. and the sample holder current, ISH, is only composed of an influ-nce current, Iinf. This influence current may be derived from thehange of the influence charge, Qinf., that is developed on the sam-le holder’ surface. This charge, Qinf., may be, in turn, deduced fromi via the continuity of displacement vector at holder–specimennterface.

With kinf ∼ 1 − [h/(h + εrw)], the result is

inf = −kinf Q (14)

In this situation, the most important result is that Qinf and Q aref opposite sign where kinf is less but very close to unity: nearly total

nfluence. Then, the initial measurement of specimen current, Ispe,eflects the initial change of Q with time including the self trapping

echanism responsible of the decrease of ıX. When all the com-ensation effects of Eq. (10) are included in ıX, one obtains from Eq.6):

inf . = ∂Qinf .

∂t= −kinf

Qinf .

∂t= − kinf ˚

◦SqıX (15)

Due to electrons coming from the ground, the time evolution ofinf. is characterized by a sharp rise at the early beginning of irra-iation followed by a slow decrease external compensation effectsrogressively take place. From the experimental point of view, the

nitial rise is limited by the time constant of the electrometer beingsed. After its initial jump, Iinf. decreases like the time derivativef VS: see Section 5.2. The possible contribution of a weak evacu-tion current is delayed by a longer time constant due to the lowigration of holes towards the rear electrode and an exception toquite negligible evacuation current is the possible migration of

onic species in the investigation of soda-lime glasses, for instancer the occurrence of a leakage.

.3. Medium thicknesses: photoelectrons crossed injectionetween specimen and substrate

When the sample thickness is situated between 3�−1 and r,he above considered self trapping effects around point I in the SEeneration layer qualitatively remain. Simultaneously, additionalnternal compensation effects take also place and they increase

hen thickness decreases. There are the migration of some holes

Fig. 8. Intermediate thicknesses, r < h < RX . Same sketch as in Fig. 7 without bandbending around point I for clarity but with a specific attention to compensationmechanisms at the sample/sample holder interface.

from the electron/hole pair generation region towards the substrateand the crossed injection of photoelectrons at the sample/substrateinterface. The sample current Iinf is not significantly modified by thecorresponding charge transfer because the induced change of Q isquite exactly compensated by the change of the influence currentof opposite sign.

Driven by electric field Fi the migration of holes towards thesubstrate is possible but their evacuation to ground is difficult toestimate because of its strong dependence upon the nature of con-tact, ohmic or Schottky, between sample and sample holder.

Involving more energetic electrons, the crossed injection of pho-toelectrons is less sensitive to the nature of this contact. As shownin Fig. 8, the involved photoelectrons are issued from the twosides of the holder/sample interface where the attenuated X-rayflux is nearly given by �◦ cos i◦x exp−(�h/cos i◦) and the respectiveSEE yields are ıX(h/s) and ıX(s/h). The SE generation and trans-port being unchanged with respect to that of bulk materials, theSEE yields for the crossed electron injection, ıX(h/s) and ıX(s/h),differs from the corresponding emissions into vacuum, ıX(h) andıX(s), by only their escape probabilities, A(h/s) and A(h). Settinga(h/s) = A(h/s)/A(h) and a(s/h) = A(s/h)/A, the initial increase (withtime) of the charge injected on the rear side of the sample, ∂Qinj/∂t,takes a form similar to Eq. (15):

∂Qinj

∂t= ˚

◦SqD (16)

with D = [exp−(�h/cos i◦)][a(s/h)ıX(s) − a(h/s)ıX(h)]Postulating the knowledge of all other parameters, application

of Eq. (16) requires the evaluation of escape probabilities at theholder/sample interface A(h/s) and A(s/h) as well as escape proba-bilities at holder/vacuum and sample/vacuum interfaces, A(h) and

A. These evaluations may be derived from the double integral overa 2� solid angle and over the SE spectral distribution of the angulartransmission probability of electrons crossing the correspondingsurface potential barriers, T(h/s), T(s/h), T(h) and T(s).

364 J. Cazaux / Journal of Electron Spectroscopy and Re

Fig. 9. Right: In polar co-ordinates and derived from numerical applications ofEq. (17), angular transmission probability, T(˛), for SEs having the most prob-able energy and arriving at different interfaces: (i) metal/dielectric (Ek1 = 10 eV;Ek2 = 2 eV); dielectric/metal (Ek1 = 10 eV; Ek2 = 1 eV); metal/vacuum (Ek1 = 12 eV;Eatn

Ea

T

tcrliirtu∼ktefttuSar√

ti∼piirti

pi

sample/holder interface: Fig. 10a. Such an accumulation of positivecharges into the specimen, tends to increase not only the surfacepotential, V(0), but also the potential function change, V(z), into thespecimen, in particular around inversion point I. In this region, theSEs are generated into a potential energy well, −qV(z), increasing in

k2 = 2 eV); dielectric/vacuum (Ek1 = 2 eV; Ek2 = 1 eV). Left: Same representation ast right but normalized to unity in the forward direction. For the case of a dielec-ric/metal, the transmission probability as a function of the inner incident angle andot as a function of the emission angle into medium 2.

