SHG from thin filmsSHG from thin filmsQuantum well states

Alkali metals ‐ plasmons

Wedge shaped metal filmWedge‐shaped metal film

AFM‐scan of Ag/Si(111)7×7

18 18 2

The wedge‐shaped metal filmis deposited by slowly movingthe sample up into the shadow

18 18 2. .× μm

Triangular domains  ~200 nmAg(111) LEED patternthe sample up into the shadow

of a fixed shield. The evaporationrate is ~1 ML per minute.

Ag(111) LEED‐pattern ‐only one type of domains

Quantum well states in Ag filmValence band spectroscopy

0,0

32

36 l

l

l

-1 5

-1,0

-0,5

ergy

(eV

)

24

28

32 l

l

l

l

l hick

ness

units

)

-2,5

-2,0

-1,5

indi

ng e

ne

16

20

l

l

l

l

easi

ng fi

lm th

sity

(ar

b.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14-3,0

B

Coverage (ML)

4

8

12 l

Incr

e

Inte

ns

4 3 2 1 00

Binding Energy (eV)

Bohr‐Sommerfeld quantization rule:

πφφ 2)()()(2 nEEEkd CB =++

Valence band spectra recorded for increasingAg film thickness starting with clean Si at thebottom and ending with 14 ML’s at the top

Two‐band model for k(E).Empirical models for boundaryphase shifts (Smith PRB 49 p 332)

bottom and ending with 14 MLs at the top.

Friedel oscillations?Friedel oscillations?Song et al. PRL 61 p1380

Oscillations due to the damping ofp g

the longitudinal field in the metal.

Only possible in p‐polarized SHG!

14

16

Ag on Si(111)7x7 p to s

8

10

12 p to p

. uni

ts)

4

6

8

SHG

(arb

0 10 20 30 40 500

2

S

Coverage (ML)Coverage (ML)

Si2p spectra – Reacted layersSi2p spectra  Reacted layers

4Cu on Si(111)7x7 Au on Si(111)7x7

3

1012141618

units

)

Cu wedge on Si(111)7x7Si2p components

Bulk

(arb

. uni

ts) 7x7

5 ML Cu 4

5

6

6

8

10

12

nits

)

Bulk Si Reacted Total signal

y (a

rb. u

nits

)

7x7

R3xR3

Si2p130 eV

2

101 100 99 98 9702468

ensi

ty (a

rb. u S_ Bulk S_

Inte

nsity

(

Binding Energy (eV) 2

3

4

101 100 99 980

2

4

6

sity

(arb

. un

Inte

nsity

0 2 4 6 8 10 12 140

1Inte

S+0

1Inte

ns Binding Energy (eV)

0 2 4 6 8 10 12 14Thickness (ML)

CuCu Sili idSili id i t f li t f l

0 2 4 6 8 10 12 14 16Coverage (ML)

AuReactedlayer

SiSi

CuCu SilicideSilicide interface layerinterface layer

Si

Au layer

R d A /Si l (4 ML)Reacted Au/Si layer (4 ML)floats on top of AuReacted Cu/Si layer

at interface

Al2p core levels

14

16

4 9 ML) its)

8

10

12

1

2

3

Al2p 130 eVrb

. uni

ts

Bulk Reacted Total

rea

(arb

. uni

4

6

8

0 2 4 6 8 100

1

nsity

(ar

Pea

k A

r

Coverage (ML)

54 55 56 57 58 59 60

0

2

Inte

n

Ki i E ( V)

Al(111) LEEDElongated spots - domains

Kinetic Energy (eV)(111) LEED + surface state ⇒ reacted layer not at free surfaceSTM (When et al. ): ~100 nm domains separated by grovesReacted part in grovesDomains of clean (111) crystals with sharp interfaces3/4 Al/Si lattice constants - 3×3 interface reconstruction

Cu buffer layerCu wedge under 10 ML Ag film

30n

Cu wedge under 10‐ML Ag film

25

g

gg

g

n

n

n

n

0

Clean Si(111)7x7

)

15

20

g

g

g

n

n

n

5

421

arb.

uni

ts

3 ML Cu: disordered film

10

g

g

g

g

n

n

n

1297

5

tens

ity (a

6‐7 ML Cu: optimum for Ag overlayer

0

5 Double peaks

g

14

2418

12

Cu VBM

Int

> 7 ML Cu: coupling of overlayerand substrate levels ‐double peaks ‐

3,0 2,5 2,0 1,5 1,0 0,5 0,00

Binding Energy (eV)

avoided crossings

Effect of Cu buffer layer

8

97x7

15 ML Al on Si(111)3,0Ag / 6 ML Cu / Si(111) Valence band 47 eV

20 ML Ag

7

8

ts)

