Large internal dipole moment in InGaN/GaN quantum dots [original]

Appl. Phys. Lett. 97, 063103 (2010); https://doi.org/10.1063/1.3477952 97, 063103

Large internal dipole moment in InGaN/GaN

quantum dots

Cite as: Appl. Phys. Lett. 97, 063103 (2010); https://doi.org/10.1063/1.3477952

Submitted: 16 June 2010 • Accepted: 20 July 2010 • Published Online: 09 August 2010

Irina A. Ostapenko, Gerald Hönig, Christian Kindel, et al.

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Large internal dipole moment in InGaN/GaN quantum dots

Irina A. Ostapenko,a兲Gerald Hönig, Christian Kindel, Sven Rodt, André Strittmatter,

Axel Hoffmann, and Dieter Bimberg

Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany

共Received 16 June 2010; accepted 20 July 2010; published online 9 August 2010兲

Direct observation of large permanent dipole moments of excitonic complexes in InGaN/GaN

quantum dots is reported. Characteristic traces of spectral diffusion, observed in

cathodoluminescence of InGaN/GaN quantum dots, allow deducing the magnitude of the intrinsic

dipole moment. Our experimental results are in good agreement with realistic calculations of

Institute of Physics.关doi:10.1063/1.3477952兴

Nitride-based self-assembled semiconductor quantum

dots 共QDs兲have attracted growing interest in recent years for

their potential application in optoelectronic devices, such as

green and blue light emitting diodes and laser diodes,1and in

quantum information processing, like high-temperature

single-photon emitters on demand.2,3Wurtzite InGaN and

GaN are remarkable for their strong spontaneous macro-

scopic polarization.4The built-in piezoelectric and pyroelec-

tric fields5,6tremendously affect optical properties of nitride

heterostructures via the Quantum Confined Stark Effect

共QCSE兲. Detailed understanding of the interplay between

confined charge carriers and electric fields is crucial for

improvement of nitride QD-based devices. Theoretical

investigations5–8of InGaN/GaN QDs and a few experimental

reports on the QCSE in single InGaN/GaN QDs 共Refs. 9and

10兲were reported so far. Experimental evidence of the in-

trinsic dipole moment is up to now lacking.

The QCSE is suggested to be the cause of spectral dif-

fusion, such as luminescence line broadening,11 intensity

quenching and random energy shifts of single QD emission

lines.12–18 One can take advantage of spectral diffusion to

assign individual lines to distinct QDs, as reported in micro-

photoluminescence 共

␮

PL兲共Refs. 9,11, and 12兲and cathod-

oluminescence 共CL兲.13,19,20

In CL experiments on single InGaN/GaN QDs, we ob-

serve unique spectral diffusion patterns. These patterns can-

not be explained within the existing model of charging and

discharging of defects in the vicinity of a QD. We propose a

novel mechanism, based on the interaction of a QD and a

gradually changing field of a propagating charge, and are

able to deduce the value of the dipole moment purely from

the QD emission energy trace. We substantiate our experi-

mental observations with realistic calculations.

We investigated different samples of InGaN/GaN QDs

grown by metal-organic chemical-vapor deposition on

Si共111兲substrate 关for further details see Ref. 19兴. The InGaN

layer has a nominal thickness of 2 nm and is capped with 20

nm GaN. The samples were covered with metal shadow

masks to allow the investigation of individual QDs.20 Single-

dot spectroscopy at liquid helium temperature was performed

with a scanning electron microscope JEOL JSM 840

equipped with a CL setup, with a spectral resolution of

310

␮

eV.19

Figure 1shows an example of the temporal variation in

CL spectra for InGaN/GaN QDs with 100 ms integration

time per spectrum. We observe here a typical pattern of emis-

sion line oscillations 共marked with ellipses in Fig. 1兲. These

oscillations with amplitudes up to 4 meV occur repeatedly

for many investigated QDs in different samples, with a ran-

dom appearance for each QD. We call this pattern “

␹

” for

simplicity. It appears always in the same manner: the line

bends to lower energies, then blinks off and reappears with a

blueshift, returning to its mean position afterwards. Such a

line trajectory has not been reported yet and does not appear

␮

PL experiments of the same samples.

