A new experimental approach for characterizing ... - Mohamed Belhaj

internal trapped charge and electric field build up in .... surface leading to a negative trapped charge Qt. .... solve the Poisson equation, DV ю qc/e ¼ 0, which.
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Nuclear Instruments and Methods in Physics Research B 194 (2002) 302–310 www.elsevier.com/locate/nimb

A new experimental approach for characterizing the internal trapped charge and electric field build up in ground-coated insulators during their e irradiation O. Jbara

a,*

, S. Fakhfakh a, M. Belhaj a, J. Cazaux a, E.I. Rau b, M. Filippov b, M.V. Andrianov b

a

Facult e des Sciences, LASSI/DTI UMR CNRS 6107, BP 1039, F-51687 Reims Cedex 2, France b Department of Physics, Moscow State University, Moscow 119899, Russia Received 27 October 2001; received in revised form 8 January 2002

Abstract An original method is proposed to investigate the dynamical trapping properties of bulk insulators during their irradiation by keV electrons when they are coated with a grounded metallic film. This method is based on the measurement of the displacement current and it allows to evaluate time constants for charging and discharging the dielectric as well as to evaluate the electric field build up and trapped charge density below the coating. This method is illustrated by the estimate of the charging and discharging time constants in e irradiated PMMA and the estimate of the magnitude of the electric field which drives the migration of the mobile ions in e irradiated glasses. Ó 2002 Elsevier Science B.V. All rights reserved.

1. Introduction The irradiation of dielectric materials concerns many areas of science and technology such as dosimetry (with the use of electrets); electron microscopy and microbeam analysis of geological and biological materials; electron beam lithography of polymers; analysis of the behavior of insulators of space vessels and satellites (including metal oxide/semiconductor (MOS) devices) submitted to cosmic radiation etc. The understanding

*

Corresponding author. Tel.: +33-03-26-013297; fax: +3303-26-913312. E-mail address: [email protected] (O. Jbara).

of the charging behaviour of an uncoated insulator has therefore generated the development of a number of characterization techniques such as use of the Kelvin probe electrometer [1], the electrostatic atomic force microscope method [2], two electron beam method [3] and the scanning electron microscope mirror method [4]. All these techniques are based on the measurement in vacuum of the trapped charge effects (electric field or potential) on the free-surface side of the specimen. Unfortunately these techniques may only be applied on bare insulators and none of them works for insulators covered by a thin conducting layer set to the ground. For such ground coated insulators, there are fewer techniques such as the thermal step method [5] or the pressure wave method

0168-583X/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 2 ) 0 0 6 6 6 - 3

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[6] or the electrical methods developed by Sessler [7] years ago. But these methods are two step methods in which the measurement of the trapped charges starts at the end of the irradiation so that they do not allow a dynamical investigation of the charging (and discharging) mechanisms during the irradiation process. Here, an original method is proposed for such a dynamical investigation of the trapping properties of coated insulating samples submitted to electron irradiation in a scanning electron microscope. The secondary electron emission is restricted to the conductive coating, and this coating avoids complications associated with the change of the secondary electron emission which may blur the trapping measurements. This method, called ‘‘electrostatic influence method’’, is based on the measurement of the displacement current on the specimen holder situated on backside of the sample when electrons are trapped below the coating on the front side of the sample. This measurement corresponds to the recording of the current induced by the charges on the specimen holder being attracted by the increasing trapped charges in the specimen. This method is inspired from a similar influence method but used on uncoated specimens [8–10]. It allows one to study charging and discharging phenomena and to determine accurately their time constants during electron irradiation. Moreover, it is possible to estimate the trapped charge beneath the coating and the corresponding internal electric field in spite of the absence of external charging effects. The illustrations concern the charging of goldcoated glass substrates and of gold-coated polymethyl-methacrylate (PMMA).