SS2,0

2,5

units

)

5

67 ML buffer layerar

b. u

ni SS

1,5

ty (

arb.

u

4

5

tens

ity (

Directlyon 7x7

1,0

Inte

nsit

2

3Int

With 7 ML Cuinterlayer

3 2 1 00,0

0,5

6 ML Cu

6 4 2 01

Binding Energy (eV)

3 2 1 0Binding Energy (eV)

Binding Energy (eV)J. Vac. Soc. Technol. 21 1431 (2003)

PRB 66, 153406 (2002)

Al QW states5

Al wedge (0-24 ML) on 10 ML Cu/Si(111)4

gy (e

V)

Al SSAl band edge

)

Cu(111)57 eV2

3

ding

Ene

rg d-band

S3

rb. u

nits

)

S1

In 0

1Bin

d

Cu sp-band

ensi

ty (a

r ncreasing th

4 8 12 16 20 24Thickness (ML)

Inte

24 ML AlAl SShickness

2

3

OO

OEF,Al

6 4 2 0Binding energy (eV)

1

2

EF,AgEne

rgy

0.0 0.1 0.2 0.3 0.4 0.50

k/G

Surf. Sci. 600,  610 (2006)

Au on Cu/Si(111)12

10

12Au wedge on 7 ML Cu/Si(111)

47 eV

8

10

24 ML Auos)

47 eV sp -band edge

6

8

oooo

o

.....Arb

. Uni

t

4 4ML Au

..

ensi

ty (A

257 eV

67 eV

77 eVInte

16 ML Au

0 38 eV

47 eV57 eV

2.0 1.5 1.0 0.5 0.0

Binding Energy (eV)

QW levels and film roughness0

)

-1

-0.5

nerg

y (e

V)

-1.5

Bin

ding

En

B i l ~1

0 2 4 6 8 10 12 14 16 18 20 22 24-2.5

-2

B Beam size on sample ~1 mm

0 2 4 6 8 10 12 14 16 18 20 22 24Thickness (ML)

Film thickness variations expected within probed areaFilm thickness variations expected within probed areaVariations within a few atomic layer give broad peaks in photoemission

SHG from thin films)()()2( )2( ⋅= EEP

rrtrωωχω

etrycentrosymmwithmaterialsofbulkin0ofelementsAll 2 =)(χt

ysensitivitinterfaceandSurfaceyy

⇒

1,0 Decay of SHG from Ag interface

0,6

0,8ω

HG

Probing buried interfaces• Large probing depth

0,2

0,4SH

2ω • Spectroscopy• Also liquid interfaces

0 20 40 60 80 1000,0

Film Thickness (ML)

Linear versus non linear reflectionLinear versus non-linear reflection

Smooth increase in linearreflection - no sign of QWeffects due to the dominating non resonant

3SHG 1.4 eV θ = 60o

Au on Si(111)

40

) dominating non-resonant Drude term in the susceptibility.2un

its)

Linear reflection1.9 eV θ = 30o

35 ctio

n (%

)

SHG is dominated by dipole-allowed resonances.

1HG

(arb

. 35

ar R

efle

c

1

SH 30

Line

a

0 5 10 15 20 25 30 35 40 45 500

Au Coverage (ML)

25

g ( )

Au on Si(111)

R t ti l i t1,01,2

7

Rotational anisotropy:Ordered structure

0 90 180 270 3600,00,20,40,60,8

SHG

5

6

p to pits)

No LEED pattern! – disorderdsurface!

0 90 180 270 360

Rotational angle (deg.)

3

4p to p

arb.

un

1

2p to s

SHG

(a

AuReactedlayer

0 10 20 30 40 500

1S

Si

Au layer

R t d A /Si l (4 ML)

Coverage (ML)

Reacted Au/Si layer (4 ML)floats on top of Au

Au on Si(111)Au on Si(111)5

1.17 eV      p to p        θ = 60o

( 3 3) t ti4 ( 3 3× ):Au

( 3 3× ) - reconstruction : Increased signal

Increased contrast in oscillations

3

Increased contrast in oscillations Same oscillation period

2SHG

7×7

1

7×7

0 10 20 30 40 50 600

Coverage (ML)

Thickness of ordered Au layer

20Anisotropic SHG from Au wedge on Si(111)

10

15

uni

ts)

P-S SHG, 1.58 eV Recorded signal Surface state contribution Thin film contribution

5

SHG

(arb

.

9 P-S SHG, 1.37 eVR d d i l

0

)

6

Recorded signal Surface state contribution Thin film contribution

(arb

. uni

ts)

Decomposition of SHG:1. Decaying surface state contribution

0

3

SH

G 2. Damped oscillations around constant level

The Au layer is ordered, only the surface is di d d!0 10 20 30 40 50

Coverage (ML)

disordered! 

