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Secondary electron emission and self-consistent charge transport in semi-insulating samples H.-J. FittingandM. TouzinCitation:J. Appl. Phys.110, 044111 (2011); doi: 10.1063/1.3608151View online:http://dx.doi.org/10.1063/1.3608151View Table of Contents:http://jap.aip.org/resource/1/JAPIAU/v110/i4Published by theAmerican Institute of Physics.Related Articles Scanning secondary-electron microscopy on ferroelectric domains and domain walls in YMnO3Appl. Phys. Lett. 100, 152903 (2012)Reflectivity of very low energy electrons (< 10 eV) from solid surfaces: Physical and instrumental aspectsJ. Appl. Phys. 111, 064903 (2012)Secondary electron image formation of a freestanding α-Si3N4 nanobeltJ. Appl. Phys. 111, 054316 (2012)Electrostatic energy analyzer measurements of low energy zirconium beam parameters in a plasma sputter-type negative ion sourceRev. Sci. Instrum. 83, 02B704 (2012)Time-of-flight-photoelectron emission microscopy on plasmonic structures using attosecond extreme ultraviolet pulsesAppl. Phys. Lett. 100, 051904 (2012)Additional information on J. Appl. Phys. Journal Homepage:http://jap.aip.org/Journal Information:http://jap.aip.org/about/about_the_journalTop downloads:http://jap.aip.org/features/most_downloadedInformation for Authors:http://jap.aip.org/authors
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Secondary electron emission and selfconsistent charge transport in semiinsulating samples 1,a)2 H.J. Fitting and M. Touzin 1 Institute of Physics, University of Rostock, Universitaetsplatz 3, D18051 Rostock, Germany 2 Unité Matériaux et Transformations, UMR CNRS 8207, Université de Lille 1, F59655 Villeneuve d’Ascq, France (Received 2 February 2011; accepted 8 June 2011; published online 31 August 2011) Electron beam induced self-consistent charge transport and secondary electron emission (SEE) in insulators are described by means of an electron-hole flight-drift model (FDM) now extended by a certain intrinsic conductivity (c) and are implemented by an iterative computer simulation. Ballistic secondary electrons (SE) and holes, their attenuation to drifting charge carriers, and their recombination, trapping, and field- and temperature-dependent detrapping are included. As a main result the time dependent “true” secondary electron emission rated(t) released from the target material and based on ballistic electrons and the spatial distributions of currentsj(x,t), charges q(x,t), fieldF(x,t), and potentialV(x,t) are obtained whereV¼V(0,t) presents the surface potential. 0 The intrinsic electronic conductivity limits the charging process and leads to a conduction sample current to the support. In that case the steady-state total SE yield will be fixed below the unit: i.e., C r¼gþd<1.V2011 American Institute of Physics. [doi:10.1063/1.3608151]
I. INTRODUCTION Insulating and dielectric materials, especially as oxides, perovskites, ceramics, and functional layers have become 1 very important in modern technology. Especially, the influ-ence of dielectric polarization and charging on the features of these materials has been investigated more intensively and reported, e.g., on the conference series on electric 2,3 charges in non-conductive materials. Furthermore, the electrical charging of insulators under different types of ion-izing irradiation (electrons, neutrons, and X-c-rays) is of con-siderable interest in many fields of technology and science, e.g., for the development of thermonuclear reactors, see Ref. 4, up to the multiform development of insulating materials 5 and microelectronic devices for satellites and spacecrafts. All these applications come within the same physical mecha-nism. Irradiation induces the injection of high energetic charges and generates electrons and holes. Secondary elec-trons are emitted but an important part of the charge carriers remains in the sample and their straggling, drift, and storage depend on the trapping and conducting properties of the ma-6 terial. Moreover, the electrical charging phenomena also play a major role in important analytical techniques like scanning electron microscopy (SEM), environmental one’s (ESEM), Auger electron spectroscopy (AES), electron energy loss spectroscopy (EELS) etc., when investigating 79 non- or partial-conductive samples. Even the invention of scanning electron microscopy by Max Knoll in 1935 was aimed to investigate the charge dis-10 tribution on insulating samples. Especially for low energy SEM the differentiation of element and charge (potential) contrast becomes difficult as demonstrated comprehensively
a) Author to whom correspondence should be addressed. Electronic mail: hans-joachim.fitting@uni-rostock.de. Fax:þ49-381-498 6802.
