Henini M. Handbook of Self Assembled Semiconductor Nanostructures for Novel devices in Photonics and Electronics

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Optical and Vibrational Properties of Self-assembled GaN Quantum Dots 259

where ω

is the optical transition frequency, n is the refractive index, and m

is the free electron

mass. Hence, the presence of strong built-in electric ﬁ elds should slow down the exciton radiative

recombination. Time-resolved PL experiments have revealed that the decay time of the emission,

, can be as high as tens of microseconds and presents a strong dependence on the QD height

[112, 113, 122, 123] . Figure 7.29 shows the measured PL decay times of a series of samples

containing a single period of GaN/AlN QDs with emission energies varying from 1.8 to 3.7 eV

[113] . The experiments were conducted at 8 K and the repetition rate of the excitation source

was either 10 Hz or adjusted in the range from 800 Hz to 82 MHz to avoid multiple excitations.

At low temperatures, it is often assumed that τ

is purely radiative and τ

 τ

since the exciton

non-radiative decay time, τ

, should be much longer. The validity of such an assumption for

hexagonal GaN/AlN QDs will be re-examined later on in this section. The variation of τ

is com-

patible with the QCSE: lower emission energies correspond to higher QDs where the separation of

electrons and holes is more pronounced and τ

is longer, and for shorter dots the emission energy

is higher and so is the overlap between the electron and hole wavefunctions leading to shorter τ

Therefore, whereas piezoelectric effects are dominant for taller QDs, the dynamics of excitons in

shorter dots are still governed by conﬁ nement effects. Solid lines in Fig. 7.29 depict the results

of a simple theoretical model based on the effective mass and envelope function approximations

that assumes a constant effective electric ﬁ eld inside the QD [113] .

3.5 3.0 2.0 1.52.5

Quantum dot height (nm)

GaN/AIN QDs

3.5

4.0

2.5 3.0

1.5

2.0

Energy (eV)

1ms

1ns

1s

Radiative lifetime

11MV/cm

9 MV/cm

7 MV/cm

Figure 7.29 PL decay time as a function of the energy of the PL maximum and the calculated QD height for differ-

Another unambiguous consequence of the existence of strong electric ﬁ elds is the dynamic

red shift of the time-resolved emission for increasing delay times after the arrival of the excitation

pulse. This is shown in Fig. 7.30a where three normalized PL spectra corresponding to different

delay times are displayed. At early times, the high density of photogenerated carriers (of the order

of 10

 2

in this experiment) screens the internal electric ﬁ eld very effectively and reduces the

QCSE (see the right-hand sketch of Fig. 7.30b ). The peak shifts to the red as the photogenerated

carriers recombine and the internal electric ﬁ eld is recovered. This red shift is faster at early times

and becomes almost negligible after 10 μ s when the “ classical ” radiative recombination regime is

reached as reported in Fig. 7.30b . The radiative lifetime decreases exponentially with the density of

electron–hole pairs [89] so that the dynamical descreening of the internal electric ﬁ eld also results

in the observed non-exponential decay of the PL intensity (see Fig. 7.30b ).

Although 3D conﬁ nement reduces the probability of non-radiative recombination, the pres-

ence of misﬁ t dislocations, often acting as nucleation centres for the QDs, may still diminish the

internal radiative efﬁ ciency of the QDs, η , deﬁ ned as

ττ







NR R

(7.7)

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260 Handbook of Self-assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics

1.8 2.0

Energy (eV)

3.02.6 2.82.2 2.4

T  8 K

t  0.23 s

t  1.8 s

t  22 s

(a)

(b)

Intensity (arb. units)

10 1000.01 10.1

2.0

3.0

2.5

Time (s)

GaN/AIN QDs

Energy (ev)

Figure 7.30 (a) Dynamic red shift of the time-resolved emission of a 3.3 nm height GaN/AlN QD. (b) Temporal

evolution of the PL maximum. The excitation density was 100 μ J/cm

per 5 ns pulse. The inset sketches represent

the dynamic descreening of the potential for electrons and holes along the QD axis [113] . With permission from

In hexagonal GaN/AlN QDs η depends not only on the sample temperature but also on the dimen-

sions of the dot. In particular, it is very much dependent on the QD height. It is reasonable to

assume that τ

is purely radiative and that η is close to 1 for the shortest dots at low temperatures.

