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 − nm 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 nm → n' ' m' = E b ,nm − 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