12 in Ref.11. However, Reimeret alalready shown that. had low energy SEM appears suitable for imaging nonconductive 13 uncoated specimens. Franket al. developed an automatic II procedure to setup the “critical” energyE, where the total 0 secondary electron yieldris equal to the unit,r¼1, and the electrical charging will be limited to a certain extent. Nowadays, electron microscopy investigations will be made in real time imaging and stroboscopic pump-and-probe investigations are imaginable by very short pulse laser exci-tation of photocathodes and usage of very short picosecond 14 electron beam pulses. Of course, this is impossible by con-ventional beam blanking methods. Thus the fast electron beam interaction dynamics will play a more and more impor-tant role. As important applications, the picoseconds catho-doluminescence was performed of InGaN quantum wells, Ref.15, and for study of exciton dynamics, Ref.16. A great number of experimental and theoretical investi-gations has been published on the charging of insulators due to electron bombardment and the related secondary electron emission (SEE). Only for short pulse irradiation, target charging is prevented and the real charging-free total second-ary electron emission yieldr0(E0) as a function of the pri-mary electron energyE0can be measured as well as has been determined theoretically for various insulators, Refs.17 and18. However, the time-dependent charging behavior under permanent electron irradiation is not yet fully understood and the stationary final state is still very complex to describe. Indeed, the total yield approachr?1 is often used to predict the sign (6) of charging and the surface potentialV0in the case of stationary electron irradiation, but experimental 19 results are not fully consistent with these predictions. It is of importance to predict the types of theory that have led to enlighten this phenomenon. One of the first attempts was the planar (1-dimensional) self-consistent
110, 0441111
V2011 American Institute of Physics C
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H.J. Fitting and M. Touzin
charging simulation of our co-author (H.J.F.) already in 1979, Ref.20, later on improved in Refs.2125. These authors use field-dependent attenuation lengthsk(F) for the ballistic transport of electrons and holes that had been found experimentally by means of electron beam induced currents 26 (EBIC) measurements as well as calculated by Monte 27 Carlo (MC) simulations. Throughout Monte Carlo calculations of the self-consist-28 ent charging were made by Vicarioet al., Ganachaudet 29 30,31 al., and Renoudet althe above mentioned. Thus, authors could demonstrate the charge build-up by a computer 28,30 animation. In previous works (Refs.20and21) we had investigated the self-consistent charging and the field-enhanced second-ary electron emission (SEE) fromthinSiO2layers (d<100 nm) on Si substrate where for low energy electron beam irra-diationE0<5 keV the total SEE rate withr>1 is main-tained by Fowler-Nordheim field injection into and through the highly positive charged SiO2layers. The motion of holes was described by a conduction and mobility formalism. In Ref.22we introduced also ballistic holes and calcu-lated the charge, field, and potential distributions inbulk Al2O3targets. Moreover, we measured the huge negative charging and surface potentialV0in real time by means of the energy-dispersive x-ray analysis (EDX) bremsstrahlung spec-tra (BS) and their high energy edge equally to the electron beam landing energyE0*¼E0þeV0. In Ref.23we have introduced a thin conducting surface cover layer (e.g., thin carbon or Au layers) often used for preventing significant charging and, indeed, the internal field and potential distributions are reduced drastically to an ines-sential magnitude. The same effect is obtained by positive ion layers on the surface as used in environment scanning electron microscopes (ESEMs). In Ref.24we investigated real existing surface leakage currents and their influence on the charging and the total SE emission rater¼gþd, wheregpresents the ratio of back-scattered primary electrons anddthe “true” secondary elec-trons released from the target materials. Of course, in that case a certain amount of charges dissipates via the sample surface and the total SE rate becomes less than the unit,r<1, even for bulk insulating samples. Moreover, we extended the simulations to layered dielectric samples like SiO2/Al2O3dou-ble layers. Of course, at the interface between the different layers we observe additional charge storage. Finally, in Ref.25we have simulated the time depend-ence of the starting-up and decaying secondary electron emis-sion in insulating dielectrics. Whereas the switching-on proceeds over milliseconds due to self-consistent charging, the switching-off process occurs much faster, even over fem-toseconds. As already mentioned above, this will find applica-1416 tion in real time and stroboscopic electron microscopy. Now, in the present and, probably last paper of this series, we want to extend the flight-drift model (FDM) by a certain natural intrinsic field conductivityc, based on even though few free electrons in the conduction band of the sample mate-rial and their limited mobility. Thus, we will consider the lim-ited charging of semi-insulating and semiconducting samples during electron irradiation.
