Development of One-Dimensional Band Structure in Artificial Gold Chains Ken Loh Ph.D. Student, Dept. of Civil & Environmental Engineering Sung Hyun Jo

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.


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.


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.


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.


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.


Linear Au ChainLinear Au Chain

Above: STM topographic images showing intermediate stages of building a Au20 chain.


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.


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


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


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


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


Quantum Well, Wire & DotQuantum Well, Wire & Dot Structure examples

Bulk Quantum Well

Quantum Wire

(On-edge growth & modulation doping) Quantum Dot


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


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


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


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


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


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


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


Resonant Tunneling Diode Resonant Tunneling Diode

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


The Width of ResonanceThe Width of Resonance

Linewidth of current resonance peak

The broadening mechanisms Inhomogeneous broadening Homogeneous broadening


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


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.


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


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


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.


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


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.



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


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))


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


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)


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)


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

Documents

Development of One-Dimensional Band Structure in Artificial Gold Chains Ken Loh Ph.D. Student, Dept. of Civil & Environmental Engineering Sung Hyun Jo