|Título/s:||In situ electrical characterization of palladium-based single electron transistors made by electromigration technique|
|Fuente:||AIP Advances, 4(11)|
|Autor/es:||Arzubiaga, L.; Golmar, F.; Llopis, R.; Casanova, F.; Hueso, L. E.|
|Palabras clave:||Electricidad; Electrones; Transistores; Paladio; Electrodos; Aleaciones de níquel; Electrostática|
| Ver+/- |
AIP Advances 4, 117126 (2014); https://doi.org/10.1063/1.4902170 4, 117126
© 2014 Author(s).
In situ electrical characterization of
palladium-based single electron transistors
made by electromigration technique
Cite as: AIP Advances 4, 117126 (2014); https://doi.org/10.1063/1.4902170
Submitted: 18 September 2014 . Accepted: 07 November 2014 . Published Online: 17 November 2014
L. Arzubiaga, F. Golmar, R. Llopis, F. Casanova, and L. E. Hueso
Paper published as part of the special topic on Chemical Physics, Energy, Fluids and Plasmas, Materials Science
and Mathematical Physics
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AIP ADVANCES 4, 117126 (2014)
In situ electrical characterization of palladium-based single
electron transistors made by electromigration technique
L. Arzubiaga,1 F. Golmar,2 R. Llopis,1 F. Casanova,1,3 and L. E. Hueso1,3
1CIC nanoGUNE, Tolosa Hiribidea 76, 20018 Donostia, San Sebastian,
Basque Country, Spain
2I.N.T.I. – CONICET and ECyT-UNSAM, San Martín, Bs As, Argentina
3IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Basque Country, Spain
(Received 18 September 2014; accepted 7 November 2014; published online 17 November 2014)
We report the fabrication of single electron transistors (SETs) by feedback-controlled
electromigration of palladium and palladium-nickel alloy nanowires. We have opti-
mized a gradual electromigration process for obtaining devices consisting of three
terminals (source, drain and gate electrodes), which are capacitively coupled to
a metallic cluster of nanometric dimensions. This metal nanocluster forms into
the inter-electrode channel during the electromigration process and constitutes the
active element of each device, acting as a quantum dot that rules the electron
flow between source and drain electrodes. The charge transport of the as-fabricated
devices shows Coulomb blockade characteristics and the source to drain conduc-
tance can be modulated by electrostatic gating. We have thus achieved the fabri-
cation and in situ measurement of palladium-based SETs inside a liquid helium
cryostat chamber. C 2014 Author(s). All article content, except where otherwise
noted, is licensed under a Creative Commons Attribution 3.0 Unported License.
The current trend of pursuing an extreme miniaturization of electronic circuits demands appro-
priate platforms for studying charge transport in systems of reduced dimensions. Single-Electron
Transistors (SETs) have attracted much interest in this matter, because they provide the means for
observing the circulation of individual electrons in a great variety of nanostructures1 such as metallic
or semiconductor nanoparticles,2–5 single molecules,6–8 carbon nanotubes9–11 or graphene nanorib-
The case of SETs constituted by metallic grains is especially interesting. On one hand, it al-
lows probing the influence of quantum confinement in electron-electron correlations and spin-orbit
interactions in a given metal. On the other hand, the possibility of alloying different metals offers
the opportunity of biasing the type of electronic interactions, for example, by the introduction of
ferromagnetism or superconductivity.2,13 Among the wide variety of metals that could be used as
an active element of a SET, palladium could add interesting features to the single electron transport
thanks to its peculiar electronic structure. This metal has a fairly strong exchange interaction between
electrons, although it has no effective magnetism in the bulk state.14 Palladium nanoparticles have
been reported to display size-dependent magnetism15 and are thus an attractive element for studying
spin-dependent effects in SETs.
The fundamental condition for obtaining a SET is having an active element with dimensions that
are low enough to induce the quantum confinement of conduction electrons. This low dimensional
element or quantum dot (QD) can be a metallic nanoparticle through which electrons must tunnel to
get from source to drain electrodes.
