# Electrical Properties of Self-Assembled Nano-Schottky Diodes

Authors: F. Ruffino; A. Canino; M. G. Grimaldi; F. Giannazzo; F. Roccaforte; V. Raineri
Journal: Journal of Nanomaterials
 (2008)

---

## Abstract

A bottom-up methodology to fabricate a nanostructured material by Au nanoclusters on 6H-SiC surface is illustrated. Furthermore, a methodology to control its structural properties by thermal-induced self-organization of the Au nanoclusters is demonstrated. To this aim, the self-organization kinetic mechanisms of Au nanoclusters on SiC surface were experimentally studied by scanning electron microscopy, atomic force microscopy, Rutherford backscattering spectrometry and theoretically modelled by a ripening process. The fabricated nanostructured materials were used to probe, by local conductive atomic force microscopy analyses, the electrical properties of nano-Schottky contact Au nanocluster/SiC. Strong efforts were dedicated to correlate the structural and electrical characteristics: the main observation was the Schottky barrier height dependence of the nano-Schottky contact on the cluster size. Such behavior was interpreted considering the physics of few electron quantum dots merged with the concepts of ballistic transport and thermoionic emission finding a satisfying agreement between the theoretical prediction and the experimental data. The fabricated Au nanocluster/SiC nanocontact is suggested as a prototype of nano-Schottky diode integrable in complex nanoelectronic circuits.


---

## Body

## 1. Introduction

Understanding  the effects  of downscaling the devices dimensions to the
nanometer size is one of the most important topics in  the modern material
science applied to microelectronics. In fact, the confinement of electrons in
dimensions typical of atoms and molecules obliges to consider their quantum behavior.
Therefore, a new class of effects are characterizing ultrascaled devices. In
the last years, these ideas led to the birth of
the “nanotechnology and nanoelectronic revolution” [1–4] with the aim to understand the effects of
downscaling the matter in the atomic range and to develop innovative
nanostructured materials and quantum effects based devices [1–4] following a bottom-up procedure with respect
to the traditional top-down scaling scheme.In particular, the nanometric level knowledge of the structural
characteristics of such innovative materials and the nanometric control and
manipulation of these characteristics acquired a fundamental importance in the
design and realization of innovative electrical nanodevices. In fact, it is
well known that the local electrical characteristics of such devices are
dramatically dependent on the local structural ones. Hence, a precise control
and manipulation (at atomic level) of the structural characteristics allow the precise
control and manipulation of the electrical ones that are always innovative
properties with respect to the traditional devices.A promising topic of nanotechnology research is, surely, the
study of the structural and electrical properties of nanometric metal clusters
deposited on or embedded in semiconductor/insulating substrates in view of the
realization of nanostructured materials with electrical properties dependent on
and tuned by the
structural ones (clusters size, density, etc.) [5].We
developed a methodology to control and manipulate the clusters structural
properties based on the self-organization mechanism of the Au nanoclusters (NCs)
on the SiC surface induced by thermal processes. The Au clustering is shown to
be a ripening process of three-dimensional structures controlled by surface
diffusion and the application of the ripening theory enabled us to derive the
surface diffusion coefficient and all other parameters necessary to describe
the entire process so that we achieved a control on size, size distribution,
clusters distance distribution, and surface fraction of area covered by the
clusters by simply controlling the process parameters.We suggest to apply the self-organization
of Au NCs as a nanotechnology step to fabricate innovative nanostructured
devices. For main example, we studied, by the conductive atomic force microscopy
(C-AFM) technique, the local electrical properties of the nanometric systems Au
NC/SiC substrate. As expected, the main result was the strongly
dependence of the electrical properties on the clusters size, density, fraction
of covered area. In particular, we observed the Schottky barrier height dependence
of the Au NC/SiC nanocontact on the cluster size. Furthermore, we propose a
model to interpret such a behavior.


## 2. Experiment

6H-SiC substrates (previously etched in 10% aqueous HF solution
to remove the native oxide) were
used. A set of substrates was covered by a 2 nm (nominally) thick Au
layer sputtered using an Emitech K550x Sputter coater apparatus (Ar plasma,10−6mbar). The samples so obtained were named “as-deposited samples.” Some as-deposited
samples were then annealed in Ar at different temperatures (873K÷1073K) for
several times (5 minutes ÷ 60 minutes) and analyzed by Rutherford backscattering spectrometry (RBS), atomic force microscopy (AFM), and scanning
electron microscopy (SEM).The RBS analyses were performed using 2 MeVHe4+ backscattered ions at 165°. The AFM analyses were
performed using a digital instruments microscope dimension 3100 in high
amplitude mode and ultrasharpened Si tips were used and substituted as soon as
a resolution loose was observed during the acquisition. The AFM images were
analyzed by using the Nanoscope III software. The SEM analyses were performed
by a Zeiss FEG-SEM Supra 25 Microscope and the SEM images were analyzed using
the Gatan Digital Micrograph software.The local transversal current-voltage (I-Vtip) analyses were
carried out at room temperature using the Veeco DI 3100 AFM, in contact mode,
equipped with the conductive-AFM (C-AFM) head and ultrasharpened diamond coated
Si tips. The conductive diamond coating is
polycrystalline and the effective tip diameter is ultimately set by the very
small diamond grain (a few nanometers) placed at the apex of the tip. For each
sample, 400 I-V acquisitions in 400 different positions were performed in a
matrix of 20×20 points with step of 500 nm.


