Full text of DOI:10.1051/epjap:2000174

Eur. Phys. J. AP 12, 85–91 (2000)
THE EUROPEAN
PHYSICAL JOURNAL
APPLIED PHYSICS
ꢀ
c EDP Sciences 2000
Charge stability on thin insulators studied by atomic force
microscopy
a
N. Felidj, J. Lambert, C. Guthmann, and M. Saint Jean
b
Groupe de Physique des Solides, Universit ´e s de Paris 6 et 7 , Tour 23, 2 place Jussieu, 75251 Paris Cedex 05, France
Received: 19 May 2000 / Revised and Accepted: 22 August 2000
2 3
Abstract. Charge diffusion in thin Al O layers has been investigated by Atomic Force Microscopy (AFM).
The layers were made by anodic oxidation of Al plates, in order to obtain plane and homogeneous amor-
phous oxides of known thicknesses. Under dry-nitrogen atmosphere, the charges are deposited by contact
electrification: a deposit voltage is applied between the Al substrate of the layer and the metallized AFM
tip brought to contact with the oxide. This process is perfectly controllable and reproducible, the quantity
of charges deposited being proportional to the deposit voltage. Afterwards the tip is lifted up and scans
the surface of the oxide in order to observe the diffusion of the deposited charges. Two behaviors were
observed for the diffusion process depending on the thickness and on the deposit voltage. These results
are interpreted by introducing an inhomogeneous trap distribution in the layer, the diffusion process being
considered mainly as diffusion by hopping transport in the bulk.
PACS. 72.20.-i Conductivity phenomena in semiconductors and insulators – 72.20.Ee Mobility edges;
hopping transport – 73.20.-r Surface and interface electron states
1
Introduction
or/and volume diffusion), we have performed new experi-
ments on amorphous alumina surfaces.
In a previous study [6], the electrification by contact or
friction of these surfaces had been extensively investigated
at submicronic scale using an atomic force microscope in
resonant mode; thus the parameters governing the tribo-
electric effect on these oxide surfaces are well controlled.
In this paper, we report the results concerning the
study of the diffusion of charges deposited on alumina
layers of various thicknesses (15 nm < d < 100 nm).
The characteristic times of diffusion are of about a few
hundred seconds and their variations with the initial de-
posited charge density σ depend on the oxide thickness: for
thin oxide layers, a single characteristic time is needed to
describe the charge diffusion whereas two time constants
are required to describe the diffusion observed for thicker
Charge transport on insulators is of great interest both sci-
entifically and technologically [1–4]. However, despite its
everyday occurrence and a very large experimental investi-
gation with various techniques, this phenomenon remains
an unsolved problem. Recently, atomic force microscopy
(
AFM) was used to scan the electronic transport phenom-
ena in insulators [5,6]. As a local probe, AFM presents
some advantages with respect to the macroscopic experi-
ments since it offers the opportunity to reduce the result
discrepancies due to the surface and bulk heterogeneities
of these materials. Moreover, the diffusion process can be
“
visualized” directly in contrast with integrated measure-
ments given by macroscopic experiments.
The most recent and complete results obtained on oxide layers.
charge diffusion by electrostatic force measurements have
The samples preparation and characterization are de-
been performed on thin silicon oxide [5]. In these experi- scribed in Section 2; Section 3 is devoted to the experi-
ments, the deposition of electrons by contact of AFM tip mental setup and protocols used to deposit and to measure
on SiO2 surfaces and their diffusion have been investigated the charges. In Section 4 we present the results concerning
under vacuum and at ambient atmosphere. However their the variations of the relaxation times with the thickness
interpretations invoke a quite mysterious “stable-unstable of the sample and the initial deposited charge densities.
phase transition” of the transferred electrons and no fur- These results will be discussed in Section 5.
ther study has been carried out to determine the param-
eters controlling this charge diffusion. In order to identify
these parameters and in particular to distinguish the dif- 2 Elaboration and characterization of alumina
ferent mechanisms involved in charge diffusion (surface
samples
a
e-mail: saintjean@gps.jussieu.fr
CNRS UA 17
Alumina layers grown on Al-plates by anodic oxidation
were chosen for these experiments for two reasons: first,
b

86
The European Physical Journal Applied Physics
they are good homogeneous insulators; when they are pre-
pared by anodic oxidation, in contrast with thermic oxida-
tion, their surfaces are smooth. In addition their thickness
is easy to check during their elaboration. This opportunity
is important because we have found in preliminary stud-
ies that the thickness of the samples played a role in the
charge diffusion process. Secondly previous experiments
on these alumina surfaces have shown that a controlled
quantity of charges of either positive or negative sign can
be deposited; thus the relaxation process of positive and
negative carriers can be studied and compared on the same
samples [6].
