Nuclear Instruments and Methods in Physics Research B 197 (2002) 114–127 www.elsevier.com/locate/nimb

Dynamic investigation of electron trapping and charge decay in electron-irradiated Al2O3 in a scanning electron microscope: Methodology and mechanisms S. Fakhfakh a b

a,b

, O. Jbara

a,*

, M. Belhaj c, Z. Fakhfakh b, A. Kallel b, E.I. Rau

d

LASSI/DTI UMR CNRS 6107, Facult e des Sciences BP 1039, F-51687 Reims Cedex 2, France LaMaCop, Facult e des sciences de SFAX, Route Soukra Km 3, BP 802, C.P. 3018 Sfax, Tunisia c IXL UMR CNRS 5818, BAT. A31-351, F-33405, Talence Cedex, France d Department of Physics, Moscow State University, 119899 Moscow, Russia Received 23 May 2002; received in revised form 9 July 2002

Abstract The charging and discharging of polycristalline Al2 O3 submitted to electron-irradiation in a scanning electron microscope (SEM) are investigated by means of the displacement current method. To circumvent experimental shortcomings inherent to the use of the basic sample holder, a redesign of the latter is proposed and tests are carried out to verify its operation. The effects of the primary beam accelerating voltage on charging, flashover and discharging phenomena during and after electron-irradiation are studied. The experimental results are then analyzed. In particular, the divergence between the experimental data and those predicted by the total electron emission yield approach (TEEYA) is discussed. A partial discharge was observed immediately after the end of the electron-irradiation exposure. The experimental data suggests, that the discharge is due to the evacuation to the ground, along the insulator surface, of released electrons from shallow traps at (or in the close vicinity of) the insulator/vacuum interface. Ó 2002 Elsevier Science B.V. All rights reserved.

1. Introduction Charge trapping in insulating materials subjected to electron-irradiation is a phenomenon frequently encountered that may affect a variety of applications. In some of them, such as scanning electron microscopy [1–3] and electron lithography [4,5], charging is considered as a source of artifacts.

*

Corresponding author. Tel.: +33-326-013297; fax: +33-326913312. E-mail address: [email protected] (O. Jbara).

Whereas, in other applications such as the formation of long-lifetime electrets [6], charging is the base of the processing itself. Whatever the specific area of interest, the knowledge of the rate at which the charge builds up under e-irradiation, the amount of the charge at saturation and its persistence after the end of the irradiation are required. A considerable amount of results correlating the charging ability of insulators and their physical properties (crystal orientation [7,8], defects [9– 11], permittivity [12,13]) were obtained by using the scanning electron microscope mirror method (SEMM) [9,14]. However, due to the SEMM

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 1 3 3 1 - 9

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process itself, the charge measurement (i.e. mirror image formation [1]) is disconnected from the charge injection (i.e. e-irradiation) and thus, no information on charging behavior during the charge injection process can be obtained. In the present work, we have studied the phenomena occurring during and after e-irradiation of polycrystalline Al2 O3 , using the displacementcurrent method [15–18]. The method is described thereafter in greater detail and a number of experimental aspects are discussed. In particular, some important limitations inherent to the use of the basic sample holder of a scanning electron microscope (SEM) chamber are pointed out. To overcome these limitations a modified experimental setup is proposed. In Section 4, the processes that occurred during and after irradiation of Al2 O3 are studied for several primary beam accelerating voltages, Vac , ranging from 8 to 29 kV. Finally, the experimental results are analyzed and the basic mechanism involved in charging–discharging and flashover of the electron-irradiated Al2 O3 is discussed. 2. General overview 2.1. Principle When the primary electrons (PEs) of landing energy EL forming a current IPE , strike the surface of the sample, secondary electrons (SEs), with energies < 50 eV, and backscattered electrons (BSEs), with energies ranging from 50 eV to EL , are emitted in the vacuum forming an electron emission current IE , IE ¼ ðd þ gÞIPE ;

ð1Þ

where d and g are, respectively, the secondary electron yield and the backscattered electron coefficient. The total electron emission yield (TEEY) is defined as r ¼ d þ g:

ð2Þ

The general behavior of r in dependence of the landing energy EL of the incoming electrons for typical uncharged insulating materials is shown in Fig. 1. This curve is measured at the very begin-

