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