The alumina layers are prepared by anodic oxidation of
Al-plates in ammonium pentaborate (NH4B5O8, 2H2O),
2
with constant current (about 1 mA/cm ) imposed be-
tween the Al-plate electrode and a platinum cathode (this
3+
2−
current induces the migration of Al and O ions inside
the layers). By measuring the potential bias ∆V inside the
oxide, its thickness is determined precisely. In order to cal-
16
ibrate ∆V , we have also evaluated the O quantity inside
the layer, which is directly proportional to its thickness,
by measuring the number of protons produced by nuclear
16
reaction between O and deutons produced in a van de
Graff accelerator [7]. The thicknesses of the samples stud-
ied were d = 15, 30, 60 and 100 nm.
Fig. 1. XPS spectrum of an alumina layer. One can recognize
peaks due to aluminum Al2s at 100 eV, Al2p at 75 eV, O1s at
530 eV. The C1s peak at 285 eV is due to carbon contamination
on the oxide surface.
The samples are transferred afterwards in the vacuum
chamber of our experimental setup, which is first out-
gassed during 24 h, then filled with dry nitrogen gas to
ensure that the oxide surface remains dry. On the other
hand, in order to evaluate the influence of contamination
on the diffusion processes, other samples of same thick-
nesses are deliberately left in ambient atmosphere before
measurements.
transferred in the vacuum chamber in a time less than
a few minutes can be considered as “freshly” prepared.
3
Experimental methods and force
measurements
The contamination of the samples left in ambient at-
mosphere is characterized by X-ray Photoelectron Spec-
troscopy (XPS) [8]. The XPS signals were recorded us-
ing a VG Scientific Scalab MKI system operating in the
constant analyzer energy mode. A Mg Kα X-ray source
was used at a power of 200 W and the by-pass en-
ergy was set at 20 eV. The pressure in the analysis
We use a homemade Atomic Force Microscope in reso-
nant mode. The tip is made of Si3N4 coated with Pt. This
metallization allows to deposit and measure charges with
the same tip and thus, to avoid any charge loss during
the measurements [6]. Moreover the Pt coating presents
the advantage of being very stable and of allowing repro-
ducible deposits.
The experimental setup is very similar to the one pre-
viously described in [6,9]. The main innovation is the ad-
dition of a vacuum chamber containing the sample and
the tip, the interferometric detection being outside the
vacuum chamber.
The nanometric metallized tip is fixed at the end of
a cantilever, the latter being excited at a frequency ωm
selected near its resonance frequency (≈ 200 kHz). When
the tip interacts with an insulator surface fixed or grown
on an underlying metallic electrode, the frequency and
quality factor of the resonance of the cantilever are modi-
fied, which induces a variation of the cantilever vibration
amplitude A(ωm) measured at ωm. Moreover, if a voltage
−8
chamber was about 5 × 10 mbar. The surface compo-
sition of various samples was determined by considering
the integrated peak areas of Al2s, Al2p, O1s, C1s. Figure 1
exhibits an XPS wide scan obtained on a freshly prepared
alumina layer (d = 15 nm). The scans display peaks due
to aluminum and oxygen arising from the alumina layer as
well as a peak due to carbon contamination on the oxide
surface. The extent of the contamination can be estimated
by measuring the relative intensities of the observed peaks.
For the d = 15 nm samples, the ratio of integrated peak
areas IC/IAl is 15 times higher for the samples exposed
to the ambient atmosphere than for the freshly prepared
samples; the same ratios were obtained for the samples of
other thicknesses.
We concluded from these measurements that the sam- V = V0 +V1 sin Ωt (Ω ≈ 50 kHz) is applied to the tip, the
ples are completely contaminated by various organic underlying metallic surface being maintained at zero po-
molecules when exposed to ambient atmosphere more than tential, an additional capacitive force F(Ω) is exerted on
a few hours after their making. Thus, only the layers the tip and induces a modulation A(Ω) of the oscillation

N. Felidj et al.: Charge stability on thin insulators studied by atomic force microscopy
87
of the cantilever at the frequency Ω. The cantilever vi-
bration is detected by optical heterodyne interferometric
detection and analyzed by two lock-in analyzers respec-
tively tuned at the frequencies ωm and Ω.