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Fig. 1. Typical total electron emission yield of an uncharged insulator. The two energies where r is unity, ECI and ECII , are known as the first and second crossover energies.

ning of irradiation just before charging affects the SE yield by using a short pulsed primary beam. According to the total electron emission yield approach (TEEYA) [2,19], if the PEs strike the insulator surface with an energy greater than the second crossover energy, ECII , (i.e. r < 1), a negative charge is injected into the insulator. If EL is comprised between ECI and ECII , a slight positive charging is expected. Recent experimental work dealing with this approach is given in [20] while its criticism is given in [21]. It is important to point out that when a permanent irradiation is used, the problem is that a negative charging is reported; even at primary energies as low as 2–3 keV where the SE yield (obtained from a short pulse excitation) is nearly at its maximum [21]. Since the PEs accelerating voltages, Vac , here involved are greater than 8 kV, r is less than unity. Thus, a negative charge, Q, is injected into the sample. This charge induces a positive countercharge (image-charge), Qim , on the grounded sample holder, Qim ¼ KQ;

ð3Þ

where K is the electrostatic influence factor. This factor depends on the thickness and dielectric permittivity of the sample and on the electrical characteristics of the media surrounding the sample [23–25]. The Q time-variation produces a displacement current Id , between the sample holder and the ground, given by Id ¼ K

dQ : dt

ð4Þ

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If K is known, the trapped charge is calculated by integrating the current Id ðtÞ measured from the grounded probe using the following relation: Z 1 t Q¼ Id dt: ð5Þ K 0 2.2. Critical analysis The basic arrangement consists of fixing a plane insulator sample on a metallic sample holder connected to the ground through a current meter. The upper surface of the insulator is irradiated by an electron beam penetrating superficially the sample. The common practice [15–17] is to assume that the sample holder current, IH , is mainly due to the charge image formation on the sample holder and hence, Id in Eq. (5) is replaced by IH [15]. Since this assumption is at the root of our trapped charge deduction, it is worth discussing its validity. (i) Let us consider, VS , the value of the surface potential produced by the built-up negative charge in the insulator. At the sample exit, in the vacuum, both SEs and BSEs are accelerated by the electric field induced by the trapped charge, in such a way that the energy distribution of emitted electrons at the insulator/vacuum interface corresponds to ½0; qðVac  VS Þ interval whereas they hit the grounded inner-walls of the specimen chamber [26,27] with an energy ranging from qVS to qVac , q being the electron charge (i.e. 1:6  1019 C). The interaction of the accelerated SEs and BSEs with the SEM inner-wall materials leads to a secondary and backscattered electron emission. These doubly-scattered electrons (from the sample surface and then from the SEM chamber-walls) form an additional electron source; they irradiate back the sample as well as the sample holder. The intensity of this source depends on VS as well as on the composition of the material constituting the SEM chamber. As it follows from the investigations conducted by us earlier [28], as soon as Vs exceeds a few kV, this intensity could reach a value as high as 30% of the PEs current intensity. A part of these stray electrons, issuing from the additional electron source, impacts the sample holder, then flows to the ground through the ammeter to form a

Fig. 2. The basic experimental setup. IH is the sample holder current.

significant time-dependent current Istray , that superimposes to Id . (ii) Numerous works [18,29–31] show that technical insulators surface may exhibit significant higher conduction than that of the bulk, due to the predominance of surface defects (shallow traps, dangling bonds, etc.). One must draw attention on the fact that at vacuum levels typical of those found in most SEMÕs (i.e. pressure from 104 to 106 Torr), the inevitable formation of hydrocarbon contamination layer [32] may also enhance the surface conductivity [33]. Therefore, the possibility of the evacuation across the surface of a part of the charge in excess to the ground can not be ruled out. Consequently, when the basic experimental setup, shown in Fig. 2 is used, IH is not only the result of Id as it is generally suggested, but includes also the two time-dependent current-components listed above. Given this, the interpretation of IH ðtÞ curve depends on the sample environment as well as on the nature of the electric contact sample/sample holder. Finally, the trapped charge deduced from Eq. (5) could be widely overestimated.

