Development of One-Dimensional Band Structure in Artificial Gold Chains Ken Loh Ph.D. Student, Dept. of Civil & Environmental Engineering Sung Hyun Jo Pre-candidate, Dept. of Electrical Engineering & Computer Science EECS 598 Intro. To Nanoelectronics September 27, 2005

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Research Motivation  While band structure engineering in semiconductor technology has been successful, it is only the beginning for the tailoring of electronic properties of nanosized metal structures.  Critical length scale smaller than semiconductors  Due to high electron density and efficient screening in metals  Possessing control over size-dependent electronic structures allow an adjustment of intrinsic material properties for a wide range of applications.  Purpose is to utilize experiments to determine the interrelation between geometric structure, elemental composition, and electronic properties in metallic nanostructures.

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Experimental Preparation  Preparation and analysis of well-defined nanosized structures remain the biggest challenge for studying the transition from atomic to bulklike electronic behavior.  Experiments take advantage of the scanning tunneling microscope (STM) to manipulate single atoms on metal surfaces.  Linear gold (Au) chains were built on Nickel Aluminide, NiAl(110), one atom at a time.

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Scanning Tunneling Microscope (STM)  Scanning Tunneling Microscope (STM) is used widely to obtain atomic- scale 3-dimensional profile images of metal surfaces.  Applications include,  Characterizing surface roughness  Observing surface defects  Determining the size and conformation of molecules and aggregates STM image, 7x7 nm, of a single zig-zag chain of Cs atoms (red) on GaAs(110) surface. STM image, 35x35 nm, of single substitutional Cr impurities on Fe(001) surface.

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 STM Operation Principles  Electron clouds associated with a metal surface extends a very small distance above the surface.  A very sharp tip is treated so that a single atom projects from its end is brought close to the surface.  Strong interaction between the electron cloud on the surface and that of the tip causes an electric tunneling current to flow under applied voltage  Tunneling current rapidly increases as distance is decreased  Rapid change of tunneling current allows for atomic resolution Left: STM image of standing wave patterns in the local density-of-states of a Cu(111) surface.

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Experimental Sample  The NiAl(110) single crystal substrate  Prepared by alternating cycles of Ne + sputtering and 1300 K.  Linear Au chains added one atom at a 12 K.  Preferential adsorption side as bridge positions on Ni troughs which alternated with protruding Al rows on alloy surface  Their electronic properties were derived from scanning tunneling spectroscopy (STS) to reveal the evolution of a 1D band structure from a single atomic orbital.

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Linear Au Chain Above: STM topographic images showing intermediate stages of building a Au 20 chain.

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Stability Issues  At low tunnel resistance (V/I < 150 kOhm), single Au atom can be moved across the surface  Jumps from one to the next adsorption site as it follows trajectory of the tip  “Pulling mode”  Increasing the resistance above 1 GOhm provide stable conditions for imaging and spectroscopy  Controlled manipulation used to build 1-D chains along Ni troughs  Atom-atom separation given by distance between Ni bridge sites (2.89 Å)  Individual Au atoms indistinguishable in chain, thus indicating a strong overlap of their atomic wave functions.

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Electronic Properties of Au Chain  Electronic properties of Au chain determined by STS.  Detects derivative of tunneling current as a function of sample bias with open feedback loop  Tunneling conductance (dI/dV) gives measure of local density-of-state (DOS)  Probing empty state of NiAl(110) at positive sample bias reveals a smooth increase in conductivity.  Reflects DOS of the NiAl sp-band

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Conductivity Spectra   Conductivity spectra for bare NiAl and for Au chains with different lengths.  Spectra taken at center of chain  Tunneling gap set at

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 What About Au?  In contrast, STS of a Au monomer dominated by a Gaussian-shaped conductivity peak centered at 1.95 V.  Enhanced conductance is attributed to resonant tunneling into an empty state in the Au atom.  Localization outside the atom in the tip-sample junction points to a lowly decaying state with sp character  Arises from hybridization of atomic Au orbitals and NiAl states

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 More Au Atoms  Moving second Au atom into neighbor position on the Ni row leads to a dramatic change of electronic properties.  Single resonance at 1.95 V splits into a doublet with peaks at 1.50 and 2.25 V  Indicates strong coupling between the two atoms  Individual conductivity resonances become indistinguishable for chains containing more than 3 atoms  Due to overlap between neighboring peaks and finite peak width of 0.35 V  Continue adding more atoms to the chain cause downshift of lowest energy peak

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Quantum Well, Wire & Dot  Structure examples Bulk Quantum Well Quantum Wire (On-edge growth & modulation doping) Quantum Dot

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 The Infinite Potential Well  The potential energy  The time independent Schroedinger’s equation  Since the electron cannot possible be found outside the well, the probability distribution function ( ) must be zero. And the boundary condition then

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 The Infinite Potential Well  The allowed energy and the corresponding wave function  The first five energy levels and wave functions (a) (b) (a)Energy levels (b)Wave functions

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Tunneling  The electron can pass through the barrier, even if the region of space is classically forbidden. An electron approaches a finite potential barrier B: Classically forbidden region The probability density function

