bandstructure and related properties from dft...

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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Bandstructure and related properties from DFT calculations

23 February; V172

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

3Schematic Illustration of Bands in Insulator, Semiconductor and Metal

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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Bandgap and Evaluation of Bands in Na

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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The crystal structure of the III-V semiconductors

Diamond and Zincblende Lattices

Unit cells for silicon (Si) and gallium arsenide (GaAs) Silicon - diamond lattice GaAs - zincblende (cubic zinc sulfide) lattice (most other III-V and many II-VI semiconductors have zincblende lattice) Diamond and zincblende lattice based on tetragonal pattern of bonds from each atom to nearest neighbors-two interlocking face centered- cubic lattices lattice parameter (or constant), a- repeat length of the unit cellse. g., GaAs, a = 5.65 Å (Angstroms) = 0.565 nm.

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

9The band structure ?

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

10First Brillouin zone E vs. k band

diagram of zincblende semiconductors

One relevant conduction band isformed from s- like atomic orbitals

“unit cell” part of wavefunction isapproximately spherically symmetric.The three upper valence bands areformed from (three) p- like orbitalsand the spin-orbit interaction splits offlowest, “split-off” hole (i. e., valence)band. The remaining two hole bandshave the same energy (“degenerate”)at zone center, but their curvature isdifferent, forming a “heavy hole” (hh)band (broad), and a “light hole” (lh)band (narrower)

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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Schokley’s Parking Garage Analogy for Conduction in Si

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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Schokley’s Parking Garage Analogy for Conduction in Si

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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Schokley’s Parking Garage Analogy for Conduction in Si

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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How to get conduction in Si?

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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Doping Silicon with Donors (n-type)

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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Doping Silicon with Acceptors (p-type)

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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Atomic Density for Si

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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Summary of n- and p-type Silicon

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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DFT Eigenvalues and Quasiparticle Energies

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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Bandstructure of an Insulator : MgO

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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The Bandgap problem [Sham,Schluter, PRL, 51, 1888 (1983).

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

29Baandgap Error in Semiconductors from LDA

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

30Calculated Badgap values of Si from various level of

Calculation

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 23 February 2011 Bandstructure & DOS from DFT

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