3. Experimental setup and methodology 3.1. Modified experimental setup and its operation To circumvent the experimental limitations discussed above (Section. 2.2), we have used the

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Fig. 3. Schematic view of the used experimental setup for the displacement current measurement.

experiment setup shown in Fig. 3. This setup is not fundamentally different from that proposed recently to investigate the electron irradiated ground coated insulators [53]. It consists of a grounded metallic enclosure made in bronze, with a hole of 1.4 mm diameter in its upper surface. The sample is placed above the hole. The metallic disk (copper) acting as an image-charge probe is set inside the enclosure on an insulating disk made of Teflon to avoid any electrical contact between the probe and the enclosure. The gap between the backside of the sample and the probe is 0.5 mm. The probe is connected to a high sensitive picoammeter, HP 4140B, interfaced to a personal computer. Using such an arrangement allows stray electrons emitted from the SEM chamber-walls or electrons lacked from the insulator to be collected by the external surface of the enclosure and next, flowed to the ground. Therefore, this minor but very important change on the experiment arrangement provides that, the current flowing from the probe, through a picoammeter to ground, represents well a net displacementcurrent Id . It is important to point out that this experimental arrangement differs from mostly encountered setups in the field, especially those operated for electrets [50], and others [18,51]. In the present setup the rear electrode is not in contact with the insulating layer, consequently only the electrostatic influence current Id is measured while in most arrangements for this type of work, the insulator being in contact with the rear electrode, a

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radiation-induced conductivity (RIC) current, IRIC , among others, is superimposed to Id . Beside the obvious physical differences, the difference between Id and IRIC is related to their different time constant (after a spontaneous increase (electrostatic effects) Id decreases rapidly at the early beginning of the irradiation) while IRIC starts to increase after a longer thickness dependent time constant (the transport time of the charge through the dielectric). The test consists first in investigating a conductor. In the case of a setup having an electrode in contact with the insulator, the measured current corresponds to I ¼ I0 ð1  rÞ þ Istray while it is nil in our case (because of the lack of trapped charge into the specimen). For some years the standard sample holder in this field has both shielding aperture above the sample and a guard ring around the sensitive electrode ([51] and references there in) but, to our knowledge, the problem of doubly-scattered electrons still remains. In our case, the latter is ruled out entirely because the sample lies on a metallic grounded enclosure. Since the sample is wholly irradiated and the charge goes in a few microns, the distribution is assumed to be a disk-like distribution. Therefore, the normal component of the electric field generated by the trapped charge decreases rapidly outward the irradiated area disk, because for a disk-like distribution of charge in plane, the electric potential is flat in the middle of the charged zone and falls off as 1=r3 outside this zone. A strong electric field is then confined in the vicinity of the primary irradiated area and the doubly-scattered electrons are deflected to impact to the grounded enclosure relatively far from the irradiated area. So the contribution of such irradiation to the amount of injected electrons in the sample may be theoretically neglected, but an estimate of its weight was done by performing additional experiments. Two experimental configurations, (i) pole pieces covered with a carbon foil (ii) pole pieces without carbon foil were used. For each configuration, the displacement current is measured. The difference between measured currents is less than 2% although the backscattering coefficient of carbon is far lower in comparison with that of the poles pieces made in stainless steel.

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3.2. Samples and handling The studied insulators produced commercially by Goodfellow, were 99% pure polycrystalline Al2 O3 in the form of cylinders, 1.5 mm thick and 1.5 mm in diameter. The flat surfaces of the samples intended to electron-irradiation were mechanically polished. Then they were cleaned in acetone in an ultrasonic bath and rinsed with distilled water. In order, to eliminate stresses and to remove any defects induced by the machining, the samples were annealed at 950 °C for 10 h under atmospheric conditions. Defects are then principally oxygen vacancies and impurities [17]. The impurities contents are listed in Table 1. The experiments were carried out in a SEM Philips 505. The vacuum was about 106 Torr. The working distance (i.e. distance between the electron gun aperture and the insulator surface) was 14 mm. The samples were irradiated over their entire surface, in fast scanning mode (50 frames/ second). All measurements were made with incident electron beam normal to the samples surfaces. The PE current was measured with the help of a Faraday cup, placed on the front of the metallic cup, which, is connected to a Keithley 610C current-meter (see Fig. 3). To avoid the influence of the remaining charge from the former irradiation, every sample was irradiated only one time. 3.3. Typical displacement current behavior Fig. 4 shows a typical example of the measured current Id during the e-irradiation stage performed at an accelerating voltage Vac ¼ 24 kV and a primary beam current IPE ¼ 2 nA. The charge decay stage is also shown when the incident beam is switched off. The corresponding time-evolution of image-charge Qim ¼ KQ, is shown in the inset. As soon as the e-irradiation begins, the sample charges negatively and a positive charge is induced Table 1 Impurity contents of investigated sample taken from Goodfellow Polycrystal