## 3. Results and Discussions

### 3.1. Self-Organization
of Au Nanoclusters on Hexagonal SiC Surface

RBS analyses  allowed to determine, in
particular, the Au atomic concentrationQ in the samples and it gave the same result (within a statistical error of 5%) for all
the  samples (as-deposited and annealed) and its value is Q=4.5×1015Au/cm2.
So we can conclude that no Au loss occurs during thermal treatments for any of
our samples (out diffusion, evaporation, reaction with C and/or Si).The change in morphology has been followed
by AFM. Despite a tip-cluster, deconvolution was considered; surface morphology
can present some
artifacts derived by
the tip-NCs interaction (not allowing an accurate determination of NCs shape
and dimension). So, for a supplementary accuracy, we compared the information acquired
by AFM with the NCs images obtained by SEM. From the AFM and SEM images, the
NCs size distributions and the distributions of center-to-center distances
between nearest NCs were determined by using a software that defines each NC area by
the surface image sectioning of a plane that was positioned at half NC height.
However, the results obtained by AFM and SEM analyses are in good agreement
(the respective results are identical within the statistical error). So, AFM
and SEM analyses were crossed to derive NC size distributions and center-to-center
NC distance distributions.As
an example, Figures1(a), 1(b) show representative AFM and SEM images for the as-deposited sample and Figures
1(c), 1(d) for the 1073 K-60 minutes sample.Figure 1
(a) AFM image of the Au
clusters as-deposited on 6H-SiC substrate, (b) SEM image for the same sample, (c)
AFM image of the Au clusters as-deposited on 6H-SiC substrate and annealed
1073 K-60 minutes, (d) SEM image for the same sample.In particular, the mean NC radius〈R(t)〉 was derived for each examined annealing temperature and time by the obtained
NC size distribution. Furthermore, if V(T,t)=(4/3)π〈R〉3 is the mean volume of the NC for each
annealing temperature T and annealing time t,
being [6] Ω=1.69×10−29m3 the Au atomic volume, then 〈n〉=〈V〉/Ω (supposing a 100% packing density) is the mean
number of Au atoms forming the NC. Therefore, Ns(T,t)=Q/〈n〉 is the mean number of NC per unit area and F(T,t)=πR2(T,t)Ns(T,t) the covered area by the NCs. The obtained
experimental F(T,t) is showed (dots) in Figure 2(a).(a) ExperimentalR4−R04 (black dots) as a function of annealing time
for each fixed temperature and the relative linear fits (continuous lines),
being K* the fits parameter. (b) Experimental (dots)
fraction F (normalized) of surface area covered by
clusters as a function of annealing time and relative theoretical simulation
(curves).
(a)(b)In the following, we briefly recall the
kinetic growth evolution of the NCs by the coarsening (or ripening) model to
explain the observed self-organization mechanism of the Au NCs on the SiC
surface.At any stage during coarsening there is a
so-called critical particle radiusR* being
in equilibrium with the mean matrix composition; particles with R>R* will
grow and particles with R<R* will
shrink [7].
Many coarsening theories are presented in literature [7–10]. In particular, the concepts that we report here (which are directly
connected with our experimental situations and data) are primarily based on the
review works of
Baldan [7] and