For a SE of kinetic energy Ek1 into medium 1 and of kinetic energyk2 into medium 2, the angular dependence as a function of thengle of emission, ˛ into the medium 2 is [24]:(

12

)= 4G1/2

[1 + G1/2]2with G = 1 + Ek1 − Ek2

EK2 cos2 ˛(17)

In Eq. (17) the kinetic energies, Eki are measured with respect tohe bottom of conduction band for metals and insulators and theorresponding kinetic energy into the vacuum, Ek, is measured withespect to the vacuum level. When the alignment of the vacuumevels are assumed (see bottom of Fig. 8), one gets: Eki = Ek + � fornsulator/vacuum interfaces and Eki = Ek + EF + � for metal/vacuumnterfaces. Fig. 9 represents in polar co-ordinates some numericalesults of such angular distributions for various interfaces and forhe most probable energy into each medium: ∼2 eV into the vac-um for a SE issued from a metal where its kinetic energy was 12 eV,1 eV into the vacuum for a SE issued from an insulator where itsinetic energy was 2 eV. Related to Fig. 4, these choices correspondo EF + � ∼ 10 eV for the metal and � ∼ 2 eV for the insulator of inter-st. This figure shows that the angular distribution of the SEs issuedrom metals is narrower than those issued from insulators becausehe SEs issued from a metal must have an inner kinetic energy inhe 10 eV range to be able to escape into a dielectric or into the vac-um while a ∼2 eV kinetic energy is sufficient for the correspondingE issued from an insulator to escape into the vacuum [24]. Then,t the interfaces, the SEs issued from a metal experience a largerefraction effect, according to the law:

Ek1 sin ˛1 =√

Ek2 sin ˛2 (18)

Obeying to sin ˛c = (Ek2/Ek1)½, there is also a critical angle ˛c forotal inner reflection in medium 1 or for emission from medium 1nto medium 2. Typical values for ˛c are ∼40◦ for insulators and25◦ for insulators when bounded by vacuum and they explain aart of the difference between ı and then ıX for the SE emission

nto the vacuum from insulators with respect to metals. When Ek1s larger than Ek2, one may consider the reverse path of SE withespect to the above situation: at normal incidence, the effect of

he surface barrier is the same, T(˛◦) and the SEs arriving at obliquencidence are deflected towards the normal to the interface.

From the above developments it results that the transmissionrobabilities A are difficult to accurately evaluate from a double

ntegration but, for each specific situation, this transmission prob-

lated Phenomena 178–179 (2010) 357–372

ability T(1/2) may be simply estimated from the evaluation of innercritical solid angle for the most probable SE energy, �c, normal-ized to 2� and weighted by the transmission probability at normalincidence, T(0◦) [24]:

T(

12

)∼ T(0◦)(1 − cos ˛c). (19)

Next, from the calculated values of parameters A(h/s), A(h), A(s/h)and A, the two coefficients a(h/s) = A(h/s)/A(h) and a(s/h) = A(s/h)/Amay be evaluated and, as seen in the bottom of Fig. 8, their values areexpected to be larger than unity because the crossed injection of SEbetween two solids is more easy than the corresponding injectioninto vacuum, the surface barrier to overcome being less.

The final insertion of various coefficients into Eq. (16) leads totwo different situations illustrated in Fig. 10a and b.

In a first situation, a(s/h)ıX(s) is larger than a(h/s)ıX(h) andpositive charges in excess are also left on the sample side of the

Fig. 10. Same sketch as in Fig. 8 but considering the two possibilities for electrontransfer at the sample/sample holder interface. (a) a(s/h)ıX (s) > a(h/s)ıX (h), theelectron injection from the sample is larger than the reverse injection. (b) Reverse sit-uation, a(s/h)ıX (s) < a(h/s)ıX (h). (c) Thin film sample with possible SE transmissionfrom the substrate to the vacuum via a transmission through the film.

and Re

dcst

isssltFdraistip[f

4

p(lipci

tdtceass

acoıtbmwiatıootwsdpbas[

J. Cazaux / Journal of Electron Spectroscopy

epth, so that an increasing fraction of them, of low kinetic energy,annot escape into the substrate and into the vacuum. This internalelf regulation effect contributes to stabilize the surface potentialo its steady state value.

In a second situation, a(s/h)ıX(s) is less than a(h/s)ıX(h) and SEssued from the substrate accumulate on the sample side of theample/holder interface: Fig. 10b. With a reference potential of theample holder set to ground, the potential function, V(z), into thepecimen takes a S shape with a negative lobe followed by a positiveobe and, at points I1 and I2, the extrema of the two lobes correspondo a direction change of the internal electric field (open arrows inig. 10b). The effect of electron injection from the substrate is toecrease the surface potential, V(0). The inner self regulation effectsesult from the shape of the corresponding potential energy, −qV(z),bump followed by a well, leading to the increase of ıX(s/h) via the

njection of a fraction of SE from sample towards grounded sub-trate combined to a decrease of the SEE, ıX, into the vacuum. Inhis second situation, the surface potential, V(0), decreases but ist able or not to reach a zero value? A possible negative surfaceotential has been previously suggested [36] but scarcely observed37,38] and a combination of Eqs. (11) and (16) provides a guide lineor optimizing this occurrence detailed in Section 4.4.

.4. Thin specimens

Besides a possible evacuation of charges through the sam-le/sample holder contact, the thickness decrease from 2r and rmaximum SE escape depth from the specimen), induces a corre-ated decrease of the surface potential, VS, via the less value of hn Eq. (11). When h is decreased there is a progressive overlap-ing between charges left by ıX on the free surface side and byharges resulting from the crossed injection at the sample/substratenterface, ıX(s/h) and ıX(h/s).

A significant change of regime is expected when the samplehickness is decreased from r down to zero. With respect to theirect influence of h on VS in Eq. (11), the main effect is the addi-ional decrease of VS due to the decrease of charge Q as a directonsequence of the decrease of ıX via the decrease of the SE gen-ration depth. For the same reason there is a decrease of ıX(s/h)nd there is also an optimization of the SE emission from the sub-trate because of a negligible attenuation of the X-ray flux in thepecimen.