Impurity

Al2 O3 99%

SiO2 0.7%

MgO 0.07%

Fe2 O3 0.07%

Na2 O 0.05%

CaO 0.03%

Fig. 4. Temporal evolution of Id . Electron-irradiation at 24 kV accelerating voltage and 2 nA primary beam current (charging process: from 10 to 58 s) followed by the blank of the electron beam.

by electrostatic influence on the metallic disk (image-charge probe) (see Fig. 3). Thus, electrons are evacuated from the metallic disk to the ground and Id becomes abruptly negative. On may note that as d is small at the beginning of irradiation, the positive charge is low and the trapped electron charge is high, therefore Id is maximum when irradiation starts. The following incoming electrons, PEs, are then decelerated by the electric field induced, in the vacuum, by previous trapped charges and their landing energy is reduced leading to the enhancement of the TEEY [2,19] and so on. Thus, a self-regulating mechanism takes place, decreasing the charge-trapping-rate until the flux of incoming electrons (IPE ) equals the flux of outgoing ones, (IE and IL ), IL being the leakage current. The trapped charge attains then a net negative saturation value, QS such as, KQS ¼ 33 pC (see, the inset of Fig. 4) and Id becomes equal to zero (dQ=dt ¼ 0). When the electron-irradiation is blanked (at toff ¼ 58 s), Id abruptly begins to decrease positively (dQim =dt < 0) reaching a zero value. This behavior is a relevant feature of a charge decay, which will be discussed below. 3.4. Calibration using change of secondary electron image size 3.4.1. Measurement of the electrostatic influence factor K In order to deduce K experimentally, the trapped charge at saturation, QS , was measured by

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using an experimental technique described previously [34]. The induced electric field in vacuum by the trapped charge may be strong enough to deflect the PE electron beam. Consequently, for a given scanning angle a, the emitted SEs and BSEs from a ‘‘point’’ M 0 , situated on the sample edge different from the initially addressed one M, are detected, as sketched in Fig. 5. Thus, the signal associated to the ‘‘point’’ M 0 is reported on the pixel M at the SEM display. This optical-aberration leads to an apparent decrease of the sample radius with a reduction factor R ¼ OM=OM 0 . The higher the amount of trapped charge is, the smaller the factor R is Fig. 6(a) and (b), show the micrographs of the Al2 O3 -disk, respectively, at the beginning of the eirradiation (t 10 s, see Fig. 4) and at charge saturation (t ¼ 58 s). The factor R takes the value of 0.85 (Fig. 6(c)). For a given working distance, PE accelerating voltage and assumed spatial-charge distribution, R is only a function of Q. Since the surface of Al2 O3 disk was irradiated as a whole, it is reasonable to assume that Q is distributed in a cylinder of radius a ¼ OM 0 and thickness zm , where, zm is the mean PE penetration depth in Al2 O3 . Since, zm toff is given by 0

Q ¼ Q0S þ DQeðttoff Þ=s ;

ð10Þ

Q0S

where is the remain stable trapped charge at saturation (i.e. after the evacuation of a part of charge). The values of Q0S and of the characteristic time of the discharging s0 , given by Eq. (10) and the data of Fig. 8, are reported in Table 2. At higher incident PE accelerating voltage, 29 kV, a different Id ðtÞ characteristics were observed (see Fig. 9). At the beginning of electron-irradia-

Table 2 Time constant and trapped charge at the steady state of the charging and discharging processes for several primary beam accelerating voltages Vac (kV)

8.7

13.8

18.7

24

QS (nC) s (s) Q0S (nC) s0 (s)

0.9 2.7 0.4 29

1.5 7.1 0.7 32

1.9 8.3 1 29

2.9 12.1 1.8 30

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Fig. 9. Id versus time under and after the electron-irradiation at 29 kV primary-beam accelerating voltage and 2 nA current. In the inset the trapped charge versus time before the occurring of the first flashover is shown.

