AtMol deliverable reporting
4D1.2: Characterization of the surface conductance anisotropy
along and across a metallic nanowire grown on Ge(001)
Unit 1: Atomic scale interconnection machines
Lead participant: Krakow (P10)
WP4.1: LT-UHV 4 STM probes systems under
an SEM planar testing
Other participants: -
Person Months (Krakow): foreseen 26/real 12
Person Months (other participant): -
Start date: M 6
Planned end date: M 24
Real end date: M 36
Introduction:
One goal of AtMol is to measure the conductance of a single surface atomic wire in a fully
planar and atomically ultra clean condition and to compare the dI/dV electronic spectrum of
this wire to the one predicted by DFT calculations and published by AtMol partners in 2013
(NanoLett. 13, 1192 (2013)). The I-V curves have to be recorded to determine the number of
surface conduction channels of these atomic wires as a function of the voltage and the variation
of its conductance with its length. For those measurements, it is necessary that the conductance
measurements be performed on the UHV nanoprobe with a precision below 1 nm. Since the
current resolution limit of the Omicron nanoprobe system operating in P10-Krakow and P11Singapore is significantly above this limit, Deliverable 4-D1.2 is related to testing the UHV
nanoprobe system capability for practical conductance measurements of a metallic nanowire
supported on the relevant semiconductor surface. Furthermore, it is important that the wires are
sufficiently decoupled electronically from the substrate, so that they could not change the
electronic band structure of the wire/substrate interface causing any anisotropy in the surface
plane.
Surface conductance 4-probe measurements:
The 2- probe conductance measurements described in detail in the report on deliverable 4-D1.1
are heavily dependent on the electronic properties of the tip to surface contact interface and its
contact resistance, difficult to control unless the contact is facilitated by the Ohmic contacts of
the metallic pads, such as Ag nano-islands and wires. Such a difficulty is not occurring for the
conductance measurements in a fully 4-probe configuration as described below and in
references [3-6]. The theoretical analysis of conductance on micrometer scale is done within
the framework of the well-known differential equation for the electrostatic potential Φ. The
equation relevant for the experimental setup reads:
.ΔΦ=α I [δ(x-x1)-δ(x-x2)]
where σ stands for the conductance of the sample and Δ is the Laplace differential operator. On
the right hand site there is the source of the current I at point x1 and the sink at the point x2,
where the current flows from the sample. α is a numerical constant depending on the detailed
contact geometry. The equation has two important features useful when analyzing the
experimental data. The first one is its linearity backing the notion of resistance, hence allowing
comparison of the data acquired for different currents. The other feature is the scaling behavior
of the equation. For any a>0 the equations:
σ. ΔaxΦ(ax)=[δ(ax-ax1)-δ(ax-ax2)]
and
σ .ΔxΦ(x)=a-dim+2[δ(x-x1)-δ(x-x2)]
are equivalent where dim stands for the dimension of the current flow. This makes evident how
solutions on different scales are related. In particular in two dimensions, there is no dependence
on the scale. This is also evident when referring to the formulas suited to our experimental setup
as described below in Fig. 1.
Fig. 1. Geometry of the 4-probe surface conductance measurements.
The experimental geometry of the measurements presented in Fig. 1 is such that the outer
electrodes supply the current to the sample. The inner ones measure the voltage drop for and
inter tip distance s. The four probes are in one line. If the current is confined to a thin layer,
there is effectively a two dimensional electronic conduction process and the resistance reads:
R2D=ln[(1-x)/(1+x)]/(πσ2dim)
where x=s/D. It makes clear, that no dependence on the absolute distance D or s remains. On
the contrary and for a three dimensions electronic conduction regime, it comes:
R3D= 1/(πσ3dim)D-1 x /(1-x2)
And in this 3D case, one cannot get rid of the absolute scale. A 4 probe measurement is therefore
a good way to characterize the 2D or 3D character of the electronic conduction process.
Description of the Deliverable results:
Metallic Ag nanowires for characterisation were fabricated following the procedure established
in AtMol Task 1T3.2, i.e., a dose equivalent to 4ML of Ag atoms was deposited from an
effusion cell on clean and well reconstructed Ge(001) surface kept elevated temperature (around
675K). The resulting structure of the nanowires, imaged by the nanoprobe high resolution UHV
SEM is presented in Fig.2 below. Typically, nanowires from few tens to few micrometers in
length are grown under those conditions with a typical width of 50 nm. 2-probe conductance
measurements [1-2] show the “Ohmic” character of the wire conductance with a slope for 0,5
m wire equal to 1/300. With STM manipulation, the Ag nanowire can be cut into 2 or more
sections and the resulting resistance is proportional to the wire length. One should note that in
a 2 probe measurements, the total measured resistance contains also the contributions from the
contact resistances of the 2 applied probes, so it is much larger than Ag nanowire resistance
alone.
