Prof. Sanjay. V. Khare Department of Physics and Astronomy,

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Ab initio calculations for properties of β-In2X3 (X = O, S, Se, Te) and β-X2S3 (X = Al, Ga, In) Prof. Sanjay. V. Khare Department of Physics and Astronomy, The University of Toledo, Toledo, OH-43606 http://www.physics.utoledo.edu/~khare/

Outline Structural details Length Scales and Techniques Ab initio method Various properties of β-In2X3 (X = O, S, Se, Te) and β-X2S3 (X = Al, Ga, In) DOS and LDOS plot of β-In2X3 (X = O, S, Se, Te) and β-X2S3 (X = Al, Ga, In)

Band structures of β-In2X3 (X = O, S, Se, Te) and β-X2S3 (X = Al, Ga, In)

Structural details Pearson Symbol: tI80 Space Group: I41/amd β-In2X3 (X = O, S, Se, Te) and β-X2S3 (X = Al, Ga, In) all belong to same space group and there details are as follows Pearson Symbol: tI80 Space Group: I41/amd Number: 141

Theoretical Techniques and Length Scales 10 – 100 nm and above: Continuum equations, FEM simulations, numerically solve PDEs, empirical relations. 1-10 nm: Monte Carlo Simulations, Molecular Dynamics, empirical potentials. < 1 nm Ab initio theory, fully quantum mechanical. Integrate appropriate and most important science from lower to higher scale.

Value of ab initio method Powerful predictive tool to calculate properties of materials Fully first principles ==> (1) no fitting parameters, use only fundamental constants (e, h, me, c) as input (2) Fully quantum mechanical for electrons Thousands of materials properties calculated to date Used by biochemists, drug designers, geologists, materials scientists, and even astrophysicists! Evolved into different varieties for ease of applications Awarded chemistry Nobel Prize to W. Kohn and H. Pople 1998

What is it good for? Pros Very good at predicting structural properties: (1) Lattice constant good to 1-10% (2) Bulk modulus good to 1-10% (3) Very robust relative energy ordering between structures (4) Good pressure induced phase changes Good band structures, electronic properties Good phonon spectra Good chemical reaction and bonding pathways Cons Computationally intensive, band gap is wrong Excited electronic states difficult

Various properties of β-In2X3 (X = O, S, Se, Te) Property β-In2O3 β-In2S3 β-In2Se3 β-In2Te3 a (Å) 6.32 7.5 7.95 8.71 c (Å) 27.202 32.1949 33.1652 34.28 c/a 4.30411 4.29025 4.17015 3.93571 B (GPa) 120.596 62.1444 46.7244 32.8733 Eg (eV) 0.6 1.02 0.23

DOS and LDOS plots for β-In2X3 (X = O, S, Se, Te)

Band structures of β-In2O3 Eg = 0.6 eV (direct band gap) Brillouin zone for tetragonal structure

Band structures of β-In2S3 Eg = 1.02 eV (indirect band gap) Brillouin zone for tetragonal structure

Band structures of β-In2Se3 Eg = 0.23 eV (indirect band gap) Brillouin zone for tetragonal structure

Band structures of β-In2Te3 No band gap Brillouin zone for tetragonal structure

Internal Parameters β-In2O3 β-In2S3 β-In2Se3 β-In2Te3 Z1 Z2 Z3 Z4 Z5 0.332512 0.333534 0.334529 0.337477 Z2 0.204951 0.203723 0.204115 0.204874 Z3 0.250872 0.250754 0.251101 0.250249 Z4 0.074560 0.078484 0.080194 0.085095 Z5 0.412490 0.413665 0.413740 0.416345

Internal Parameters β-In2O3 β-In2S3 β-In2Se3 β-In2Te3 Y1 Y2 Y3 Y4 Y5 -0.007515 -0.021255 -0.023265 -0.036737 Y2 0.250000 Y3 -0.002573 -0.005846 -0.010579 -0.016192 Y4 0.029477 0.005619 0.004753 0.000550 Y5 0.021686 0.021310 0.026458 0.032940

Various properties of β-X2S3 (X = Al, Ga, In) Property β-Al2S3 β-Ga2S3 β-In2S3 a (Å) 6.9664 7.0373 7.50 c (Å) 29.6158 30.0123 32.1949 c/a 4.25122 4.26474 4.29025 B (GPa) 79.6222 76.13778 62.1444 Eg (eV) 1.48 0.9 1.02

DOS and LDOS plots for β-X2S3 (X = Al, Ga, In)

Band structures of β-Al2S3 Eg = 1.48 eV (indirect band gap) Brillouin zone for tetragonal structure

Band structures of β-Ga2S3 Eg = 0.9 eV (indirect band gap) Brillouin zone for tetragonal structure

Band structures of β-In2S3 Eg = 1.02 eV (indirect band gap) Brillouin zone for tetragonal structure

Internal Parameters β-Al2S3 β-Ga2S3 β-In2S3 Z1 Z2 Z3 Z4 Z5 0.331432 0.330343 0.333534 Z2 0.205795 0.206360 0.203723 Z3 0.251597 0.251340 0.250754 Z4 0.078314 0.077213 0.078484 Z5 0.412824 0.412028 0.413665

Internal Parameters β-Al2S3 β-Ga2S3 β-In2S3 Y1 Y2 Y3 Y4 Y5 -0.020405 -0.019844 -0.021255 Y2 0.250000 Y3 -0.008816 -0.005678 -0.005846 Y4 0.009629 0.009880 0.005619 Y5 0.022118 0.21126 0.021310

Institutional Support Collaborators Prof. S. Marsillac. (Department of Physics and Astronomy, The University of Toledo, Toledo, OH-43606.) N. S. Mangale. (Department of Electrical Engineering and Computer Science, The University of Toledo, Toledo, OH-43606.) Institutional Support Photovoltaic Innovation and Commercialization Center (PVIC) Ohio Supercomputer Cluster National Center for Supercomputing Applications (NCSA)

Thank You

Evolution of theoretical techniques The physical properties of any material are found to be related to the total energy or difference between total energies. Total energy calculation methods which required specification of number of ions in the material are referred to as ab initio methods. Ab initio make use of fundamental properties of material. No fitting parameters are involved.

Ab initio techniques and approximations Density functional theory Pseudopotential theory Iterative diagonalization method Approximations: Local density approximation Generalized gradient approximation Different codes like SIESTA, VASP, CASTEP are used. VASP - Vienna Ab initio Simulation Package Graph showing the comparison of wave function and ionic potential in Pseudopotential theory.

Details of our ab initio method LDA, Ceperley-Alder exchange-correlation functional as parameterized by Perdew and Zunger Used the VASP code with generalized ultra-soft Vanderbilt pseudo-potentials and plane wave basis set Supercell approach with periodic boundary conditions in all three dimensions Forces converged till < 0.01 eV/ Å Used supercomputers of NCSA and OSC Our calculations were performed in the framework of density functional theory (DFT), within the local density approximation (LDA) using VASP. The single-particle wave functions were expanded in a plane-wave basis using a 150 eV kinetic energy cutoff which was determined by convergence tests to be sufficient. As a test of the pseudopotentials used, we computed for bulk Si, and Ge. For Ge a lattice constant of 0.5638 nm and bulk modulus of 72.57 GPa, in excellent agreement with experimental values of 0.5658 nm and 75 GPa respectively. The theoretical lattice constant was used in all the later calculations.