1. Matthew Lane, Professor J. Staunton.
Ab initio modelling of thermoelectric materials using density functional theory
Matthew Lane, Professor J. Staunton.

2. Density functional theory
A brief summary.

3. DFT
Hartree approximation – many electron wavefunction as a product of single electron orbitals.

4. DFT
Hartree approximation – many electron wavefunction as a product of single electron orbitals.
Hartree-Fock approximation – introduction of indistinguishability and spin using slater determinant. 2
Coulomb
Exchange

5. DFT
Hartree approximation – many electron wavefunction as a product of single electron orbitals.
Hartree-Fock approximation – introduction of indistinguishability and spin using slater determinant.
Hohenberg-Kohn theorems – ground state electron density contains the same information as the wavefunction.

6. DFT
Hartree approximation – many electron wavefunction as a product of single electron orbitals.
Hartree-Fock approximation – introduction of indistinguishability and spin using slater determinant.
Hohenberg-Kohn theorems – ground state electron density contains the same information as the wavefunction.
Kohn-Sham equations – write in terms of an auxiliary system of non-interacting particles.

7. DFT
Hartree approximation – many electron wavefunction as a product of single electron orbitals.
Hartree-Fock approximation – introduction of indistinguishability and spin using slater determinant.
Hohenberg-Kohn theorems – ground state electron density contains the same information as the wavefunction.
Kohn-Sham equations – write in terms of an auxiliary system of non-interacting particles.
Density Functional Theory (DFT) – use fictitious potential of auxiliary system and self consistent field approach to iteratively minimise.

8. DFT until self consistent Initial potential
Intuit a reasonable guess at the potential.
Generate density function
Use initial potential with Kohn-Sham equations.
Wavefunction
Determine improved wavefunction.
Update potential function
Use wavefunction to correct potential.
until self
consistent

9. Modelling thermo-power
[5]
Modelling thermo-power
Extracting information from the density of states and maximising the thermoelectric figure of merit.

10. The seebeck coefficient
Large slope in the DOS at the Fermi energy.
Free electrons will diffuse from warmer to colder.
From the Drude model:
More realistically, using the energy dependant electrical conductivity:

11. Figure of merit A good thermoelectric material:
High Seebeck coefficient S
High electrical conductivity σ
Low thermal conductivity κ
Maximise the thermoelectric figure of merit.
Seebeck coefficient dominant.

12. Magnesium silicide

13. Rigid band approximation
Modelling the effect of doping.

18. [5]
Running simulations
Generating new data.

19. Tin alloy
Evidence that alloying with tin on the Silicon site improves Seebeck coefficient.
Want to know how much tin, and then suggest doping.

20. Tin alloy

32. Matthew Lane, Professor J. Staunton.
Ab initio modelling of thermoelectric materials using density functional theory
Matthew Lane, Professor J. Staunton.