Development of One-Dimensional Band Structure in Artificial Gold Chains

1
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

2
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.

3
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.

4
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.
5
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.
6
Experimental Sample

• The NiAl(110) single crystal substrate
• Prepared by alternating cycles of Ne sputtering
  and annealing _at_ 1300 K.
• Linear Au chains added one atom at a time _at_ 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.

7
Linear Au Chain
Above STM topographic images showing
intermediate stages of building a Au20 chain.
8
Stability Issues

• At low tunnel resistance (V/I lt 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.

9
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

10
Conductivity Spectra

• Conductivity spectra for bare NiAl and for Au
  chains with different lengths.
• Spectra taken at center of chain
• Tunneling gap set at

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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

12
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

13
Quantum Well, Wire Dot

• Structure examples

Quantum Well
Bulk
Quantum Wire (On-edge growth modulation doping)
Quantum Dot
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The Infinite Potential Well

• The potential energy
• The time independent Schroedingers equation
• Since the electron cannot possible be found
  outside the well, the probability distribution
  function ( ) must be zero. And the
  boundary condition
• then

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The Infinite Potential Well

• The allowed energy and the corresponding wave
  function
• The first five energy levels and wave functions

(a)
(b)

1. Energy levels
2. Wave functions

16
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
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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)

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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
,
)
19
Tunneling

• The tunneling probability of arbitrary shape
  potential (WKB approximation)

Wave function of a particle with energy E
tunneling through a quantum barrier
20
Resonant Tunneling Diode

• Band diagram of resonant tunneling diode

1. Band diagram of n-type resonant tunneling
   structure
2. The ground state wave function in the well

21
Resonant Tunneling Diode

• Band diagram and voltage-current characteristic
  of a resonant tunneling structure under different
  bias

22
The Width of Resonance

• Linewidth of current resonance peak
• The broadening mechanisms
• Inhomogeneous broadening
• Homogeneous broadening

23
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.

24
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 En . 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.

25
Experiment

• The observed conductivity pattern ( dI/dV )
  results from
• The electron transport through the 1D quantum
  well is limited to a finite number of En
• 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

26
Conductivity Patterns versus Bias

• We can expect that each conductivity pattern has
  peaks with finite width (linewidth)

Experimental results
The contribution of to
conductivity patterns will vary continuously
according to the bias depends on energy
and has a peak with finite width
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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
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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
29

• 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 En in quantum well

Selected coefficients obtained from the fitting
procedure of conductivity patterns
30
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. B39 13149 (1989))
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Dispersion Relation

• The allowed energy
• The points are aligned on a parabolic
  curve. From fitting to the theoretical dispersion
  relation

Dispersion relation of electronic states for a
Au20 chain
32

• Mapping the conductivity at different positions
  along a chain reveals a characteristic intensity
  pattern

At the both ends of the chain there are non ideal
properties (e.g. surface state)

• Conductivity spectra taken along Au20 with
  tunneling gap set at Vsample 2.5V, I1nA
• (C) Vertical cuts through dI/dV spectra shown (A)
  at three exemplary energies

33

• 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)

34
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