Sum-Frequency Spectroscopy on Bulk and Surface Phonons of a N

oncentrosymmetric Crystal

Wei-Tao Liu, Y. Ron Shen

Physics Department,

University of California at Berkeley

Optical Spectroscopy Techniques for Probing Phonons

IR Raman

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 -1)

Existing Techniques To Probe Surface Phonons

• He scattering: Often limited to < 30 meV

• EELS: Difficult for insulating crystalsOften probing surface phonon-

polaritons

• Infrared-visible sum-frequency spectroscopy

(2)1 2 1 2

(2)(2) (2)

(2)

(2)

( ) : ( ) ( )

( )

0 in media with inversion symmetry

0 at surfaces or interfaces

S

BS

B

S

P E E

i k

�

�

�

�

(2) 21 2

(2) (2)

2

ˆ ˆ ˆ |e : |

qNR

q q q

SFG e e

A

i

�

As 2 q, or el,

SFG is resonantly enhanced,

Spectroscopic information.

1

2

1

2

2

1

SF

SF

Sum-Frequency Spectroscopy

Measurements with different polarization combinations independent (2)ijk

1, 0.2 -2

2, 0.42 -10 s

s

To detectorand computer

Experimental Setup

Surface Phonons of Diamond (111)(A Centrosymmetric Crystal)

Raman spectrum

SFG spectrum

Pandey model

(cm-1)

Ra

ma

n S

ign

al

IRSF Vis

Surface Phonons of Noncentrosymmetric Crystals

(21 out of 32 crystallographic point groups are non-centrosymmetric)

(2) 21 2

(2)(2) (2)

ˆ ˆ ˆ |e : |

( )BS

SFG e e

i k

�

�

SF output is overwhelmed by bulk contribution unless can be suppressed,

Achievable with selective sample geometry and input/output polarization combination

(2)B

Basic Idea: Surface and Bulk have different structural symmetry.

Si

OSi-OH

Si-O-Si

Example: Quartz(0001)(relevant in many areas of science and Technology)

D3 point group

[0001]

Side view Front view

)2(,

)2(,

)2(,

)2(, babBbbaBabbBaaaB )2(

,)2(

, bacBabcB

)2(,

)2(, bcaBacbB )2(

,)2(

, cbaBcabB

Bulk and Surface Nonlinear Susceptibilities of Quartz(0001)

4 Nonvanishing elements of bulk nonlinear susceptibilities:

3 Nonvanishing elements of surface nonlinear susceptibilities for the (0001) surface:

)2(,cccS )2(

,)2(

, bbcSaacS

)2(,

)2(,

)2(,

)2(, cbbScaaSbcbSacaS

W.T.Liu, Y.R.Shen, PRL (2008)

(2) (2) (2), , ,[ cos3 / ]SSP eff S aac B aaaC i k

(2) (2) (2) (2), 1 , 2 , 3 , cos3 /PPP eff S aaz S ccc B aaaC C C k

2)2()( effIRvisSFS

SF Output from (0001) –Quartz with SSP and PPP Polarization Combinations

Bulk contribution dominates unless ~ 0

SF Phonon Spectra of Quartz

750 800 1000 1100 1200 1300

0

1

2

3

4

5

I SF

G (

a. u

.)

Wavenumbers (cm-1)

x5

0

30

6090

120

150

180

210

240270

300

330

Properties of bulk -quartz

D3 point group

SF signal from bulk -quartz can be suppre

ssed at certain sample orietations.

Surface modes observed with bulk signal suppressed.

-Quartz (0001) surface: vibration modes

2)2()2(BulkSurfaceSSPI

)2(Surface Isotropic

)2(Bulk )3cos(

Surface and bulk signals are separable

W.-T. Liu and Y. R. Shen, PRL 101, 016101 (2008)

Si-OH

Si-O-Si

Mode assignment: OTS titration

…

Si-OH

850 900 950 1000 1050

1

2

3

4

Wavenumbers (cm-1)

Hydrated surface Baked @ 100C Rehydrated

I SS

P (

arb

. u

nit)

SiOH+SiOH SiOSi+H2O

Effect of Baking

500C baking disrupts the ordered surface lattice structures

Irreversible surface structural change

SF I

nten

sity

Quartz

Fused Silica

• After baking at 500C

• Rehydroxylated

• After boiled in water

Boiling

S. Yanina et al., Geochimica 70, 1113 (2006)

Deteriorated LEEDpatterns after 500C

F. Bart et al., Surf. Sci 311, L671 (1994)

T. Goumans et al., PCCP 9, 2146 (2007)

Surface structure: Si-O-Si bonding geometry

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

Si-O-Si ~ 120o-135o

• Max 30o on partly hydrated -quartz (0001);

• Silanol groups has a broader distribution on fuse

d silica.

Surface structure: Si-OH orientation

Bulk terminated surface

Partially hydrated

• Surface vibrations of non-cen

trosymmetric crystals can be

obtained with SFG;

• Example: -quartz (0001)

980 cm-1: Si-OH stretch

880 cm-1: (strained) Si-O-Si vi

bration;

Si-OH

Si-O-Si

Summary

Probing Bulk Phonons

Infrared spectroscopy IR active modes

Raman spectroscopy Raman active modes

SF spectroscopy IR and Raman active modes

For quartz, only E(TO) modes are both IR and Raman active – 3 out of 11 existing phonon modes between 700 and 1300 cm-1

750 800 1000 1100 1200 1300

0

1

2

3

4

5

I SF

G (

a. u

.)

Wavenumbers (cm-1)

x5

0

30

6090

120

150

180

210

240270

300

330

Raman spectrum

SF spectrum

Sum-Frequency Spectroscopy on Bulk Phonons of Quartz

Three-fold Symmetry from Bulk SFVS

(2) 2,

(2) (2) (2) 21 , 2 , 3 ,

(2) (2) (2) 21 , 2 , 3 ,

,(2) (2), ,

| sin 3 |

| sin 3 |

| sin 3 |

( )

SSS B aaa

SPP B aaa B bca B abc

PSP B aaa B cba B abc

q ijkB ijk NR ijk

q IR q q

S A

S B B B

S C C C

A

i

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, (2)

, 0NR ijk

,

,

,

1

/ Raman polarizability ratio

ij kq ijk

q q q

q bca bc aa

q aaa q q

AQ Q

A

A Q Q

SF Spectroscopy for Bulk Phonons

• Complementary to IR and Raman spectroscopy:Identify modes both IR and Raman activeSimple 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.

ManuelHappy 75th Birthday!