J. Appl. Phys.110, 044111 (2011)
II. THEORETICAL BACKGROUND A. Primary electron (PE) scattering and injection The injection of primary electrons (PE) and their crea-tion of secondary electrons (SE) and holes (H) (see also Fig. 1) have been described thoroughly in Refs.3235based on empirical results of the electron penetration into and through thin films, see “film-bulk method” in Refs.33and34and the review description in Ref.35. By means of this method, the resulting PE current density in dependence on the target depthxand the PE initial energyE0was found:    pðZÞ x jPEðx;EÞ ¼j0ð1gÞexp4:605 (1) RðE0;ZÞ
withj0as the impinging PE current density and the material parameters for materialsZ:gthe backscattering coefficient, p the transmission exponent. A new equation for the maxi-mum rangeR(E0) of electrons reached by 1% of PE in de-pendence on their initial energyE0was deduced from many-fold experimental data, see Ref.36. Whereas in former descriptions, the maximum electron rangeR(E0) had to be distinguished for high and low primary electron beam ener-n giesE010 keV with power formulasR/Eandn¼1.7 0 and 1.3, respectively, the new formula covers the general energy range of SEMs from aboutE0¼1keV up to 30 keV. In this energy range, the exponent changes ton¼1.45 and the electron range formula may be modified to
93:4 1:45 RðE0;ZÞ ¼E; 0:91 0 q Z
whereRis given in nm, the mass densityqZof the material 3 Z in g/cm , and the electron beam energyE0should be inserted in kiloelectron volts. For an exact charge balance, the exhausted PEs in the depthxhave to be added to the excited secondary electrons
FIG. 1. (Color online) Electron irradiation of an insulating target in a scan-ning electron microscope (SEM):I0- incident PE current,rI0- backscat-tered (BE) and secondary electron (SE) part,ITE- tertiary electrons backscattered from the chamber, IS- surface leakage current,IC- real con-duction current,IP– instationary displacement current during charge trap-ping and polarization,IS– surface leakage current,ISC¼ICþIPþIS resulting sample stage current.
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H.J. Fitting and M. Touzin
(SE), which are generated in parity to the positive holes (H). The PE exhaustion density, or better said PE–SE conversion functiongPE, is given by the negative first derivative of the PE penetration current of Eq.(1):
djPE j0gPE¼  dx h   i p 4:605x p1 ¼j0ð1gÞpðZÞxexp4:605:(3) p R R PE–SE conversion functionsg(x,E) have been presented PE 0 in Ref.23. Of course, these exhausted and deposited PE will continue their motion like created common SE and should be added finally to the SE generation functiongSEof Eq.(4)as will be done in Eq.(9). On the other hand, the spatial SE generation rate g(x,E) excited by PE is proportional to the spatial energy SE 0 lossdE/dxof the impinging and straggling primary electrons (PE), i.e., proportional to the spatial PE energy transfer to the target volume:
1dE gSEðx;E0Þ ¼a; Eidx
whereEiis the mean creation energy for one SE andaa 37 yield factor of nearly unit. According to Klein and Alig 38 and Bloom, the SE creation energy increases with the energy gapEgof a given target material
resulting inEi28 eV for SiO2and Al2O3withEg¼9 eV consistent with the dielectric electron energy loss function Im(1/e(hx)) and MC calculations in Ref.39. Then with Eq.(4)and an empirical expressions fordE/ dxfrom Ref.34, we may write the SE generation rategSE, e.g., in the dielectrics SiO2and Al2O3targets, in the form of a semiempirical equation     2 1:544E0x gSEðx;E0Þ ¼gSHðx;E0Þ ¼ 7:50:3: RðE0ÞEiR (6)
Of course, secondary electrons (gSE) and holes (gSH) are cre-ated in parity presenting a spatial Gaussian distribution with the maximum shifted tox¼0.3Rfrom the surface into the target volume as also shown in Ref.23.