SHG from Au wedge in free air

3,5

3,0

Au on Si(111)

θ = 60o, P to P Pump photon energy: 1.4 eV

2,0

2,5p p gy

nits

)

QW oscillations reducedin amplitude below ~10 ML

1,5

,

G (a

rb. u

in amplitude below ~10 ML

0 5

1,0

in situ growth

SHG

0 10 20 30 40 50 60 700,0

0,5 g wedge scan in free air

Coverage (ML)

Resonances in thin films – Ag on Si(111)7x7

12

1.4 eV pump photon energyRT growth (300 K)

Monotonous growth of the signal at LT due to plasmons in the small Ag 

10

its]

RT growth (300 K) LT growth (170 K) LT growth +

annealling to RT

p gdomains.

hωP=2.8 eV

8

[arb

. un

4

6

nten

sity

High‐contrast oscillations for annealed LT grown film– Quantum Well resonances.

2

4

SHG

In

Q

0 10 20 30 40 50 600

Ag Coverage [ML] Surface Science 482‐485, 735 (2001)

SHG from Ag wedge on Si(111)

5

6

7p to p

2 66 Vts)

2

3

4

5 2.66 eV

G (a

rb. u

nit

⊥ polarization

0 10 20 30 400

1

2

63.44 eV

SH

G

Long period ~14 layers 

4

5 p to s2.66 eV

units

)

1

2

3

SH

G (a

rb.

|| polarization

Short period ~7 layers0 10 20 30 40

0

Film Thickness (ML)

3.44 eV

S Short period  7 layers

( )

Oscillations: Quantum well resonances – period depends on ħω

SHG from Ag wedge on Si(111)

1 2

1,0

2 4

2,0

V)

2 6252,6502,6752,7002,7252,7502,7752,8002,8252,8502,8752,9002,9252,9502,9753,000

1 6

1,4

1,2

3 2

2,8

2,4

ergy

(eV

1 8751,9001,9251,9501,9752,0002,0252,0502,0752,1002,1252,1502,1752,2002,2252,2502,2752,3002,3252,3502,3752,4002,4252,4502,4752,5002,5252,5502,5752,6002,625

gy (e

V)

2 0

1,8

1,6

4 0

3,6

3,2

hoto

h E

n

1 1501,1751,2001,2251,2501,2751,3001,3251,3501,3751,4001,4251,4501,4751,5001,5251,5501,5751,6001,6251,6501,6751,7001,7251,7501,7751,8001,8251,8501,8751,900

ton

Ene

r

E0/E1

2 4

2,2

2,0

4 8

4,4

4,0

SH

Ph

0,50000,52500,55000,57500,60000,62500,65000,67500,70000,72500,75000,77500,80000,82500,85000,87500,90000,92500,95000,97501,0001,0251,0501,0751,1001,1251,150,

Pho

t

E2

0 10 20 30 402,4 4,8

Film Thickness (ML)

• Interface resonance at E0/E1 transition• Resonance at Ag bulk plasma frequency• Double peaks at low energies

PRB 73, 125440 (2006)

p g• Long period – interference between surface and interface parts

Periodic structure in SHG versus thickness

• Oscillations die out as d grows• Electronic levels →continuum 8

9

10

• Roughness grows

•Double peak structure 4

5

6

7

EF

ergy

(eV

)

Interference between interface

and surface contributions4.0

0 2 4 6 8 10 12 14 16 18 20 22 240

1

2

3

Ene

3.0

3.5

p to p

Ag wedge on Si(111)7x71.43 eV

ts)

Resonances at fundamental

0 2 4 6 8 10 12 14 16 18 20 22 24

Coverage (ML)

1.5

2.0

2.5

7 ML

14 ML

(arb

. uni and SH frequencies.

Faster oscillations with higherphoton energy.

0 0

0.5

1.0p to sS

HG

Different periods for

isotropic and anisotropic

-5 0 5 10 15 20 25 30 35 40 45 500.0

Film Thickness (ML)contributions

Modification of free surface

Ag wedge with 0.5 ML Cs

Ag

p to p

Ag wedge with 0.5 ML Cs

p to s

715 nm

)

Ag/Csx10 715 nm

0.5 ML Cs:Ag wedge with 0.5 ML Cs

x10 775 nm

rb. u

nits

)

Ag wedge with 0.5 ML Cs

775~10 x signal for ⊥ pol.

SHG

(ar 775 nm

Ag wedge with 1 ML Au Ag wedge with 1 ML Au

Large surface cotrib.

