development of one-dimensional band structure in artificial gold chains ken loh ph.d. student, dept....
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Development of One-Dimensional Development of One-Dimensional Band Structure in Artificial Gold Band Structure in Artificial Gold
ChainsChains
Ken LohPh.D. Student, Dept. of Civil & Environmental Engineering
Sung Hyun JoPre-candidate, Dept. of Electrical Engineering & Computer Science
EECS 598 Intro. To NanoelectronicsSeptember 27, 2005
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Research MotivationResearch 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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Experimental PreparationExperimental 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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Scanning Tunneling Microscope (STM)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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
STM Operation PrinciplesSTM 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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Experimental SampleExperimental Sample The NiAl(110) single crystal substrate
Prepared by alternating cycles of Ne+ sputtering and annealing @ 1300 K.
Linear Au chains added one atom at a time @ 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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Linear Au ChainLinear Au Chain
Above: STM topographic images showing intermediate stages of building a Au20 chain.
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Stability IssuesStability 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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Electronic Properties of Au ChainElectronic 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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Conductivity SpectraConductivity Spectra Conductivity spectra for bare
NiAl and for Au chains with different lengths.
Spectra taken at center of chain Tunneling gap set at
VVsample 5.2
nAI 1
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
What About Au?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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
More Au AtomsMore 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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Quantum Well, Wire & DotQuantum 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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
The Infinite Potential Well 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
0( ) 0
( ) 0 and P
P
E x E x L
E x x x L
2 2
0* 2
( )( ) ( ) 0
2
d xE x E x x L
m dx
2 2
* 2
( )( ) ( ) ( ) 0 and
2
d xx E x x x L
m dx
(0) ( ) 0L
( ) sin( ) sinn n
n xx C K x C
L
*
E
x0x x L
0E E
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
The Infinite Potential Well The Infinite Potential Well The allowed energy and the corresponding wave function
The first five energy levels and wave functions
2 2 2 22
0 * * 2( )
2 2K
KE E E n
m m L
2( ) sinn
n xx
L L
0x x L123
4
5
0x x L1E2E
3E
4E
5E
(a) (b)
(a) Energy levels
(b) Wave functions
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
TunnelingTunneling The electron can pass through the barrier, even if the
region of space is classically forbidden.
aE
bE
cE0x x L
A B C
aE
bE
cE0x x L
A B C
E
An electron approaches a finite potential barrier
B: Classically forbidden region
*
The probability density function
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
TunnelingTunneling
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)
* 2(2 / )( )aj m E E xjKxa Ae Ae
* 2(2 / )( ) ( 0)bm E E xb bAe E E
* 2 * 2 * 2
* 2 * 2
(2 / )( ) (2 / )( ) (2 / )( )
(2 / )( ) (2 / )( )
( ) ( )
C ( )
c b c
c b
j m E E x m E E L j m E E xc b
j m E E x m E E L
x L e Ae e
e C Ae
x L
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
TunnelingTunneling 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)
* 2(2 / )( )bm E E xb Ae
* 22 (2 / )( )2* bm E E xA e
* 2*
2 (2 / )( )
*
( )
(0)bm E E Lb b
b b
Le
(e.g. as for , )
*01ev, 2 & bE E L nm m m
* 292 (2 / )( )
1.1 10bm E E Le
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Tunneling Tunneling The tunneling probability of arbitrary shape potential (WKB
approximation)
1
0 0
1
0
( ) 2 * ( )
2 2 * ( )
( ) (0) (0)x x
LB
k x dx m U x E dx
II II II
m U x E dx
x e e
T e
Wave function of a particle with energy E tunneling through a quantum barrier
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Resonant Tunneling DiodeResonant 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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Resonant Tunneling Diode 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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
The Width of ResonanceThe Width of Resonance
Linewidth of current resonance peak
The broadening mechanisms Inhomogeneous broadening Homogeneous broadening
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
The Width of ResonanceThe 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.
E t
E
t
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Experiment ProcessExperiment 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.
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Experiment 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;
2( )n k
/dI dV
2/ DOS ( ) ( : coefficient)n n ndI dV E c c
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Conductivity Patterns versus BiasConductivity Patterns versus Bias We can expect that each conductivity pattern has peaks
with finite width (linewidth)
2/ DOS ( ) n ndI dV E c
The contribution of to conductivity patterns will vary continuously according to the bias
depends on energy and has a peak with finite width
2
n
nc
Experimental results
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Formation of Energy BandsFormation 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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
The Lowest peak?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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 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 En in quantum well
, ( )nc E
Selected coefficients obtained from the fitting procedure of conductivity patterns
2/ DOS ( ) n ndI dV E c
nc
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
Dispersion RelationDispersion 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))
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 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 RelationDispersion Relation
2 2 2 22
0 * * 2( )
2 2n
KE E E n K n
m m L L
2 20( ) / 2 *E k E m k
( )nE k
0 00.68 , * 0.5E m m
Dispersion relation of electronic states for a Au20 chain
Development of One-Dimensional Band Structure in Artificial Gold ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 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 Au20 with tunneling gap set at Vsample =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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 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 ChainsDevelopment of One-Dimensional Band Structure in Artificial Gold ChainsEECS 598 Nanoelectronics – Tuesday, September 27, 2005
ConclusionConclusion
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