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

Structure – Spectra relationship:

QD morphology: Single-dot spectroscopy:

Ga1-xInxAs QDs

(~105 atoms)(P. A. Dalgarno &

R. J. Warburton)

Structure – Spectra relationship:

QD morphology: Single-dot spectroscopy:Theory:

Input structure

Strain minimization

Solve the single-particle

problem

Solve many-particle

Problem (CI calc.)

Emission Spectra

Ga1-xInxAs QDs

(~105 atoms)(P. A. Dalgarno &

R. J. Warburton)

Structure – Spectra relationship:

QD morphology: Single-dot spectroscopy:Theory:

Input structure

Strain minimization

Solve the single-particle

problem

Solve many-particle

Problem (CI calc.)

Emission Spectra

Ga1-xInxAs QDs

(~105 atoms)(P. A. Dalgarno &

R. J. Warburton)

Self-assembled QDs are usually alloyed:

Ga1-xInxAs:

In

In

Ga

As

Random realization (RR) -

particular random assignment

of the In and Ga atoms onto

the cation sublattice.

Self-assembled QDs are usually alloyed:

Ga1-xInxAs:

In

In

Ga

As

Different local environments:

Random realization (RR) -

particular random assignment

of the In and Ga atoms onto

the cation sublattice.

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?

X0: Fine structure splitting (FSS)

X0: FSS & Polatization directions vs RRs?

S. Seidl et al., Physica E 40, 2153 (2008) –Conference proceedings.

X0: FSS & Polatization directions vs RRs?

S. Seidl et al., Physica E 40, 2153 (2008) –Conference proceedings.

?

X0: Linear Polarization Ratio (P) vs RRs?

I. Favero et al., APL 86, 041904 (2005).

• 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?

X0: Linear Polarization Ratio (P) vs RRs?

I. Favero et al., APL 86, 041904 (2005).

?• 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?

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

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

FSS exhibits significant dependence on the RRs (from 1.1 - 8.5 μeV)

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.

X0: Polarization Directions vs RRs

Vladan Mlinar and Alex Zunger, Phys. Rev. B 79, 115416 (2009)

X0: Polarization Directions vs RRs

Vladan Mlinar and Alex Zunger, Phys. Rev. B 79, 115416 (2009)

X0: Polarization Directions vs RRs

Vladan Mlinar and Alex Zunger, Phys. Rev. B 79, 115416 (2009)

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

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.

X-2: Conflicting experimental results

Poem et al., PRB 76, 235304 (2007):

• Polarization directions of the optically

active transitions oriented along

[120] and [2-10]

• Optically active transitions of X-2 have

well define polarization directions

Ediger et al., PRL 98, 036808 (2007):

Polarization directions of the optically

active transitions oriented along

[110] and [1-10]

X-2: Conflicting experimental results

Poem et al., PRB 76, 235304 (2007):

• Polarization directions of the optically

active transitions oriented along

[120] and [2-10]

• Optically active transitions of X-2 have

well define polarization directions

Ediger et al., PRL 98, 036808 (2007):

Polarization directions of the optically

active transitions oriented along

[110] and [1-10]

Different X-2 emission lines DO NOT have fixed polarization directions!

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.

Thank you for your attention!

Vladan Mlinar and Alex Zunger, Phys. Rev. B 79, 115416 (2009)

Comparison with other calculations:

PRB 77, 113305 (2008): This work:

• Investigated effect of intermixing profiles

• EBOM does not have atomic resolution

•Uniform composition profile vs.

nonuniform profile

• Linear polarization ratio as a tool for

structural characterization

• Investigated effect of atom-by-atom

random substitution

• LCBB full atomic resolution

•Uniform composition profile, but

different random realizations

• Linear polarization ratio cannot be used

as a tool for structural characterization

FSS & Polarization Directions of Multiexcitons

FSS vs RRs of Multiexcitons:

Polarization Directions of Multiexcitons: