SHG from thin films SHG from thin films Quantum well states Alkali metals ‐ plasmons
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