From the measurement of the amplitude A(Ω) we can
determine the contact potential Vc associated to the tip-
surface system as well as the deposited charge [6,9]. With
no deposited charge, A(Ω) is proportional to (V0 +Vc); Vc
is measured by tuning V0 until A(Ω) becomes zero which
corresponds to V0 = −Vc. When charges are on the sur-
face, the additional charge-tip force induces a variation of
the amplitude A(Ω) when the tip scans over the charge.
By comparing the A(Ω) measurements before and after
contact, the deposited charge can be determined. Simul-
taneously, the output signal A(ωm) is introduced into a
feedback loop to control the tip-surface distance. The feed-
back signal at ωm is used to image the surface topography;
in particular one can verify that its corrugation has not
changed after charge deposition.
The charges are deposited by “injection”. The tip stays
in contact with the same point of the oxide surface, a “de-
posit voltage” Vd being applied to the tip: initially far
from the oxide, the tip is softly put into contact with
the surface by slowly shifting the reference value of the
feedback loop. During this down motion, the tip is main-
Fig. 2. A typical A(Ω) versus time variation curve obtained
on a thin Al O layer. The variation of the amplitude Amax(Ω)
2 3
with time is simply the envelop of the curve. The amplitudes
A0, A1 and A2 are represented. The duration of the decrease
is approximately 10 mn.
The experiments were performed taking V0 = −Vc in
order to cancel the mean electrostatic field due to the tip in
the layer. A(Ω) and A(ωm) are measured simultaneously
by using the classical topographic feedback loop procedure
in order to be sure the variation of A(Ω) is not due to a
possible mechanical drift of the piezoelectric ceramic.
tained at V0 = 0 V. When the contact is established, a 4 Results
voltage Vd (−25 V < Vd < +25 V) is applied during td
seconds, then the tip is raised far from the surface, the
Figure 2 presents a typical recorded decrease of Amax(Ω)
voltage Vd being in this phase maintained for tr seconds
1 ms < tr < 10 s) to avoid any charge back flow [11].
with time. Two quantities can be extracted from such a
curve: the ratio R of the quantity of charges that have
left the oxide after a few minutes with respect to the to-
tal quantity of deposited charges, and the time constant τ
characterizing the diffusion of the mobile charges. In order
to obtain R, we measure three parameters on the recorded
curves: the signal amplitudes A0 just before the contact
electrification, A1 immediately after deposition and A2
when the signal does not vary anymore, thus R is defined
as the ratio (A1 − A2)/(A1 − A0). The time constants τ
describing the relaxation process are determined by fit-
ting the variations of Amax(Ω) with time decreasing ex-
ponentials. In order to compare easily the different results
obtained for different samples, the signal amplitude A0 is
subtracted from the amplitude Amax(Ω) and normalized.
In order to prove that R and τ are relevant to describe
the diffusion process, we have checked their reproducibility
by comparing their values obtained for similar conditions
of deposit. In previous studies, we have shown that the
(
We emphasize that the same tip is used for the deposition
of charges and for their reading. This requires very strict
control of the conditions of experiments. In particular we
have verified, performing SEM studies on the tip before
and after friction, that the tip and its metallic coating were
not damaged during the experiments. In previous experi-
ments, we had shown that no variation of the magnitude of
the deposited charge was observed when the times td and
tr were tuned between 1 ms and 10 s [6] (in the results pre-
sented here, td is 100 ms). In addition, we had exhibited
the linear variation of the quantity of transferred charges
−
3
−2
with Vd: σ = 10 Vd C m
.
The tip scans a line of about 1 µm around the charge
deposit during a few minutes. The maximum of ampli-
tude Amax(Ω) is recorded. It corresponds to the tip being
exactly above the deposit, the A(Ω) = 0 reference corre-
sponding to the signal far from the deposit.