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Tunneling  The wave function of the incident electron in region A  In the forbidden region (neglecting the reflection at the boundary)  At, must be continuous. Then, in region C (neglecting the reflection at the boundary)

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Tunneling  The probability density function in forbidden region (the region B)  The probability density function is a decaying exponential function  The probability that the electron will penetrate the barrier (by neglecting the reflection at the boundaries) ( e.g. as for, )

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Tunneling  The tunneling probability of arbitrary shape potential (WKB approximation) Wave function of a particle with energy E tunneling through a quantum barrier

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Resonant Tunneling Diode  Band diagram of resonant tunneling diode (a)Band diagram of n-type resonant tunneling structure (b)The ground state wave function in the well

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Resonant Tunneling Diode  Band diagram and voltage-current characteristic of a resonant tunneling structure under different bias

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 The Width of Resonance  Linewidth of current resonance peak  The broadening mechanisms  Inhomogeneous broadening  Homogeneous broadening

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 The Width of Resonance  Inhomogeneous broadening mechanisms caused by inhomogeneities of the structure  Quantum well thickness fluctuations  Alloy fluctuations in the well and barriers  Homogeneous broadening mechanisms caused by lifetime broadening  The uncertainty principle  The energy of a quantum mechanical state can be obtained with highest precision (small ), if the uncertainty in time is large, i.e. for transitions with a long lifetimes. The energetic width of transitions given by the uncertainty principle is called the natural linewidth. is the time that the electron dwells in the quantum well.

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Experiment Process  The one of the goals is to reveal the dispersion relation (E-K diagram) of Au chains and to verify the related theories.  What we can do are the preparation of nanosized Au chains & the measurement of conductance versus applied voltage from the samples.  Then how?  From the results of dI/dV patterns, we can obtain a set of finite number of discrete energy levels E n. After this step, by using an applicable theoretical dispersion relation model, the E-K relation can be described. Or inversely, we can verify the correlated theories.

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Experiment  The observed conductivity pattern ( dI/dV ) results from  The electron transport through the 1D quantum well is limited to a finite number of E n  The conductivity is determined by the squared wave function  The each energy levels has the finite width  More than one state contributes to the differential conductance at a selected sample bias patterns are superposition of several wave functions;

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Conductivity Patterns versus Bias  We can expect that each conductivity pattern has peaks with finite width (linewidth) The contribution of to conductivity patterns will vary continuously according to the bias depends on energy and has a peak with finite width Experimental results

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Formation of Energy Bands  We already know well regarding a single atom and bulk itself. And we also know some theories. However we need to confirm those things again by actual experimental data. Experimental results As the N atoms are brought together, the discrete energy level split into N levels. (The Bonding & the anti-bonding orbital) Each conductivity peaks is indistinguishable The energy band is formed

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 The Lowest peak?  In density of states of 1D, there is a instant start. As the number of the Au atoms goes to infinity, the result can be more ideal. Experimental results

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005  To determine the coefficient is fitted to the observed dI/dV pattern  It is reasonable to consider the position of energy that has peak value as the energy position of an electronic state E n in quantum well Selected coefficients obtained from the fitting procedure of conductivity patterns

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Dispersion Relation  Because of the well defined geometry of Au chains on NiAl(110), a 1D quantum well with infinite walls can be used. And the presence of a pseudo band gap in the DOS of NiAl(110) locate above the Fermi level (a) (b) (a) Real space representation of the NiAl (110) surface (b) The first layer is rippled (S. C. Lui et al. Phy. Rev. B (1989))

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005  The allowed energy  The points are aligned on a parabolic curve. From fitting to the theoretical dispersion relation Dispersion Relation Dispersion relation of electronic states for a Au 20 chain

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005  Mapping the conductivity at different positions along a chain reveals a characteristic intensity pattern (A)Conductivity spectra taken along Au 20 with tunneling gap set at V sample =2.5V, I=1nA (C) Vertical cuts through dI/dV spectra shown (A) at three exemplary energies At the both ends of the chain there are non ideal properties (e.g. surface state)

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005  The 1D particle in the box model oversimplifies the electronic properties in Au chains  The interaction between single Au atoms in the chains results from a direct overlap between the Au wave functions and substrate-mediated mechanisms (e.g. Friedel oscillation)  Beside forming direct chemical bonds at short separations, atoms and molecules interact indirectly over large distance via relaxation in the lattice of substrate atoms on which they are absorbed.  The effect of the indirect interaction depends on the adsorbate separation and is important for adsorbate-metal systems with weak ad- ad bonds or a weakly corrugated surface.  The strong electron-phonon coupling occurring in 1D system changes the periodicity along atomic chains (Peierls distortion)

Development of One-Dimensional Band Structure in Artificial Gold Chains EECS 598 Nanoelectronics – Tuesday, September 27, 2005 Conclusion  This experiments demonstrate an approach to studying the correlation between geometric and electronic properties of well- defined 1D structures  The investigation of 2D and even 3D objects built from single atom is envisioned