2. University of California at Berkeley
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

3. Optical Spectroscopy Techniques for Probing Phonons
Raman IR
SFS
For bulk and surface phonons

4. Bulk phonons  Bulk structure Surface phonons  Surface structure
Microscopic surface phonons
different from
Fuchs-Kliwer surface phonon-polaritons (Re e = -1)

5. Existing Techniques To Probe Surface Phonons
He scattering: Often limited to < 30 meV
EELS: Difficult for insulating crystals Often probing surface phonon- polaritons
Infrared-visible sum-frequency spectroscopy

6. Sum-Frequency Spectroscopy2 1
SF 1 2 
As 2 q, or el,
SFG is resonantly enhanced,
 Spectroscopic information. 1  2
Measurements with different polarization combinations  independent

7. Experimental Setup 1, 0.2 -2  To detector and computer
2,  s
To detector
and computer

8. Surface Phonons of Diamond (111) (A Centrosymmetric Crystal)
Raman spectrum
Pandey model
Raman Signal
(cm-1)
SFG spectrum SF
Vis IR
Pi-bonded chain model: (b) Dimerization with no buckling proposed by Larlori et al, and c) slight buckling with no dimerization proposed by Bechstedt and Ricahrdt.
SF spectrum is observed when the sample is heated above 1200K. Sample surface reconstructs from C(111)(1x1) to C(111)(2x1). The spectrum disappears wit 0.04 ML dosing of H, reversing the surface to C(111)(1x1). Low frequency mode or modes come from C-C bonds connecting the top layer, and high frequency mode or modes from C-C bonds connecting top and second layers, as supported by the polarization dependence of the modes.

9. Surface Phonons of Noncentrosymmetric Crystals
(21 out of 32 crystallographic point groups are non-centrosymmetric)
SF output is overwhelmed by bulk contribution unless can be suppressed, Achievable with selective sample geometry and input/output polarization combination
Basic Idea: Surface and Bulk have different structural symmetry.

10. Example: a-Quartz(0001) (relevant in many areas of science and Technology)
D3 point group Si O
Si-OH
Si-O-Si
[0001]
Side view
Front view

11. Bulk and Surface Nonlinear Susceptibilities of a-Quartz(0001)
W.T.Liu, Y.R.Shen, PRL (2008)
4 Nonvanishing elements of bulk nonlinear susceptibilities:
3 Nonvanishing elements of surface nonlinear susceptibilities for the (0001) surface:

12. Bulk contribution dominates unless f ~ 0
SF Output from (0001) a–Quartz with SSP and PPP Polarization Combinations
Bulk contribution dominates unless f ~ 0

13. SF Phonon Spectra of Quartz

14. Properties of bulk a-quartz
First I briefly review the bulk property of alpha-quartz.
It belongs to D3 point group, and this is how it looks along the (0001) direction, which is also parallel to the 3-fold axis.
In the cm-1range, strong bulk vibration modes can be observed in SFG spectra, and they all belong to the E irreducible representation.
What’s noticeable is that all three modes are anisotropic wrt to the crystal orientation, as shown in the inset, and can be suppressed simultaneously at certain angles. Therefore, the surface modes shall be observable if their chi(2) have different orientation dependence.
SF signal from bulk a-quartz can be suppressed at certain sample orietations.
D3 point group

15. a-Quartz (0001) surface: vibration modes
 Isotropic 
 Surface modes observed
with bulk signal suppressed.
Knowing that, we expect for the SSP pol. comb.that the surface contribution will be independent of the azimuthal angle phi, and the bulk contribution can be suppressed at phi=30deg.
Here are the experimental results
Black curve corresponds to phi=30deg, and the bulk vibration at 1064 cm-1 is almost completely suppressed. It increases dramatically when phi changes by 1.8deg.
On the other hand, the two bands at 880 and 980 cm-1 are not varying with phi. And as they do not have any bulk correspondence, we attribute them to surface vibrations.
Surface and bulk signals are separable
W.-T. Liu and Y. R. Shen, PRL 101, (2008)

16. Mode assignment: OTS titration
Si-OH …
Si-O-Si
Si-OH
To further verify that there are surface modes, we deposit an OTS SAM on it.
And indeed we see the spectrum changes dramatically upon OTS deposition.
Similar effect was also seen on fused silica surfaces.
The observation confirms that the spectra are indeed surface originated, We know that the bare quartz surface shall be partically covered by silanol groups, which will be replaced by OTS molecules.
and we can immediately assign the 980 cm-1 mode on quartz to be due to silanol groups.
The assignment is consistent w/ previous experiments on high surface area silica powders.
The 880 cm-1 mode is less perturbed by the OTS monolayer and shows up only on quartz spectra. Therefore, it should come from the ordered Si-O-Si lattice structure on the (0001) quartz surface.