2. Experimental 2.1. Experimental arrangement A schematic diagram of the experimental arrangement is shown in Fig. 1. This arrangement is not fundamentally different from that previously proposed by authors for electron irradiated bare insulators [10]. It consists of a grounded cup with a hole of diameter 3 mm in its upper surface. The

303

Fig. 1. Setup for electron charging of insulators and for the influence current measurements.

coated insulator is placed under this hole and its metallic coating is in electrical contact with the cup. The metallic disk acting as an image-charge probe is set inside the cup on an insulating disk made of Teflon to avoid any electrical contact between the probe and the cup. In order to prevent any leakage current which may come from the bulk or the surface of the sample, the backside of the sample is separated from the probe by a narrow vacuum gap (about 200 lm). The probe is connected to a high sensitive picoammeter, HP 4140B interfaced to a personal computer. This picoammeter is able to measure currents ranging from as low as 1015 A up to 1 mA. The grounded cup also acts like a shield to prevent stray electrons (i.e. electrons emitted from the SEM chamber-wall (SE þ BSE)) to be collected by the probe disk and therefore to disturb the measure of the current displacement (i.e. the current flowing from the probe to ground). In order to measure the primary beam current a Faraday cup is placed on the grounded cup connected to the ground via a sensitive electrometer. The experiments were carried out in SEM Philips 505. The vacuum was about 106 Torr. The working distance (i.e. distance between electron gun aperture and the insulator surface) was 14 mm. The sample surface under the hole was irradiated in fast scanning mode (TV-rate). The

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irradiated area was 3 mm in diameter. The displacement current, (Id ) was directly monitored in integration mode (0.2 s) by a low impedance and high sensitive picoammeter. For bulk insulators coated with a metallic grounded layer, as investigated in electron probe microanalysis (EPMA), the secondary electron emission is restricted to the grounded coating, so that only negative charges are implanted below the surface leading to a negative trapped charge Qt . This charge produces positive ‘‘influence’’ charges (i.e. image charges) in all metallic pieces of the SEM chamber and mainly in the specimen holder. The image charge developed on the holder and opposite in sign to the trapped charge is given by the following expression:

2.2. Experimental results

Qim ¼ KQt ;

2.2.1. Glasses Fig. 2 presents a typical example of the measured current, on a glass sample during the electron irradiation stage performed at a primary beam energy E0 ¼ 18:5 keV and a primary beam current I0 ¼ 3 nA. The charge decay stage is also shown when the incident beam is switched off. The insert

ð1Þ

where K is the electrostatic influence factor depending on the experimental geometry as given by Eq. (9) (see Section 3.2). The trapped charge Qt which is a function of secondary and backscattered electrons and also of the leakage current IL (i.e current flowing between the sample and ground) is as follows: dQt ¼ I0 ð1  rÞ  IL ; dt

The samples used in this study are a series of PMMA and glass pieces having a thickness of 1 and 0.95 mm respectively. The dielectric constant and the density of the PMMA are 2.6 and 1.2 g/cm3 respectively and those of glass are 3.9 and 2.60 g/cm3 . Before being introduced into a vacuum evaporator, where a 15 nm thick gold film was deposited onto their surfaces, the samples were carefully degreased in a methanol, cleaned ultrasonically in deionized water, and dried in warm air. In order to avoid any remaining charge which may result from previous electron irradiation, each measurement was done using a new and chargefree sample.

ð1aÞ

where I0 is the primary beam current and r is the total electron yield. r is equal to d þ g (d: secondary electron yield; g: backscattering coefficient). The charge trapping induces a displacement current (Id ), Id ¼ K

dQt ðtÞ ; dt

ð2Þ

where Qt ðtÞ is the amount of trapped charge during electron irradiation. If K is known, the trapped charge could be measured at any time t from Id , Z 1 t Id dt: ð2aÞ Qt ðtÞ ¼ K 0 Consequently, the time integration of the measured displacement current represents the time evolution of the trapped charge (with a factor 1=K).

Fig. 2. Experiments on glass. Evolution of the displacement current during electron irradiation (charging process) and after blanking of the electron irradiation (discharging process). The image charge evolution Qim is shown in insert (left hand scale and open circle) with also the corresponding evolution of the electric field in the vacuum gap (right hand scale and solid line). The primary beam energy is 18.5 keV and the beam current is 3 nA.

