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 / WP4.1: LT-UHV 4 STM probes systems under an SEM planar testing
Lead participant: Krakow (P10) / 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 afully 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 AtMolpartners in 2013(NanoLett. 13, 1192 (2013)).The I-V curves have to be recorded to determine the number of surfaceconduction channels of these atomic wires as a function of the voltage and the variation of its conductance withits length. For those measurements, it is necessary that the conductance measurements be performed on the UHV nanoprobewith a precision below 1 nm. Since the current resolution limit of the Omicron nanoprobe system operating in P10-Krakow and P11-Singapore is significantly above this limit, Deliverable 4-D1.2 is related to testing the UHV nanoprobesystem 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 x1and 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 nanowirecan 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 contributionsfrom 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)