Following the procedure proposed by Terris et al. [10] deposition is a reproducible mechanism [6]. Let us now
and using the method of images to determine the elec- compare the ratio R and the time evolution of charges de-
trostatic force between the tip and the surface, we had posited under the same conditions: Figure 3a shows the
previously developed a simple model describing the tip- amplitude decrease versus time for negative charges de-
surface force and had shown that the main contribution posited in the same conditions at three different points
to the measured amplitude A(Ω) is due to the interaction of the same “fresh” alumina surface. The corresponding
between the deposited charge Q and q1 = 4πε0R(V0 + values of R are identical. In order to compare the dif-
Vc)V1 sin Ωt which describes the tip charge due to the ferent experiments we have defined a normalized ampli-
applied potential. Neglecting all the other contributions tude a = (Amax(Ω) − A2)/(A1 − A2). After normalization
to the force applied to the tip, we can then consider (Fig. 3b), the three curves are perfectly superposed. Thus,
that Amax(Ω) is proportional to the quantity of deposited our recent results allow to consider the diffusion process as
charges [6,12].
reproducible, and confirm that the parameters (R, τ) are

88
The European Physical Journal Applied Physics
1
2
1
1
0
5
0
5
0
d =15nm
1
5v t
20v t
5v t
2
0
.1
0
100 200 300 400 500
WꢀꢁVꢂ
0
200 400 600 800 1000
WꢀꢁVꢂ
Fig. 4. Normalized amplitude variation in logarithmic scale.
On a fresh 15 nm thick Al layer, the charge diffusion has
O
3
(
a)
2
only one characteristic time, depending on the deposit voltage,
here 15 V, 20 V and 25 V.
1
.2
1
1
d =100nm
0
0
0
0
.8
-
-
-
10v
15v
20v
.6
.4
.2
0
0
200 400 600 800 1000
WꢀꢁVꢂ
0
.1
0
100 200 300 400 500
WꢀꢁVꢂ
(
b)
Fig. 5. Normalized amplitude variation in logarithmic scale.
On a fresh 100 nm thick Al layer, the charge diffusion has
Fig. 3. (a) Amax(Ω) versus time. These three curves are ob- two characteristic times depending on the deposit voltages,
tained on different spots of the same Al
layer using the here −10 V, −15 V and −20 V.
same deposit conditions (d = 30 nm,V = 10 V). The Y -axis
2
O
3
2
O
3
d
scale is graduated in arbitrary units; (b) here is represented
the normalized variation of Amax(Ω), i.e. a = (Amax(Ω) −
pA e2 r )i /m ( pA o1 sa−b Al e .2 ). After normalization, the three curves are su-
contrast, this ratio is equal to 1 for the thinnest samples
d = 15 nm). This means that all the charges have disap-
peared. The crossover thickness for storage capacity being
about 30 nm.
(
Another thickness-dependent behavior is the variation
of Amax(Ω) with time. For the thinnest samples, the decay
of Amax(Ω) can be described with only one characteristic
relevant to characterize the diffusion processes and can be
used to compare the results obtained for different samples.
First, let us present the results obtained for freshly time whereas for the thickest samples, two times are re-
prepared samples of different thicknesses (d = 15, 30, 60 quired to describe the evolution of the force applied to
and 100 nm). On each layer, different quantities of charges the tip. As for the R ratio, the crossover seems to oc-
were deposited. These experiments were carried out under cur for a thickness about 30 nm. For instance, Figure 4
dry-N2 atmosphere.
presents the recorded decrease of Amax(Ω) when negative
The first important result is that the quantity of charges are deposited on 15 nm samples, with various de-
charges stored on/in the oxide a long time after the posit voltages Vd. Whatever the deposit voltage is, the
deposit depends on the sample thickness. The ratio R dependence of Ln(Amax(Ω)) with time is roughly linear,
for sample thicknesses larger than 15 nm is systemati- thus indicating that, in this case, the diffusion process can
cally smaller than 1 whatever the initial charge quan- be described by only one time constant. In contrast, the
tity is, indicating that the deposited charges have not measurements obtained for a d = 100 nm sample clearly
completely diffused and that some of them are stored exhibit two characteristic times as shown in Figure 5. For
in the oxide layer, trapped on surface or bulk sites. In the three injection voltages, Amax(Ω) decays at first with

N. Felidj et al.: Charge stability on thin insulators studied by atomic force microscopy
89
Table 1. Thickness d = 15 nm.
Deposit voltage V Characteristic time τ
5 Discussion
d
From now on, we shall only discuss the results obtained
on fresh samples. Different conduction mechanisms can be
invoked in insulating materials with traps. Some of them
involve the conduction band whereas others only consider
the hopping conduction between traps [13–18]. The pre-
dominance of either phenomenon depends on the strength
of the electric field in the layer and on the temperature.