Fixing η  0.8 for h  2.5 nm, Simon et al. [112] have deduced the size dependence of η at low tem-

peratures, ﬁ nding that it falls down to 0.25 for h  3.6 nm. Such a radical decrease follows from

an almost size independent τ

(~10 ns) and a fast increase in τ

for taller QDs due to the drop

in the oscillator strength, see Eq. 7.6 . As a result, non-radiative processes have a more signiﬁ cant

contribution in the emission of taller QDs even at low temperatures. The temperature dependence

of η shows that a decrease with increasing temperature ( η  0.27 for h  2.5 nm at room temper-

ature) occurs due to the reduction of τ

by an order of magnitude while τ

remains almost con-

stant [112] . The latter is expected for a 0D system. On the other hand, the decrease of τ

is more

pronounced for shorter dots as the wavefunctions of the conﬁ ned carriers penetrate more into the

barrier making them more sensitive to nearby defects, such as threading dislocations.

7.4.4 Single quantum dot studies

Although optical spectroscopy on ensembles of QDs gives access to valuable information, the

large inhomogeneous broadening of the spectral lines still hides many other fundamental

aspects, such as the exciton ﬁ ne structure, the homogeneous broadening of the emission lines,

etc. Microscopic measurements where the emission of a single QD is resolved have proliferated

for zinc-blende materials since the mid 1990s. Despite the interest that short-wavelength single-

photon emitters convey [124] the study of self-assembled GaN QDs has evolved at a much slower

pace. This is partly due to the poor control over the dot density described in section 7.2. The ﬁ rst

μ PL spectra showing single QD features were achieved in the group of Y. Arakawa in 2004 on

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Optical and Vibrational Properties of Self-assembled GaN Quantum Dots 261

samples grown by MOCVD [8] . Almost simultaneously, near-ﬁ eld scanning optical microscopy

images were published showing the emission of relatively large (20 nm height and 150 nm

diameter) single GaN QDs [125] . Previously, single QD CL measurements [126] were performed

in uncapped GaN dots grown on AlGaN by MOCVD using TESi as antisurfactant. The density of

dots in the samples grown by this method was small enough to ensure the observation of sin-

gle dot emission without the need of isolation techniques. The position of a QD of a diameter of

100 nm and a height of 40 nm was determined by high-resolution ﬁ eld emission scanning elec-

tron microscopy. Its CL spectrum was characterized by a peak at 3.47 eV, ascribed to the dot, and

a second peak centred at 3.71, characteristic of the AlGaN layer. The large width of the single QD

emission (50 meV) was attributed to the presence of Si impurities introduced in the dot during

growth. More recently, the combination of detailed CL mappings obtained at various emission

wavelengths ( Fig. 7.31 ) and AFM micrographs [127] allowed the establishment of a direct cor-

relation between the emission characteristics of the individual dots and their size and density.

Figure 7.31 CL images of 4  4 μ m

regions taken at (a) 260 nm, (b) 290 nm, (c) 300 nm (d) 330 nm, (f) 350 nm,

(g) 370 nm, and (i) 410 nm at 300 K and V

acc

 3 kV of GaN QDs grown on an AlN buffer layer on (0001) 6H-

SiC by MOCVD [127] .

The isolation of a few QDs by μ PL requires either etching submicron mesa patterns [8] or

opening submicron holes in an opaque metallic mask [9] on a sample containing a low density

of QDs (  10

 2

). Single QD PL lines measured on a 200 nm mesa are shown in Fig. 7.32 .

For low excitation powers, a single emission peak is observed and is attributed to the conﬁ ned

exciton (X). With increasing power, a second peak, labelled XX, appears on the high energy side.

Two additional peaks of unknown nature appear in the P

 9 mW spectrum. Notice that while

the intensity of X scales linearly with P

, XX presents a superlinear (quadratic) power depend-

ence. Hence, X and XX can be assigned to the exciton ground state and the biexciton transitions,

respectively. According to that allocation, the biexciton binding energy is negative and of the

order of 30 meV. Biexciton binding energies are most often positive. The negative binding energies

observed in GaN QDs are a consequence of the spatial separation of electrons and holes (see Fig.

7.23b ) which leads to, on the one hand, a reduction of the electron–hole binding energy and, on

the other hand, an increase of the electron–electron and hole–hole binding energies [128] .