B. Ballistic currents of secondary electrons and holes After generation secondary electrons and holes are fly-ing and straggling ballistically over certain distances, so-called attenuation lengthskdepend on the presence of an electric fieldFand its direction. We have demonstrated this process by Monte Carlo simulation in Ref.39(see Fig.2) and have measuredk(F) directly by electron beam induced 26 currents EBIC. As a main result, we get attenuation proba-bilitiesWEFfor ballistic electrons (E) expressed by field-de-pendent mean attenuation lengths:
kexpkEðFÞ ¼E;0ðbEFÞ
J. Appl. Phys.110, 044111 (2011)
FIG. 2. (Color online) Mean SE energy<E>(above) during the relaxation timet, with rapid cooling due to impact ionization and cascading at the be-ginning followed by slow attenuation due to phonon emission and final ther-malization toEth¼40 meV¼3/2kTR(room temperature) at the bottom of the conduction band, see Ref.27, followed by the processes in Fig.3.
  Dx WEF¼expkE;0expðbEFÞ
in (F>0) and against (F<0) field direction. HerekE,0 presents the field-free attenuation length andbEthe elec-tron field attenuation parameter. Similar expressions can be written for ballistic holes withkH,0andþbH, respectively, shown in Ref.23. Assuming an isotropic SE generation, one half of the created SE: 0.5j0gSE(x,E0)Dxwill move into the bulk sam-ple, i.e., in the direction toward the sample support, called transmission (T), and the other half toward the sample sur-face, called reverse direction or remission (R). Then the re-spective continuity equation in 1-dimensional form for ballistic SE or hole currents in transmission (T) direction to-ward the sample substrate (holder) or in reverse or remission 23 (R) direction toward the surface can be written as        1 BER BER jðxÞ ¼jðx6DxÞ þj g BET BET0SEx;E0þ;E gPEx0Dx WEF 2 (9)
and for holes, respectively, but without thegPEterm. The first term in the brackets presents the convection part from the neighboring cellDx; the second one the genera-tion of inner SE: (gSEþgPE) or holes (gSH¼gSE) followed by the ballistic attenuation probabilitiesWEF(x) for electrons andWHF(x) for holes over the small distanceDxin the target depthx. These attenuation probabilities have been described by Eqs.(7)and(8). The part of ballistic SE moving toward the surface jBER(x) and being reflected at the surface (x¼0) presents the initial rate of transmitting SE at the surfacejBET(x¼0), i.e., rffiffiffiffiffiffiffi v jBETðx¼0Þ ¼jBERðx¼0Þ 0:3jBERðx¼0Þ(10a) ESE
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H.J. Fitting and M. Touzin
forv¼0.9 eV as the surface electron affinity andESEthe mean kinetic energy of SE in the conduction band, e.g., of Al2O3or SiO2, see Ref.22. The part of SE non-reflected at the surface is emitted into the vacuum presenting the current jSEEand the rate of “true” SEd¼jSEE/j0:  rffiffiffiffiffiffiffi v jSEE¼1jBERðx¼0Þ 0:7jBERðx¼0Þ:(10b) ESE
Thus, the total secondary electron emission rater(t) is given by
jðx¼0;tÞ rðtÞ ¼gþdðtÞ ¼1þ; j0
including the fractiongof backscattered PE and the “true” SE released from the target material with the rated(t) chang-ing with time due to the charging of non- and partial-conduc-tive targets, see also Fig.1.
J. Appl. Phys.110, 044111 (2011)
FIG. 3. (Color online) Scheme of the flight-drift model (FDM) including the excitation of ballistic electrons and holes into the conduction (Ec) and valence (Ev) band, respectively, their flight and attenuation, followed by drift or dif-fusion, trapping or recombination, and/or Poole-Frenkel (PF) release, see Eqs.(12)(14).