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shows the corresponding evolution of image charge Qim with time as obtained by integrating the specimen holder current Id . The negative sign of Id during the first stage, corresponds to a situation where the electrons move from the rear disk (i.e. probe) to the ground while the sign change (relative to the start) of the current in the second stage (at the stop) indicates the evacuation to the ground of a part of the excess electrons when the incident beam is switched off. For both stages, the equilibrium state is reached when the current Id is zero (i.e. dQim =dt ¼ 0). This observed behavior for Id ðtÞ is very similar to the one previously described for electron irradiated bare insulators [10] except the fact that the amounts of trapped charge are different. As soon as the sample is subjected to irradiation, the positive image charge, Qim as well as the negative trapped charge Qt increases with irradiation time to approach a saturation value Q1 and is well fitted by the first order charging kinetics given by the following expression: Q ¼ Q1 ð1  et=s Þ:

ð3Þ

s is the characteristic time constant of charging and its value is 48 s (see Fig. 5). When the electron beam is blanked (at toff ), some of the trapped charges released. The charge evolution at a time t > toff is nearly given by, Q ¼ Q1  DQeðttoff

Þ=s0

ð4Þ

which also applies for the positive image charge Qim as well as for the negative trapped charge Qt . One may note that the sample is not practically discharged, the remaining charge at the steady state is Q’s and the amount of the released charge is DQ ¼ Q1  Q0S (see Fig. 5). s0 is the characteristic time of the charge relaxation. Here its value is 11 s. 2.2.2. Poly-methyl-methacrylate Fig. 3. shows the behaviour of the displacement current for PMMA during a 18.5 keV e irradiation (beam current 2 nA) and after this irradiation. In the inset the evolution of image charge Qim with time is presented and the general evolution is not significantly different from that of the glass. The characteristic time of charging and discharging are 98 and 46 s respectively (see Fig. 6).

305

Fig. 3. Similar experiments on PMMA. The primary beam energy is 18.5 keV and the beam current is 2 nA.

From the experimental measurements, the most obvious result being established is that only a few charges are evacuated to the ground when the irradiation is stopped and most of them remain trapped into the dielectric despite the presence of a conductive coating on the surface.

3. Calculations It is possible to use simple electrostatic considerations to deduce the electric field built up and the trapped charge, Qt , from the above described measurements. 3.1. Electric field in the vacuum gap From elementary electrostatic considerations, the electric field in the gap (vacuum) may easily be directly deduced from the measurement of Qim . It is given by EV ¼ rim =e0 ;

ð5Þ

where rim corresponds to Qim =S and is the surface density of the image charge (in C/cm2 ); S being the surface of the scanned area (7 mm2 ) and e0 is the permittivity of the vacuum. The field in the nonirradiated area, Eout , may also be deduced from the continuity of the normal component of the

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dielectric displacement condition at the vacuum dielectric interface, Eout ¼ EV =er ;

ð6Þ

er is the relative permitivity of the dielectric.The time evolution of EV is reported on the right hand scale of the insert of Figs. 2 and 3. 3.2. Estimate of trapped charge, Qt To correlate the measured image charge Qim to the trapped charge Qt and then to determine the proportionality coefficient K, there is the need to simplify the corresponding electrostatic problem. In the present study, a coated insulator of dielectric constant e1 and of uniform thickness t, bounded by vacuum (dielectric constant e0 at z ¼ 0 is considered. The metallic specimen holder is at z ¼ h and at a distance h  tS (see Fig. 4) from the backside of the dielectric. The boundary conditions used here agree with a simplified structure of the set up shown on Fig. 1. The top boundary of the region corresponds to the grounded coating, and the bottom boundary corresponds to grounded specimen holder. The insulator is considered to be amorphous and it is assumed to be irradiated by an incident beam scanned over a large area during analysis (the lateral dimensions, 3 mm, of the scanned area are far larger than the thickness of the studied insulator) or its surface is exposed to

a broad electron beam. For such conditions, the electric potential function, V, and fields, E, build up are only a function of z coordinate and the density of trapping centers is uniform. For the sake of simplicity, the charge distribution qc (x,y,z) (resulting from the charges trapped in the specimen) is considered to be a constant up to a depth R, equal to the maximum penetration depth of incident electrons. This model for the charge distribution is similar to that previously used to explain the field assisted diffusion of mobile species in grounded coated glasses [11] or to predict some charging effects in EPMA of insulators [12,13]. It has also be used on uncoated insulating specimens for explaining the correlation between the secondary electron emission and charging [14,15]. In such a one dimensional problem, one has to solve the Poisson equation, DV þ qc =e ¼ 0, which takes the simplified form d2 V =dz2 þ qc =e ¼ 0;