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262 Handbook of Self-assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics

Another interesting characteristic of the single QD PL displayed in Fig. 7.32 is the broad line-

width of the X peaks. The FWHM of the emission lines is of the order of a few meV, almost three

orders of magnitude larger than the typical values observed for InAs QDs and one order of mag-

nitude larger than those for InGaN. Such large homogeneous broadening is far beyond the value

expected for phonon dephasing and results from ﬂ uctuations in the exciton energy, the so-called

spectral diffusion produced by the variations in the strength of the internal ﬁ eld caused by charge

ﬂ uctuations in the vicinity of the QDs. The spectral diffusion has been observed experimen-

tally following the time evolution of the continuous wave μ PL spectrum of single GaN/AlN QDs

over several minutes [9] . These studies have identiﬁ ed two types of spectral diffusion: a discrete

one where the emission peak jumps abruptly in an energy range of the order of 10 meV; and

a continuous shift of the transitions producing an inhomogeneous broadening of the spectral

lines. Both scenarios can be explained by the changes in the QD internal electric ﬁ eld produced

by charges trapped in defects in the vicinity of the dots. The discrete drift is produced by closer

defects and more distant charges induce the continuous shift [9] .

Single QD spectroscopy has allowed the demostration of QCSE by the application of an external

electric ﬁ eld in different geometries [129, 114] . Figure 7.33a shows the evolution of the peak energy

of a single exciton emission line as a function of the strength of an applied vertical electric ﬁ eld. The

sample contained a single period of GaN/AlN QDs of 3 nm average height grown by MOCVD on

n -doped 6H-SiC. A Cr/Au semitransparent Schottky contact was deposited on the top surface of the

sample. The PL blue shifts linearly for increasing positive ﬁ elds as electrons and holes are pushed

towards the centre of the QD and the effect of the built-in ﬁ eld is partly compensated. Changing the

geometry of the experiment and applying the electric ﬁ eld along the QD plane should induce a red

shift of the emission line resulting from the polarization of the electron–hole pairs. The experimen-

tal observations reported in Fig. 7.33b correspond to an experiment performed on a similar sample

with Al/Au interdigital electrodes with 200 nm spacing and prove that the emission is blue shifted

for any direction of the ﬁ eld instead. There is a slight asymmetry in the energy shift due to the pres-

ence of a weak vertical component in the applied ﬁ eld which produces an asymmetric shift as seen

in Fig. 7.33a . The increase of the emission energy in the case of in-plane external ﬁ elds reﬂ ects the

decrease in the exciton binding energy as electrons and holes are taken apart from each other and

the cancellation of the energy shifts of the electron and hole conﬁ ned state energies [114] . The lat-

ter occurs because there are different conﬁ nement potentials acting on electrons and holes since the

internal electric ﬁ eld pushes their wavefunctions to the top and bottom part of the QD, respectively.

3.30 3.153.203.25

Emission energy (eV)

1.5

0.5

0.0

1.0

2.0

2.5

3.0

375 395390380 385

Wavelength (nm)

 9 mw

 1 mW

 70 W

Intensity [arb. units]

Figure 7.32 Single dot PL spectra of a GaN/AlN QD for increasing power of the 266 nm laser line focused on a

4 μ m diameter spot. The dots were grown by MOCVD and had average height and diameter of 4 and 20 nm, respec-

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Optical and Vibrational Properties of Self-assembled GaN Quantum Dots 263

7.4.5 QDs grown along non-polar directions

Avoiding the undesired effects of the built-in electric ﬁ eld present in polar III-nitride heterostruc-

tures is the main motivation for growing their non-polar counterparts. In the case of QDs two

different strategies have proved a drastic suppression of the ﬁ eld effects: the growth of GaN QDs

with zinc-blende structure and the growth of hexagonal dots along non-polar directions.

Zinc-blende GaN QDs embedded in an AlN matrix exhibit a strong emission in the UV without

any thermal quenching up to room temperature [23] . The lack of an internal electric ﬁ eld also

results in a faster and size independent recombination rate [112] .

The situation of hexagonal non-polar QDs is more complex since the polar c -axis is now con-

tained in the plane of the dot and still crosses GaN/AlN interfaces. Thus an electric ﬁ eld should

still be present inside the QD. However, the optical properties of a -plane GaN/AlN QDs grown on

(

1120

) 6H-SiC indicate that the ﬁ eld is very much reduced. Figure 7.34 shows the room tem-

perature PL of a sample containing 18 layers of non-polar dots for different excitation powers

together with that of a polar sample. Among the differences between the two types of QDs, the

lack of screening effects and the much narrower linewidth of the non-polar QD emission are

100

5 10 510050 5 10 15

Voltage (V)

Energy shift (meV)

(b)

(a)

Figure 7.33 PL energy shift as a function of the voltage of an applied electric ﬁ eld parallel (a) and perpendicular