tion, Id is negative and the charging behavior is similar to that observed for lower energies (see Figs. 4 and 8). Afterwards, when the trapped charge reaches a critical value, Qc ¼ 3:3 nC (see, the inset of Fig. 9) a succession of spasmodic and brief local discharges occurs. These abrupt and rapid discharges are the signature of the surfaceflashover phenomenon [18,35–38]. 4.2. Deflection correction and error estimation Taking into account the deflection correction, it is possible to deduce the real trapped charge kinetics. The method consists in determining the time t elapsed to reach a given trapped charge Q using t ¼

corr Ninj ðtÞ t; Ninj ðtÞ

ð11Þ

where the superscript corr corresponds to the surface density of injected electrons corrected from electron beam deflections. Since t is less than t, the kinetics of trapped charge is affected as shown in Fig. 10 where a comparison between the temporal evolutions of trapped charge at 24 kV accelerating voltage with and without deflection correction is given. One may point out that the steady state is reached more rapidly when no deflection occur but the corresponding trapped charge remains

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electron trapping (i) and charge compensation process (ii and iii) is established (i.e. c ¼ 1). Then, the trapped charge reaches a saturation value, given by Z 1 ð1  cðtÞÞdt: ð13Þ QS ¼ IPE 0

Fig. 10. Comparison between the temporal evolution of trapped charge. Open circle: with deflection correction; Open square: without deflection correction.

unchanged in both situations. The corrected time constant is 11.1 s (Fig. 10) instead of 12.1 s (Table 2). The relative error is about 8%.

5. Discussion 5.1. Charge regulation-mechanisms and trapped charge at saturation During the electron injection (e-irradiation), between the capture of a fraction of the PEs that induces a negative charge (electron trapping (i)) and a charge regulation processes that tends to counterbalance the negative charge, a dynamic competition occurs. The counterbalance mechanism is mainly based on two phenomena: (ii) The creation of holes, as a consequence of the secondary electron emission. (iii) The charge transport to the ground (leakage current IL ). At any time, the trapped charge has to satisfy the following charge balance equation: IPE ¼ cðtÞIPE þ

dQ ; dt

ð12Þ

where cðtÞ ¼ b þ d þ g is the charge-compensation-process rate (b ¼ IL =IPE Þ. If c is less than 1, a negative charge build-up until the balance between

Knowing that the PE penetration-depth has an order of magnitude of a few microns, it is interesting to notice that an excess of trapped electrons density of about 1021 electrons/m3 can be achieved at the steady state. This value being much lower than those typically expected, for intrinsic traps content in Al2 O3 , that is to say, 1023 m3 in materials with low defects content [39] (i.e. single crystals of high purity) and three order of magnitude greater and more for polycrystalline [40] and amorphous [41] Al2 O3 . Obviously, the charging capability of most technical insulators is not directly limited by the lack of a possible electrontraps content, but largely limited by the efficiency of the charge regulation processes [20,21]. Clearly, the material properties (defects, surface roughness, etc.) affect the insulator charging capability by acting on the mechanisms of charge regulation. Thus, to understand the charging behaviors, it is important to get a clear picture of these charge regulation processes. Presently, the TEEYA is often used to describe the charge regulation mechanism and to predict the magnitude of the surface potential. According to this approach, when the insulator is irradiated with a primary beam energy qVac higher than ECII , a negative surface potential, Vac  ECII =q, at the steady state is predicted [2,22,42] and therefore the PE landing-energy at saturation, ELS , remains unchanged. However, as illustrated in Fig. 11, our data exhibit an increasing of ELS when Vac increases, instead of being constant. We should mention that similar behaviors of ELS versus Vac , have been observed previously on MgO [27] and sapphire [28]. As shown in Fig. 11, the values of ELS deduced from the present method are confirmed nicely by the direct experimental results obtained from the shift occurring on energy spectra of secondary SEs and BSEs emitted from the surface sample and measured by a highly compact electron toroidal spectrometer specially adapted to SEM applications.

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Fig. 11. The PEs landing energy at charge saturation ELS , as a function of the primary beam accelerating voltage. The primary beam current was 2 nA. Open circle: present method; open square: electron toroidal spectrometer.