In the thickness range of interest the decreasing values of ıX

nd of ıX(s/h) may be overcompensated by ıX(h/s) and a negativeharging is possible. Unfortunately a precise evaluation of such anccurrence is difficult because the difficulty to evaluate ıX and ofX(s/h) for thin films. This difficulty is due to the multiple SE reflec-ion/refraction effects at the two interfaces of the sample that maye experienced by a fraction of SEs issued from the substrate, trans-itted through the specimen and escaping or not into vacuum asell as by a fraction of SEs generated into the sample and experienc-

ng similar zig-zag paths. Despite the lack of a precise estimate fornegative charging it is clear that the best situation corresponds to

hin samples of a low absorption coefficient and having a SEE yield,X, far less than that of the substrate, ıX(h/s). From the developmentsf Section 2.2, these best situations correspond to the investigationf thin polymers deposited on a gold substrate while the inves-igation of large SEE emitters such as CsI on a carbon substrateould be unsuccessful. Indirect verifications of the role of the sub-

trate composition on the SEE yield may be related to the observedamaging effects of photoelectrons as a function of substrate com-

osition: For a polymer specimen, the use of a gold substrate haseen found more damaging than the use of a silicon substrate [39]nd films of poly(vinyl alcohol) on silicon, copper and gold sub-trates were allowed to degrade with relative rates of 1:∼33:∼4140].

lated Phenomena 178–179 (2010) 357–372 365

Even when VS remains positive it decreases because of thecombined decrease of Q and of h in Eq. (11). This trend may beextrapolated down to the nanometer range but not below: forthicknesses in the monolayer scale the discontinuous nature of thesample makes that the mean surface potential value approacheszero but with relatively large fluctuations around it, because of itsthickness heterogeneities.

5. Compensation mechanisms from outside and timeevolution

5.1. Compensation mechanisms from outside

Compensation effects from outside have be listed elsewhere [1]but most of them, such as the role of the vacuum pressure sur-rounding the specimen, are difficult to quantify and are specific toeach experimental arrangement and operating mode. Then presentinvestigation is limited to general mechanisms resulting from emit-ted SEs returning back to the specimen compensating, then, thepositive charges initially left by SEE. This compensation effect isdriven by the electric field progressively established in the vacuumgap, width w, between the sample surface at potential V(0) andgrounded pieces of the instrument: spectrometer or final windowof the X-ray source. For the defocused mode in a parallel geometry,Figs. 5a and 7 (Section 3.2), this field, Fe = −VS/w is supposed to beuniform and given by Eq. (12).

In such a simple situation the equations of motion of SE electronsare:

m∂2X

∂t2= 0;

m∂2z

∂t2= qVs

w(20)

Then, with ES = qVS, the trajectories of SE of initial energy Ek andangle of emission ˛ (to the normal) obey to:

z

w= −

(ES

4Ek

)(x

wsin ˛

)2+

(x

w

)cot ˛ (21)

Using reduced coordinates, z/w and x/w, Fig. 11 illustrates vari-ous SE trajectories derived from numerical applications of Eq. (21),first (top) when the initial SE kinetic energy, Ek, is less than theirabsolute potential energy, |q|VS, and next (bottom) when the initialSE kinetic energy is larger than qVS.

As expected, the attraction by a positive potential distorts theSE trajectories. All the emitted SEs of initial kinetic energy Ek ≤ qVSreturn back to the sample and sample holder but the return pathalso concerns SEs of initial kinetic energy Ek larger than ES, Ek ≥ qVSwhen their initial normal component Ek (⊥) is less than qVS. Fromelementary properties of parabolas, the angular limit, ˛lim., for thereturning SEs may be easily established:

cos ˛lim . =√

Es√Ek.

(22)

The fraction of SE non-returning back to the sample or to thesample holder may be evaluated from the surface integral of func-tion T(S/V) from angle ˛ = 0 to angle ˛lim of the angular distributionof Eq. (17) for each kinetic energy Ek of the spectral distribution,∂ı ∂Ek. Normalized to the surface integral, SE, over half the space,each integral may be performed in a numerical form from thediscrete sum of the elementary contributions relative to emissionangles ˛ ± �˛i (Fig. 12a):

�

(∂ı

∂E

)=

∑T(

S

V

)i2�(sin ˛i) �˛i (23)

k

The result of such a procedure is illustrated by the dashed linein Fig. 12b that has been evaluated for a surface potential VS of 1 Vand a material affinity � of 1 eV. In this figure the area betweenthe full line, uncharged spectral distribution, and this dashed line

366 J. Cazaux / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 357–372

Fig. 11. Derived from Eq. (21), various SE trajectories into the vacuum for electrons ofdifferent initial emission angles and different initial kinetic energy. Top: Ek = |q|VS/2aco

rwt

itaissalofi

darsaonlpiahtit6

Fig. 12. Evaluation of the fraction of SE non-returning back to the sample or tothe sample holder. (a) Evaluation of Eq. (21) from decomposition of the angular

of their recombination with holes. In addition, during this flight

nd Ek = |q|VS. Bottom: Ek = 2|q|VS and Ek = 3|q|VS. At the same scale, the dotted lineorresponds to the SE angular distribution at the dielectric/vacuum interface shownn the left of Fig. 9.

epresents the fraction of SEs returning back to the sample holderhile the dashed-dotted line represents the self trapped frac-

ion.Under the assumption of a uniform field into the vacuum an

mportant consequence of present analysis is that the spectral dis-ribution of non-returning SEs does not show a sharp cut-off at qVSnd the same remark also holds when a conductive specimen isnvestigated with a positively biased sample holder [41]. Such aharp cut-off at qVS may only be obtained with concentric hemi-pherical constant potential surfaces obtained from a point sourcend a point sample surrounded by a concentric hemispherical col-ector at ground. For all the other external geometries the fractionf non-returning SE is a function of the more or less complicatedeld established into the vacuum.