In a SET the QD is directly connected to two terminals (source and drain electrodes) by means of
two tunnel junctions with resistance > R0 (where R0=h/2e2 is the resistance of a single conductance
channel). A third terminal (gate electrode) is used to tune the electrochemical potential in the QD
by electrostatic field-effect. When the QD is a metallic nanoparticle of more than a few nanome-
ters, as it is the present case, electrons require an additional amount of energy for tunneling into the
2158-3226/2014/4(11)/117126/7 4, 117126-1 ©Author(s) 2014
117126-2 Arzubiaga et al. AIP Advances 4, 117126 (2014)
QD. This extra amount of energy, known as the “Coulomb charging energy”, allows overcoming the
electrostatic repulsion created by the electrons confined in the dot.
The observation of a single electron transport requires EC to be larger than the thermal energy
(EC >> KBT, where KB is the Boltzmann constant and T is temperature). If EC >> KBT, an electron
tunnels into the QD when the applied source-drain voltage (VSD) provides enough energy to overcome
EC. The devices that meet these conditions show a negligible conductance when a low source-drain
voltage (VSD) is applied, which is a situation known as Coulomb blockade. Thus, the QD acts as a
bottleneck in the circuit where electrons are forced to pass one at a time.1
There are interesting examples in literature describing the fabrication of SETs based on metallic
QDs. Such techniques comprehend one or more steps for creating nanoelectrodes (employing lithog-
raphy or alternative techniques), followed by the addition of metallic nanoparticles obtained by chemi-
cal or physical methods.16–18 The use of electromigration for the fabrication of SETs is quite extended,
as it has enabled the fabrication of transistors with channel lengths as small as 1 nm.3,6–8
Electromigration consists on passing a high electrical current density through a metallic wire of
nanometric cross-section, until it breaks by electrical stress. Metallic QDs can then be placed and elec-
trically contacted in the gap between the obtained electrodes. The combination of certain experimental
conditions during the electromigration process and the intrinsic properties of the nanowire material
can favor the simultaneous formation of metallic nanoclusters or nanoparticles at the breaking point.
The newly formed metallic nanoparticles have the advantage of being already embedded in the gap
between two electrodes. Hence, the as-fabricated device would be ready for electrical characterization
without further manipulation.
The formation of SETs with metallic quantum dots as a consequence of electromigration has
already been reported.7,19 These devices have generally been regarded as undesired by-products when
the aim was obtaining single molecule transistors (SMTs). We would like to show that the spontaneous
formation of SETs during electromigration could also be used to our advantage.
We used electron-beam lithography for defining palladium devices on top of p-doped silicon
chips coated with 150 nm of thermally grown silicon oxide (SiO2). The lithography was carried out
on a double layer polymethyl metacrylate (PMMA) resist system spun onto the thermal SiO2 surface,
followed by metal deposition by magnetron sputtering and lift-off in acetone. We fabricated devices
with 99.99% purity Pd.
Each device consisted of a palladium nanowire (around 300 nm long, 25 nm thick and 65 nm
wide) terminated with a pair of macroscopic electrodes for electrical contact. The as-fabricated palla-
dium devices were cleaned with acetone and isopropanol, followed by 10 seconds of oxygen plasma,
before placing them in a liquid helium cryostat.
All the electromigration and electrical characterization experiments were carried out at 1.8K in-
side a liquid He cryostat (with 10 mTorr He atmosphere). A home-made LabView program controlled
the electromigration process with the aid of an appropriate feedback algorithm. The nanowires were
gradually broken by electromigration. The strategy consisted on applying series of increasing voltage
ramps and limiting the extent to which the electromigration took place in each ramp. This was done
by continuously monitoring the conductance (G) measured across the device and limiting the amount
it changed in the last measured 40 data points. Fig. 1 shows the conductance of a device as it evolved
in a typical electromigration process. At the beginning of each voltage ramp the conductance of the
device decreased slightly, due to the increase of electron scattering events as the circulating current
got higher. The observation of a sudden decrease of conductance marked the starting point of elec-
tromigration. We will refer to the values of voltage and current at the onset of electromigration as
the critical voltage (VC) and critical current (IC), respectively. Typically, we limited the decrease of
conductance to a 1.5% in the last measured 40 data points, after which the applied voltage was reset
to zero and a relaxation time of 5 seconds was allowed. These conditions ensured that the electromi-
gration in the nanowire occurred only partially in each voltage ramp. As the gradual breaking process
of the nanowires was carried out, the value of VC decreased. When the onset of electromigration took
place at VC values lower than about 500 mV, we allowed the nanowire to electromigrate beyond the
previously set limits. During the final voltage ramps the nanowires suffered a sudden and major break
(which could bring the device resistance up to several KΩ). Afterwards, the evolution of the conduc-
tance entered a different regime in which sudden jumps of random character were often observed.