the theoretical work of Lifshitz-Slyozov-Wagner [8, 9] (LSW
theory), Allmang-Feldman-Grabov [10].The aim of mathematical modeling of
ripening process of particles dispersed (Au in our case) in/on a matrix is to
calculate the growth rate of individual particle. Despite the particular differences
derived by the
boundary conditions relative to the particular case examined, the general
theory of ripening process based on the LSW ideas has the same result for the
asymptotic temporal evolution of the system, and is summarized as follows [10]: the
mean particle radius R evolves as a function of time (for time
sufficiently great, i.e., in stationary state) according to (1)Rn(t)−R0n=K*t with R0 the radius of the particle at time t=0,
and K* an appropriate constant depending on the
diffusion coefficient. In particular, the fundamental formulations of the
ripening theory differ themselves by the value of n: n=2 (2D/2D case) for the growth of two-dimensional
(2D) particles on a surface (2D); n=3 (3D/3D case) for the growth of
three-dimensional (3D) particles embedded in a bulk matrix (3D); n=4 (3D/2D case) for the growth of three-dimensional
(3D) particles on a surface (2D).The Au on SiC has a strong nonwetting
nature [11],
being its adhesion energy on SiC Eadh(Au/SiC)=445mJ/m2 [11] much lower than the Au surface energy γAu=1500mJ/m2 [12], so that the Au NCs have grown on
SiC as 3D structures.According to this considerations, if the
Au clustering on SiC surface, in the examined temperature range, is guided by a
ripening process of 3D structures limited by diffusion, the temporal variation
of the mean NC radius〈R〉 should be regulated by (1) with n=4; it is demonstrated by the data reported in Figure 2(a). In such a figure are reported the experimental data 〈R〉4−〈R0〉4 (dots) for all the investigated temperature
and the lines (continuous, dashed, and dotted) represent the theoretical fits
by (1) (using n=4), being K* the fit parameter. The good agreement between the experimental data and the
fits is evident.Therefore,  in the assessed growth modes,
the mean radius of the Au NCs on SiC in the examined temperature and time
ranges increases with time as indicated by (1) with n=4 and with K* defined by [13] (2)K*=8N0DsγΩ245kBTln(L) being Ds the surface diffusion coefficient of the Au
atoms on the SiC surface, L≈3 a characteristic length (in units of 〈R〉), N0 the density of nucleation sites, Ω the Au atomic volume, γ the Au surface energy (N0=1.22×1015cm−2, Ω=1.69×10−29m3, γ=1.5J/m2) [6, 12]. The fit of
experimental data by (1) (with n=4), reported in Figure 2(a) for the different
annealing temperatures, allowed us to determine K*(T) for the three  examined temperatures. Moreover,
inversion of (2) allowed us to determine the diffusion coefficient of Au on SiC: Ds(873K)=1.67×10−15cm2/s, Ds(973K)=3.52×10−15cm2/s, Ds(1073K)=6.58×10−15cm2/s.
Such values are consistent with an Arrhenius behavior Ds(T)=D0e−Ea/kBT so as predicted for a thermally activated
diffusion process [14].  The
fit of the experimental Ds(T) with this activated form allows as to obtain
the preexponential factor D0=(2.6×10−12±1.6×10−13)cm2/s and the activation energy Ea=(0.55±0.01)eV/atom.Furthermore, the exposed model allows simulating theF(t) behavior: in fact, in Figure 2(b) the continuous lines
represent the prevision according to the exposed model and it is evident the
good agreement with the experimental data.


