Pseudopotential calculations of excitonic transitions in semiconductor quantum dots

1
Pseudopotential calculations of excitonic
transitions in semiconductor quantum dots
Andrew Williamson Lin-Wang Wang Huaxiang Fu Alex
Zunger
National Renewable Energy Laboratory, Golden,
Colorado
2
Summary

• Description of Atomistic Methods
• Pseudopotentials, Folded Spectrum Method
• electron-hole Coulomb interaction
• Free Standing Dots
• CdSe, InAs Excited state spectra
• Embedded Quantum Dots
• GaAs / InAs SK dots Dependence on size, shape
  and pressure

3
Calculation of single particle states
Relax Strain (VFF)
Empirical Pseudotential Hamiltonian

• No EMA
• No Parabolic bands
• No limit on no. bands
• Realistic shape
• Realistic surface
• Full strain

Folded Spectrum Method
4
Calculation of excited states
20 conduction states
jth conduction State
ith valence State
40 valence states
Coulomb Energy
Transition Probability
Absorption Spectrum
5
Calculated absorption spectra (CdSe)

• Few main peaks
• Spacing decreases
• with size

6
Free standing CdSe

• EPM explains up to 8 peaks
• Correct scaling with size

7
Free standing InAs
8
Differences with k.p
1. Different order of levels
k.p
EPM
-0.2
InP EPM s above p (VB to CB allowed)
k.p p above s (VB to CB forbidden)
PF
-0.3
SD
SD
H. Fu et al. Appl. Phys. Lett. 71 (1997)
P
-0.4
(eV)
PF
2. Different assignment of some excitons
DG
D
VBM
bulk
-0.5
SD
SD

E
-
i
E
-0.6
-0.7
-0.8
0
2
4
0
2
4
9
Conclusions - Free standing dots

• Eigenstates and energies
• Coulomb energies, excitation energies
• Transition probabilities, absorption spectra
• Good agreement with experiment even for
• high order exciton

10
InAs / GaAs wavefunctions 101

• Electron states Single band works well

• Hole states Multiband mixing

11
Effect of shape on conduction states
101
105
113

• Same order of states
• Same shape of wavefunctions

12
Effect of size InAs/GaAs 101
(3)
(4)
(4)

• Gap decreases with size
• Number bound electron states
• increases
• No change in order of states

(5)
CBM
VBM
13
Effect of pressure, InAs/GaAs 105
14
Conclusions - SK dots

• Eigenstates and energies
• Coulomb energies, excitation energies
• Size dependence of energy levels
• Pressure induced type I II transition