C. Drift currents with trapping and recombination Ballistic electrons and holes are scattered over field-de-pendent attenuation lengthskE(F) andkH(F), respectively, as given by Eqs.(7),(8), and(9)and in their time dependence in Fig.2. In the following, they will continue their motion by drift and diffusion until they will recombine or be trapped, see the main scheme in Fig.3. As a consequence, we have a convection term from the neighboring adjacent cellsx6Dxas well as sources (genera-tion) of drift carriers from the attenuated and exhausted, i.e., absorbed ballistic electrons and holes:jBE(x) (1WEF(x)) andjBH(x) (1WHF(x)), respectively, given by Eq.(9)for electrons. Thus, we may write for drifting (D) electrons (E) in reverse (R) and transmission (T) directions:
DER DER jðxÞ ¼jðx6DxÞþcFðxÞHð6FÞ þconvectionþconduction DET DET þ½jBERðxÞ½1WEFRðxÞ þjBETðxÞ½1WEFTðxÞ þgeneration by ballistic attenuation þqðxÞW E1 E1PFþqE2ðxÞWE2PF FEðxÞg detrapping by PooleFrenkel effect         q q E1 E2 expN1SE1DxexpN2SE2Dxe0e0 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} WE1WE1 trapping probability2shallowð1Þand deepð2Þstates     q q H1 H2 expSEH1DxexpSEH2Dx:recombination probability with holes e0e0 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} WEH1WEH2
2025 Here, with respect to previous works, an additional intrinsic conduction term withj(x)¼cF(x)H(6F) has been added based on the presence and mobility of free electrons. They will maintain a certain conduction current even through the unradiated bulk part of the semi-insulating/semiconduct-
ing sample. Of course, the Heaviside step functionH(6F) adds the conduction current in case ofF>0 to the current in reverse directionjDER, in case ofF<0 to the transmission directionjDET. The first convection term describes incoming and out-going drifting electrons in the depth elementDx; the second
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H.J. Fitting and M. Touzin
term presents the above explained intrinsic field conduction, the third generation term presents the sources of drifting electrons by attenuated (exhausted) ballistic electrons and 40 the fourth (detrapping) term is given by the Poole-Frenkel emission of electrons from traps, presenting also a source of drifting electrons. The Poole-Frenkel release of charges (here electrons) from trapsEnin dependence on sample tem-peratureTSand present electric fieldFis given by   EnDEPF W EPF¼fEexp(13) kTS
with trap barrier loweringDEPFby an electric fieldF:  1=2 3 e 1=2 DEPF¼2F: 4pe0er
The anisotropy field factorFE(x) in Eq.(12)describes the anisotropic field directed motion of the generated drifting electrons (DE) in the present electric fieldF(x), see Ref.24:
1F FE¼tanh: 2FE0
Finally, as electron drains we see the trapping and recombi-nation terms with trap concentrationsNnand actual charges qnas well as the respective cross sectionsSn, all as presented DHR in Fig.3. Of course, the current density equationjfor DHT drifting holes (DH) looks adequate with the respective trap-ping parameters of holes, as already described in Refs.20 and24. The resulting charges will be counted from the balance of trapping and detrapping:
qðx;tÞ ¼ qqþqþq: E1 E2 H1 H2
On the other hand, we may account and normalize the charges and the fields from the total current flux, i.e., divergences:
@ @qðx;tÞ@ @ jðx;t¼Þ ¼ e0erFðx;tÞ @x@t@t@x
as it has been described in detail in Ref.23.
III. RESULTS AND DISCUSSION The first simulations have been performed for 3 mm thick (bulk) samples comparable in mass density with alu-3 mina (Al2O3):q3.8 g/cm . Thus we have a comparison to more or less insulating Al2O3materials of previous 2125 works. The respective material parameters are mostly given in Ref.22(Table I); others are described already in the respective text parts of this paper. In order to protect the samples from thermal irradiation effects and material modifi-cations, we used in our measurements as well as simulations a slightly “defocused” electron beam of 100 nA impinging 2 an area of 1 mm leading to a primary electron current den-5 2 sity ofj0¼. This planar geometry of 100010 A/cm lm beam width versus only 5lm irradiation depth maintains the assumption of the planar 1-dimensional target model.
