فونون اولیه در Cu2ZnSnSe4 (سی‌زدتی‌اس) نوع کاستریت (Kesterite) و استانیت (Stannite)

ABSTRACT Ab initio Phonons in Kesterite and Stannite-Type Cu2ZnSnSe4

Cu₂ZnSnSe₄ (CZTSe), a promising indium-free material for photovoltaic applications, has a body-centered tetragonal crystal structure derived from CuInSe2 chalcopyrite via double substitution of indium atoms, in an ordered manner, by zinc and tin. This can be done, e.g., producing the sequence of (001) cation planes . . ./Cu+Zn/Cu+Sn/. . . and hence the kesterite (KS) structure, or . . ./Cu+Cu/ Zn+Sn/. . . and hence stannite (ST). In both structures, a given atom species has the same nearest coordination, dictated by the need to satisfy the octet rule, but at longer ranges the connectivity patterns differ. This affects electronic structure, e.g., optical properties, but also lattice dynamics, that might become useful for characterizing, or recognizing, the structures of these materials. The identification of phonon modes is rarely straightforward, and usually is much helped by having first-principles calculation results as a benchmark.

In the following, from first-principle calculations done in the framework of the density functional theory, we calculate and compare vibration frequencies and eigenvectors in KS and ST phases of CZTSe. The method technically used for electronic structure calculations is SIESTA,1) which relies on norm-conserving pseudopotentials and atom-centered numerical basis functions with finite confinement radii; the force constants are collected from applying small finite displacements of all atoms, whereupon the phonon frequencies and eigenvectors follow from diagonalizing the dynamical matrix by an auxiliary code. The details of calculation are explained elsewhere.2) Exchange–correlation was treated in the local density approximation. From a number of previous studies on similar systems3–7) it is known that the band structure obtained this way is not good for analyzing optical properties, since the calculated band gap is (wrongly) negative. However, the phonons, being a groundstate property, can be reasonably well calculated.

The zone-center projected density of vibration modes, 21 in total, resolved into contributions from individual constituents, is shown in Fig. 1, after calculations done for the single CZTSe unit cell. Similarly to the case of CuInSe2 chalcopyrite studied earlier,8) we found transversal optical phonons to be arranged into three groups, at 60–90, 174– 187, and 209–254 cm1. ‘‘Zone-center projected’’ above implies that the vibration eigenvectors, before being taken to square for yielding the weights of spectral lines, are first summed up over the like atoms in the unit cell (see Postnikov et al.9) for details). This suppresses those contributions of Cu and Se which include opposite move.