Phase shift in oscillations775 nm

Ag

Ag/Au775 nm

No change in || pol.Interface signal

0 10 20 30 0 10 20 30

Ag/Au

Film Thickness (ML)

Interface signal

1 ML Au:Lattice match‐ no change!g

Au wedge on Si(111)0,5 1

Au on Si(111)eV

)

1

1,0

3

2

gy (e

V)

nerg

y (e

32,0

1,5

4

3

nits

)

1.27 eV

on E

nerg

hoto

n E

n

E0/E1

1

2

2,5 5

SH

G (a

rb. u

n

1 72 eV H P

hoto

ump

Ph E2

0 10 20 30 40 500 10 20 30 40 50

3,0 6S 1.72 eV

SHP

Film Thickness (ML)Film Thickness (ML)

Resonance at E0/E1 transitionOnly 2 eV to d bandsOnly 2 eV to d‐bands

Al/Si(111)7x7‐ Isotropic Contribution

6 57,07,5

ngt

725

705 nm 2,5O2 on Al/Si(111)

4 04,55,05,56,06,5

n

n

ng

g

g

t

t

t

800 nm

760 nm

740 nm

725 nm

units

)

1,5

2,0

2 ( )780 nmp to p polarization

. uni

ts)

Clean 10 L 50 L 300 L

1 52,02,53,03,54,0

ng

g

g

g

t

t

t

t 940 nm

880 nm

840 nm

800 nm

SHG

(arb

. u

0,5

1,0

SH

G (

arb.

0 5 10 15 20 25 30

0,00,51,01,5 g

gt 980 nm

Al/Si(111)7x7 p to p

S

0 10 20 30 40 500,0

S

Coverage (ML)0 5 10 15 20 25 30

Film Thickness (ML)

Oxidation only changes top layerDecay of overall signal level ‐ decay of oscillationsDouble peak structure:   high‐coverage part decays fasterp g g p y

Periodic structure in SHG versus thicknessAssume resonances vary periodically – alternating odd and even wavefunctions

Periodic structure in SHG versus thickness

wavefunctions SHG sensitive to symmetry ⇒ one SHG period includes odd + even wavefunction (2×period of linear optics) Two limits:

1. |χS|≈|χI|: Contributions from d QW l l l every second QW level cancel

Kirilyuk et al. PRL 77 4602 ⇒ long oscillation period

2. χS|>>|χI| (or |χS|<<|χI|) : No interference ⇒ short oscillation period )()()2( 22 21 ωχχω φ EeeeE dikdiki

IS +=

ΑI >>Αs (a)

Corresponds to anisotropicres lts Interface dominates

ts)

(b)

results: Interface dominates

Αs=ΑIφ

S=φ

Ι

(arb

. uni

t (b)

SH

G

Corresponds to Isotropic results: Both surface and

Αs=ΑIφS-φI =0.4π

(c)

results: Both surface and Interface contribute

0 5 10 15 20 25 30 35 40Film Thickness (ML)

SHG from QWSHG from QW

IS

∑ −−=

3,2 3112

321,

)2(, )2)((

)(ωω

ωχEE

ZZZf ISj

IS

)2( 22

22

nnnEij Δ+Δ=πh

Energy difference Eij between n and n+Δn

)2(2 2 nnn

mdEij Δ+Δ

πdkn F=Assume first level close to Fermi level, then

∑IS

jfC

,)2( )(

Assume first transition dominates the QW oscillations

∑Δ

⎟⎟⎠

⎞⎜⎜⎝

⎛−−Δ

=n F

jIS

indm

kf

Cγωπ

ωχ2

)2(, )(

h

Thi k d dThickness dependence

SimulationsSimulations

1)( =Sjf )1()( )1( −−= jI

jfAlternating odd and even wavefunctions:

Si

SSSeAE χφ= dikdki

Ii

II eeeAE I ωωχφ 22=

dikdkiBB eeE ωωχ 22=

Quantum well signals:

Background – Si interface layer: BB

∑ +=

im

B ief m

γωωωχ

φ

2)2()2(

g y

Interband resonances in interface+−m mm iγωω2

Simulations‐ Ag on SiDouble peak structure

id d i

g

Avoided crossing atinterface resonances

1

1.2

or

0

0.2

0.4

0.6

0.8

nanc

e Fa

cto

Real

0 0.5 1 1.5 2-0.6

-0.4

-0.2

0

Relative Frequency

Res

o

Phase

|| polarization dominated by interface

⊥polarization from both interfaces

I f d dInterface resonances detected

PRB 73, 125440 (2006)

Conclusions on thin filmsConclusions on thin films

• Film growth can be followed in situ• Burried layers and interfaces can be tested• Quantum well effects! Not seen in linear optics for metal

films