What is the reason of the often-noticed deviation of experimental data from those predicted by the TEEYA? To address this question, let us consider two particular situations: in the first one (situation 1), the insulator is irradiated with a PE accelerating voltage, Vacð1Þ and in the second one (situation 2) the insulator is irradiated with a PE accelerating voltage Vacð2Þ > Vacð1Þ . As the charging progresses, the primary electron landing energy EL decreases in such a way that, for a given EL , the quantity of the trapped charge Q2 in the situation 2 is higher than Q1 in the situation 1 (see, Fig. 12(a)). Now, let us analyze the effect of the trapped charge on the regulation mechanism components of the charge, namely d, b and g: (1) Secondary electron yield, d. The production rate of inner SEs is proportional to the spatial energy transfer of the primary electron to the target-interaction-volume. Since, for both situations (1 and 2) we consider a time where the primary-beam landing energies are equal, the secondary electron production rate should be the same at this time. Nevertheless, on the vacuum side of the insulator/vacuum interface, the external electric field, F, induced by the negative space charge leads to a Schottky barrier lowering [21], Dv, that can be expressed as

Fig. 12. (a) A schematic illustration of the landing energy decreasing as the negative trapped charge grows: Q1 and Q2 (Q2 > Q1 ) are the trapped charges for a given landing energy EL (ECII < EL < qVacð2Þ ). (b) Dv1 and Dv2 are the Schottky barrier lowering on the vacuum side of the insulator/vacuum interface for, respectively, situation 1 and situation 2 (Dv2 > Dv1 ). (c) A schematic illustration of the evolution of the secondary emission electron yield (full lines) and the leakage current (dashed lines) for both situations (1) and (2). Situation 1: the primary beam accelerating voltage is Vacð1Þ : arrow O1 S1 . Situation 2: the primary beam accelerating voltage is Vacð2Þ > Vacð1Þ : arrow O2 S2 .

 1=2 er  1 Dv ¼  q jF j ðin eVÞ; e0 ðer þ 1Þ

ð14aÞ

where F ¼

4Q : e0 ð1 þ er Þa2

ð14bÞ

For a typical trapped charge of 1 nC (see Table 2), the strength of the external electric field at the

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vacuum/insulator interface is about 8  105 V cm1 and hence Dv can reach a value as large as 2 eV. The electronic affinity (i.e. the difference between the vacuum level and the bottom of the conduction band) could be appreciably decreased, leading to a notable increase of the SEs escape probability [21,43,44]. Since Q2 > Q1 , the secondary electron yield is certainly higher in the situation 2 than in the situation 1 (see, Fig. 12(b)). (2) The so-called leakage current, b. The dynamics of the charge migration towards the electrode serving to discharge the sample and measuring the leakage current is mainly due to three mechanisms [30]: (i) surface conduction; (ii) surface charges spreading due to there own mutual Colombian-repulsion; (iii) bulk space charge motion with volume conductivity playing a negligible role. b is expected to increase as the trapped charge or/and the electric field increases. This consideration is supported by several experimental works [18,45]. Hence, b should be greater in situation 2 than in situation 1. (3) Backscattered electron coefficient, g. An increase of g, when the trapped charge increases, was reported in a previous work [27]. According to Kotera and Suga Monte-Carlo simulations [46], this increase results from the deceleration of the primary beam electron in the vacuum due to the external electric field. This deceleration causes a decrease in the depth of the electron diffusion region, and hence an increase of the escape probability of scattered electrons in the sample. As a consequence, the backscattering coefficient would be the same for both situations, 1 and 2, where the PEs landing energies are chosen to be equal. The interesting result which may be deduced from the above analysis is that for a given primary beam landing energy (EL > ECII ), c is higher in situation 2 than in situation 1. The higher the primary beam accelerating voltage is (i.e. initial primary electron beam energy), the more effective are the charge compensation mechanisms, as sketched in Fig. 12(c). Consequently, Es shifts towards higher energies when Vac increases. This analysis also shows that further adaptations of TEEYA (taking into account the dependence of charge transport and secondary electron

escape probability on the build up electric field) are needed in order to be able to predict the sign and magnitude of the surface potential. 5.2. Charge decay The data presented in Fig. 8 shows that a charge decay occurs immediately when the e-irradiation is stopped. To make rigorous analyses of the discharging mechanism; the knowledge of electrons and hole transport parameters and e–h recombination lifetimes are required. This is a formidable task, made more difficult by the presence of the internal electric field, which, in turn affects the carrier transport equations and the e–h recombination parameters. However, some features of the present experimental data can be exploited to give some qualitative information on the mechanism of discharging: (i) Fig. 13 shows the evolution of the fraction a ¼ DQ=QS , of the released charge as a function of the primary beam accelerating voltage used to charge the samples. The mean PE penetrationdepth is also shown in Fig. 13 (left ordinates). This depth is assumed to be similar to the Kanaya– Okayama range resulting from Monte Carlo simulations [47]. This range is a generally accepted