(b) to the QD axis. In (a) positive voltage corresponds to electric ﬁ elds pointing the sample top [129, 114] . With

2.2 2.4 2.6 3.6 3.82.8 3.0

Energy (eV)

Intensity (arb. units)

c-plane QDs a-plane QDs

W cm

2

W cm

2

W cm

2

Figure 7.34 PL spectra of a -plane GaN/AlN QDs as a function of the average power density of a pulsed laser

(2 ps pulse at 76 MHz repetition rate). The spectra of c -plane GaN QDs is also shown for comparison. The spectra

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264 Handbook of Self-assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics

highlighted. Indeed, single QD studies have reported linewidths which go down to 0.5 meV, i.e.

one order of magnitude lower than those of polar QDs [130, 131] .

The emission also evolves in a much faster dynamic than those described in section 7.4.3 for

polar QDs. The a -plane QD PL decay curves for two different energies are depicted in Fig. 7.35 .

The curves can be ﬁ tted by single exponentials with characteristic decay times well below 1 ns.

Since non-radiative recombination does not have a large impact in the low-temperature dynam-

ics of these systems, the fast decay of the PL indicates a fast radiative lifetime of the exciton and,

hence, an increased wavefunction overlap for electrons and holes in the dots.

0 1200200 400 600 800 1000

Time (ps)

Intensity (in units)

500

400

300

200

3.60

3.64 3.68

3.72

3.76

Energy (eV)

(I)

(h)

(I)

(h)

Decay time (ps)

Figure 7.35 Time evolution of the PL intensity for two energies at the high- and low-energy side of the a -plane

The overall phenomenology just described points out a strong reduction of the internal electric

ﬁ eld. A possible explanation for the lack of electric ﬁ eld effects becomes evident after the analy-

sis of the strain-induced piezoelectric polarization. The determination of strain through Raman

scattering presented in section 7.3.4 allows the estimation of the mean piezoelectric polarization,

, for the GaN QD and the AlN barrier through the piezoelectric coefﬁ cients as

Pe e

pz xx yy zz



31 33

().εε ε

(7.9)

The values obtained are 0.027 C/m

and  0.013 C/m

for the barrier and the QD, respectively.

These should be added to the spontaneous polarization calculated by Bernardini et al. [105] which

are

AlN 2

C/m0 081.

and

QD 2

C/m0 029.

. Finally, the total polarization difference

between AlN and the a -plane QDs is Δ P   0.012 C/m

, i.e. seven times smaller than that found

in quantum dots grown along the c -axis [61] . Such a strong reduction would then result in a

proportional reduction of the internal electric ﬁ eld. This is in very good agreement with the theo-

retical results of Fig. 7.36 , where the electric ﬁ eld along the [0001] direction along the centre of

a non-polar GaN/AlN QD is shown. The value of the electric ﬁ eld diminishes by a factor 10 with

respect to that found in the polar QD of Fig. 7.22 . A second striking difference between Figs 7.22

and 7.36 arises from the piezoelectric contribution to the potential induced by strain (dashed

line) which now has an opposite sign. As a consequence, the total potential, obtained by adding

both contributions, is considerably reduced.

7.5 Intraband absorption

The large conduction band offset characteristic of GaN/AlN heterostructures (~2 eV) offers the

possibility of tuning intersubband transitions at very short wavelengths. Due to the high ionicity

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Optical and Vibrational Properties of Self-assembled GaN Quantum Dots 265

of GaN, the electron–LO-phonon interaction is largely enhanced, so that the absorption recovery

time was found to be extremely short, of the order of 150 and 370 fs in QW heterostructures, for

intersubband transitions at 4.5 and 1.7 μ m, respectively [132, 133] . In contrast to QWs, the 3D

conﬁ nement of electrons in quantum dots allows intraband transitions with a polarization com-

ponent in the layer plane (TE) or along the growth axis (TM).

The ﬁ rst observation of intraband absorption in GaN/AlN QD superlattices was reported by

Moumanis et al. [134] . Various absorption peaks were identiﬁ ed, with energies around 0.6 eV,

which varied by several tens of meV with sample substrate.

The differential absorption under s -polarized radiation (electric ﬁ eld contained in the layer

plane) was found to be a factor two or three smaller than that for p -polarized light. It amounts to

5.6  1 0



(1.7  1 0

 4

) for the sample grown on Si (sapphire) determined for the main absorp-

tion peak. This absorption is attributed to the transition from the s -like to the p -like orbital states

of the conduction band.