117126-3 Arzubiaga et al. AIP Advances 4, 117126 (2014)
FIG. 1. Evolution of the device conductance (G) during the electromigration process of a palladium nanowire. A series of
increasing voltage (V) ramps are applied while the decrease of G in each V ramp is limited to a 1.5%. The solid arrow
indicates the starting point of the first V ramp, while the dashed arrow shows the order of the successive V ramps throughout
the process. The gradual decrease of G indicates that the cross-section of the nanowire is decreased after each V ramp. After
the nanowire suffers a major break (observed as a sharp jump in G) it becomes unstable. G evolves in random jumps until a
target G value (corresponding to a device resistance of around 40 kΩ, indicated by a dotted line) is reached. Inset: Evolution
of the conductance (G) in units of quantized conductance (G0=2e2/h) in the last stage of the electromigration for a similar
nanowire. The appearance of quantized conductance steps indicates the formation of a narrow constriction before the failure
of the nanowire.
The applied voltage was steadily increased until a target conductance value was reached (typically
corresponding to a device resistance of around 40 KΩ), after which the voltage was reset to zero and
the process was finished. At this point, the low bias resistance of the devices had a value in the order of
1 to 100 MΩ (measured at 20 mV and 1.8 K) and the measured current versus voltage curves became
During an electromigration process the nanowires develop constrictions that grow gradually
throughout several voltage ramps until they finally break.20 This is consistent with the steady decrease
of G measured during the first few voltage ramps of the process (Fig. 1). As regards the more random
evolution and the sudden jumps of G observed in the last stage of the process, they are generally attrib-
uted to rearrangements of the metal grains. We could occasionally observe the conductance decreasing
in quantized steps in this last stage. This quantization indicated the formation of a constriction with
a few conductance channels just before the complete breakdown of the nanowire.
The source-drain current (ISD) versus voltage (VSD) curves of the electromigrated devices were
non-linear, with a plateau of almost negligible source-drain current near the zero bias region. On the
other hand, most of the obtained devices showed a periodic modulation of the described transport
features as a function of the applied gate potential (VG). This last observation confirmed that after
the electromigration of the nanowires, the devices had indeed transformed into SETs in which the
current passed through a QD. The modulation with VG occurs because the electrostatic energy of the
QD is shifted with respect to the Fermi energy (EF) of the source and drain electrodes by field effect.
The effect of VG is more easily analyzed in the differential conductance curves (dI/dV), which
are obtained by calculating the derivative of the recorded ISD vs VSD traces. The circulation of single
electrons into or out of the QD is marked by peaks in the dI/dV. These peaks appear at different VSD
values depending on the applied VG. We calculated the dI/dV curves for a range of gate voltages and
we plotted them as a function of VSD and VG. The resultant graphs, commonly known as “stabil-
ity diagrams”, constituted a conductance-map of the devices. Some of our devices showed stability
diagrams with the characteristic pattern of a SET, in which we observed periodic diamond-shaped
regions of almost negligible conductance (Fig. 2).
The average number of electrons inside the QD is fixed in each of the so-called Coulomb dia-
monds. Hence, contiguous diamonds represent charge states that differ by just one electron. The
117126-4 Arzubiaga et al. AIP Advances 4, 117126 (2014)
FIG. 2. Stability diagram of palladium SET obtained by electromigration. Plotting the derivative of the drain current
(dI/dV) as a function of bias voltage (VSD) and gate voltage (VG) results in a pattern of diamond-shaped regions of almost
negligible conductance. These conductance features are a signature of the Coulomb blockade regime and they indicate the
transformation of the palladium nanowires into QDs after electromigration.
