The electronic structures of 2D atomically

uniform thin film

S.- J. Tang, T. Miller, and T.-C. ChiangDepartment of Physics, University of Illinois at Urbana-

Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080

Surface state and Quantum well state

Surface

Thin Film

Vacuum

Vacuum

Substrate

SS

SSqw

Photoemission

Re d uc e d wa ve ve c to r

Va le nc e b a nd

C o n d uc tio n b a n d

Ef

Ev

EF

Ei

Ele

ctr

on

En

erg

y

Excited electron and hole states

Excited hole state

Excited electron state (photoelectron)

Photon

(Final)

(Initial)

Work function

Ef –Ei = Ek +e = Ei+

k

One particle picture to many body effect

Many body interaction

Spectral function 220 ),(Im),(Re)(

),(Im),(

kkk

kkA

Spectra function in the form of a Lorentzian

I ~

Photoemission intensity

Quasi particle One state -----> One single Lorentzian peak

Quantum well states

Nt

EEnk is

2

)()(2

)( kEEn

Bohr-Sommerfeld quantization rule

n: Quantum number, 1,2,3,..

: interface phase shift

Nt: thickness

Ph

oto

em

issi

on

inte

nsi

ty (

arb

. u

nits

)

-3 -2 -1 0Energy (eV)

4

6

8

10

13

17

23

25

27

36

42

Ag/Ge(111)

(ML)

Normal emission

qws

ss

All the information of substrate bands are embedded in i

Quantum size effect

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

Bin

ding

Ene

rgy

(eV

)

0.100.00-0.10k||(Å

-1)

n=1

n=2

n=3

n=4

15 ML 16 ML

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

Bin

ding

Ene

rgy

(eV

)

1.31.21.11.00.9kperpendicular(Å

-1)

Ag bulk band perpendicular to the surface

Ag qws bands parallel to the surface, which

are normally similar to the corresponding

bulk band dispersions

Atomically uniform film revealed by photoemission

qws peak

1 ML 1.5 ML

1 ML

qws peak

1 ML 2 ML

Atomically uniform + quantum size effect

Thickness changes (uniform films)

The allowed quantized k’s changes

The energy positions of the QWS changes

Properties of films change

Surface energy, work function, thermal stability, adsorption, superconductivity transition temperature, magnetic interlayer coupling……….

J. J. Paggel, T. Miller, and T.-C. Chiang, Phys. Rev. Lett.81, 5632 (1998); Science 283, 1709 (1999)

Substrate effect

Substrate

Thin film

My three major findings on substrate effect 1. Many body interaction between the quantum well

state and substrate state

Kink dispersion S.-J. Tang, L. Basile, T. Miller, and T.-C. Chiang, Phys. Rev. Lett. 93, 216804 (2004)

2. Strong hybridization between the surface state and substrate bands

Display of HH,LH and SO

major substrate bands

S.-J. Tang, T. Miller, and T.-C. Chiang, Phys. Rev. Lett. 96, 036802 (2006).

3. Diffraction from the substrate surface

QWS of second kind

S.-J. Tang, Y. R. Lee, S. -L. Chang, T. Miller, and T. -C. Chiang, Phys. Rev. Lett. 96, 216803 (2006)

Surface Brillouin zone for Ag(111) and Ge(111)

M

K M

'M

G

K K

KK

K

'M

M

M

'M

The band structures of atomically uniform thin film of Ag/Ge(111)

21 ML ss QW 1 2 3 4 5

K M

Band dispersions of Ag/Ge(111)

Two types of splitting !!

KinkDramatic linewidth change of QWS across substrate band edge

Layer resolutionThe band structures of QWS in 8.6 ML are equal to the linear combination of 8ML and 9ML.

Emission Angle ()

ss QW n= 1.2 …

Type 2

Type 1

Atomically uniform filmAg/ Ge(111)

Atomically Uniform Film

1. moving discretely from its 8 ML ( 9 ML) position to the 9 ML (10 ML) position.

2. The 8ML (9ML) peak is absent in the 9ML (10ML) spectrum and vice vesra.

Quantum well peak

Non quasiparticle behavior

The two-peak line shape across the substrate band edge is non quasiparticle

2/1

0

2

1Im

1Im

1

sqq iEEVAiEEGE

dgiE

ViEEEG

E

sqq

0

21

0

0

EE

Ag

One dimensional form of the density of the states for the substrate band edge

Spectral function

Retarded Green function for a single electron state entering into the bulk band continuum.

Surface state

2D electron state residing on or near the surface

The product of reduced symmetry

)cos()( pzez qz

iqpk

Nt1/q

When 1/q NtDecay length Thickness

Substrate

film

Vacuum

Something interesting happens !!!

Surface state touches down to the substrate

The anomalous lineshape of the surface state at

lower thickness P

hoto

emis

sion

Inte

nsity

(A

rb. U

nits

)

-3 -2 -1 0Energy (eV)

6 ML

7 ML

8 ML

9 ML

10 ML

hv = 50 eV

Thickness dependence SS

QWn = 1

n = 2

Ph

oto

em

issi

on

In

ten

sity

(A

rb.

Un

its)

-3 -2 -1 0 Energy (eV)

9 eV

22 eV

50 eV

Thickness 6ML

Photon energy dependence SS

QWn = 1

Ag/Ge(111), Normal emission

Quantum well state ? Substrate state ?

Thickness dependence of the surface state dispersion

Decay length of Ag surface state 12ML

Surface state energy shifts with the thickness

VtE )(

)2exp()0( tE

New finding !!!