### 3.2. Electrical
Properties of the Au Nanoclusters/SiC Contacts

The knowledge of the details of the
self-organization mechanisms of Au NCs on SiC surfaces is a fundamental step towards
innovative nanodevices design. For example, once the knowledge of the details
of the Au NCs self-organization mechanisms on the SiC surface was established, we
were able to probe the electrical behavior of the Au NCs/SiC nano-Schottky
contacts observing their dependence on NCs size and fraction of area covered by
cluster. Hence, by opportune annealing process we are able to control the
structural properties of the fabricated nanostructured materials and, as a
consequence, the electrical properties of nanodevices based on such systems.The samples considered in these analyses were the as-deposited sample and
the 873 K-5 minutes, the 973 K-20 minutes, the 973 K-60 minutes, and the 1073 K-60 minutes
annealed samples. They showed NCs with mean diameter of(1.46±0.03)nm, (2.78±0.12)nm, (4.54±0.11)nm, (5.98±0.09)nm, (6.82±0.12)nm and a mean
center-to-center distance between nearest NCs of (4.31±0.18)nm, (6.53±0.18)nm, (10.9±0.13)nm, (14.15±0.15)nm, (17.6±0.19)nm,
respectively.According to Giannazzo et al. [15],
a biased C-AFM tip in contact with a continuous ultrathin metal film on a semiconductor forms a
nano-Schottky diode due to the nanometric localization of the current across the
metal-semiconductor (MS) interface. In our case of discontinuous film, for each
tip position on the sample surface, the typical rectifying Schottky contact I-V
characteristics were found, with the threshold voltage (correlated to the
Schottky barrier height (SBH)) depending on the tip position. As an example, in
Figure 3 are compared the characteristics recorded in bare SiC (Figure 3(a))
and in SiC covered with Au NCs of different size (Figures 3(b), 3(c)). Each I-Vtip curve is typical of thermoionic emission [16], and in the reference sample the
I-Vtip characteristics belong to a unique family that can be
associated to the Schottky contact between the diamond tip and the 6H-SiC
substrate. In Au covered samples, the I-Vtip curves are splitted in
two families: one corresponds to the diamond/6H-SiC Schottky contact (area not
covered by Au) and the second one corresponds to the Au NC/SiC Schottky
contact. The second family shift towards higher voltage when the mean NCs size
increases. To determine the SBH, the current onset region of each I-V curve was
fitted with a parabolic function and the SBH value was determined as the
parabola vertex derived by the fits, as described in [13]. So the SBH spatial distribution for each sample was obtained and reported
in the normalized distributions of Figure 4(a) for
the reference sample (sample without Au clusters). The SBH distribution is
peaked at (1.24±0.02)eV, with a broadening due to statistical
fluctuations. This measured value of 1.24 eV is associated
to the SBH of the diamond-tip/6H-SiC Schottky contact. For
the samples with Au clusters on the surface, by increasing the mean cluster sizes, the SBH distributions exhibit a
bimodal shape (see Figures 4(b), 4(c), 4(d)), with two broad peaks fitted by
two Gaussian curves. For all the samples, the first peak is centred at 1.24 eV,
that is, the value of the tip-diamond/6H-SiC SBH. Hence, the presence of this
first peak can be associated to the surface regions in which the diamond tip is
directly in contact with the 6H-SiC substrate. Interestingly, the position of
the second peak changes with the NCs average dimension. The SBH values in the
hystograms around the second peak can be associated to the direct contact with
a single Au NC, that is, to a single Au NC/6H-SiC
nano-Schottky diode. In fact, according to the used tip shape and to the
average cluster-distance/cluster-dimension ratio (and the step of 500 nm
between each point), it is quite unlikely that more than one cluster could be
simultaneously contacted by the tip. Hence, when the tip is in contact with a
single NC, the nearest NCs can contribute to the total current only by a tunnel
component through the air that is negligible, being, according to realistic
estimations, at least  two orders of magnitude smaller than the current due to
the direct tip-NC-substrate contact. Moreover, such a hypothesis is supported by the
fact that the fraction of I-Vtip curves belonging to the family in
which the tip is in contact with Au corresponds to the fraction of covered area
by Au NCs for that sample (Figure 5), measured by the structural analyses.I-Vtip curves measured (by C-AFM)
in SiC covered with Au nanoclusters with different sizes.
(a)(b)(c)Schottky
barrier height distributions. (a) Reference sample (sample without Au cluster);
sample with Au cluster mean diameter of (b)(1.46±0.03)nm,
(c) (2.78±0.12)nm,
and (d) (6.82±0.12)nm.
(a)(b)(c)(d)Figure 5
Comparison
between the data concerning the fraction of covered area by the Au clusters
(normalized) derived by the structural analyses (square dots) and by the
electrical ones (circular dots).The data of Figure4
demonstrate the dependence of the SBH on the NC