17. Effect of Baking SiOH+SiOH  SiOSi+H2O
The assignment is also supported by thermal treatments of the sample.
This is the spectrum of a fresh, hydrated (0001) surface.
After baking the sample at 100C for half an hour, the 980 cm-1 mode drops appreciably while the 880 cm-1 increases. This clearly corresponds to the well known reaction that silanol groups will condense and form siloxane during heating.
The reaction shall also be reversible. And indeed after rehydration, the spectrum recovers to the original condition.

18. Irreversible surface structural change
Quartz
Fused Silica
SF Intensity
After baking at 500C
Rehydroxylated
After boiled in water
With SFG spectra, we had some interesting observation of the qz surface. For example we observed an irreversible surface structual change at high temperature baking.
Unlike the case when we baked the qz at 100C, as baked at 500C, the 880 cm-1 drops instead of increases. And it cannot be brought back by simple rehydration process (indicated by the grey curve)
Instead, the overall spectral shape becomes very similar to that of fused silica, indicating that the surface lattice is disrupted and randomized after being baked at 500C.
To confirm that, we know that amorphous quartz has slightly higher solubility compared to qz in hot water. And indeed the spectra recovered after we boiled the sample in hot water.
 500C baking disrupts the ordered surface lattice structures

19. S. Yanina et al., Geochimica 70, 1113 (2006)
Deteriorated LEED
patterns after 500C
F. Bart et al., Surf. Sci 311, L671 (1994)
Boiling
S. Yanina et al., Geochimica 70, 1113 (2006)
The result agrees fairly well with previous LEED study that found deteriorated diffraction pattern from (0001) qz after baking it at 500C; also with AFM study that found boiling can indeed remove dead, amorphous layer on the qz surface.
The whole thing is interesting because 500C is well below any transition temperature for bulk quartz, and it shows that it can be dangerous to assume surface will simply behave following the bulk properties.

20. Surface structure: Si-O-Si bonding geometry
Si-O-Si ~ 120o-135o
Bulk
Si-O-Si 795 cm-1
Si-O-Si = 143.7o
Surface
Si-O-Si 870 cm-1
Si-O-Si ~ 130o
For the Si-O-Si structures that contribute to the 880 cm-1 mode, we notice ab initio calculations predict that on dehydrated (0001) surface, the Si-O-Si bonding angle becomes much smaller than the bulk correspondence, which shall lead to a shift of Si-O-Si stretch frequency
For bulk quartz, the Si-O-Si stretch is found at 795 cm-1, corresponding to a Si-O-Si bonding angle at 143.7deg. If we assume the bond length and force constant remain the same for the surface lattice, we found for a bonding angle at 130deg, the Si-O-Si stretch frequency shifts to 870 cm-1, which is quite close to the 880 cm-1 mode we observed.
Therefore, the surface structure contributing to the 880 cm-1 can be strained Si-O-Si structures with a strained bond angle.
T. Goumans et al., PCCP 9, 2146 (2007)

21. Surface structure: Si-OH orientation
Bulk terminated surface
Partially hydrated q
Having the modes assigned, we can now deduce the corresponding structual information.
First, we estimate the orientation of silanol groups.
On a bulk terminated (0001) surface, silanol groups shall tilt by around 50deg from the surface normal. However, in ambient conditions, the surface shall be partially hydrated, which leads to an reorientation of silanol groups closer to the surface normal.
And indeed we found the tilting angle of silanol groups to be within 30deg.
We also found a broader angular distribution for silanol groups on the fused silica surface, which is physically expected.
qMax  30o on partly hydrated a-quartz (0001);
Silanol groups has a broader distribution on fused silica.

22. Summary
Si-OH
Si-O-Si
Surface vibrations of non-centrosymmetric crystals can be obtained with SFG;
Example: a-quartz (0001) 980 cm-1: Si-OH stretch 880 cm-1: (strained) Si-O-Si vibration;
To our knowledge, these surface vibrational modes are observed for the first time on well-defined single crystalline quartz surface.

23. 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

24. Raman spectrum
SF spectrum

25. Sum-Frequency Spectroscopy on Bulk Phonons of a-Quartz

26. Three-fold Symmetry from Bulk SFVS

28. Fitting of the experimental results yields
wq = 795, 1064, cm-1
and the corresponding nonvanishing
Aq,aaa , Aq,bca  Aq,cab , Aq,bca = 0,

29. 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.

30. 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.

31. Manuel
Happy 75th Birthday!