In amorphous materials like alumina, the high resistivity
is generally attributed to localized states in the forbidden
band [17,18]. Moreover, our previous results [6] indicated
that the traps played a central role in the electrification
of these oxides: the charges are transferred on trap lev-
els, the large concentration of trapped charges inducing
the pinning of the chemical electropotential in the surface
insulator. This indicates that the mechanism of the car-
rier transport through these oxides is certainly controlled
by hopping process, the large values of the observed time
constants confirming this assumption [19].
−
+
+
+
20 V
10 V
20 V
25 V
80 s
250 s
150 s
120 s
Table 2. Thickness d = 100 nm.
1 2
Deposit voltage V Characteristic times τ and τ
d
−
−
−
10 V
15 V
20 V
100 s
100 s
100 s
400 s
200 s
100 s
a characteristic time of about 100 s followed by a slower
process characterized by a second time constant (Tab. 2).
The same behavior is observed with a 60 nm thick layer,
the first time being in this case about 50 s.
Once the tip is retracted, the charge transport is dom-
inated by the conduction induced by the electric field in
the bulk of the insulator. The electric field is produced
We have studied the variations of these characteristic by the deposited charges and by their images in the Al-
times with the potential Vd which is proportional to the substrate. One could argue that the tip contributes to the
number of charges initially deposited [6]. For d = 15 nm charge displacement via the V0 +V1 sin Ωt voltage applied
samples, the only relaxation time τ observed decreases between the tip and the aluminum electrode. Actually
with the amplitude of the deposit voltage (see Tab. 1). three reasons make this contribution negligible: firstly, the
For thicker samples, the first time constant τ1 is indepen- V0 voltage is chosen to be equal to −Vc so that there is
dent of the deposit voltage, whereas the second long re- no continuous voltage between the bulk of the insulator
laxation time τ2 is voltage-dependent, as for thin samples. and the tip. Secondly, the frequency Ω of the alternative
The higher the voltage is, the faster the amplitude de- voltage V1 is 50 kHz, which is much too high when com-
creases (see Tab. 2). The variations of the time constants pared to the characteristic times observed experimentally
with Vd are similar for both polarities, however smaller (hV1 sin Ωtiτ = 0), and thirdly because the tip sweeps a
times are measured for negative Vd.
large area compared to the charge extension and is most
of the time too far from the charges to influence them.
In this scheme our interpretation is based on the fact
At last, in order to evaluate the influence of the surface
contamination on the diffusion process, negative and pos- that the hopping characteristic time depends on the bar-
itive charges were deposited on surfaces which had been rier height between the traps, which is modified by the
left a few days in ambient atmosphere. The observed time electric field in the oxide, and on the inter-trap dis-
evolutions are radically different from those observed for tance [13,18]. Since we observe two characteristic times
“
freshly” prepared samples kept in dry nitrogen gas. The in the charge spreading, the main assumption to interpret
first point is that, whatever the oxide thickness or the our results is to consider the oxide layers as inhomoge-
deposit voltage are, all the measured ratios R are equal neous with respect to the trap distribution. Let us point
to 1. This result indicates first that the totality of the de- out that, since the inter-trap distance dependence of the
posited charges systematically disappears when oxide sur- hopping characteristic time is exponential, this inhomo-
faces have been exposed to ambient atmosphere. Charges geneity is not necessarily very large: for instance, the char-
˚
can be deposited but not stored in this type of sam- acteristic time can vary from 26 s for a 30 A trap distance
ples. The second point concerns the time dependence of to 12.5 min for a 33 A trap distance [18,20]. This assump-
˚
Amax(Ω). For two deposit voltages(Vd = 15 V and 20 V), tion is justified by several experimental results. The very
the charge diffusion on a sample of thickness 15 nm can fast and important charge transfer observed in previous
be described by only one characteristic time. The relax- triboelectricity experiments suggested a quasi-equilibrium
ation of charges deposited on 100 nm samples for similar between the tip and a region under the surface with a
Vd potentials can also be described by a single time con- large concentration of traps, the characteristic penetra-
stant. This time, as for thin samples, is about 200 s and is tion length being about 50 nm [6]. The change in the time
independent of the deposit voltage. The likeness of these behavior of the amplitude (crossover between one char-
behaviors suggests that the diffusion of charges for these acteristic time and two characteristic times) observed in
polluted samples occurs exclusively on the surface of the the present experiments when the oxide layer thickness
insulator and is probably due to the contaminants or to is about 30 nm confirms the order of magnitude of this
the water film present on the surface.