In present parallel geometry and for a sample of infinite lateralimension, the fact that a returning SE emitted at a point I reachespoint J significantly distant from I is not important because of the

everse path of a SE emitted at point J and arriving at point I and theurface potential remains, in theory, uniform. In practice, the irradi-ted area has finite dimensions and such crossed trajectories cannotccur at the borders of this area. The resulting surface potential iso longer uniform at around these borders. Another point is the

arge distance between point I and point J, several w units. For sam-les of small dimensions or for small insulating details embedded

n a conductive matrix, the arriving points such as J may be situ-ted on the sample holder where they do contribute to the sampleolder current, ISH, of Fig. 5a but they do not compensate the posi-

ives charges left in the sample. Such lateral effects are specificallymportant in the focused mode, small spot XPS, and then addi-ional details would be given in the corresponding section (Section.2).

distribution into a set of annuli parallel to the surface. (b) Calculated spectral dis-tribution of the non-returning SE (dotted line) for Vs = 1 V. and � = 1 eV compared tothe same distribution with Vs = 0 V.(full line). The dashed dotted line corresponds tothe approximate spectral distribution of SE self trapped around point I.

In an idealized geometry where all the SEs returning back tothe sample surface contribute to the external compensation effect,the progressive increase with time of the surface potential V(0)increases the electric field strength into the vacuum and next thedistortion of emitted SE trajectories. The result is an increasingnumber of SEs participating to the external compensation mech-anism, including the most energetic ones. Such an external selfregulation process is illustrated in Fig. 13. The exact evaluationof the time dependence and of the limit of VS attained at thesteady state is of a terrific complexity but it is possible to esti-mate the approximate delay of the compensation mechanismsconsidered here. This delay is correlated to the finite time of flightfor a SE to move from I to J. The velocity of a SE of 1 eV-kineticenergy is v(SE) = (2qV /m)1/2 ∼ 0.6 × 106 m/s and, for IJ = 1 cm, therelated value of t(tof) is ∼ IJ/v(SE) or ∼2 × 10−8 s. This time of flightlooks very short but it is probably longer than the injection timeof photoelectrons from the substrate and of the few picoseconds

other secondary electrons are emitted from the sample and thecloud of flying photoelectrons is submitted to the excess of non-compensated positive charges being left in the sample. Such extradistortions may be significant under high fluence rate, ∂�◦/∂t, con-

J. Cazaux / Journal of Electron Spectroscopy and Re

Fif

do∼vSpas

hpamfolmrs

oitlrk

5

ds

iaarc

As expected the general shape of the evolution of VS as a func-tion of irradiation time, Fig. 14, is modified by the crossed injectionof SE at the sample/substrate interface. When a(s/h)ıX(s) is largerthan a(h/s)ıX(h), i.e. d = 0.5, and when the X-ray attenuation into the

Fig. 14. Change of qV during irradiation time t(irr.) as derived from Eqs. (25) and

ig. 13. Progressive influence of the increase of VS on the SE trajectories with thencreased re-attraction (and external compensation) of emitted SE towards the sur-ace. Insert: external homogenization effect for a non uniform surface potential.

itions. For instance synchrotron sources allow to obtain fluxesf around ∼109 ph/(�m2 s) [4], so that, during a time of flight2 × 10−8 s., the theoretical increase of �VS is ∼10 V for the samealues previously used for the numerical application of Eq. (9) inection 3.1: h ∼1 mm; εr = ε/ε0 ∼ 3.4, ıX ∼ 0.1. For accelerating thisrocess by limiting the SE time of flight and the lateral SE spreading,practical solution is to reduce the distance w between the sample

urface and the grounded pieces of the surrounding.When laterally heterogeneous samples are investigated, the

omogenization process is mainly due to returning SE. An exam-le is shown in insert of Fig. 13 for a two-component specimen, 1nd 2, at different surface potentials, V1 and V2 (with V1 > V2). Theain effect is the difference in the SE trajectories. Some SE issued

rom medium 1 are re-attracted towards this medium while somethers are pushed away from medium 2 (dashed arrows) while a

arger fraction of SE issued from medium 2 are attracted towardsedium 1 instead of returning back to their initial medium. The

esult is a progressive decrease of V1 approaching V2 but with alowed down homogenization process.

When thickness h falls into the ‘r’ range, the more rapid decreasef VS with h and Q (Section 4.4) makes that the field strength

nto vacuum, Fe = −VS/w, is decreased in proportion. The distor-ion of SE trajectories are minimized for SE of initial kinetic energyarger than qVS and the external compensation mechanism is nearlyestricted to the decreasing number of returning SE having an initialinetic energy less than qVS.

.2. Attempt for an initial evolution of charging

Gathering all the analyses detailed above, the various timeependence of charging as a function of sample thickness may beummarized as follows:

For thick samples where h is RX, the initial evolution of VSs, in theory, governed by Eq. (9) but two compensation mech-

nisms rapidly take place: a spontaneous inner trapping effectnd a slightly delayed external effect mainly due to the increasede-attraction of SE’s. The two mechanisms increase with VS in aomplicated way. In particular, the complications concern the exter-

lated Phenomena 178–179 (2010) 357–372 367

nal compensation effect which depends upon the specific geometrysurrounding the sample into the vacuum. To go deeper into the sub-ject and for obtaining, at least, orders of magnitude, one may admitthat these two mechanisms lead to a sharp cut-off at qVS in the SEspectral distribution of Fig. 12b. In a way similar to that recentlydeveloped for electron irradiation in the positive charging region[42], the VS-dependence of ıX is then given by

ıX (Vs) ∼∞∫

qVs

(∂ı

∂Ek

)dEk (24)

Using the spectral distribution of Eq. (5), this integral is easilyperformed in an analytical form with, in particular, a normalizationfactor F = 2�ıX(0). The insertion of ıX(VS) into Eq. (9) leads to[

1 + y2

(1 + 2y)

]y = t

t◦ (25)

In Eq. (25), t◦, the reduced unit for time irradiation, ist◦ = �ε/�◦ı(0) hq when � is expressed in eV and y is y = qVS/�. Thecorresponding evolution is shown in Fig. 14.