where qc is the density of trapped charges (in C/ cm3 ) and is negative (trapping of incident electrons). qc ¼ Qt =RS or qc ¼ rt =R with rt the negative surface density of trapped charge in C/cm2 . Integrating Eq. (7), in each region of the coated sample and taking into account the boundary conditions (continuity of potential and continuity of the normal component of the displacement vector D ¼ eE), the V ðzÞ and EðzÞ functions are then easily established and the result is illustrated in Fig. 4. In the dielectric and inside the irradiated area (0 < z < R), the potential function takes a parabolic form and it reaches a minimum value near z  R, Vm  rt R=2e;

Fig. 4. Depiction of the boundary conditions of negatively charged insulator (thickness tS , dielectric constant e). The electric field (dashed line) and potentials (solid line) are also schematically represented as a function of depth.

ð7Þ

ð8Þ

where R is the maximum penetration depth of the incident electrons. In the same region, the internal field, Ein , directed towards the bulk, takes its maximum value, EMax at the coating/specimen interface and it decreases linearly down to nearly R. In the dielectric but outside the irradiated area, R < z < tS , and in the gap (vacuum) between the insulator and the metallic probe tS < z < h, there is no trapped charge then the fields are uniform and the potential function decreases linearly.

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The final result is the relationship between the image (or influence) charge developed on the metallic probe Qim and the trapped charge Qt : Qim ¼ KQt where K is given by K¼

R=2tS : er ð1  h=tS Þ  1

ð9Þ

This result is a function of the penetration depth, R, of incident electrons. Various expressions have been proposed for R. Here and only for an estimate, the Kanaya and Okayama expression may be chosen [16], R ðlmÞ ¼

0:0276AE01:66 ; Z 0:89 q

ð10Þ

where E0 is the primary beam energy in keV, A is the average atomic weight in g/mol; q is the density in g/cm3 , and Z is the average atomic number. In the case of a glass sample with a mean atomic number Z ¼ 10 and the mean weight A ¼ 20 g/mol the electron penetration depth is 3.5 lm at E0 ¼ 18:5 keV. The corresponding K factor is estimate to be 103 . This K estimate may be used to evaluate the trapped charge density rt as a function of time under and after electron irradiation as well as the corresponding evolution of the maximum internal field (at the coating/dielectric interface). The results are shown in Fig. 5 and the

Fig. 6. Estimated time evolution of the trapped charge density rt (left hand scale and open circles) and of the maximum electric field, at the coating/dielectric interface (right hand scale and open triangles). Deduced from the experimental results obtained on PMMA (Fig. 3).

maximum value of the field reaches the 107 V/cm range. In the case of PMMA the corresponding K factor was estimated to be 2 103 for E0 ¼ 18:5 keV. The trapped charge density rt as a function of time under and after electron irradiation as well as the corresponding evolution of the maximum internal field (at the coating/dielectric interface) are summarized on Fig. 6. The maximum value of the field is in the 9.5.106 V/cm range.

4. Discussion of the results

Fig. 5. Estimated time evolution of the trapped charge density rt (left hand scale and open circles) and of the maximum electric field, at the coating/dielectric interface (right hand scale and open triangles). Deduced from the experimental results obtained on a glass (Fig. 2).

The values of EV are directly deduced from the measurements of the image charge (see Eq. (5)) and their uncertainty is directly related to the experimental errors which are less than 5%. The same precision holds for Eout (Eq. (6)). In opposition, the estimated values of the maximum field EMax and of the trapped charge density rt result from the numerical application of Eqs. (7) and (8). More than the underlying assumptions of the naive model of charge distribution being used to establish Eq. (9), there is the problem of the estimate of R. Eq. (8) corresponds to the penetration depth of an uncharged specimen while the electric field progressively established induces an electric slowing down of the primary electrons, below the

