Contributed talk at the 2009 American Physical Society March Meeting: http://meetings.aps.org/Meeting/MAR09/SessionIndex2/?SessionEventID=104219

1. Effect of Atomic-Scale Randomness on the
Optical Polarization of Semiconductor
Quantum Dots
Vladan Mlinar and Alex Zunger
National Renewable Energy Laboratory,
Golden, Colorado USA
Vladan.Mlinar@nrel.gov

2. Structure – Spectra relationship:
QD morphology: Single-dot spectroscopy:
Ga1-xInxAs QDs (P. A. Dalgarno &
(~105 atoms) R. J. Warburton)

3. Structure – Spectra relationship:
QD morphology: Theory: Single-dot spectroscopy:
Input structure
Ga1-xInxAs QDs Strain minimization
(P. A. Dalgarno &
(~105 atoms) R. J. Warburton)
Solve the single-particle
problem
Solve many-particle
Problem (CI calc.)
Emission Spectra

4. Structure – Spectra relationship:
QD morphology: Theory: Single-dot spectroscopy:
Input structure
Ga1-xInxAs QDs Strain minimization
(P. A. Dalgarno &
(~105 atoms) R. J. Warburton)
Solve the single-particle
problem
Solve many-particle
Problem (CI calc.)
Emission Spectra

5. Self-assembled QDs are usually alloyed:
Ga1-xInxAs:
As
In
Ga
In
Random realization (RR) -
particular random assignment
of the In and Ga atoms onto
the cation sublattice.

6. Self-assembled QDs are usually alloyed:
Ga1-xInxAs:
As
In
Ga
In
Random realization (RR) -
particular random assignment
of the In and Ga atoms onto
Different local environments: the cation sublattice.

7. Optical Properties vs Atomic-Scale Randomness
Ga1-xInxAs:
Large bulk solids: different random
realizations (RRs) get self-
averaged, so the measured physical
property does not resolve features
of individual RRs.
Finite nanosystems (≤105 atoms):
self-averaging of RRs may not be
complete, so we can observe the
effect of individual RRs (atomic-
scale alloy randomness effect).
What is the effect of atomic-scale randomness on the
optical properties of Gax-1InxAs QDs?

8. X0: Fine structure splitting (FSS)

9. X0: FSS & Polatization directions vs RRs?
S. Seidl et al., Physica E 40, 2153 (2008) –Conference proceedings.

10. X0: FSS & Polatization directions vs RRs?
?
S. Seidl et al., Physica E 40, 2153 (2008) –Conference proceedings.

11. X0: Linear Polarization Ratio (P) vs RRs?
• P is a measure of the in-plane polarization
anisotropy
P = (Ix - Iy)/(Ix + Iy)
Where Ix and Iy are intensities defined along [110] and
[1-10] direction
• Atomic-scale randomness vs geometrical
anisotropy?
I. Favero et al., APL 86, 041904 (2005).

12. X0: Linear Polarization Ratio (P) vs RRs?
?
• P is a measure of the in-plane polarization
anisotropy
P = (Ix - Iy)/(Ix + Iy)
Where Ix and Iy are intensities defined along [110] and
[1-10] direction
• Atomic-scale randomness vs geometrical
anisotropy?
I. Favero et al., APL 86, 041904 (2005).

13. X0: FSS changes by more than a factor 7 with RRs

14. X0: FSS changes by more than a factor 7 with RRs
FSS exhibits significant dependence on the RRs (from 1.1 - 8.5 μeV)

15. X0: FSS changes by more than a factor 7 with RRs
FSS exhibits significant dependence on the RRs (from 1.1 - 8.5 μeV)
FSS shows almost no sensitivity to piezoelectric field, irrespective of
piezoelectricity was included via linear term only, or both linear and
nonlinear terms.

16. X0: Polarization Directions vs RRs
Vladan Mlinar and Alex Zunger, Phys. Rev. B 79, 115416 (2009)

17. X0: Polarization Directions vs RRs
Vladan Mlinar and Alex Zunger, Phys. Rev. B 79, 115416 (2009)

18. X0: Polarization Directions vs RRs
Vladan Mlinar and Alex Zunger, Phys. Rev. B 79, 115416 (2009)

19. X0: P is not affected only by geometrical elongation
• Even 50% elongation in [100] direction
gives the same range of P, as in
geometrically symmetric QD!
• Measuring P cannot tell:
(1) the geometrical anisotropy
(2) composition

20. FSS & Polarization Directions of Multiexcitons
• QD can be charged by controllable number of electrons and holes: X-2, XX0, XX-1, XX+1
• FSS of multiexcitons is sensitive to RRs.
• Optically active transitions of different multiexcitons do not have fixed polarization
directions
Poem et al., PRB 76, 235304 (2007): Different multiexcitonic transitions have well defined
polarization directions.

21. X-2: Conflicting experimental results
Poem et al., PRB 76, 235304 (2007): Ediger et al., PRL 98, 036808 (2007):
• Polarization directions of the optically Polarization directions of the optically
active transitions oriented along active transitions oriented along
[120] and [2-10] [110] and [1-10]
• Optically active transitions of X-2 have
well define polarization directions

22. X-2: Conflicting experimental results
Poem et al., PRB 76, 235304 (2007): Ediger et al., PRL 98, 036808 (2007):
• Polarization directions of the optically Polarization directions of the optically
active transitions oriented along active transitions oriented along
[120] and [2-10] [110] and [1-10]
• Optically active transitions of X-2 have
well define polarization directions
Different X-2 emission lines DO NOT have fixed polarization directions!

23. Conclusions:
We provided a clear evidence for the effect of atomic-scale
randomness on the optical properties of alloyed Ga1-xInxAs QDs.
• Fine structure splitting of the monoexciton changes by more than a factor
of 7 with RRs.
• For multiexcitons, the polarization directions strongly depend on the atomic
scale randomness, so different multiexciton emission lines do not have
fixed polarization directions.
• Optical polarization is affected both by atomic-scale randomness and by
possible geometric elongation of the QD in one direction.
Vladan Mlinar and Alex Zunger, Phys. Rev. B 79, 115416 (2009)
Thank you for your attention!

24. Comparison with other calculations:
PRB 77, 113305 (2008): This work:
• Investigated effect of intermixing profiles • Investigated effect of atom-by-atom
random substitution
• EBOM does not have atomic resolution • LCBB full atomic resolution
•Uniform composition profile vs. •Uniform composition profile, but
nonuniform profile different random realizations
• Linear polarization ratio as a tool for • Linear polarization ratio cannot be used
structural characterization as a tool for structural characterization

25. FSS & Polarization Directions of Multiexcitons

26. FSS vs RRs of Multiexcitons:

27. Polarization Directions of Multiexcitons: