Sum-Frequency Spectroscopy on
Bulk and Surface Phonons of a
Noncentrosymmetric Crystal
Wei-Tao Liu, Y. Ron Shen
Physics Department,
University of California at Berkeley
Optical Spectroscopy Techniques
for Probing Phonons
Raman
IR
SFS
For bulk and
surface phonons
Bulk phonons  Bulk structure
Surface phonons  Surface structure
Microscopic surface phonons
different from
Fuchs-Kliwer surface phonon-polaritons
(Re e = -1)
Existing Techniques To Probe
Surface Phonons
• He scattering:
• EELS:
Often limited to < 30 meV
Difficult for insulating crystals
Often probing surface phononpolaritons
• Infrared-visible sum-frequency spectroscopy
Sum-Frequency Spectroscopy
P ( = 1  2 ) =  : E (1 ) E (2 )
(2)
S
 (2) = (  S(2) 
 B(2)
 B(2)
2
1
SF
)
ik
= 0 in media with inversion symmetry
SF
 S(2)  0 at surfaces or interfaces
1
SFG  |eˆ   (2) : eˆ1eˆ2 |2

(2)
=
(2)
NR

q
Aq
 2   q  i q
As 2 q, or el,
SFG is resonantly enhanced,
 Spectroscopic information.

2
1

2
Measurements with different polarization combinations  independent
ijk(2)
Experimental Setup
s
1, 0.2 -2 
To detector
and computer
s
2, 0.42 -10 
Surface Phonons of Diamond (111)
Raman Signal
(A Centrosymmetric Crystal)
Raman
spectrum
Pandey model
(cm-1)
SFG spectrum
SF
Vis
IR
Surface Phonons of
Noncentrosymmetric Crystals
(21 out of 32 crystallographic point groups are non-centrosymmetric)
SFG  |eˆ   (2) : eˆ1eˆ2 |2

(2)
= (
(2)
S

 B(2)
ik
)
SF output is overwhelmed by bulk contribution
(2)

unless B can be suppressed,
Achievable with selective sample geometry and
input/output polarization combination
Basic Idea: Surface and Bulk have
different structural symmetry.
Example: aQuartz(0001)
(relevant in many areas of science and Technology)
D3 point group
Si
Si-OH
[0001]
O
Si-O-Si
Side view
Front view
Bulk and Surface Nonlinear
Susceptibilities of aQuartz(0001)
W.T.Liu, Y.R.Shen, PRL (2008)
4 Nonvanishing elements of bulk nonlinear susceptibilities:
)
)
)
)
 B(2,aaa
=  B(2,abb
=  B(2,bba
=  B(2,bab
)
)
 B(2,acb
=  B( 2,bca
)
)
 B(2,abc
=  B( 2,bac
)
)
 B(2,cab
=  B( 2,cba
3 Nonvanishing elements of surface nonlinear susceptibilities
for the (0001) surface:
)
 S( 2,ccc
)
)
 S( 2,aac
=  S( 2,bbc
)
)
)
)
 S(2,aca
=  S(2,bcb
  S(2,caa
=  S( 2,cbb
SF Output from (0001) a–Quartz with
SSP and PPP Polarization Combinations
S ( SF = vis   IR )  

(2)
SSP,eff
= C[
(2)
S ,aac
 i
(2)
B,aaa
( 2) 2
eff
cos3 / k ]
(2)
(2)
(2)
(2)
PPP
=
C


C


C

,eff
1 S ,aaz
2 S ,ccc
3 B, aaa cos3 / k
Bulk contribution dominates unless  ~ 0
SF Phonon Spectra of Quartz
Properties of bulk a-quartz
5
120
60
30
150
4
ISFG (a. u.)
90
180
0
3
330
210
2
240
270
300
x5
1
0
750
800
1000
1100
1200
1300
-1
Wavenumbers (cm )
SF signal from bulk a-quartz can be
suppressed at certain sample orietations.
D3 point group
a-Quartz (0001) surface: vibration modes
I SSP  
( 2)
Surface
( 2)
 Surface
( 2)
 Bulk