In order to achieve absorption at shorter wavelengths suitable for unipolar intersubband devices

operating at ﬁ bre-optics telecommunication wavelengths (1.3 μ m, 1.5 μ m), Tchernycheva et al.

[135] investigated samples with very small dot heights of approximately 1 nm. The samples studied

in this work were grown by plasma-assisted MBE on AlN-on-sapphire. They consisted in 20 periods

GaN QD layers, formed by the deposition of 4 ML GaN, with 3 nm thick AlN spacer. A detailed study

of the different growth parameters and structural characteristics of the QDs that affect the intra-

band transitions and allow telecommunication wavelengths to be achieved was reported elsewhere

[136] . The absorption observed for the different samples for p -polarization peaked between 0.81 eV

(1.53 μ m) and 0.878 eV (1.41 μ m), and showed FWHM as small as 88 meV. The absorption char-

acteristics was found to depend on the interruption growth time in Si-doped samples. On the other

hand, nominally undoped samples showed residual intraband absorption as well as light-activated

absorption. They were attributed to the detrapping of electrons in the AlN barriers and subsequent

capture in the dots. No absorption was observed for s -polarization.

A communication wavelength photodetector based on intersubband transition in GaN/AlN

self-assembled quantum dot heterostructures was reported in [137] . The photodetector is based

on in-plane transport and has a room temperature spectral peak responsivity of 8 mA/W at a

wavelength of 1.41 μ m. The authors used photoluminescence, transmission, and photocurrent

spectroscopy in order to explore the energy level scheme of the device. The sample investigated

consisted of 20 periods of Si-doped GaN QD layers (1.2 nm QD height and 15 nm diameter) sepa-

rated by 3 nm thick AlN barriers, and was grown on an AlN-on-sapphire template. Figure 7.37

presents the results of three techniques: photocurrent spectroscopy (PC), transmittance (T) and

0.4

0.2

0.0

0.2

0.4

15 0

z (nm)

55101510

0.6

0.3

0.0

0.3

0.6

0.9

Electric field (MV/cm)

TOT

Potential (V)

Figure 7.36 Variation of the electrostatic potential components along the wurtzite c -axis of a non-polar QD. The

strain-induced piezoelectric contribution is shown with a dashed line and spontaneous polarization term with a dot-

ted line. Their sum corresponds to the total potential (solid line). The variation of the z -component of the electric ﬁ eld

along the c -axis is represented by a dashed–dotted line.

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266 Handbook of Self-assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics

P photoinduced

absorption

S photoinduced

absorption

0.6 0.9 1.1 1.210.80.7

Ener

y (eV)

0.84 (eV)

0.86 (eV)

0.87 (eV)

S transmittance

P transmittance

T  300 K

(arb. units)

P photocurrent

S photocurrent

Figure 7.37 Photoconductive, transmission and photoinduced absorption spectra of the QD device in wedge illumi-

normalized photoinduced absorption ( Δ T/T). For the experiments, a multipass wavelength geo-

metry was used, in which the sample was illuminated through the 45° wedge and a polarizer was

used to select s- or p -polarization. The p -polarized PC peak takes place at 1.41 μ m (0.88 eV), while

that corresponding to the transmission and absorption spectra appear at slightly lower energies

(20–40 meV). All the peaks are strongly p -polarized and show similar widths of about 150 meV.

In order to investigate the origin of the observed transitions and photocurrent spectral

response, calculations of the electron energy levels in the QDs and in the WL were performed

by means of an eight-band k  p model that takes into account lattice mismatch and strain,

but neglects the in-plane conﬁ nement of the carriers. Good agreement between the calculated

transition energies and the experiment was found. The calculations showed that the second QD

electronic level ( p

) overlaps in energy with the ﬁ rst electronic level of the WL. There is therefore

an efﬁ cient transfer of the excited carriers from the QDs into the WL. This overlap accounts as

well for the observed blue shift of the PC peak relative to that measured by absorption ( Fig. 7.37 ).

The QDs of smaller size have a p

energy larger than the ﬁ rst electronic state of the WL. They are

therefore more likely to contribute to the lateral transport in the WL, resulting in a PC spectral

peak of higher energy in comparison with that of absorption measurements.

Acknowledgements

The authors are thankful to the Ministry of Science and Education of Spain (Grant MAT 2006-

01825, FEDER), European Network SANDIE (NMP4-CT-2004-500101) and the Generalitat

Valenciana for their ﬁ nancial support.

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