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)
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
Structural details
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
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 0
Various properties of β-In2X3 (X = O, S, Se, Te)
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 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 -0.007515 -0.021255 -0.023265 -0.036737
Y2 0.250000 0.250000 0.250000 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
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
Various properties of β-X2S3 (X = Al, Ga, In)
DOS and LDOS plots for β-X2S3
(X = Al, Ga, In)
Band structures of β-Al2S3
Brillouin zone for tetragonal structure
Eg = 1.48 eV (indirect band gap)
Band structures of β-Ga2S3
Brillouin zone for tetragonal structure
Eg = 0.9 eV (indirect band gap)
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 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 -0.020405 -0.019844 -0.021255
Y2 0.250000 0.250000 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
•Photovoltaic Innovation and Commercialization Center (PVIC) •Ohio Supercomputer Cluster
•National Center for Supercomputing Applications (NCSA)
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.)
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
• Techniques:
1. Density functional theory 2. Pseudopotential theory 3. 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
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