The Charged Exciton in an InGaN Quantum Dot on a GaN Pyramid
Chih-Wei Hsu,1,a) Evgenii S. Moskalenko,1,2 Martin O. Eriksson,1 Anders Lundskog,1 K.
Fredrik Karlsson,1 Urban Forsberg,1 Erik Janzén1 and Per Olof Holtz1
1
Department of Physics, Chemistry and Biology (IFM), Linköping University, S-581 83,
Linköping, Sweden.
2
A. F. Ioffe Physical-Technical Institute, RAS, 194021, Polytechnicheskaya 26, St. Petersburg,
Russia
a)
Author to whom correspondence should be addressed. Electronic mail:cwhsu@ifm.liu.se
The direction and the degree of polarization
The polarization dependent emission spectra of QD2 were done by passing the collected
emission through a rotatable half-wave retardation plate followed by a linear-polarization
filter fixed at a specific direction before entering the monochromator. The linear-polarization
filter was kept in the same angle to ensure fixed incident geometry of the emission with
respect to the grating, avoiding the anisotropic responsivities between different incident
geometries. By recording the emission spectra with the half-wave retardation plate rotated
systematically between 0o and 180o, the in-plane polarization characteristics of the emission
can be revealed. 36 emission spectra corresponding to every 10o interval from 0o to 360o were
recorded for XA and XB, respectively. The intensities of XA and XB with respect to different
polarization directions were measured and separated in two groups. Both XA and XB groups
were divided by the maximum value found in individual groups for the normalization. The
normalized intensities of XA and XB were plotted as a function of the polarization direction as
shown in Fig S1. Two polarization features, namely the degree of polarization and the
polarization angle, can thus be determined. The definitions and details can be found in
reference 15. The fitted degree of polarization for XA and XB is 0.96 and 0.97, respectively.
The fitted polarization angle is 97o for both XA and XB.
Normalized Intensity
90
1.0
0.8
150
0.6
0.4
0.2
0.0 180
0.2
0.4
0.6
210
0.8
1.0
120
90
60
XA
120
30
330
300
270
XB
150
0
240
60
180
30
0
330
210
240
300
270
FIG. S1. Polar plots of the normalized emission intensities of XA (left) and XB (right). The
fitted curves to obtain the polarization angles are shown in red dash lines.
Exciton dynamics based on TRµPL spectroscopy
For a simple cascade biexciton-exciton recombination scheme, the recombination of a
biexciton will leave an exciton as the intermediate state and give an exciton emission later.
The time-dependent intensity of the single exciton is expected to reach its peak intensity with
a delay in relation to the peak intensity of the biexciton. Both time-dependent intensities of
the single exciton and the biexciton can be formulated by means of rate equations (ref 16 and
17). In the presented TRµPL results (Fig. S2), the Pex was set to 15 µW to generate significant
IXB, as revealed by the ratio of IXB/IXA~0.5. If we assumed XB to be biexciton and computed a
decay curve for the single exciton (XA) based on the experimental input of their individual
decay times (τXA=290±20 ps, τXB=140±10 ps) and intensities. The decay times of XA and XB
are obtained by fitting the experimental data with mono-exponential functions. It should be
noted that a more pronounced delay of XA is expected in the case of stronger IXB, which can
be obtained by increasing Pex. According to our measurements, the emission intensity of QD
saturates at ~40 µW. However, the background luminescence associated with the adjacent
InGaN layer is also magnified, causing uncertainty in background subtraction. Therefore, we
selected a moderate Pex of 15 µW to conduct the TRµPL, allowing background subtraction
with a high confidence level. Although the intensity ratio of ~0.5 is lower than the ideal ratio
of 1 (assuming biexciton and exciton), we believe that the intensity of XB under our
experimental condition is strong enough to influence the decay curve of XA as depicted by
the computed curve (FIG. S2). The computed decay curve of the exciton does not match well
with the experimental one, implying that the assumption of XB being a biexciton is not true.
Although the decay time ratio between XA and XB is ~2, an ideal expected value for
exciton and biexciton, the argument of XA and XB being single exciton and biexciton based
on the number of radiative pathways could be over simplified and is often not the case for IIInitride QDs. As has been reported by G. Bacher et al. (ref 17), the decay time ratio between
exciton and biexciton varies significantly depending on their spin structure and the spatial
wavefunction coupled to the radiation field. If the hole wavefunction becomes less localized,
the decay time for biexciton will be prolonged, shifting away from the ideal ratio of 2 to ~1
(ref 17). Such an effect is predicted to be more pronounced for asymmetric and large QDs.
Although the number of publications related to the TRµPL of III-nitride is limited, the
reported decay time ratio between the single exciton and the biexciton is typically ~1 in IIInitride QDs (ref 5 and 16). This result probably reflects a fact that the QD is asymmetric and
large. Since the actual structural information about the QD is not available, the decay time
ratio between the exciton and the biexciton is not believed to be a good indicator for the
identification of the biexciton.
FIG. S2. The transient properties of both XA and XB measured by TRµPL spectroscopy. The
experimental results of XA and XB are shown in red and black lines, respectively. The blue
line is the computed decay curve for XA assuming XB is a biexciton with a cascade biexcitonexciton recombination scheme as described in reference 16.