How impurities affect optical properties of solids? Beryl - Be3Al2(SiO3)6

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How impurities affect optical properties of solids?

Beryl - Be3Al2(SiO3)6

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Intra-atomic excitations (doped insulators)

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Real crystals are never perfect, there are

always defects

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vacancies

Point defects

Defect

concentration

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Antistructural defects

Point defects

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MoS antisites

Monolayer MoS2

S - vacancies

electron microscope picture (Wikipedia)

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Green diamonds – carbon vacancies

Diamonds

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Colour centers in ionic crystals

KBr

F - center electron trapped at the anion site

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Edge dislocation Screw dislocation

Line defects

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Twinnings

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From the point of view of electron binding there are two regimes possible:

 

cr

defect r V

U  Weakly bound defects

 

cr

defect r V

U  Tightly bound defects (localized)

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Donors: P, As, Sb Acceptors: B, Al, Ga, In Substitutional impurities in Si - weakly bound

Produce shallow electron levels

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c k k

r ) = C (k ) (r )

(

i k r

k

r ) = C (k ) e F (

 

Shallow impurities – the effective mass method

Hydrogen-like equation

r ) = (E - ) F (r )Eg 2 2

2 2

e 0 s

- - e F (

2m 4  r

Donor

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 

aD

r

D

a e r

F 1 2

3

1 ) /

( π

Ry .

m Ry R m

s e

D 1 0 001

2

  Ry = 13,6 eV

B s e

D a

m a  m

n2

En   RD

r ) = (E - ) F (r )Eg 2 2

2 2

e 0 s

- - e F (

2m 4  r

F(r) – envelope function

Donor

Shallow impurities – the effective mass method

Hydrogen-like equation

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Eg

D c

v

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Ground state energies of shallow impurities

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Absorption processes involving shallow impurities

donor-acceptor transitions

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Probability of electron transitions from the valence band to donor levels

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 

aD

r

D

a e r

F 1 2

3

1 ) /

( π 2 2 2

2

5 1

1 8

) (

)

( /

D D

k a k a

C

π

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Defect localization in r- space and k- space

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 

2

g A D

0 s

= - E E + E + e

4 R

   

Donor-acceptor transitions

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Donor-acceptor transitions

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Donor-acceptor transitions

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valence band – D i A – conduction band

v – D A - c

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Case of GaP:N

Real space localization k- space delocalization

Indirect band gap

Quasi-direct

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Deep defects

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EL2 (AsGa) defect in GaAs

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