dimensions and shape of the diagram can be used to extract information about the studied systems.2,3,5,7
The longest dimension of the Coulomb diamonds in the VSD axis is related to the charging energy
(∆VSD = 2EC/e). The charging energy can be written as EC = e2/2C, where C is the total capacitance
of the quantum dot. The capacitance is related to the size of the QD and therefore, we can extract
information about its approximate dimensions using a simple model, such as that of a conducting
sphere into a dielectric environment. In this case we can use the expression for the self-capacitance
of a sphere C = 2εd, where ε is the absolute permittivity of the dielectric media and d is the diameter
of the conducting QD. According to these expressions, we extracted the following values from the
left (1) and right (2) diamonds, in the stability diagram of Fig. 2: EC (1) = 6.47 x 10-21 J and EC (2)
= 4.22 x 10-21 J for the charging energy; C (1) = 1.98 x 10-18 F and C (2) =3.04 x 10-18 F for the total
capacitance; d (1) = 9.1 nm and d (2) = 14 nm for the approximate diameter of the QD (assuming a
spherical shape and the value ε = 3.45 x 10-11 F/m for the silicon dioxide gate dielectric, on top of
which the QD was located). It is not unusual to observe differences in the size of the Coulomb dia-
monds, as in the present case on Fig 2. They are a consequence of the background charge in the silicon
oxide surrounding the QD, which may vary when applying the gate potential, as the charge traps in
the oxide get or release electrons. The biggest dimension of the Coulomb diamond in the VG axis is
related to the gate capacitance (∆VG = e/CG), whereas the capacitance between the quantum dot and
the drain (source) electrodes can be extracted from the positive (negative) slope of the diamonds (α+
= CG/(CG+CD) and α− = -(CG/CS). Based on these expressions, we extracted the following values
from the slopes of the diamonds in Fig. 2: CG = 3.72 x 10-20 F, CS = 6.48 x 10-19 F and CD = 1.29
x 10-18 F, which agree fairly well with literature. As expected, the capacitance with the gate electrode
was one or two orders of magnitude smaller than with the source and drain electrodes. This was
consistent with the approximate distances from the QD to the gate (150 nm, the thickness of gate
oxide), source and drain (tunnel barriers of a few nm).2,3,5 Similarly, the periodicity of the diamonds
in the VG axis is related to the gate coupling. Using the expression ∆VG = EC/eβ we can extract an
approximate value of 0.019 for the gate coupling (β). This number is close to the value expected for
a SiO2 gate dielectric of 150 nm thickness.5
We must note that although approximately a 90% of our devices showed Coulomb blockade,
only around a 15% displayed clearly distinguishable Coulomb diamonds, consistent with the charge
transport through a single quantum dot. The formation of several nanoparticles conducting in parallel
was often observed, giving as a result a pattern of superposed diamonds in the stability diagram that
was not appropriate for extracting useful information about the QDs.5
117126-5 Arzubiaga et al. AIP Advances 4, 117126 (2014)
FIG. 3. Unusual conductance features in palladium devices. Unusual features in the form of symmetric and sharp resonance
peaks appeared in a number of palladium devices. Inelastic tunneling processes involving spontaneous magnetization of the
atomic-sized palladium structures have been proposed as a possible explanation. a) Detail of the resonance peaks appearing
consistently into two clusters, around VSD =0.5 and below VSD=0.3 V (as shown in the inset). b) Temperature dependence in
the position and intensity of the peaks at high bias (left) and low bias (right).
More unusual conductance features appeared in some devices, such as the sharp resonance peaks
shown in Fig. 3. The observed conductance features appeared in two different sets, which were
symmetrically located with respect to VSD. The first set appeared at low bias and comprised a clus-
ter of small peaks of different sizes. The other one consisted of two bigger peaks (with several µS
intensity) located around VSD = 0.4 V. Same as reported in literature,14 both the intensity and position
of these peaks depended on temperature. They shifted to lower VSD values and decreased in size
when increasing the temperature. The low-bias features became imperceptible at a temperature of
about 4K, while the high-bias peaks were visible up to 10K. However, neither of these features was
affected by applied magnetic fields or VG. The origin of these peaks remains still unclear, although the
authors of the cited work ruled out several physical mechanisms after exhaustive experimental and
theoretical studies. Inelastic tunneling processes involving spontaneous magnetization were finally
proposed as a possible explanation. This hypothesis is consistent with the onset of ferromagnetism
predicted for palladium nanoparticles and atomic-sized contacts,21,22 although further experiments
would be needed for a full understanding.
