Polarized Raman scattering study of kesterite type Cu2ZnSnS4 single crystals Maxim Guc1,4,*, Sergiu Levcenko2, Ivan V. Bodnar3, Victor Izquierdo-Roca4, Xavier Fontane4, Larisa V. Volkova3, Ernest Arushanov1, Alejandro Pérez-Rodríguez4




Дата канвертавання30.04.2016
Памер22.05 Kb.
Polarized Raman scattering study of kesterite type Cu2ZnSnS4 single crystals
Maxim Guc1,4,*, Sergiu Levcenko2, Ivan V. Bodnar3, Victor Izquierdo-Roca4, Xavier Fontane4, Larisa V. Volkova3, Ernest Arushanov1, Alejandro Pérez-Rodríguez4,5
Supplementary information

The group theoretical analysis [27] for the zone center phonons, applied to kesterite CZTS (Fig. S1), with respect to Wyckoff position of all atoms (Ref. [14]), are given in Table S1.


Table S1. Atomic coordinates, Wyckoff Position, atom sites symmetry and irreducible representations for the atoms of the tetragonal CZTS.

Atom

Wyckoff position

Symmetry

Irreducible representations

Cu(1)

2a





Cu(2)

2c





Sn(1)

2b





Zn(1)

2d





S(1)

8g





Modes classifications

IR

Raman

Acoustic










Figure S1. CZTS kesterite unit cell structure.
The Raman intensity, I, is given by [45]

(S1)
where vi is the incident light polarization, vs is the scattered light polarization and is the Raman tensor for the phonon mode. Here (X Y Z) is the laboratory system associated with (1 1 2)-crystal plane, where X, Y and Z correspond to , and crystallographic directions, respectively. For the arbitrary value of the in-plane angle, θ, the incident and scattered light polarization vectors are defined by

, (S2)

where is parallel and is perpendicular geometry.



To apply Eq. (S1) we used results of the Ref. [28], where tensors for the kesterite (1 1 2)-plane were already determined. For clarity we provide these in Table S2, too. Finally, the calculated angular dependence for the A, B and E-symmetry modes and the selection rules for the considered geometries and are collected in Table S3.
Table S2. Calculated Raman tensors for kesterite type structures in case of (1 1 2) crystal plane.

Mode

Raman tensor

A



B(Z)



E(X)



E(Y)





Table S3. Angular dependence of Raman mode intensities for kesterite type structure in case of (1 1 2) crystal plane (upper part of the Table) and intensity values for the selected geometries (lower part of the Table).

Mode

||



A





B(Z)





E(X)





E(Y)






Mode





A

a2

((a+2b)/3)2

B(Z)

d2

d2/9

0.5×E(X)+0.5×E(Y)

0

(4/9)(f2+e2)




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