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coating of about Vm [11,12]. Consequently a better estimate consists in combining Eqs. (8) and (9), to obtain Vm ,    r t   h im S Vm ¼ 1 ; ð11Þ er 1  tS e and to insert this value in Eq. (10) with ðE0  qjVm jÞ1:66 (q is the elementary charge) instead of E01:66 (a procedure similar to that used for the estimate of the maximum compression of the depth distribution of ionization or UðqzÞ function in EPMA [12]). In the case of a glass and when the steady state is attained, the voltage drop is of about jVm j  EMax R=2 or 1.5 kV. This means that, to evaluate R from Eq. (10) at the steady state, the effective energy is not E0 (18.5 keV) but it is close to E0  qjVm j (17 keV) and the corrected value of K is probably 15% less than the calculated value using the uncharged expression for R. In other words, the permanent rearrangement of the charge distribution during the irradiation leads rapidly to an equilibrium between different processes in competition [14,15]. Due to the decrease in the length of the trajectories by the electric field slowing down, the maximum penetration depth R of incident electron is shortened in presence of trapped charges and our initial calculation overestimates R and underestimates therefore the amount of trapped charges and the maximum field EMax . Consequently the coefficient K evolves during the irradiation (it decreases) and this fact may also be deduced from K calculations based on the same amount of trapped charges Qt but with a different charge distribution qc . It certainly also evolves slightly in the opposite direction when the beam is off because the detrapping processes progressively expend the irradiated volume, leading to an increase of K and then the present evaluation of DQ is slightly underestimated. This procedure has been also used on PMMA with a primary beam energy changing from 14 up to 24 keV. The experimental results are shown in Fig. 7 and the calculated values for EMax and rt are shown in Fig. 8. These results shows that the maximum electric field (at the coating dielectric interface) is nearly a constant. This may be understood by the influence of such kind of self

Fig. 7. Experimental evolution of the image charge density (full circles) and of the field in the vacuum gap (full squares) as a function of the primary beam energy E0 . Left: calculated value of Vm from Eq. (11) (full triangles).

Fig. 8. Calculated change of the trapped charge density (open squares and left y-axis), the maximum penetration depth R (full squares and left y-axis) and the maximum field (at the coating dielectric interface) (open circles and right y-axis) as a function of the primary beam energy E0 . Results obtained on PMMA by using Eq. (10) but changing E01:66 into ðE0  qjVm jÞ1:66 . Deduced from Fig. 7.

regulation effect in which a critical electric field in the 109 V/m induces detrapping mechanisms and the evacuation of detrapped electrons via the conductive coating. The most important result is that the present method gives an order of magnitude value of the electric field build up below a grounded coating, and this field value is surprisingly high. Another

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important result is the time constant for charging. This time constant is certainly a function of the density of traps in the specimen and of the incident dose [14,15]. The doses used here are very low and these low values lead to time constants in the 10– 100 s range which permit following the dynamic of the phenomenon. Higher doses would lead to too rapid evolutions which would prevent good precision on the measurements. There is also the fact that there is no full discharging when the incident beam is switched off. This not surprising too because it is known that the detrapping process may be very long (as it is for the electrets for instance) and it is facilitated by the increase of temperature, or by the application of electric fields or UV or X-ray radiation [15]. The novelty of our experimental results is the estimate of the fraction DQ of the charges that are detrapped when the beam is switched off. They are easily evacuated to the ground, because there are close to the coating and are situated in a region where the electric field is maximum. Finally from the technical aspect of the method being used, one may observe that the contact between the specimen and the rear electrode is minimum and this fact prevents any radiation-induced-current (RIC) to be superimposed with the displacement current. This is an important aspect from the experimental point of view even if the two contributions may be distinguished between each other because they have very different time constants [15]. The response function of the system to the displacement current is very fast while the time propagation of the RIC through thick specimens is expected to be far longer being the results of successive trapping and detrapping processes up to the collection electrode. From the point of view of applied physics, there is the problem of the quantification of insulating specimens investigated by electron beam techniques such as EPMA. The present experiment proves that the grounded coating of the insulator surface does not suppress the field effects below the surface. The field shortens the penetration depth of incident electrons and induces changes in many measurable quantities such as the characteristic X-ray signal intensities. The present estimate of the internal electric field build up, in the 109 V/m

309

range, corresponds to values where the distortions of the Uðqz) function become significant [12,13]. To improve significantly the quantification procedure, it would be possible in the future to take into account these distortions by inserting into the Monte Carlo calculations the effect of a field measured by applying the present method [13,17]. A correlated problem that may be solved by the present experimental approach is the migration of the mobile ions that are driven by the internal electric field [11]. In some experiments developed on glasses, the migration of mobile species is stopped when the electron beam is off [18] while the present results show that associated decay of the internal electric field is very low (Fig. 2) and this point has to be clarified by systematic studies.