size. As an example, in the as-deposited sample, the average cluster size is ∼1.46 nm with a
Gaussian distribution (full width height maximum σ=0.03nm). Correspondingly, Figure 4(b)
shows that most of NC/6H-SiC contacts present a
SBH around 1.35 eV while only a low number of
contacts present smaller or larger SBH. Similarly,  in the other samples the peak corresponding to the
tip-Au-substrate contact is centred on the SBH value corresponding to the mean
Au cluster size with dispersion due to the cluster dimensions. Accordingly, we
associated to each sample a unique SBH corresponding to the cluster mean size
(the peak at higher SBH in Figure 4)  and the error bar on each SBH value was evaluated from
the σof each hystogram in Figure 4.In Figure6, the evaluated SBH
(dots) is reported as a function of the mean NC size. It increases with
increasing average NC size, tending asymptotically to the ideal SBH value of a
continuous Au film/SiC contact (∼1.9 eV) [17]. This latter evidence indicates that the larger Au NCs (>7 nm) on SiC approach the behavior
of the Schottky barriers formed by continuous Au films.Figure 6
Experimental
values (dots) of the SBH as a function of mean cluster size and theoretical
prediction forΦB=1.85eV, m*=0.08,
and m*=m.
The inset shows the
considered band diagram of the system (AFM) tip-cluster-SiC substrate.We based our interpretation of the SBH
dependence on the NCs size considering the
thermoionic transport theory through the MS barrier coupled with the concept of
ballistic transport and the constant interaction (CI) model for the electron
transport in few electrons quantum dots [18]. The
process was schematized as indicated in the inset of Figure 6. For a forward
(positively) biased tip, an additional electron from the substrate overcomes
the SBH by thermoionic emission and falls on the lowest unoccupied energy level μ(N+1) within the 3D box containing N electrons (NC). As the electron
mean free path λe for the considered
electron kinetic energy in the Au NCs is ranging between [19] 10 and 20 nm (i.e., λe larger than the average
cluster dimension), the
electron moves ballistically within the Au dot and it is collected to the tip
in ohmic contact with the Au grain. Hence, the Au Nc/SiC SBH is given by ΦB(N)=ΦB0−Δμ(N),
with Δμ(N) the energetic distance between EF and μ(N+1) (inset of Figure 6) and ΦB0 the Schottky barrier height as defined for the
macroscopic contact. According to the CI model of few electron quantum dots, Δμ(N)=(e2/C)+ΔE where Ec=e2/C is the electrostatic energy (“charging
energy”) necessary to add or subtract one electron to the dot, taking into
account the Coulomb interactions of that electron with all other electrons, in
and outside the dot. We derived the capacitance C as C=C0+nsCc; C0=2πεrε0L is the self-capacitance of the dot, that is,
the capacitance of a sphere of diameter L embedded in a dielectric of constant εr, Cc≈(π3εrε0L2)/4(s+L) is an approximated expression for the coupling
capacitance between two nearest clusters, described as two spheres with the
same diameter L and sited at center-to-center distance s+L (s is the surface-surface distance between the
two clusters). Finally, ns is the number of nearest neighbour clusters whose analytical
expression is derived starting from the results exposed in Section 3.1.
According to those results, the surface clusters density is expressed by Ns(L)=3QΩ/4πL3,
where Q is the Au atomic surface concentration. In a random distribution of the clusters on the surface,
a circular symmetry around each fixed cluster can be assumed, so that ns=2π(s+L)Ns.
So: (3)ΦB(L)=ΦB0−e22πεrε0L+(3QΩ/4π)(π3εrε0/2)L1/2−(13π2)1/3(π6Ω)−1/3ℏ2π2m*L3. Clearly, ΦB(L) tends to saturate to ΦB0 for sufficiently large L values, that is, the behavior of large NCs
approaches that of the bulk material. By (3) it is evident that, decreasing L,
the barrier height ΦB becomes zero for a certain L* value, which in
our case is L*=0.85nm. For L<L*, ΦB would be negative. Since ΦB(L)=Φm−χ−Δμ(L)=Φmeff(L)−χ, a negative ΦB value is equivalent to an effective metal
work-function Φmeff(L) lower than the electron affinity χin the semiconductor. In such a
situation, the Au NC/6H-SiC contact would be not any more a Schottky contact,
but an ohmic one and the transport mechanism at the interface would change in
consequence. Although the developed
model is valid for T=0,
it gives a good approximation even at room temperature (our experimental case)
for which (e2/C)≫kT.Comparing the theoretical prediction by (3) with the experimental data
of Figure 6 using the values ΦB0=1.85eV, εr=1, Q=4.5×1015cm−2 (by RBS analyses), and Ω=1.69×10−29m3,
the continuous curve reported in Figure 6 is obtained. The only free fitting
parameter was m*.
The best agreement was obtained for m*=0.08m.
For NCs characterized by size larger than 10 nm, it is evident that . As a consequence NCs with size larger than 10 nm acquire bulk properties. This is confirmed by other experimental evidences as Au NCs melting
point and structural properties dependence on size [20].