Emission Angle ()

T. C. Hsieh, T. Miller, and T. C. Chiang, Phys. Rev. Lett. 55, 2483 (1985)

11.7

Thickness dependence of the surface state dispersion

Strong hybridization between the surface state and substrate states makes the photoemission intensity proportional to the density of states for substrate bands

2 2

SI E E E g E M g E

3

1

i

i i i

Ag E

E E E E

Three major Ge bands of HH , LH and SO cross this area

Emission Angle ()

Fitting the data with the model

(a)

(b)

(c)

(a)

(b)

(c)

Fitting result from the model

Image processed

Comparison with the calculated Ge bands and other measurements

En

erg

y (

eV

)

-0.6

-0.4

-0.2

0.0

k|| (Å-1)

-0.2 -0.1 0.0 0.1 0.2

En

erg

y (

eV

)

-0.6

-0.4

-0.2

0.0

(a)

Theory Expt

Expt

(b)

HH

LH

SO

HH LH SO Expt

Cyclotron measurements

0.30 0.034 0.21

0.33 0.043 0.095

Effective Mass

Spin-orbital Splitting

Expt 0.301 eV

0.296 eV Optical measurements

Quantum well state of the second kind

M (Ge)

Ag bulk bands projected to (111) direction

Surface Brillouin zone for Ag(111) and Ge(111)

M

K M

'M

G

K K

KK

K

'M

M

M

'M

Vacuum

Substrate

(k||,k) (k||,-k) (0,-k) (0,k) (-k||,k)(-k||,-k)

First Kind

The Ge substrate working as a diffraction grating

),( kk

M

GKKMM

MKG

2

Vacuum

),( kkM

),( kk

M),( kkM

1 2 3 4

Second Kind

Generalized Bohr-Sommerfeld quantization rule

  

,d= Nt , t=2.36 Å for 1ML of Ag in (111) direction

4,3,2,1,2*)( 4321 nndkkkk

ndEkEkEkEk 2*))()()()(( 4321

ndEK NEW 2*)(

Due to energy conservation

ndEkEkEkEk 2*))()()()(( 44332211

Hybridization between qws of the first kind and qws of the second kind

Thickness dependence of hybridization between two different kinds of quantum well

states

9MLbands and bands anti-cross interactions

'4

3

2

1

5

4

3

2

1

000

000

000

000

0000

0000

0000

0000

0000

ˆ

EVVVVV

EVVVVV

EVVVVV

EVVVVV

VVVVE

VVVVE

VVVVE

VVVVE

VVVVE

H

V (d) = ?

Relationship between quantum well state and surface state from 5 ML

down to 1ML

Pho

toem

issi

on In

tens

ity (

Arb

. Uni

ts)

-3 -2 -1 0Energy (eV)

Ge(111)

2x8

1 ML1 ML

5 ML

4 ML

3 ML

2 ML

hv = 50 eV, NE

Ag/Ge(111)

QWS

SS

QWS +SS ?

Second kind of quantum well from 5ML down 1ML

Substrate is the key

Doping effect on the quantum well states

e-

e-

Lightly doped n type substrate

Heavily doped n type substrate

film

Depleting areafilm

Electronic Fringe Structure in Silver Films on Highly Doped Silicon, N. J. Speer,S. -J. Tang, T. Miller, and T.-C. Chiang*, recently accepted by Science.

Atomically uniform film+ quantum size effect + substrate

effect

High Tc

Magnetism

bulk film

Substrate

Future research plan

Photoemission1. Investigate the temperature dependence of the surface states,

energy shift and electron-phonon coupling, on the metal surfaces like Be , Be , Al(100), Al (110) surfaces. The central idea is to study the interplay between the electron structures and lattice structures on the surfaces.

2. Investigate the structures and behavior of surface states and film states (quantum well states) in an atomically uniform thin filmfor various systems like Ag/Ge(111), Pb/Ge(111), Co/Ge(111) and Ag/Cr(100).

3. Study the electronic structure of quantum wire, quantum dots, nanotubes and complex materials.

)0110( )0211(

Future research planLow energy electron microscopy (LEEM)

1. Study the surface morphology of metal surface or metal cluster. (Time dependence and Temperature dependence) example Cr(100)

    Sublimation of Atomic Layers from a Chromium Surface, S. -J. Tang, S. Kodambaka, W. Swiech, I. Petrov, T. -C. Chiang, Phys. Rev. Lett., in press.

2. Study the quantum size effect of metal thin film ( the intensity of the islands oscillates with electron energy) example Ag/Cr(100)

445 C

467 C

1 HOUR LATER

Ag/Cr(100)

7.5 eV 16.7 eV

38.5 eV 51.5 eV

Ag/Cr(100)

I V curve300

250

200

150

100

50

Inte

nist

y (

arb.

uni

ts)

5040302010Energy (eV)

Ag island

IV curve

qwsqws

qws

Surface Superconductivity on )0110(Be

22)0( MIN

)62.01(

)1(04.1exp45.1

DCBTk

Bulk Be =0.24 , Tc = 0.024 K

=0.646 , Tc = 17 K )0110(Be Localized S1 stateSmall coherence length

)2/( CBF Tk

HTSC Dominant e-p coupling with 50-80 meV optical phonon

MgB21. Light atoms

2. covalent like sp B-B bonding with DOS at Fermi level

3. Dominant coupling with in-plane B-B vibration phonon about 64 meV

Back bonding model rehybridzation of broken surface bonds

Hybridization between

S2 and SR states

SR S2

Charge density distribution of SR and S2

on (0010) cut plane

1

4

5

89

12

S and Pz type Py type

(J-H Cho )

Back bonding model rehybridzation of broken surface bonds

Hybridization between

S2 and SR states

SR S2

Charge density distribution of SR and S2

on (0010) cut plane

1

4

5

89

12

S and Pz type Py type

(J-H Cho )

k

k

M

M

'M

'M

Inversion symmetry

G