These sharp resonances had only been observed in electromigrated palladium devices, according
to literature and consequently, they had been attributed to an intrinsic phenomenon particular only to
this metal. Interestingly, we also observed similar features in a nickel device (see Figure 4), which
pointed toward the fact that such peculiarities in the conductance could perhaps be attributed to the
formation of specific nanostructures, instead of to the inherent properties of palladium itself. We note
the resemblance of the observed differential conductance peaks with the ones arising from the Van
Hove Singularities (VHS) in the DOS of a one dimensional system, such as a carbon nanotube. The
117126-6 Arzubiaga et al. AIP Advances 4, 117126 (2014)
FIG. 4. Unusual conductance features in nickel devices. Sharp resonance peaks in the differential conductance curve of
an electromigrated nickel device at T=1.8K. The resemblance of these features to the peaks observed in several palladium
devices seems to indicate that they belong to the same type of resonance or excitation.
VHS would account for the sharp peaks presented in the differential conductance curves of Figures
3 and 4.
In the case of the nickel device of Figure 4 the peaks at low bias are not so well defined and
intense as those observed in the palladium device in Figure 3. Their shape and intensity are closer
to the traces recorded at higher temperatures in the palladium devices (see the graph on the right in
Figure 3(b)). With regard to the peaks at high bias, we observe that they are sharper than in the case
of palladium. The shape of the peaks observed for nickel devices is fairly asymmetric, since they
show a very abrupt drop when decreasing bias, while the decay is more gradual for increasing bias.
Qualitatively speaking, this detail resembles again the typical profile of the VHS.
Preliminary tests of electromigration with palladium alloy devices (Pd0.5Ni0.5) were also carried
out following the same strategy as explained for palladium devices. Again, we observed Coulomb
diamonds, confirming that our method was also valid when alloying the palladium with nickel up to
a 50 atomic %. This opened up the possibility of fabricating and studying a series of alloyed devices
covering the whole range from 0 to 50 atomic % nickel content. We would expect Pd to play a role in
the magnetic properties, due its strong exchange interactions. However, studying electronic correla-
tions at this level implies working at dilution-refrigerator temperatures for enabling the observation
of the individual electronic energy levels of the metallic grains,2 which for the time being has been
impossible for us.
In conclusion, we have obtained devices working in the single electron transport regime by per-
forming feedback-controlled electromigration of palladium nanowires. Breaking palladium nanowires
at low temperature by a gradual electromigration process resulted in the simultaneous formation
of closely separated nanoelectrode pairs (source and drain) and metallic quantum dots. The newly
formed quantum dots showed an adequate coupling to source, drain and back-gate electrodes for
exploring single electron physics. The formation and subsequent measurement of these nanostruc-
tures inside a virtually inert atmosphere of a He cryostat allowed skipping additional fabrication steps.
Additionally, we have shown that the fabrication method can be extended to palladium-based alloys,
such as Pd0.5Ni0.5, which offer the opportunity of studying magnetic effects. This result suggests that
Pd could be used as a medium for driving the formation of SETs with small amounts of other elements,
which is an attractive prospect. Precisely, one of the difficulties of obtaining SETs with magnetic
nanoparticles is that they tend to oxidize, since metallic nanoparticles have enhanced reactivity when
compared to bulk metals. Hence, the proposed approach, in which the samples are fabricated and
measured in situ, would be most convenient for studying non - noble metals.
The authors would like to acknowledge financial support from the European Union 7th Frame-
work Programme under the European Research Council (Grant 257654-SPINTROS), the Marie Curie
Actions (PIRG06-GA-2009-256470), and the NMP project (NMP3-SL-2011-263104- HINTS); the
Spanish Ministry of Economy under Project No. MAT2012-37638 as well as the Basque Government
117126-7 Arzubiaga et al. AIP Advances 4, 117126 (2014)
through Project No. PI2011-1. The author L. Arzubiaga would like to thank J. A. Arregi, O. Idigoras
and L. Fallarino from the Nanomagnetism Group of CIC nanoGUNE for their advice regarding the
preparation of metallic alloys by co-sputtering.
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