## 3.1. Self-Organization
of Au Nanoclusters on Hexagonal SiC Surface

RBS analyses  allowed to determine, in
particular, the Au atomic concentrationQ in the samples and it gave the same result (within a statistical error of 5%) for all
the  samples (as-deposited and annealed) and its value is Q=4.5×1015Au/cm2.
So we can conclude that no Au loss occurs during thermal treatments for any of
our samples (out diffusion, evaporation, reaction with C and/or Si).The change in morphology has been followed
by AFM. Despite a tip-cluster, deconvolution was considered; surface morphology
can present some
artifacts derived by
the tip-NCs interaction (not allowing an accurate determination of NCs shape
and dimension). So, for a supplementary accuracy, we compared the information acquired
by AFM with the NCs images obtained by SEM. From the AFM and SEM images, the
NCs size distributions and the distributions of center-to-center distances
between nearest NCs were determined by using a software that defines each NC area by
the surface image sectioning of a plane that was positioned at half NC height.
However, the results obtained by AFM and SEM analyses are in good agreement
(the respective results are identical within the statistical error). So, AFM
and SEM analyses were crossed to derive NC size distributions and center-to-center
NC distance distributions.As
an example, Figures1(a), 1(b) show representative AFM and SEM images for the as-deposited sample and Figures
1(c), 1(d) for the 1073 K-60 minutes sample.Figure 1
(a) AFM image of the Au
clusters as-deposited on 6H-SiC substrate, (b) SEM image for the same sample, (c)
AFM image of the Au clusters as-deposited on 6H-SiC substrate and annealed
1073 K-60 minutes, (d) SEM image for the same sample.In particular, the mean NC radius〈R(t)〉 was derived for each examined annealing temperature and time by the obtained
NC size distribution. Furthermore, if V(T,t)=(4/3)π〈R〉3 is the mean volume of the NC for each
annealing temperature T and annealing time t,
being [6] Ω=1.69×10−29m3 the Au atomic volume, then 〈n〉=〈V〉/Ω (supposing a 100% packing density) is the mean
number of Au atoms forming the NC. Therefore, Ns(T,t)=Q/〈n〉 is the mean number of NC per unit area and F(T,t)=πR2(T,t)Ns(T,t) the covered area by the NCs. The obtained
experimental F(T,t) is showed (dots) in Figure 2(a).(a) ExperimentalR4−R04 (black dots) as a function of annealing time
for each fixed temperature and the relative linear fits (continuous lines),
being K* the fits parameter. (b) Experimental (dots)
fraction F (normalized) of surface area covered by
clusters as a function of annealing time and relative theoretical simulation
(curves).
(a)(b)In the following, we briefly recall the
kinetic growth evolution of the NCs by the coarsening (or ripening) model to
explain the observed self-organization mechanism of the Au NCs on the SiC
surface.At any stage during coarsening there is a
so-called critical particle radiusR* being
in equilibrium with the mean matrix composition; particles with R>R* will
grow and particles with R<R* will
shrink [7].
Many coarsening theories are presented in literature [7–10]. In particular, the concepts that we report here (which are directly
connected with our experimental situations and data) are primarily based on the
review works of
Baldan [7] and
the theoretical work of Lifshitz-Slyozov-Wagner [8, 9] (LSW
theory), Allmang-Feldman-Grabov [10].The aim of mathematical modeling of
ripening process of particles dispersed (Au in our case) in/on a matrix is to
calculate the growth rate of individual particle. Despite the particular differences
derived by the
boundary conditions relative to the particular case examined, the general
theory of ripening process based on the LSW ideas has the same result for the
asymptotic temporal evolution of the system, and is summarized as follows [10]: the
mean particle radius R evolves as a function of time (for time
sufficiently great, i.e., in stationary state) according to (1)Rn(t)−R0n=K*t with R0 the radius of the particle at time t=0,
and K* an appropriate constant depending on the
diffusion coefficient. In particular, the fundamental formulations of the
ripening theory differ themselves by the value of n: n=2 (2D/2D case) for the growth of two-dimensional
(2D) particles on a surface (2D); n=3 (3D/3D case) for the growth of
three-dimensional (3D) particles embedded in a bulk matrix (3D); n=4 (3D/2D case) for the growth of three-dimensional
(3D) particles on a surface (2D).The Au on SiC has a strong nonwetting
nature [11],
being its adhesion energy on SiC Eadh(Au/SiC)=445mJ/m2 [11] much lower than the Au surface energy γAu=1500mJ/m2 [12], so that the Au NCs have grown on
SiC as 3D structures.According to this considerations, if the
Au clustering on SiC surface, in the examined temperature range, is guided by a
ripening process of 3D structures limited by diffusion, the temporal variation
of the mean NC radius〈R〉 should be regulated by (1) with n=4; it is demonstrated by the data reported in Figure 2(a). In such a figure are reported the experimental data 〈R〉4−〈R0〉4 (dots) for all the investigated temperature
and the lines (continuous, dashed, and dotted) represent the theoretical fits
by (1) (using n=4), being K* the fit parameter. The good agreement between the experimental data and the
fits is evident.Therefore,  in the assessed growth modes,
the mean radius of the Au NCs on SiC in the examined temperature and time
ranges increases with time as indicated by (1) with n=4 and with K* defined by [13] (2)K*=8N0DsγΩ245kBTln(L) being Ds the surface diffusion coefficient of the Au
atoms on the SiC surface, L≈3 a characteristic length (in units of 〈R〉), N0 the density of nucleation sites, Ω the Au atomic volume, γ the Au surface energy (N0=1.22×1015cm−2, Ω=1.69×10−29m3, γ=1.5J/m2) [6, 12]. The fit of
experimental data by (1) (with n=4), reported in Figure 2(a) for the different
annealing temperatures, allowed us to determine K*(T) for the three  examined temperatures. Moreover,
inversion of (2) allowed us to determine the diffusion coefficient of Au on SiC: Ds(873K)=1.67×10−15cm2/s, Ds(973K)=3.52×10−15cm2/s, Ds(1073K)=6.58×10−15cm2/s.
Such values are consistent with an Arrhenius behavior Ds(T)=D0e−Ea/kBT so as predicted for a thermally activated
diffusion process [14].  The
fit of the experimental Ds(T) with this activated form allows as to obtain
the preexponential factor D0=(2.6×10−12±1.6×10−13)cm2/s and the activation energy Ea=(0.55±0.01)eV/atom.Furthermore, the exposed model allows simulating theF(t) behavior: in fact, in Figure 2(b) the continuous lines
represent the prevision according to the exposed model and it is evident the
good agreement with the experimental data.


