Optical Properties of Solids from DFT - Universitetet i...

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 16 March 2011 Optical properties of solids from DFT

1

Optical Properties of Solids from DFT

16 March 2011; V172


2Microscopic Theory of Linear Optical Properties of Semiconductors


3


4


5


6


7


8Optical Properties


9Beer –

Lambert Law


10

Absorption in Semiconductors : processes


11Absorption in semiconductors: processes cont.


12

Optical Properties: Semiconductors & Insulators


13

Optical Properties : Impurities


14

Urbach

Tail in Absorption


15

Absorption in semiconductors: band-to-band


16Direct band gap and Indirect band gap


17

Comparing Direct and Indirect Bandgap Absorption


18

Interband

absorption


19

Direct versus indirect absorption


20Interband

absorption above the band gap


21

Silicon band structure


22Optical absorptions in Si


23Summary of Indirect optical transitionsMany important semiconductors including Si,Ge,


24

Semi-classical Theory of Interband

Transitions


25


26

One can predict optical properties from DFT calculations


27


28Joint Density of States


29

Joint Density of States (JDOS)


30

Dielectric Function and Critical Points in Ge


31Band edge absorption in direct gap semiconductors


32Radiative and Non-radiative Recombination


33

Feasible Recombination Processes


34Excitonic

Effect : Two particle (e-h) interaction


35

Absorption via Excitons


36

Electron-Hole interaction: Excitons

The annihilation of a photon in exciting an


37Experimental Absorption Edges with exciton


38Exciton Effect above the bandgap


39Plasma reflectivity : metals (from intraband

transitions)


40Drude

Model


41

Interband

transitions in metals


42

Noble Metals : Copper


43Band structure and DOS in Copper


44Doped Semiconductors


45Optical transitions in semiconductors: Impurities


46

Donor absorption in n-type silicon


47

Light

Scattering: Interband

transition

ES

intraband transitioninterband transition

Ener

gy

wave vector

EF

band structure

kc

kv


48Linear optical

parameters

Kramers-Kronig relations

Complex dielectric tensor:

Optical conductivity:

Loss function:

Absorption coefficient:

Reflectivity:

Complex refractive index:


49Intraband Contributions: Metals

Drude-like termsDielectric Tensor:

Optical conductivity:

Plasma frequency:


50


51

Optical Sumrules


52Optical Anisotropy


53

Symmetry of Dielectric Tensor

cubic

monoclinic (,=90°) orthorhombic

tetragonal, hexagonal

triclinic


54

Convergence : Al

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

25

50

75

100

125

150

175

0 1000 2000 3000 4000 500012.012.112.212.312.412.512.612.712.8

p

k-points in IBZ

165k 286k 560k 1240k 2456k 3645k 4735k

In

terb

and

Im

Energy [eV]


55

0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5 165 k-points 4735 k-points Experiment

Nef

f [el

ectro

ns]

Energy [eV]

Sumrules : Al


56Optical Properties of Metals.


57

Loss Function

Exam

ple:

Al

0 5 10 15 200

20

40

60

80

100

120

total

intraband

interband

Lo

ss fu

nctio

n

Energy [eV]


58Optical Properties of Metals: Al and Pd


59Optical Properties of Metals: Cu and Cd


60

Dielectric Function (Real and Imaginary parts)


61Comparison of theory vs. Experiment: ε2(ω) for Ge


62

Absorption Coefficient : α(ε)


63

Index of Refraction: n(ω)


64

Sensitivity of Reflectivity to Surface Contamination


65


66


67

Band structure of Au: relativistic effects


68

DOS and Joint DOS for Au: relativistic effect


69

Dielectric function for Au: relativistic effect


70

Reflectivity: Theory vs. Experiment for Pt


71

Optical Spectra : Impact on Solar Cells


72

Optical Spectra : Impact on Solar Cells


73

Current Developments

Gradient Corrections (GGA) LDA + UExact Exchange (EXX)

Self-interaction correction (SIC)Non-local exchange / screened exchange

Kohn-Sham theory

Generalized Kohn-Sham theory

Time dependent DFT

band gap problemexcitonic effects

non-local effectscorrelation effectsband gap problem

Many-body perturbation theoryGW + Bethe-Salpeter equation

response to time-dependet perturbation

Date post:	21-Jul-2018
Category:	Documents
Upload:	dinhliem
View:	222 times
Download:	0 times

Optical Properties of Solids from DFT - Universitetet i...

Documents