5. Conclusion An original method has been proposed for a dynamical investigation of the trapping properties of coated insulating samples submitted to the electron irradiation. It is possible to estimate the trapped charge beneath the coating and the corresponding internal electric field in spite of the absence of external charging effects. In opposition to the investigation of bare specimens the investigation of the trapping mechanism is not disturbed by the complication related to the change of the secondary electron emission during the charging process [14]. Illustrations on gold coated glass substrates and on gold coated PMMA have been given and the precision of the measurements has been discussed while some possible improvements have been proposed. The applications of the method concern the physics of insulators with the investigation of the trapping mechanisms. The influence of the primary beam energy on the amount of trapped charges has to be investigated systematically as well as the role of the dose on the time constants and maximum trapped charge for different classes of insulating materials. The most important point is that (to the authors’ knowledge) this method is the single one which permits to follow the dynamic of charging

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of ground coated specimens, without the complications occurring in bare insulators and related to the change of the secondary electron emission when charging mechanisms take place during their irradiation. It has been established that the electric field build up below the coating may reach the 109 V/m range and is nearly a constant for PMMA when the beam energy changes from 14 to 24 keV. Of course the present study is only a preliminary investigation that have to be improved by choosing, in particular, a more realistic charge distribution and to be extended in the future to other dielectrics and a larger energy range. It is believed that this method opens the possibility of many interesting investigations. It may also be easily adapted to other types of charged projectiles such protons and other ions.

References [1] M. Bai, R.F.W. Pease, C. Tanasa, M.A. McCord, D.S. Pickard, D. Meisburger, J. Vac. Sci. Technol. B. 17 (1999) 2893. [2] H.J. Wintle, Meas. Sci. Technol. 8 (1997) 508.

[3] M. Bruner, E. Menzel, J. Vac. Sci. Technol B. 1 (1983) 1344. [4] B. Valayer, G. Blaise, D. Treheux, Rev. Sci. Instrum. 70 (1999) 3103. [5] A. Cherifi, M. Abou Dakka, A. Toureille, IEEE Trans. Elect. Insul. 27 (1992) 1125. [6] C. Alquie, G. Dreyfus, J. Lewiner, Phys. Rev. Lett. 47 (1981) 1483. [7] G.M. Sessler, G.M. Yang, CSC’3 Proceedings SFV, 1998, pp. 38. [8] J. Bigarre, S. Fayeulle, O. Paulhe, D. Treheux, Conference on Electrical Insulation and Dielectric Phenomena, IEEE Annual Report, 1997, p. 101. [9] J. Liebault, Ph.D. Thesis, Ecole Nationale Superieure des Mines de Saint-Etienne 1998, unpublished. [10] M. Belhaj, O. Jbara, D.J. Ziane, S. Fakhfakh, Proceedings of fourth International Conference on Electric Charges in Non-Conductive Materials, Tours (France), 2001, p. 338. [11] O. Jbara, J. Cazaux, P. Trebbia, J. Appl. Phys. 78 (1995) 868. [12] J. Cazaux, X-ray Spectrom. 25 (1996) 265. [13] O. Jbara, B. Portron, D. Mouze, J. Cazaux, X-Ray Spectrom. 26 (1997) 291. [14] J. Cazaux, J. Appl. Phys. 85 (1999) 1137. [15] J. Cazaux, J. Electron. Spectrosc. Relat. Phenom. 105 (1999) 155. [16] K. Kanaya, S. Okayama, J. Phys. D 5 (1972) 43. [17] M. Kotera, H. Suga, J. Appl. Phys. 63 (1988) 261. [18] F. Autefage, J.J. Couderc, Bull. Mineralogie 103 (1980) 623.