Second-order Phase Transition at a Pressure in Snse Crystal

Abstract

The existence ofsecond-order structural phase transition in the SnSe at a pressure of10GPa has been proved theoretically. The calculation is performed using the plane-wave pseudopotential approach to density-functional theory within the local-density approximation (LDA) withthe help ofthe ABINIT software package. Theabrupt change inbulk module jointly with unit cell volume continuous changeofthe crystalis the clear evidence of the second-order phase transition. It is shownthat the phase transitionis caused bythe softening of thelow-frequency fully symmetric interlayer shear modewithincreasing pressure. As a result, displacement type phasetransition (PT) take placewith the changeof translational symmetryof the crystalfrom the simple orthorhombic to thebase-centeredorthorhombic.

Introduction

Modern microelectronicsbased on the useof thinfilms grown onvarious substrates. A lattice parameters mismatch ofthe film and ofthe substrateresults in compressionor tensionin thin films. Due to the differencein thermal expansion coefficientsof the film andsubstrate biaxialdeformations take place, also. The structural parametersof the latticeand the electronic properties ofthe crystalschange substantially under appliedpressure, and this should betaken into account inthe development of variousdevices. Thus, the study of the effect of pressureon the structural, elastic andelectronic parameters of thecompounds is of greatinterest. In recent years, great efforts are aimed at creating photovoltaic devices from non-toxic materials with a simple, low cost production technology. In this regard, very promising were semiconductor compounds of group A4B6. Preliminary solar celldevices incorporating SnSe nanocrystals into a poly[2-methoxy-5-(3′, 7′-dimethyloctyloxy)-1, 4-phenylenevinylene] matrix demonstrate a significant enhancement in quantum efficiency and short-circuit current density, suggesting that this earth-abundant material could be a valuable component in future photovoltaic devices.

As we know two experimental studies of the effect of hydrostatic pressure on the structural parameters SnSe have been published in recent years. Mossbauer measurements have been made on SnSe under hydrostatic pressure in the range 0. 001 to 55 kbar and temperature and pressure induced phase transition in IV-VI compounds. No phase transition was detected in these works.

In this paper, we theoretically investigate the possibility of Phase Transition at a pressure in SnSe crystal. 2. The crystal structure SnSe belongs to group of layered semiconductor compounds of A4B6 type. The crystal structure consists of four atomic planes in sequence of Sn-Se-Se-Sn. The unit cellof the crystal contains two layers related by the inversion symmetry operation. Intralayer bonds have predominantly covalent character, whereas the bond between the layers is weak and presumably is van derWaalstype. Both types of atomsoccupy positions (4c): ±(x; y, 1/4) и ±(1/2 − x, 1/2 + y, 1/4), (seeFig. 1). The lattice parameters are : a = 4. 445Å, b = 11. 501Å, c = 4. 153Å, xSn = 0. 1035, ySn = 0. 1185, xSe = 0. 4819, ySe = 0. 8548.

The method of calculation

All calculations are performed using the ABINIT software package. Equilibrium parameters at zero temperature have been obtained by total-energy minimization. The lattice parameters and the equilibrium position of the atoms in a unit cell were determined by minimization of Hellmann-Feynman forces acting on the atoms. The minimization procedure for eachspecified pressure was carried out until the force modules become less than Hartree/Bohr. The lattice dynamics was determined using of the density functional perturbation theory (DFPT), according to which the static linear response to phonon distortions is determined by the electronic properties of the ground state. The dynamical matrices and phonon frequencies were calculated on an homogeneous grid in k-space using the Monkhorst-Pack grid with shift of k-grid by (0. 5, 0. 5, 0. 5). Then, the interatomic force constants in the configuration space were determined by performing the Fourier transform with the ANADDB program from the ABINIT software package. In calculations have been used norm-conserving Hartvigsen-Goedekker-Hutter (HGH) pseudopotentials and basis sets including plane waves up to a kinetic-energy cutoff of 40 Ha.

The convergence of the structural parameter xsn to zero and the convergence of the structuralparameter xse to 1/2 indicate the change in the symmetry of the crystal at the pressure of 10GPa. Fig. 5 shows thepressure dependence ofthe linear compressibilityof the crystalSnSeobtained fromthe calculated values componentsof the compliance tensorat different pressures. The continuous change of lattice constants andthe unit cell volume of the crystal with pressure and the discontinuityin the change ofthe linear compressibilityand the bulk module suggests that near the pressure of10GPatakes place second-order structural phase transition. Our calculationsof the phononspectrum of the crystal show the softening of thelow-frequency fully symmetric mode Ag as the pressure approaches 10 GPa.

Simultaneously with this there is a growth in of the amplitude of displacement of atoms in these vibrations in [100] crystallographic direction. As a result, occurs displacement typephase transitionwith a changeof translational symmetryof the crystalfrom the simpleorthorhombic structure to thebase-centeredorthorhombic structure (Pnma ( ) → ( )).

Conclusion

In this paper have been investigated the vibrational spectrum of SnSe crystal in the framework of the density functional theory within the local-density approximation. Wedeterminedthe relativechange in volumewith pressure, the pressure dependence ofthe bulk modulusof compressibility, the pressure dependencesof the componentsof the compliance tensor, and the pressure dependence of the internal parametersof SnSe crystal. We established the existence of the second-order PT nearthe pressure of10GPa. This second-order structure phase transition is displacement type and is induced by the softening of thelow-frequency fully symmetric interlayer shear vibration mode Ag.