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University of Sidi Mohammed Ben Abdallah Faculty of Science Dhar El Mahraz-Fes

The Effects of an external field and LO phonons on the Optical Properties of Shallow Impurities in CdSe Quantum Dot M. Ahlal, I. Zorkani & A. Jorio Laboratory of Solid State Physics

Absorption Coefficient

Introduction The bandgap in a quantum dot will always be energetically larger than The bandgap in the bulk semiconducteur; therefore, we refer to the radiation from quantum dots to be "blue shifted" reflecting the fact that electrons must fall a greater distance in terms of energy and thus produce radiation of a shorter, and therefore "bluer" wavelength.

On-centre impurity 1 α // ( ω ) = α 4π

1 × FS n rε 0R

n= 2 l= 1 m= ,± 1

(

  X0 2 + Y0 2  ( E − E ) 2 + γ 2  nlm   100 ,nlm λ 100 ,nlm  

) + (E

 δ ( E − E − ω ) ) − E Z  nlm λ nlm λ 100 ,nlm  2

2

0

Off-centre impurity

Linearly polarized radiation α

// ( ω ) =

3 α 4π

1 n rε 0R

FS

∑ ( E nlm − E λ ) 2 Z100,nlm

2

n= 2 l = 0 ,1 m= 0

δ ( E f − E i − ω )

Circularly polarized radiation α

CdSe Quntum Dot

Bulk semiconductors

⊥ ( ω ) =

3 α 8π

Size Dependant color

FS

1 n rε 0R

n= 2 l= 1 m= ± 1

(

 X  100 ,nlm ± Y100 ,nlm 

) (E 2

2 nlm − E λ ) +

γ 2(X

100 ,nlm

 Y100 ,nlm

) δ (E 2

f

− E i − ω )  

Quatum Dot Quantum Well The peak value of the absorption coefficient for infinite CdS QD as a function of the photon energy for two magnetic field values B=0T and B=5T when the electromagnetic field is polarized parallel to ri . strong geometric confinement regime

The absorption coefficient as a function of photon energy for several values of the dot radius and for a magnetic field value B=20T

Quantum Dots Energy levels in the presence of a magnetic field EC ED

Light Et

B

EG EA

EV

Magneto-absorption Coefficient: LO phonons Effect

Ni

Interbande

Via défauts/ impuretés

Intrabande

An electron is Excited across the Bandgap

Optical Transitions in Semiconductors 2

 1 2 2 2 + γ L z + γ r sin ( θ ) + Vconf ( r ) 2 2 4 r + ri − 2r ri cos( θ )

H = − ∆ r,θ ,ϕ −

H = − ∆ r ,θ ,ϕ

H = H e + H LO + H e − LO + H ion − LO

 1 2 2 2 + γ L z + γ r sin ( θ ) + V ( r ) 4 (

α

J1 2 ( k10 r )   1 2 2  2 2 ( ) ( ) N r , λ exp − λ r + r − 2 r r cos θ exp  − γ r sin ( θ )  , i i ϕ i ( r, θ , ϕ ) =  i r  4   0, r>R 

)

(

E i (λ ) = min λ ϕ i H ϕ i

r≤ R

  (  + m + 1) (  − m + 1) − (  + m ) (  − m )  1 2 2 2  E = k + m γ + γ N Λ 1 −  nm n n  ( 2 + 1) ( 2 + 3) ( 2 + 1) ( 2 − 1)  4    J  + 1/ 2 ( k n r ) ψ m ( ) ( ) r = N Y θ , ϕ n   n  m r

 2 π2 Ι3  Ι1 γ  R  Ι 2 = min λ  λ + 2 + γ − γ R +  − 1 − 2  R T 2 π T R T    

The peak value of the absorption coefficient for infinite CdS QD as a function of the photon energy and for a set of the magnetic field values running from 0 to 15 T, when the electromagnetic field is polarized perpendicular to ri. E1 and E2 correspond to transitions involving donor at the edge and at on-center of the QD respectively

The peak value of the absorption coefficient for infinite CdS QD as a function of the photon energy for two magnetic field values B=0T and B=5T when the electromagnetic field is polarized parallel to ri. weak geometric confinement regime and

e − ph

=

1 α 4π

FS

)

2  Ei − E ef− ph ψ ef X ψ ie e − ph   2 1 i f ψ ef Y ψ  + E e − ph − E e − ph 3 n r ε 0 R ω   + E ei − ph − E ef− ph 2 ψ ef Z ψ 

( (

) )

2

i e i e

  2  i f  δ E p − E p − ω  2  

(

α (ω ) = α

e

(

)

α

(ω ) +

e

α

(ω ) =

1 α 4π

FS

e − ph

)

 (E i − E f )2 + (γ R* )2 ψ f X ψ i 2  e B e e  e    2 1  i f 2 * 2 f i i f + ( E − E ) + ( γ R ) ψ Y ψ   δ ( E p − E p − ω ) e e B e e 3 n r ε 0 R ω   2 2 i f f i   + ( Ee − Ee ) ψ e Z ψ e  

(

)

(ω )

16

*

Transition energy (R )

14

B=0T B=10T B=20T

12

(

)

ET nm → n' ' m' = E b ,nm − E b ,n' ' m

10

∆  = ± 1, ∆ m = 0 , ± 1

8 6

Absorption coefficient as function of the photon energy.In the absence (a) and in the presence (b) of e-LO Phonons interaction for finite potentiel barrier

4 2 0 0

5

10

15

20

*

Dot radius (a )

1s-2p+ transition energy of a CdSe quantum as a function of the dot radius for magnetic field values from 0 to 20T.

The transition energies between 1s (ground state of the donor) and some excited states of the conduction levels as a function of the magnetic field, for an on-center donor (open circles) and for an off-center donor (full circles).

Absorption coefficient as function of the photon energy.In the absence (a) and in the presence (b) of e-LO Phonons interaction


P12-23