1. 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

2. 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)

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

4. 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:

5. 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.

6. 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

7. 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

8. 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
34.28
c/a
B (GPa)
Eg (eV)
0.6
1.02
0.23

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

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

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

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

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

14. Internal Parameters β-In2O3 β-In2S3 β-In2Se3 β-In2Te3 Z1 Z2 Z3 Z4 Z5 Z2 Z3 Z4 Z5

15. Internal Parameters β-In2O3 β-In2S3 β-In2Se3 β-In2Te3 Y1 Y2 Y3 Y4 Y5 Y2 Y3 Y4 Y5

16. 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)
c/a
B (GPa)
Eg (eV)
1.48
0.9
1.02

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

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

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

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

21. Internal Parameters β-Al2S3 β-Ga2S3 β-In2S3 Z1 Z2 Z3 Z4 Z5 0.331432 Z2 Z3 Z4 Z5

22. Internal Parameters β-Al2S3 β-Ga2S3 β-In2S3 Y1 Y2 Y3 Y4 Y5 -0.020405 Y2 Y3 Y4 Y5

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

24. Thank You

27. 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.

28. 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.

29. 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 nm and bulk modulus of GPa, in excellent agreement with experimental values of nm and 75 GPa respectively. The theoretical lattice constant was used in all the later calculations.