( 2) 2
Bulk
 Isotropic
cos(3 )
 Surface and bulk
signals are separable
 Surface modes observed
with bulk signal suppressed.
W.-T. Liu and Y. R. Shen, PRL 101, 016101 (2008)
Mode assignment: OTS titration
Si-OH
Si-O-Si
…
Si-OH
Effect of Baking
4
Hydrated surface
Baked @ 100C
Rehydrated
SiOH+SiOH  SiOSi+H2O
ISSP (arb. unit)
3
2
1
850
900
950
1000
-1
Wavenumbers (cm )
1050
Irreversible surface structural change
Quartz
SF Intensity
Fused
Silica
• After baking at 500C
• Rehydroxylated
• After boiled in water
 500C baking disrupts the ordered surface lattice structures
Deteriorated LEED
patterns after 500C
F. Bart et al., Surf. Sci 311, L671 (1994)
Boiling
S. Yanina et al., Geochimica 70, 1113 (2006)
Surface structure: Si-O-Si bonding geometry
Si-O-Si ~ 120o-135o
Bulk
Si-O-Si stretch @ 795 cm-1
Si-O-Si = 143.7o
Surface
Si-O-Si stretch @ 870 cm-1
Si-O-Si ~ 130o
T. Goumans et al., PCCP 9, 2146 (2007)
Surface structure: Si-OH orientation
Bulk terminated surface
q
• qMax  30o on partly hydrated a-quartz (0001);
• Silanol groups has a broader distribution on
fused silica.
Partially hydrated
Summary
Si-OH
• Surface vibrations of noncentrosymmetric crystals can
be obtained with SFG;
• Example: a-quartz (0001)
980 cm-1: Si-OH stretch
880 cm-1: (strained) Si-O-Si
vibration;
Si-O-Si
Probing Bulk Phonons
Infrared spectroscopy  IR active modes
Raman spectroscopy  Raman active modes
SF spectroscopy  IR and Raman active modes
For aquartz, only E(TO) modes are both
IR and Raman active – 3 out of 11 existing
phonon modes between 700 and 1300 cm-1
Raman spectrum
5
120
60
30
150 spectrum
SF
4
ISFG (a. u.)
90
180
0
3
330
210
2
240
270
300
x5
1
0
750
800
1000
1100
1200
-1
Wavenumbers (cm )
1300
Sum-Frequency Spectroscopy on
Bulk Phonons of aQuartz
Three-fold Symmetry from Bulk SFVS
S SSS =| A B(2),aaa sin 3 |2
S SPP =| B1  B(2),aaa sin 3  B2  B(2),bca  B3  B(2),abc |2
S PSP =| C1  B(2),aaa sin 3  C2  B(2),cba  C3  B(2),abc |2

(2)
B ,ijk
=
(2)
NR ,ijk

q
Aq ,ijk
(IR  q  i q )
Fitting of the experimental results yields
q = 795, 1064, 1160 cm-1
and the corresponding nonvanishing
Aq,aaa , Aq,bca  Aq,cab , Aq,bca = 0,
Aq ,ijk
(2)
NR
,ijk  0
1 a ij k

q Qq Qq
Aq ,bca
Aq ,aaa
a bc a aa
=
/
= Raman polarizability ratio
Qq Qq
SF Spectroscopy for Bulk Phonons
• Complementary to IR and Raman spectroscopy:
Identify modes both IR and Raman active
Simple spectrum.
• One fixed beam geometry is often sufficient to
characterize the detected modes, such as
Raman polarizability ratio.
• Reflected SF signal comes from a surface layer
thickness of reduced wavelength.
IR-visible sum-frequency spectroscopy can be
used to probe bulk phonons of crystals,
complementary to IR and Raman spectroscopy.
It can also be an effective tool to probe surface
phonons of crystals with or without inversion
symmetry.
Manuel
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