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)

4