Title: Theory of semiconductor nanostructures
1Theory of semiconductor nanostructures Funded by
BES LAB 03-17
Alex Zunger Alberto Franceschetti Gabriel
Bester Joonhee An
2- Theory of is generally available in two size
regimes - Tiny dots (lt100 atoms)
- First-principles LDAGW calculations are
feasible - 2. Huge dots (gt107 atoms)
- Empirical effective mass models are OK
-
- Theory is not available for 103 -106atom quantum
dots - (most interesting size range)
3What we offerAtomistic theory for 103-106 atom
nanostructures
Step 1 Relax atomic positions
Step 2 Solve single-particle problem
Step 2 Solve many-particle problem
4Summary of present methodAtomistic theory for
103-106 atom nanostructures
Step 1 Relax atomic positions
Valence-force field (VFF)
Step 2 Solve single-particle problem
Step 2 Solve many-particle problem
5Step 1 Relax atomic positions
Example InAs/GaAs dot molecule
Hydrostatic Strain Field
Valence Force Field model (VFF)
The strains on the two dots are different, even
when the dots are identical
6Summary of present methodAtomistic theory for
103-106 atom nanostructures
Step 1 Relax atomic positions
Semi-empirical pseudopotential method (EPM)
Step 2 Solve single-particle problem
Step 2 Solve many-particle problem
7Step 2 Solve the single-particle Schroedinger
equation
- Input
- Atomic positions Ri
- Screened atomic potentials vi (fitted to bulk
electronic structure) - Output
- Single-particle energies ei and wave functions
yi
- Pseudopotential method includes
- Inter-band coupling
- Inter-valley coupling
- Spin-orbit coupling
- Anisotropy of effective masses
- Realistic potential barrier
8Folded Spectrum Method
?dot?(r) ?i ci ji (r)
Hi, j lt ?i H ?j gt
ji (r)
plane waves
Ai, j lt ?i (H Eref )2 ?j gt
bulk wave functions
(E?- Eref )2
E
Conduction band
Valence band
Eref
The lowest eigenvalue of A is the eigenvalue of H
closest in energy to Eref
Up to 1,000,000 atoms !
Memory N CPU time N
9Summary of present methodAtomistic theory for
103-106 atom nanostructures
Step 1 Relax atomic positions
Step 2 Solve single-particle problem
Configuration interaction method (CI)
Step 2 Solve many-particle problem
10Step 3 Solve the many-body problem
Example Biexciton
e-e interaction
e-h interaction
h-h interaction
Configuration interaction
11Configuration-interaction Hamiltonian
Coulomb and exchange integrals
W screened Coulomb potential
is diagonalized in a basis set of electronic
configurations
12 Modern theory of nanostructures Current
capabilities
Materials Si, Ge, GaAs, InAs, InP, GaP, CdSe,
PbSe Dimensionality Films (2D), Wires (1D),
Dots (0D) Physical properties/effects Optical
absorption Emission Excitons,
bi-excitons, multi-excitons Auger
cooling rates Radiative recombination
rates Impact ionization rates
Charging energies Excitonic fine
structure
13ExampleCarrier multiplication in PbSe
nanocrystals
Ellingson et al., Nano Letters (2005)
Schaller and Klimov, PRL (2004), APL (2005)
Carrier multiplication One photon in ? several
electron-hole pairs out
14Mechanism of carrier multiplication in quantum
dots
(a)
II
II
AR
AR
(c)
(b)
15 II and AR transition rates
W screened Coulomb interaction
Open questions1. Is II faster than AR? 2. What
is the energy threshold for II?
161. II vs AR transition rates
PbSe dot R15.3 Å
Transition rate (arb. units)
II becomes faster than AR
II is 500 times faster than AR
172. II threshold
Impact ionization threshold
A. Franceschetti, J.M. An, A. Zunger, Nano
Letters (in press)
18 Modern theory of nanostructures Current
capabilities
Materials Si, Ge, GaAs, InAs, InP, GaP, CdSe,
PbSe Dimensionality Films (2D), Wires (1D),
Dots (0D) Physical properties/effects Optical
absorption Emission Excitons,
bi-excitons, multi-excitons Auger
cooling rates Radiative recombination
rates Impact ionization rates
Charging energies Excitonic fine
structure