Fig. 2. SEM image of the Ag nanowire obtained by depostion of 4ML o silver on Ge(001) surface kept
675 K. The 2 probe conductance measurements for roughly 0,5 m long wire yielded “Ohmic” I(U)
dependence with the conductance 1/R = 1/(300). The top right panel shows the situation after cutting
the wire into 2 sections.
In order to test any anisotropy in the surface conductance caused by the Ag nanowire supported
by the Ge(001) surface, P10-Krakow has used various configurations of the four point-probe
measurements [3-6]. In each configuration, the two Fig. 1 inner STM tips are measuring the
voltage drop and two outer STM tip act as contacts through which the current was applied. In
every measurement the inner probes (voltage probes) were placed in one position and two outer
probes (current probes) where moved in such a way that the angle between axis of symmetry
of the voltage probes and the current probes were changed from 0 to 90. A schematic outline
of this situation for the 4-probe geometry of measurements is shown in Fig. 3.
Fig. 3. A scheme of the four point-probe conductance measurement for Ge(001) supported Ag
nanowire. A) a view from above, B) a side view, C) SEM image of the 4-probe system in one
of the measurement configuration. Two inner probes are measuring the voltage drop, and two
outer probes are applying and collecting the current. The voltage probes could be connected
or not to the wire, but in the last situation they were kept in contact with Ge(001)substrate very
close to the 2 ends of the wire.
A comparison was also made with the 4-probe conductance measurements for the clean,
reconstructed Ge(001) surface without nanowires preserving the same geometry and spacing
between the probes as seen in Fig. 4.
Fig. 4: 4-probe conductance measurements for the clean, reconstructed Ge(001) (nominally
undopped, n-type) surface. The R over x dependence (x=s/D) obtained for various distances of
the outher probes D are fitted with the equation describing 2D model of the surface
conductance.
Conclusion:
1) When the voltage probes are electrically connected to the wire, the voltage drop along the
wire (so at the same time resistance) between inner probes oscillates near zero, i.e., it is very
small, below the accuracy of our measurements (voltage drop < 50 V), effectively the wire is
shorting the conduction path between the current probes;
2) When the voltage probes are connected to the substrate in a close vicinity of the nanowire
ends (but not providing an “Ohmic” contact to the wire) the situation is changing, in such a way
that the drop of voltage corresponds to the one measured in the linear 4-probe geometry for the
substrate (Ge(001)) alone, providing that the inner probe separation is essentially the same as
the wire length. When the voltage probes are in one line with current probes the voltage
drop/resistance reaches the maximum value. With the change of the outer probe axis angle the
resistance is decreasing to reach the minimum value for perpendicular orientation of the current
probes with respect to the voltage probe axis. This is quite expected situation for clean
germanium since for a perpendicular orientation, the potential at both voltage probes location
is the same because the probes are at the same distance from both current tips. It is clear that
the presence of Ag nanowires aligned along the reconstruction rows of the Ge(001) surface
alone is not causing any anisotropy of the substrate surface conductance. The experiment
demonstrates the feasibility of the 4-probe conductance measurements for semiconductor
surface supported nanowires with the accuracy provided by the current version of the Omicron
4-probe system.
With those measurements by P10-Krakow about the surface conductance anisotropy along and
across a metallic nanowire grown on Ge(001) semi-conductor surface the Deliverable 4-D1.2
was delivered at M36.
Ref. Publications:
1. M. Wojtaszek, M. Kolmer, S. Godlewski, J. Budzioch, B. Such, F. Krok, M. Szymonski,
“Multi-probe characterization of 1D and 2D nanostructures assembled on Ge(001)
surface by gold atom deposition and annealing” in “Advances in Atom and Single
Molecule Machines”, Springer Series on Advances in Atom and Single Molecule
Machine, ed. Christian Joachim (2012) ISBN 978-3-642-28171-6.
2. Hofmann, P., Wells, J. W.: Surface-sensitive conductance measurements. J. Phys.:
Condens. Matter 21,013003 (2009)
3. W. Mönch, Semiconductor Surfaces and Interfaces, Springer-Verlag, Berlin Heidelberg
New York, 2001
4. E. Landemark, C. J. Karlsson, L. S. O. Johansson, R. I. G. Uhrberg, Phys. Rev. B 49,
16523 (1994)
5. C. Jeon et al., Phys. Rev B 74, 125407 (2006)
6. P. E. J. Eriksson, M. Adell, K. Sakamoto and R.I.G. Uhrenberg, Phys. Rev. B 77,
085406 (2008)