Fig. 13. Left ordinates and dashed line: the fraction of the detrapped charge (a ¼ DQ=QS ) as a function of the primary beam accelerating voltage. Right ordinates and solid line: mean penetration depth in Al2 O3 versus the accelerating voltage according to Kanaya–Okayama range [47].

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description for the interaction volume of the electron beam in the SEM theory [52], zm ðlmÞ ¼

0:0276AVac1:67 ; Z 0:89 q

ð15Þ

where Vac is the PE accelerating voltage in kV, A is the average atomic weight in g/mol, q is the density in g/cm3 , and Z is the average atomic number. For Al2 O3 , A, q and Z are respectively 22 g/mol, 3.9 g/cm3 and 11. Let us note that when the mean-electron penetration-depth increases, a decreases. We inferred from this behavior that the more concentrated the space charge was close to the sample surface the more unstable it was. (ii) The values of characteristic times of the charge decay s0 , given in Table 2 indicate that s0 is independent of the amount of the trapped charge QS . This result suggests that the released charge is evacuated to the ground following a process based on a conduction mechanism as was mentioned by WintleÕs theoretical works [30,31]. Following this work, the time constant of conductive mechanism is independent of the magnitude of the initial charge, whereas in the charge electric field driven mechanism there is an explicit dependence due to the nonlinearity of the transport equation. Knowing that there are three time constants for discharging: the detrapping time constant which is very long for excellent insulators; the transport, from the trap site to the surface, time constant (governed by the DC conductivity and the dielectric constant of the material) and the evacuation to the ground (through the surface) time constant, a charge decay by bulk conduction mechanisms would have a longer time constant of several hours [23] rather than the observed second-time-scale because the bulk electric resistivity of Al2 O3 is in the range of 1014 –1016 X cm and its relative dielectric constant er ¼ 9. Therefore, due to the building-up of a hydrocarbon contamination layer [32], for instance, the surface conductivity is usually significantly higher than that of the bulk, it is reasonable to suggest that the observed charge decays is mainly due to: (i) the detrapping of electrons from shallow traps at the insulator/vacuum interface and then (ii) their evacuation to the ground by a conduction

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mechanism along the insulator surface. These considerations are also supported by Song et al. work in PMMA [18], showing that the leakage current is unrelated to the sample thickness. Adding to the charge decay due to the surface conduction, let us draw attention on the fact that other possible phenomena can take place, such as the neutralization of the surface-charge by ionic species from the residual atmosphere via a mechanism similar to that involved in environmental electron scanning microscope [48,49]. However this effect would be quasi-instantaneous and can not explain the observed discharge time of about 30 s.

6. Conclusion Experimental aspects associated to the measurement of the trapped charge in e-irradiated insulators in SEM by means of the displacement current were analyzed. To overcome a number of experimental shortcomings inherent to the use of the basic sample holder in a SEM chamber, a redesign of this holder is proposed and tests have been done to verify its operation. The charging and discharging behaviors of polycristalline Al2 O3 submitted to several electron beam accelerating voltages were investigated. Various behaviors were noticed: (1) During e-irradiation with primary beam accelerating voltages ranging from 8.7 to 24 kV, the charging behaviors are characterized by a monotonous growth of a negative trapped charge, followed by charge saturation. The value of the trapped charge (or the value of surface potential) at saturation increases as the primary beam accelerating voltage increases. We noticed a divergence between the experimental results and those predicted by the TEEYA approach. This divergence was discussed and explained. (2) At higher primary beam accelerating voltage, 29 kV, the monotonous growth of the trapped charge was altered, by a spasmodic and local abrupt discharging. This behavior was attributed to the occurrence of a flashover. A correlation between this abrupt discharge and a critical trapped charge (or electric field) was noticed.

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