For a sample thickness, h, of ∼1 mm, εr = ε/ε0 ∼ 3.4 and withıX(0) ∼ 0.1, a numerical application of Eq. (25) shows that t◦ is ofthe order of 2 × 10−3 s. for X-ray fluxes of the order of that used inlaboratory instruments ∼109 ph/(mm2 s). but it may be of around2 × 10−10 s. in soft X-ray spectro-microscopy developed with syn-chrotron sources because a SEE yield one order of magnitude largerin the soft X-ray domain and because of the six-order of magnitudelarger fluxes, ∼109 ph/(�m2 s). being available with such intensesources [4,43]. Being derived from Eqs. (7) and (14), the charges Qand Qinf evolve in proportion.

For samples of medium thicknesses, RX < h < r, the crossed injec-tion at the sample/sample holder interface has to be taken intoaccount. This additional contribution corresponds to Eq. (16) wherecoefficient D may be considered as an extra algebraic contributionto the normal yield ıX(0). With d = D/ıX(0), the insertion of thisadditional contribution into Eq. (25) leads to[

1 + y2

(1 + 2y)

]y = (1 + d)

t

t◦ (26)

S

(26) and using reduced co-ordinates: y = |q|VS/� and t◦ = �ε/˚◦ı(0) h|q|. Parameter dis d = D/ıX(0) with D given by Eq. (16). d = 0 corresponds to a thick specimen where thecrossed injection of SE at specimen/substrate interface is negligible and the initialslope, dashed line, is equal to unity; d = 0.5 corresponds to an injection from thesample larger than that from the substrate and d = 5 corresponds to the reverse.

3 and Related Phenomena 178–179 (2010) 357–372

settiiin∼ts

aofitfliwmeteVfvAreafmoF

itsobodgoeicie

6

6

iftemstbpT

Fig. 15. Non-parallel geometry. In the vacuum the constant potential surfaces V1; V2;V3, (faint lines) between an initially uniform surface potential VS and the groundedpieces of the surrounding are not parallel to each others. The different trajectoriesof SE such as SE1 and SE2 of same initial kinetic energy Ek and emission angle ˛ lead

68 J. Cazaux / Journal of Electron Spectroscopy

ample is negligible, the evolution of qVS/� is slightly above that ofvolution corresponding to a thick sample. When a(s/h)ıX(s) is lesshan a(h/s)ıX(h), i.e. d = 5, the evolution of qVS/� is below that of ahick sample. For the comparison between the three regimes shownn Fig. 14, it must be kept in mind that the horizontal co-ordinates expressed in reduced time units so that the real time irradiations proportional to incident flux and inversely proportional to thick-ess h. Then, for photon fluxes available with synchrotron sources,109 ph/(�m2 s), the increase of the surface potential may be faster

han the time needed for the acquisition of several photoelectronpectra so that it is difficult to measure [43].

In fact the main drawback of present investigation is to find thesymptotic limit attained by VS at the steady state: VS(∞). In the-ry this limit is VS(∞) = h�/q at maximum and not infinity as chosen,or simplicity, in the upper limit of integral 24. But a precise limits difficult to evaluate because it results from external compensa-ion effects that are more or less independent from the incidentux such as the atmosphere, pressure and composition, surround-

ng the specimen. In terms of charge compensation, Qcomp., theireight is often low but, expressed in volts, their influence on VS(∞)ay be very large because of the rapid decrease above Ek ∼ a few

V of the SE spectral distribution ∂ı/∂Ek. In laboratory experimentshe incident flux is low and the time acquisition of a spectrum isnough long to permit these compensation effects to take place andS(∞) scarcely exceeds a few volts. The situation is quite different

or experiments based on the use of synchrotron radiation wherealues of VS(∞) of several hundred volts are rapidly attained [43].lso pointed out in [43], another upper limit of VS(∞) is the occur-

ence of leakage in thin films when the ratio VS(∞)/h reaches thelectric breakdown value of the insulator of interest. Despite thebove difficulties, it is hoped that present analysis provides a use-ul guide line for the initial evolution of surface potential in XPS or

ore generally for X-ray irradiation into vacuum including the usef short pulse excitations: see the initial slope the curves shown inig. 14.

Finally there is the time evolution of charging when the beams off. For thick samples, the initial time decay of VS(∞) is expectedo be due to the neutralization of surface charges by the atmo-phere surrounding the specimen but a partial internal chargingf the specimen remains for a very long time because the chargeselow the first atomic layers cannot be de-trapped except the usef external strengths: temperature, applied electric field, UV irra-iation, etc. A practical consequence of the remaining charges is aeneral rule forbidding the XPS investigation of a specimen previ-usly irradiated because some charges remain. The best strategy tovaluate the decay of the charge Q when the incident beam is offs to measure this decay via the integral of the measured influenceurrent by a rear electrode not in contact with the sample: see fornstance, the experimental arrangement used by Farkhfakh et al. forlectron irradiation [44].

