RESONANT RAMAN SCATTERING IN TiO2

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RESONANT RAMAN SCATTERING IN TiO2

J. Camassel, B. Gil, P. Merle, H. Mathieu, J. Pascual

To cite this version:

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JOURNAL DE PHYSIQUE

CoZZoque C6, suppZ6ment au no 12, Tome 42, de'cembre 1981 page c6-682

RESONANT RAMAN SCATTERING IN T i 0 2

*

J. Camassel, B. G i l , P . Merle, H. Mathieu and J. Pascual

Universite' des Sciences e t Techniques du Languedoc, C.E.E.S., U.S.T.L., 34060 Montpe

Z

tier-Cedex, France

*

Universitat ~utknoma de BarceZona, BeZZaterra, BarceZona, Spain

Abstract. - One investigates t h e resonant behavior of Raman active phonons in Ti0 for incident laser energies ranging between 2.0 and 2.75 eV. One finds

2

the ehhancement to be dominated by the quadrupolar interaction.

14 Ti0 (rutile) i s a wide band gap semiconductor which belongs to the Dqh sym-

2

metry group. The fundamental absorption edge has been well characterized from experiments performed at liquid helium temperature('). The result of both experiments and theoretical calculations") concerning the ordering of electronic energy levels at t h e center of the Brillouin zone is schematically drawn in Fig. 1. The lowest absorption edge i s associated with a first-order forbidden quadrupolar interaction. Dipole-allowed transitions correspond to perturbations with

r

l 2 ( E l l ? ) and

r r 5

( E L F )

symmetry, respectively. If one refers to the crystallographic directions, the polariza- ( 3 )

bility tensor of the first-order non-resonant Raman process corresponds to :

We have studied the resonant scattering tuning the incident phonon energy fiul close to t h e exciton energy of t h e fundamental gap. I n this case, of the six terms contributing to the scattering probability per unit time(4) one becomes the strongest compared to all other terms which can approxiamted b y a constant C . Thus, inreso- nant Raman scattering (RRS) the scattering probability i s written as :

where I F l > corresponds to the unperturbed ground state of the crystal ; _{* 1 ( 3 )}

and

H are the exciton-radiation and exciton-phonon interactions, respectively ;Ij>andlk> 2

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denote intermediate states in which excitations a r e created in the solid ; wl( us) is t h e energy of the incident (scattered) light, C? t h e energy of the phonon and w.(w ) the

J k

energy of the intermediate state.

( 3) All experiments have been performed using previously described techniques

.

The incident propagation was along t h e c axis, the collected one along a. All incident frequencies were provided by i ) an argon-ion laser, ii) a C.W. dye laser using R6G in

0

the range 5700-6000 A, iii) a pulsed dye laser punped by 1 MWatt nitrogen laser.

r

(A ) : 76 meV / 612 cm-I Raman-line

-1-lg

The most resonant electronic process first includes the creation of a direct exciton in an excited state of symmetry / j

= r 3 )

by means of a quadrupolar interaction H1 ( r

1.

3 1 The exciton is next scattered to the exciton ground state Ik

= r

) by the

r

phonon.

3 1

Finally the exciton anihilates by quadrupolar interaction H 3 (r3L). Other processes in- volving two dipolar interactions from the ground state to higher excited states with symmetry

r5, are far from resonance. The scattering probability is then given by

:

Near resonance :

P (Alg) Q

A~

( 3 . 0 5 + 0 . 0 7 6 - +iy)2 ( 3 . 0 5 - f ~2 ~ )

The solid line in Fig.2 has been calculated using = 0.16 and accounts satisfactorily for the dispersion of experimental cross section

The different excitation processes involve different immediate states. Two of them a r e summarized in t h e expression of t h e scattering probability :

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JOURNAL DE PHYSIQUE

The solid curve in Fig. 3 has been calculated using B~ = 1.75 and, again, compares satisfactorily with the experimental results.

We did not find a process which permits the enhancement of phonons with symmetry

r3

with quadrupolar-allowed transitions. The allowed process with lowest exciting energy includes two dipolar interactions with excited states of symmetry

r5,

:

crl

I H )

(rijL

I

r5,> <r5,1

H~ W3)I

r 5 0

Q5.

I

H1 (r51)

1 rl

>

+ ( 5 - 2 1 9 ) ( 5 - h w 1 )

-1

_1

I n agreement with experimental data, the solid line in Fig. 4 displays a negligible dispersion in our range of investigation

References : 1) J . Pascual, J . Camassel and H . Mathieu,Phys.Rev.Let. 39,1490,1977 2) N . Daude, C . Gout and C. Jouanin, Phys. Rev. B15, 3229, (1977).