In the last years, Tin dioxide SnO₂, present one of the most important materials because of their optical properties. This oxide present a large band gap energy of 3.6eV[5]. We define a several domains of application of SnO₂, for example, solar cells, detection of toxic gas, catalysis[1] ...etc.  The rutile phase of tin dioxide (SnO₂) has a tetragonal structure with space group  and two molecules per unit cell.

Both experimentally and theoretically studies[1,2,4], proved that the presence of oxygen vacancies is responsible of amelioration of several properties, for example: magnetic; electronics and optical properties. For this reason, we focused our intention on the optical properties.

The aim of this investigation is firstly, to calculate the RAMAN and IR frequencies of fundamental modes of vibrations at G point of the first Brillouin zone for SnO₂ rutile without and with oxygen vacancies. In the second stage, we compare our results with those obtained experimentally and theoretically in the literature. The comparison with fundamental optical modes of SnO₂: G=A_1g+A_2g+B_1g+B_2g+E_g+A_2u+2B_1u+3E_u[2]. Where, the symmetrical modes A_1g, B_1g, B_2g and E_g are Raman active modes, whereas, A_2u and E_u modes are IR active modes. The modes A_2g and B_1u are neither Raman active nor IR active.

Theoretical calculations of RAMAN and IR frequencies are released with CRYSTAL09[3] program, using SCF-LCAO with different Hamiltonians of periodic DFT approximation: hybrid B3LYP and a combination with non-local and local approximations: LDA, GGA and BPE. The creation of vacancies need a use of supercells of (2x2x2)p, contain 48 atoms (16 Sn and 32 O).

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References

[1] R. Fabricio Sensato, Rogerio Custodio, Monica Calatayud, Armando Beltran, Juan Andres, R. Julio, Sambrano, Elson Longo, Periodic study on the structural and electronic properties of bulk, oxidized and reduced SnO2(110) surfaces and the interaction with O₂, Surf. Sci. 511 (2002) 408–420.

[2] R. S. KATIYAR  et al. Dynamics of the rutile structure III. Lattice dynamics, infrared and Raman spectra of SnO2, J. Phys. C: Solid St. Phys., 1971, Vol. 4.

[3] R. Dovesi, V.R. Saunders, C. Roetti, R. Orlando, C.M. Zicovich-Wilson, F. Pascale, B. Civalleri, K. Doll, N.M. Harrison, I.J. Bush, Ph. D'Arco, M. LIunell, CRYSTAL09, University of Torino, 2010.

[4] L.Z. Liu, T.H. Li, X.L. Wu, J.C. Shen and P.K. Chu, J. Raman Spectrosc. 2012, 43, 1423-1426.

[5] V.E. Henrich, P. A. Cox, The Surface Science of Metal Oxides, Cambridge University Press, Cambridge, 1966.