. Some other experimental situations

.1. Non-parallel geometry and angle-resolved XPS

In a non-parallel geometry and more generally when the samples rotated, the form of Eq. (9) is unchanged because the initial sur-ace potential is expected to not change with cos i◦: Section 3.1. Alsohe inner compensation mechanisms remain nearly unchangedxcept the change as RX/cos i◦ of the border between thick andedium thicknesses and the main change results from compen-

ation mechanisms due to SE returning back to the sample. Inhe vacuum the constant potential surfaces of Fig. 15, V1; V2; V3,etween an initially uniform surface potential VS and the groundedieces of the surrounding are not, now, parallel to each others.hen it results that the trajectories of SE having the same initial

to an asymmetry of external compensation effect and then to a non-uniform surfacepotential, VS(x). The corresponding peak broadening increases with dimension ofthe analyzer entrance slit, SA and with the angle � of PE collection with respect tothe normal of the specimen.

kinetic energy Ek and emission angle ˛ are not identical because ofthe breaking of the z-axial symmetry: see SE1 and SE2 in Fig. 15.The asymmetry of external compensation mechanisms induces asmooth change of the surface potential, VS(x) leading to a peakbroadening of the analyzed photoelectrons lines. This broadeningincreases with the dimension of analyzer entrance slit, SA, and withthe angle � of PE collection with respect to the normal to the sample.

More spurious artifact may occur in angle resolved XPS becausethe surface charges are not spontaneously evacuated and they accu-mulate during the successive angular experiments. Then there isan increasing charging shift due to the correlated increase of thesurface potential that is sometimes incorrectly attributed to a truechemical shift due to some in-depth compositional change. Thistype of misinterpretation may be avoided by coming back to theinitial position after the end of the full angular exploration in orderto verify the reversibility of measurements.

6.2. Focused mode and small spot XPS

When a fine incident X-ray beam, diameter d◦, irradiates ahomogeneous insulating sample, the SE emission generates a local-ized positive charge (Fig. 16a): Q+ = q�◦ıXd◦2t/4. In this situation,the electric field and potential functions may be obtained by solvinga two-dimensional Poisson equation when it is possible to take thez-axis symmetry into account. An alternative approach consists inusing the electric image theory following which the field and poten-tial at a point M into the vacuum experienced the field and potentialdue to the real charge Q+ weighted by a factor K = (εr–1)/(εr + 1), andthose due series of electric images symmetric to the real chargewith respect to the two interfaces: sample/sample holder and vac-uum/sample interfaces. Another series of images may be taken intoaccount for a point P inside the sample. Details on this type of cal-culation may be found elsewhere [26,45] and the important point isthat the main effects are due to the real charge and to its first image,of opposite sign, in the sample holder (Fig. 16b). The first image

effect increases when the sample thickness, h, is decreased whilethe effect of the image of a single point charge q on itself is negligi-ble excepted when this point charge is at sub-nanometer distancesfrom an interface. Then the influence of the sample thickness is sim-ilar to that obtained from solutions of the Laplace equation in the

J. Cazaux / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 357–372 369

Fifi

oat4E

cvtfuAmpptfao0udbwFc

V

sp

Fig. 17. Small spot XPS. (a) Top view of the negative halo due to some returning

ig. 16. Small spot XPS. (a) Sketch of some surfaces of constant potential: V1; V2 lead-ng to concave mirror effects. (b) Decrease of the magnitude of the surface potentialunction for a decreasing thickness, h, via the increasing effect of the first electricmage I1 of opposite sign as the real charge Q+.

ne-dimensional problem. In particular, the compensation mech-nisms from inside, self trapping effect and crossed injection fromhe sample/substrate interface, look like those described in Section. An exception is the evaluation of the influence coefficient, kinf (inq. (14)), that is slightly more complicated.

Because of the finite lateral dimension of charge Q+, the mainhanges concern the electric field and potential established in theacuum above the specimen and then their influence on the SErajectories. The surface potential is no longer uniform over the sur-ace; it is a function of the lateral coordinates, V(x, 0), dependingpon the radial distribution of photons inside the incident beam.s previously reported, the observed shifts and distortions of theeasured photoelectron lines reflect the change of V(x, 0) over the

rojected area of the spectrometer entrance slit [1]. For uniformhoton densities, the lateral charge distribution may be assimilatedo that of a uniformly charged disc and the potential function has theorm of a plateaus followed by a sharp decrease at around x = d◦/2nd next by a smooth decrease towards zero at the grounded placesf the surface [26]. For a Gaussian radial distribution of photons, V(x,) has a bell-shape form similar to that shown in Fig. 17. In the vac-um, the surfaces of constant potential evolve as a function of theistance ‘l’ from the central point O. Around point O, they start toe nearly parallel to the surface with a value close to V(x, 0). Next,hen ‘l’ is ‘l’ > > d◦ they become nearly hemispherical as shown in

ig. 16a for V = V1. Again with K = (εr – 1)/(εr + 1), their values nearlyorrespond to:

KQ

(‘l’) ∼

4�ε0‘l’(27)

Next these constant potential surfaces become nearly ellip-oidal, Fig. 16a, for V = V2 to finally take the shape of the groundedieces of the surrounding when approaching them.

SE back to the specimen. (b) Sketch of the surface potential function, V(x, 0) whenQ+ > |Q−|, ıX being <1. (c) When more SE are returning back to the specimen, Q+ < |Q−|and V(x, 0) change sign along x-axis.

The SE trajectories are distorted by the complicated potentialfunction established into the vacuum and, experiencing some kindof internal mirror effect, the SEs are reflected back to the sampleand sample holder surface when their kinetic energy is equals totheir potential energy: Eki = qVi. Then SE emitted with very low Ekvalue (spectrum of Fig. 4) may return at a point J close to theiremission point I where they may compensate some positive chargesbut most of the others may return back to the sample and to sampleholder but at points J rather far from the central spot. In contrast tosituation of Section 5.1, there is no possible crossed compensationbetween point I and point J.