Spectral diffusion is commonly explained as follows:

free carriers trapped in defects in the vicinity of the QD and

in neighboring QDs induce randomly fluctuating local elec-

tric fields and thus cause an energy shift of the luminescence

lines via the QCSE.9,11,12 The dependence of transition en-

ergy shift ⌬Eon the external electric field Fcan be ex-

pressed as21

⌬E共F兲=兺

i=x,y,z

共

␮

iFi−

␣

iFi

2兲,共1兲

where

␮

iare the components of the QD excitonic dipole

moment and

␣

iis related to excitonic polarizability.

a兲Electronic mail: [email protected].

FIG. 1. 共Color online兲Temporal evolution of CL spectra showing a single

emission line from an InGaN/GaN QD. The intensity is coded in gray scale

and the integration time for each spectrum is 100 ms. Circles result from

Gaussian fits for the peak center energy. Ovals depict typical

␹

–patterns.

One of them is presented in the inset, as time-dependence of energy shift.

The solid curve in the inset results from a fit with ⌬E共t兲=

␮

zFz共t兲

⬃共t/共constant+t2兲3/2兲关see Eq. 共2兲兴.

APPLIED PHYSICS LETTERS 97, 063103 共2010兲

However, the observed

␹

-pattern cannot be explained

with random charging and discharging of defects. Stochastic

carrier trap and release processes would result in random

discrete energetic jumps or linewidth broadening11 and could

not give the smooth trajectory shown in Fig. 1, with the same

geometry for all occurrences. Many lines show

␹

-patterns

but only a few are synchronous in time. Therefore, the origin

must be close to the QD: fluctuating charges on interfaces or

in traps lying at larger distances relative to the interdot spac-

ing would result in similar field changes for several neigh-

boring QDs, giving a similar spectral diffusion pattern for all

spectral lines.

For the occurrence of the

␹

-pattern the following condi-

tions must be fulfilled: 共1兲the field Fchanges gradually for a

continuous, smooth change in peak position. 共2兲The varia-

tion in Faccounts for both positive and negative energy

shifts of equal magnitude around the mean emission energy.

This cannot be fulfilled by a quadratic response of the system

to the changes in F, and consequently

␮

iFiⰇ

␣

iFi

2in Eq. 共1兲.

Hence, the observed patterns present direct experimental evi-

dence of the large dipole moment in InGaN/GaN QDs. 共3兲

For the abrupt change of sign of the line shift, the field F

changes its direction relative to the position of the QD once.

For quantitative estimations, we have to apply a detailed

model, describing the pattern. The only originator of the

electric field fulfilling the above three conditions is a charge,

propagating smoothly through the material. We assume a

charge qthat propagates through the material approximately

on a straight line with an average speed v

␮

, and consider the

induced electric field within the QD and the resulting time-

dependent line shift. More complex charge trajectories do

not change the results significantly.

The central symmetry of the

␹

-pattern with the same

amplitude in positive and negative shift direction is only

achieved when the propagation direction has a component

共anti-兲parallel to

␮

. The field created by a moving charge

fulfills all three conditions above. The induced oscillation of

the emission energy around its average energetic position

⌬E关F共t兲兴共see inset in Fig. 1兲is

⌬E关F共t兲兴 ⬇

␮

ជ

·F

ជ

␮

⬃

␮

共d⬜

2+t2v

␮

2兲3/2,共2兲

with time t=0 in the center of the

␹

-pattern, v

␮

—average

charge velocity along growth direction, d⬜—lateral distance

between the charge and QD center at t=0.

Calculations for InGaN/GaN QDs deliver field strengths

in the dot center up to 1.6 MV/cm 共Refs. 5and 8兲and a

significant permanent dipole moment due to the separation of

electron and hole states within a QD.6Here we theoretically

investigate the excitonic dipole moment and the influence of

additional electric fields and nearby charges on the exciton

emission energy.