J. Appl. Phys.110, 044111 (2011)
So we may use mean ballistic attenuation lengths for secondary electronsk¼5 nm, for holesk¼2 nm and E,0 H,0 respective attenuation field factorsbE¼4.6 cm/MV and bH¼0.8 cm/MV in accordance with Refs.2022. More diffi-cult is the selection of appropriate electron and hole trap con-centrationsN,H; their capture cross sectionsSE,SH; their
FIG. 4. (Color online) Internal electron diffusion current:jDER– in reverse direction to the surface (top),jDET– in transmission direction to the substrate (middle),jtot– total current (bottom), and sum of all components, see Eq. (18). In the steady-stationary statejtotbecomes constantjtot¼j0(1r(t1)), 7 here for a sample conductivityc¼10 S/m.
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H.J. Fitting and M. Touzin
FIG. 5. (Color online) Internal space chargesq(x,t): positive in the SE escape zone beneath the surface (above) and negative within the sample vol-7 ume (below); sample conductivityc¼10 S/m.
thermal activation energiesEE,EH; and recombination cross sectionsSandS, as given in Fig.3. For the calculations EH HE presented here, we choose the following data: shallow trap 203 concentrationsNE1¼NH1¼10 cm corresponding to high concentrations of self-trapping by small polaron formation; 13 2 their capture cross sectionsSE1¼SH1¼10 cm and ther-mal activation energiesEE1¼EH1¼0.1 eV. Of course, the 18 deeper traps possess less concentrations:NE2¼NH2¼10 313 2 cm ,SE2¼SH2¼, and10 cm EE2¼EH2¼3 eV. The Coulomb-attractive recombination can be described by a 11 2 relatively high cross sectionSEH¼SHE¼10 cm . A more diversive trap parameter selection and optimization should be done in direct comparison with experimental data. The samples possess an open, non-covered surface, and the secondary electron emission is only limited by the height of the surface barrier, i.e., by the electron affinity, taken here v¼0.9 eV, as valid for SiO2and Al2O3. Of course, all holes and also low energy drifting electrons will be totally reflected at this surface barrier. As an example, in Fig.4the current densities of drifting electrons in reverse (R) direction toward the surfacejDER(x,t) and in transmission (T) direction into the sample volumejDET(x,t) are presented in their spatial and temporal distributions. Moreover, at the bottom of Fig.4 the total currentj(x) of all moving charge carriers is tot presented:
jtot¼ jPEþjBERjBETjBHRþjBHTþjDERjDET jDHRþjDHT:(18)
J. Appl. Phys.110, 044111 (2011)
FIG. 6. (Color online) Internal electric fieldF(x,t) with a spatial plus-minus structure (above) and the resulting potentialV(x,t) controlled mainly by the 7 huge negative volume charge, see also Fig.5; (c¼10 S/m).
The respective total chargeq(x) and fieldF(x) distributions in dependence on electron beam irradiation time 5 2 t¼(10100) ms forE0¼30 keV, andj0¼are10 A/cm shown in Figs.5and6. On the top of Fig.5, the charge dis-tributions are given in a zoomed nanometer scale immedi-ately beneath the surface where especially the emerging secondary electrons are coming from. Here we see the built-up of a positive charge distribution with a center of gravity at about 2.5 nm. In this region beneath the surface, the field is increasing positively, Fig.6, enforcing field-enhanced sec-ondary electron emission into the vacuum. The field remains positive up to a depth of 1.5lm sweeping electrons toward the surface and holes into the bulk. Then, beyond 1.5lm, the field changes to negative values and keeping almost con-stant up to the support electrode at the depthx¼d¼3 mm, Fig.6. This almost constant field over a large distance pro-duces high linear potentials slopesV(x), but, then near the surface appearing already almost constant, see Fig.6(bot-tom) The valueV(x¼0)¼V0means the “surface potential”. For full-isolating samples (c¼0) the drifting and finally trapped charges form a fourfold charge distribution: plus-2325 minus-plus-minus as we had found in former works and presented here in Fig.7. The positive surface charge is due to emitted SE and remaining holes as mentioned already in
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