Then the role of this external compensation effect is now alsoa function of the lateral dimension of the insulating area of theinvestigated sample.

For a small insulating region on a conductive surface, most ofthe returning electrons are evacuated to ground where they con-tribute to the specimen holder current ISH. The corresponding lackof compensation effect leads to a rapid increase of the potential atpoint O and this increase in turn increases the re-attraction of newSE towards this spot, following then a mechanism similar to that

shown in Fig. 13.

For large and thick sample, the key result is to expect a negativehalo surrounding the central spot on the surface: see Fig. 17a. Whenthe SEE yield, ıX, is less than unity the surface potential function is

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FoEm

70 J. Cazaux / Journal of Electron Spectroscopy

lways positive (Fig. 17b) but V(x, 0) may change sign, from posi-ive at around point O to negative at distances x d◦ when, ıX being1, more SE are returning back to the sample than there are emittedrom it: Q+ < |Q−|:Fig .17c. A signature of the generation of a negativealo, Q−, may be obtained from the decrease and eventually fromhe change of sign of influence current Iinf. When a fixed fine butntense probe is used a practical consequence of the shape of V(x,) is a large radial electric field, Fx(x, 0) at around x ∼ d◦/2, and thiseld is able to drive laterally the migration of mobile ions if therere. In Scanning Photoelectron Microscopy, another practical con-equence of the shape of V(x, 0) is the change of the charging shifthen a line profile is performed after a longer stay at the starting

oint. Such negative halo has also been predicted for electron irra-iation in the positive regime where the total yield is larger than

nity [11,46,47]. In fact during irradiation the negative halo aroundhe central spot modifies, in turn, the trajectories of a fraction of newmitted SEs pushing them towards the spot while a remaining frac-ion is deflected towards external regions of this circle. The results a lateral self compensation effect with stabilized positive charge

ig. 18. Unconventional use of a flood gun (courtesy of Dr B. Pelissier, CEA-LETI, Grenoblbtained without (left) and with (right) the flood gun on. (b) Sketch of the electron induce◦ across E1 permits the change the sign of charging from negative to positive. (c) The coarked I with respect to unchanged ‘conductive’ Si2p lines marked C.

lated Phenomena 178–179 (2010) 357–372

around the central spot because of the re-attraction of some SEstowards this spot and the lateral expansion of the initial negativecircle farer and farer than its initial position around a circle.

In the two cases, small insulating region or large insulating sam-ple, the time evolution of charging is different because of the lackof negative halo in the first case but its detailed evolution is com-plicated to predict in detail because it requires long step-by-stepcalculations of SE trajectories depending also upon the specificgeometry of the grounded pieces of the sample surroundings. Thefinal state would be the steady state only attained for t(iir.) = ∞when no spurious effect, such as a leakage or sample degradation,occurs.

The decrease of sample thickness leads to the increase of theinfluence of electric images and in particular of the first image in

the conducting specimen holder and the magnitude of the surfacepotential decreases. The large normal field component Fz(0, z) dueto the attraction of the image of opposite sign in the specimenholder increases enhancing the adhesion of the insulator on themetallic holder [26,45]. Simultaneously the crossed injections at

e). (a) sketch of the investigated sample, central part surrounded by the O(1 s) lined SEE yield, ı = f(E◦), around critical energy E1. Increasing the electron beam energyntrolled increase of EFG permits to reverse the position of the ‘insulating’ Si2p line

and Re

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J. Cazaux / Journal of Electron Spectroscopy

he specimen/specimen-holder interface progressively take placeeducing in proportion the role of external compensation effectsnd the situation around point O becomes more and more similaro that of the defocused mode.

.3. Unconventional use of a flood gun

The use of low energy electron flood guns is a traditional way ofompensating for charging effects in XPS [3–6,48–50]. This methodonsists in replacing into the sample the emitted SEs with electronsssued from an electron gun and having nearly the same kineticnergy, EFG, of a few eVs. These additional electrons have the sameenetration depth as the escape depth of the emitted SEs and theyre, then, able to fill the holes left by photoemission. In addition thisnergy EFG, corresponds to the linear part of the electron-inducedield curves, ı ∼ AE◦/Ese (derived from Eq. (3) when R is �s), where◦ is below the critical energy E1 (∼Ese/A ∼ 40 eV) at which the yieldis equal to unity. From Fig. 18b, it results that the neutraliza-

ion efficiency of one electron of the flood gun increases when EFGecreases down to zero where its efficiency nearly reaches unity.hen a conventional use of a flood gun is to operate it energies as

ow as possible. In the context of present paper organized aroundhe SE emission, the unconventional use of a flood gun consists inperating it at energies EFG larger than E1. At such energies � is >1nd the normally positive charging of the sample is increased viahe controlled increase of EFG.

The advantage of this approach is illustrated in the top, a, ofig. 18 for a part of a microelectronic device obtained from a Plasmatching process, where oxygen atoms are present on an isolated partf the sample and on the conductive substrate. When the flood gun

s off, there is an overlap of the two O(1s) lines so that the existencef the two species is questionable while they are easily identifiedy the additional positive shift of the insulating line due to the elec-ron gun operated at an energy above E1. The controlled increasef EFG permits to reverse the position of the ‘insulating’ Si(2p) linemarked I in Fig. 18c) with respect to unchanged ‘conductive’ Si(2p)ines (marked C in Fig. 18c).

This strategy permits to obtain a physical decomposition ofhe XPS lines instead of a mathematical decomposition. It may bepplied to any type of samples composed of insulating and con-uctive phases of similar chemical composition. The controlledhift of the additional positive charging also facilitates the 2d-ompositional mapping of insulating phases separated from theapping of conductive phase. This example also permits to end

he body of present paper by a positive consequence of positiveharging in XPS.