We performed self-consistent Hartree calculations for an

exciton trapped in lens shaped QDs. The calculations, based

on eight-band k·pstates, include strain, piezoelectricity and

pyroelectricity, spin-orbit, and crystal-field splitting. The lat-

eral diameter of the model QD presented here is 5.2 nm and

its height 2 nm. The QD is placed ina2nmthick In0.1Ga0.9N

layer, with the In content inside the QD linearly rising up to

a maximum of In0.49Ga0.51N at the center of the QD. This

model system is embedded in a matrix of pure GaN. The

parameters were chosen to match the structural investiga-

tions of the samples.19 The predicted exciton emission en-

ergy is ⬃2.92 eV. The dipole moment, calculated from the

electron and hole functions density distribution, is

␮

z=1.9

⫻10−28 C·m=1.2e·nm and

␮

x,y=0. Change in the model

QD structure, leading to the change in the emission energy

within the experimentally observed range, does not result in

significant change in

␮

. Applying homogeneous capacitor-

like fields in x,yand zdirection with a magnitude of

⬃10 kV/cm, chosen to reproduce the observed energy

shifts, yields the same

␮

It is, however, not obvious, to what extent Eq. 共1兲is

applicable for electric fields, that are spatially inhomoge-

neous across the QD. To verify our model of a traveling

charge, we also calculated the exciton energy shifts, caused

by external electrostatic fields of a negative elementary point

charge, placed onto different positions close to the model

QD—see Fig. 2. The circles depict numerical results, the

contour plot shows a fit with Eq. 共1兲, resulting again in the

same

␮

. The inset of Fig. 2shows line traces for different

constant lateral distances to the QD. It is easy to see the

similarity to the observed experimental data 共inset Fig. 1兲.

We find the energy shifts, induced by nearby point charges,

still well described by Eq. 共1兲. Particularly our simulations

show that the

␹

-patterns are induced by external fields, more

than two orders of magnitude smaller than the built-in fields

of the QDs. Hence, the energy shift, caused by the quadratic

term in Eq. 共1兲, is much smaller than the one caused by the

linear term, and it is justified to set

␣

x,y,z=0 in the analysis of

the experimental results.

We can now directly deduce the value of the excitonic

dipole moment from the amplitude of the

␹

-pattern. The av-

erage QD radius and average distance between the QDs is

2.5 nm and 10 nm, respectively.19 Then with the d⬜in the

range of 2.5 to 8 nm and a maximum observed shift ampli-

tude of 4 meV, we obtain dipole moment values between

␮

z=0.7⫻10−28 C·m=0.3e·nm and 7⫻10−28 C·m=3e·nm,

respectively. Theoretical prediction6and our numerical re-

sults agree quantitatively. Therefore, our observations allow

to determine the magnitude of the dipole moment of the

InGaN/GaN QDs in growth direction.

FIG. 2. 共Color online兲Contour plot of the calculated exciton energy shift for

a point charge at 共x,z兲. The QD center is located at x=0, z=0. The circles

represent results of Hartree calculations for each charge position. The

color-coded contour plot results from a fit ⌬E关F

ជ

共x,z兲兴=

␮

zFz+

␣

F2. Inset

shows the energy shift of an emission line of the model QD for a charge of

different lateral distances, d⬜, to the QD.

063103-2 Ostapenko et al. Appl. Phys. Lett. 97, 063103 共2010兲

The identical geometry of all

␹

-patterns lets us conclude

that we observe the influence of either only one type of

charge carriers or of the motion of positive and negative

charges in exactly opposite directions. Remarkable is the

slow time scale of the emission line shifts, which does not

comply with diffusion-time constants of hot carriers. From

experimental data and fit with Eq. 共2兲, we obtain a carrier

velocity on the order of ⬃20 nm/s. It could be a weakly

bound charge, propagating slowly along a threading disloca-

tion line. Another driving force for the moving charge may

be the excitation mechanism in CL: excess carriers are in-

jected into the sample resulting in a vertical gradient of

charge carriers.

In conclusion, we report the experimental proof of large

dipole moments in InGaN/GaN QDs. Our results are based

on the observation of characteristic traces in the spectral dif-

fusion of the CL emission lines from single QDs. From ex-

periment we identify built-in dipole moments as large as 0.7

to 7.0⫻10−28 C·m. Realistic calculations using eight-band

k·ptheory and the Hartree model yield dipole moments of

similar values. A recurrent energy-shift pattern in the lumi-

nescence of single InGaN/GaN QDs is caused by the inter-

action of the excitonic dipole moment of the QD and a

gradually changing electric field. We propose as explanation

the interaction of the QD and the changing field of a moving

charge, propagating on a straight line through the material.

This work was supported by Deutsche Forschungsge-

meinschaft in the frame of SFB 787.

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063103-3 Ostapenko et al. Appl. Phys. Lett. 97, 063103 共2010兲