## 3.2. Electrical
Properties of the Au Nanoclusters/SiC Contacts

The knowledge of the details of the
self-organization mechanisms of Au NCs on SiC surfaces is a fundamental step towards
innovative nanodevices design. For example, once the knowledge of the details
of the Au NCs self-organization mechanisms on the SiC surface was established, we
were able to probe the electrical behavior of the Au NCs/SiC nano-Schottky
contacts observing their dependence on NCs size and fraction of area covered by
cluster. Hence, by opportune annealing process we are able to control the
structural properties of the fabricated nanostructured materials and, as a
consequence, the electrical properties of nanodevices based on such systems.The samples considered in these analyses were the as-deposited sample and
the 873 K-5 minutes, the 973 K-20 minutes, the 973 K-60 minutes, and the 1073 K-60 minutes
annealed samples. They showed NCs with mean diameter of(1.46±0.03)nm, (2.78±0.12)nm, (4.54±0.11)nm, (5.98±0.09)nm, (6.82±0.12)nm and a mean
center-to-center distance between nearest NCs of (4.31±0.18)nm, (6.53±0.18)nm, (10.9±0.13)nm, (14.15±0.15)nm, (17.6±0.19)nm,
respectively.According to Giannazzo et al. [15],
a biased C-AFM tip in contact with a continuous ultrathin metal film on a semiconductor forms a
nano-Schottky diode due to the nanometric localization of the current across the
metal-semiconductor (MS) interface. In our case of discontinuous film, for each
tip position on the sample surface, the typical rectifying Schottky contact I-V
characteristics were found, with the threshold voltage (correlated to the
Schottky barrier height (SBH)) depending on the tip position. As an example, in
Figure 3 are compared the characteristics recorded in bare SiC (Figure 3(a))
and in SiC covered with Au NCs of different size (Figures 3(b), 3(c)). Each I-Vtip curve is typical of thermoionic emission [16], and in the reference sample the
I-Vtip characteristics belong to a unique family that can be
associated to the Schottky contact between the diamond tip and the 6H-SiC
substrate. In Au covered samples, the I-Vtip curves are splitted in
two families: one corresponds to the diamond/6H-SiC Schottky contact (area not
covered by Au) and the second one corresponds to the Au NC/SiC Schottky
contact. The second family shift towards higher voltage when the mean NCs size
increases. To determine the SBH, the current onset region of each I-V curve was
fitted with a parabolic function and the SBH value was determined as the
parabola vertex derived by the fits, as described in [13]. So the SBH spatial distribution for each sample was obtained and reported
in the normalized distributions of Figure 4(a) for
the reference sample (sample without Au clusters). The SBH distribution is
peaked at (1.24±0.02)eV, with a broadening due to statistical
fluctuations. This measured value of 1.24 eV is associated
to the SBH of the diamond-tip/6H-SiC Schottky contact. For
the samples with Au clusters on the surface, by increasing the mean cluster sizes, the SBH distributions exhibit a
bimodal shape (see Figures 4(b), 4(c), 4(d)), with two broad peaks fitted by
two Gaussian curves. For all the samples, the first peak is centred at 1.24 eV,
that is, the value of the tip-diamond/6H-SiC SBH. Hence, the presence of this
first peak can be associated to the surface regions in which the diamond tip is
directly in contact with the 6H-SiC substrate. Interestingly, the position of
the second peak changes with the NCs average dimension. The SBH values in the
hystograms around the second peak can be associated to the direct contact with
a single Au NC, that is, to a single Au NC/6H-SiC
nano-Schottky diode. In fact, according to the used tip shape and to the
average cluster-distance/cluster-dimension ratio (and the step of 500 nm
between each point), it is quite unlikely that more than one cluster could be
simultaneously contacted by the tip. Hence, when the tip is in contact with a
single NC, the nearest NCs can contribute to the total current only by a tunnel
component through the air that is negligible, being, according to realistic
estimations, at least  two orders of magnitude smaller than the current due to
the direct tip-NC-substrate contact. Moreover, such a hypothesis is supported by the
fact that the fraction of I-Vtip curves belonging to the family in
which the tip is in contact with Au corresponds to the fraction of covered area
by Au NCs for that sample (Figure 5), measured by the structural analyses.I-Vtip curves measured (by C-AFM)
in SiC covered with Au nanoclusters with different sizes.
(a)(b)(c)Schottky
barrier height distributions. (a) Reference sample (sample without Au cluster);
sample with Au cluster mean diameter of (b)(1.46±0.03)nm,
(c) (2.78±0.12)nm,
and (d) (6.82±0.12)nm.
(a)(b)(c)(d)Figure 5
Comparison
between the data concerning the fraction of covered area by the Au clusters
(normalized) derived by the structural analyses (square dots) and by the
electrical ones (circular dots).The data of Figure4
demonstrate the dependence of the SBH on the NC
size. As an example, in the as-deposited sample, the average cluster size is ∼1.46 nm with a
Gaussian distribution (full width height maximum σ=0.03nm). Correspondingly, Figure 4(b)
shows that most of NC/6H-SiC contacts present a
SBH around 1.35 eV while only a low number of
contacts present smaller or larger SBH. Similarly,  in the other samples the peak corresponding to the
tip-Au-substrate contact is centred on the SBH value corresponding to the mean
Au cluster size with dispersion due to the cluster dimensions. Accordingly, we