. Conclusion

The present article is devoted to some fundamental aspects ofharging in XPS. Despite the fact that they are often correlated toharging effects, damaging effects and the wide field of their appli-ations have been kept out of present purpose and the interestedeaders are refereed to [51–55 and ref. inc.]. Also the positive oregative biasing, VH, of the specimen holder is not explicitly here1,8,10,56,57]. Such a biasing changes the V(z) potential functionhown in Fig. 7. It modifies in particular the inner trapping effectsround point I but the main change may be deduced from the addi-ion of an additional term, VH, in the expression of the surfaceotential, V(0), on the left side of Eq. (11) (see Eq. (16) in [1]). Thehange of V(0) modifies the field into vacuum and then the SE trajec-

ories are modified. Similarly to a positive charging, the main effectf a positive bias would be an increase of re-attraction of some out-oing secondary electrons and, similarly to Fig. 12b, the correlatedecrease of the effective value of ıX(VS). A negative bias would pushway the emitted SEs without changing significantly ıX [1].

lated Phenomena 178–179 (2010) 357–372 371

Such as the role and composition of the vacuum surrounding ofthe sample, difficult to quantify, some other compensations effectshave not been taken into account here but some present consid-erations restricted, in principle, to insulators may be extended tosemiconductors. The best example is given by the insert of Fig. 13where the two regions, at V1 and V2, may represent a pn-junctionwhere V1 represents the surface potential in the n-doped regionand V2 the surface potential in the p-doped region. For such a sam-ple, the external homogenization process would lead to a decreaseof the voltage drop between the two regions in a way similar to thedoping contrast reported for the SEM investigation of this type ofdevice [58].

Within the above limitations, the main results of present inves-tigations are:

1. Order of magnitude, dependence on photon energy andclassification of insulators by the increasing value of their X-ray-induced SEE yield, ıX, have been given (Section 2.1).

2. Knowledge of ıX(h�) is important because it is the single respon-sible of charging effects but it may also play a role in thecompensation mechanisms at the sample/sample holder inter-face (Eq. (16)).

3. A possible strategy to minimize charging effects by changingphoton energy has been suggested (Section 2.3).

4. A precise value of the SEE yield ıX cannot be predicted fromknowledge of only the main chemical composition of a samplebut, via the role of � in Eq. (2), the general trend is the increase ofıX with the mean atomic number: the SEE yield of organic insu-lators such as polymers is far less than that of high Z inorganicinsulators.

5. Close correlation between electron-induced and X-ray inducedSEE yield ı and ıX permits to deduce the evolution of ıX(h�) fromthe best fit of ı(E◦) experiments or calculations (Figs. 2 and 3)

6. Initial evolution of the surface potential may be estimated fromEqs. (6) and (9).

7. Some effects of the subsurface composition, such as strati-fication of the specimen or of sample mounting, have beenindicated (Section 3.1)

8. The sample holder current, ISH, has not to be confused withthe evacuation, Iev that is often negligible for thick insulators(Section 3.2 and Fig. 5a).

9. The measurement of only the influence current Iinf may pro-vide useful information on the charge evolution when the X-raybeam is on but also on its evolution when the beam is off (Sec-tions 4.2 and 5.2).

10. The fact that the surface potential, VS, decreases with samplethickness is known from a long time [59] but, here, three distinctregimes have been distinguished as a function of the range ofthis thickness with respect to the maximum penetration depthof incident X-rays and with respect to the maximum escapedepth of the secondary electrons.

11. Three main causes of regulation effects have been identified:(i) trapping of SEs in the charged layer of the sample; (ii)compensation effects at the sample/substrate interface; (iii)compensation effects from the external environment.

2. An equation (Eq. (16)) has been established to evaluate thecrossed SE injection at the specimen/substrate interface. Therole of the substrate composition and the stringent conditionsfor a negative charging have been established (Sections 4.3 and4.4).

13. The angular distribution of emitted SEs and the distortion of

their trajectories have been investigated (Figs. 8 and 11; Eq.(17)). For the first time, the compensation role played by return-ing SE back to the sample been analyzed in detail with itsdependence on the external geometry inside the vacuum cham-ber (Eq. (22) in Section 4.3), and with the influence on lateral

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72 J. Cazaux / Journal of Electron Spectroscopy

heterogeneities (Section 5.1 and insert of Fig. 13) as well as, inthe focused mode, the lateral dimension of the sample (Section6.2).

4. To reduce the time of flight of the SE and their lateral expan-sion, the decrease of the distance between the sample and thegrounded pieces of its environment has been suggested.

5. Also for the first time, an equation, Eq. (25) and Fig. 14, hasbeen suggested for describing the time evolution of the surfacepotential as a function of experimental parameters such as theincident flux, sample thickness, etc.

6. Artifacts associated to a non parallel geometry and to angle-resolved XPS have been pointed out in Section 6.1 and Fig. 15.

17. In small spot XPS, the possible existence of a negative halo atthe beginning of the irradiation and some of its consequenceshave been pointed out: Section 6.2 and Fig. 17.

8. An experimental decomposition of overlapping photoelectronlines from the unconventional use of a flood gun is suggestedin Section 6.3.

9. Finally, all across this paper, various numerical applicationsconcerning either conventional XPS or X-ray PhotoelectronSpectro-microscopy (developed with the use of intense focusedsynchrotron X-ray sources) have been given.

cknowledgment

This author is deeply indebted to Dr B. Pelissier, LTM-CNRSrenoble (F) for providing the illustration of Fig. 18 and for stimu-

ating discussions on his experiments.

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