penetration length. Hence we assumed here that the trap

90
The European Physical Journal Applied Physics
distribution is very large at distances from the surface suggest that they describe the same relaxation process.
less than 30 nm and weaker for larger distances. This as- Once τ2 and τ are considered to be alike, the fact that
sumption is in agreement with the literature comments on this time is independent of the oxide thickness is a sup-
electronic levels in oxide surfaces which mention trap con- plementary argument in favor of the localized character
centrations differing by a few orders of magnitude between (here the Al2O3 Al interface) of the process it is related
−
the surface and the bulk [18,21].
to. The second point is that the first time τ1, which is likely
to describe the “bulk region” crossing, increases with the
oxide thickness. It is found to be independent of the initial
transferred charge (or deposition potential Vd); indeed the
electric field is small and the characteristic time between
two jumps is roughly proportional to the exponential of
the distance between traps (the concentration of trap be-
ing small).
The migration across the “bulk region” permits to ex-
plain why the measured values of the ratio R are system-
atically inferior to 1 for thick oxides. During the migration
process some charges are kept by traps as the electric field
becomes too weak to ease their migration.
Under this assumption, thin oxides (d < 30 nm)
present only one large concentration of traps. Since these
traps are “instantaneously” filled during the injection, the
hopping time between them is very short with respect to
the measured time constants. Once the tip is removed, all
the charges located in the insulator bulk migrate under
the force exerted by their images to the traps that are
the nearest to the Al2O3 Al interface. The characteris-
−
tic time of this migration is similar to the injection one,
since the hopping process involved is the same. Therefore
this migration will be considered as instantaneous as well.
Then, the charges trapped near the Al2O3 Al interface,
−
being assisted by the electric field, begin to jump in the
conductor. In this case, the observed decrease of the am-
plitude is due to charges passing from the insulator to 6 Conclusion
the metallic Al electrode and is therefore characterized
by only one time constant τ. The other main observation Our studies of the diffusion of charges deposited on thin
concerning this characteristic time is its deposit voltage alumina layers using an AFM in resonant mode led us
dependence. The results obtained can be explained by the to a better understanding of the phenomena involved in
fact that the electric field being proportional to the de- the charge diffusion in alumina layers. First, the ability for
posited charge density, the barrier-height of the Al2O3
Al charge storing depends on the layer thickness. The thicker
−
interface is lowered when Vd increases. So, the higher the the layer, the larger is the quantity of charges retained. No
initial charge concentration, the smaller is the diffusion charge can be stored on samples thinner than 30 nm. Sec-
time. The third point about the measures performed on ondly, the time dependence of the diffusion process is also
thin layers is the value of the ratio R. It is found systemat- strongly dependent on the layer thickness. Whatever the
ically equal to 1, so that one could assume that the total- layer thickness is, the storage and the diffusion are in-
ity of the deposited charges leave the insulator. Yet, some terpreted using charge trapping/detrapping mechanisms.
residual charges could remain trapped since, during this Two successive processes are proposed to explain the ob-
oxide discharge, the local electric field is decreasing; this served behaviors: the transport of charges across the bulk
decrease would cause the characteristic time to increase and their passing through in the Al electrode. In a pre-
beyond the recording duration. Nevertheless this increase vious article we had discussed the charge diffusion during
should occur for very low concentrations of charges since the contact electrification [6]. The results presented here
R = 1.
show that, except for the contaminated layers, the sur-
face diffusion mechanism can be neglected, the dominant
diffusion occurring in the bulk.
Beyond these results related to alumina oxides, these
experiments show that the AFM microscopy is a promis-
ing technique to study the charge transport processes in
insulators.
The situation is very different for thicker layers: one
can distinguish two regions corresponding to two different
trap concentrations. The “surface region” (at distances
smaller than about 30 nm from the surface) presents a
higher concentration of traps than the “bulk region” (at
distances higher than about 30 nm from the surface). Dur-
ing the injection, only the “surface region” traps are filled
instantaneously. Once the tip is retracted, these trapped
carriers are attracted by their image charges. The carri-
ers trapped in the “surface region” first cross the “bulk
region” and, once they are located in the nearest Al elec-
trode traps, jump in the metal. This process permits to
explain the two-times behavior of the amplitude decrease:
the first characteristic time is associated to the migration
of the charges across the “bulk region” whereas the second
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