associated to each sample a unique SBH corresponding to the cluster mean size
(the peak at higher SBH in Figure 4)  and the error bar on each SBH value was evaluated from
the σof each hystogram in Figure 4.In Figure6, the evaluated SBH
(dots) is reported as a function of the mean NC size. It increases with
increasing average NC size, tending asymptotically to the ideal SBH value of a
continuous Au film/SiC contact (∼1.9 eV) [17]. This latter evidence indicates that the larger Au NCs (>7 nm) on SiC approach the behavior
of the Schottky barriers formed by continuous Au films.Figure 6
Experimental
values (dots) of the SBH as a function of mean cluster size and theoretical
prediction forΦB=1.85eV, m*=0.08,
and m*=m.
The inset shows the
considered band diagram of the system (AFM) tip-cluster-SiC substrate.We based our interpretation of the SBH
dependence on the NCs size considering the
thermoionic transport theory through the MS barrier coupled with the concept of
ballistic transport and the constant interaction (CI) model for the electron
transport in few electrons quantum dots [18]. The
process was schematized as indicated in the inset of Figure 6. For a forward
(positively) biased tip, an additional electron from the substrate overcomes
the SBH by thermoionic emission and falls on the lowest unoccupied energy level μ(N+1) within the 3D box containing N electrons (NC). As the electron
mean free path λe for the considered
electron kinetic energy in the Au NCs is ranging between [19] 10 and 20 nm (i.e., λe larger than the average
cluster dimension), the
electron moves ballistically within the Au dot and it is collected to the tip
in ohmic contact with the Au grain. Hence, the Au Nc/SiC SBH is given by ΦB(N)=ΦB0−Δμ(N),
with Δμ(N) the energetic distance between EF and μ(N+1) (inset of Figure 6) and ΦB0 the Schottky barrier height as defined for the
macroscopic contact. According to the CI model of few electron quantum dots, Δμ(N)=(e2/C)+ΔE where Ec=e2/C is the electrostatic energy (“charging
energy”) necessary to add or subtract one electron to the dot, taking into
account the Coulomb interactions of that electron with all other electrons, in
and outside the dot. We derived the capacitance C as C=C0+nsCc; C0=2πεrε0L is the self-capacitance of the dot, that is,
the capacitance of a sphere of diameter L embedded in a dielectric of constant εr, Cc≈(π3εrε0L2)/4(s+L) is an approximated expression for the coupling
capacitance between two nearest clusters, described as two spheres with the
same diameter L and sited at center-to-center distance s+L (s is the surface-surface distance between the
two clusters). Finally, ns is the number of nearest neighbour clusters whose analytical
expression is derived starting from the results exposed in Section 3.1.
According to those results, the surface clusters density is expressed by Ns(L)=3QΩ/4πL3,
where Q is the Au atomic surface concentration. In a random distribution of the clusters on the surface,
a circular symmetry around each fixed cluster can be assumed, so that ns=2π(s+L)Ns.
So: (3)ΦB(L)=ΦB0−e22πεrε0L+(3QΩ/4π)(π3εrε0/2)L1/2−(13π2)1/3(π6Ω)−1/3ℏ2π2m*L3. Clearly, ΦB(L) tends to saturate to ΦB0 for sufficiently large L values, that is, the behavior of large NCs
approaches that of the bulk material. By (3) it is evident that, decreasing L,
the barrier height ΦB becomes zero for a certain L* value, which in
our case is L*=0.85nm. For L<L*, ΦB would be negative. Since ΦB(L)=Φm−χ−Δμ(L)=Φmeff(L)−χ, a negative ΦB value is equivalent to an effective metal
work-function Φmeff(L) lower than the electron affinity χin the semiconductor. In such a
situation, the Au NC/6H-SiC contact would be not any more a Schottky contact,
but an ohmic one and the transport mechanism at the interface would change in
consequence. Although the developed
model is valid for T=0,
it gives a good approximation even at room temperature (our experimental case)
for which (e2/C)≫kT.Comparing the theoretical prediction by (3) with the experimental data
of Figure 6 using the values ΦB0=1.85eV, εr=1, Q=4.5×1015cm−2 (by RBS analyses), and Ω=1.69×10−29m3,
the continuous curve reported in Figure 6 is obtained. The only free fitting
parameter was m*.
The best agreement was obtained for m*=0.08m.
For NCs characterized by size larger than 10 nm, it is evident that . As a consequence NCs with size larger than 10 nm acquire bulk properties. This is confirmed by other experimental evidences as Au NCs melting
point and structural properties dependence on size [20].


## 4. Conclusion

The possibility of controlling and
modeling size and size distribution of Au NCs deposited on SiC surface by
process parameters such as thermal treatments has been demonstrated.The clustering kinetic process and surface
diffusion of Au on SiC substrates were experimentally characterized by Rutherford backscattering spectrometry, scanning electron
microscopy, and atomic force microscopy. The evolution kinetics has been
interpreted by classical models involving surface diffusion limited ripening of
spherical three-dimensional clusters on a substrate. From the mass transfer
surface diffusion coefficients of gold on SiC hexagonal and SiO2 surfaces, determined in the 873K÷1073K temperature range, activation energy of (0.55±0.01)eV/atom was obtained. The knowing of the details of
the self-organization mechanisms of Au NCs on SiC allowed us to fabricate nano-Schottky
diodes with tunable electrical properties by tuning the parameters
characterizing these mechanisms.



---

*Source: 243792-2008-10-21.xml*