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 249

7.4.1 Conﬁ nement effects

Increased thermal stability and improved emission efﬁ ciency at room temperature are well-

established consequences of zero-dimensional conﬁ nement and common probes for identifying

QD luminescence. In GaN/AlN heterostructures the 2.8 eV band gap mismatch between the dot

and the barrier materials ensures a deep localization potential. Indeed, strong carrier conﬁ ne-

ment was already demonstrated in the ﬁ rst optical studies performed on GaN/AlN QDs grown in

the SK mode by MBE [23] and by MOCVD [17, 84] and on GaN/Al

1

N ( x  0.2) QDs grown

in the VW mode by using Si as a surfactant [16, 85] . Figure 7.17 shows the resonantly excited

PL spectrum of a GaN/AlN QD superlattice grown by MBE on a commercial GaN substrate at two

different temperatures. While the emission from the bulk GaN substrate is visible at low tempera-

ture only, a broader emission band centred at 3.75 eV and attributed to the GaN QDs remains

almost unchanged, both in shape and intensity, with temperature. The blue shift of the QD emis-

sion with respect to the bulk band gap is a consequence of the conﬁ nement potential and the

large inhomogeneous broadening reveals the wide distribution of dot sizes probed in this experi-

ment. The integrated intensity of the QD emission stays constant up to room temperature, as can

be seen in Fig. 7.18 , because migration to non-radiative centres is hindered by strong conﬁ ne-

ment. On the contrary, a severe quenching in the PL intensity of GaN bulk and QW systems is

observed as temperature increases due to the high density of threading dislocations and other

defects that act as non-radiative traps.

Bulk GaN

GaN quantum dots

T  300K

T  2K

3.4 3.5 3.6 3.7 3.8 3.9 4

Photon energy (eV)

PL intensity (arb. units)

Figure 7.17 PL of a 20 period GaN/AlN QD superlattice grown by MBE on a GaN MOCVD-grown substrate.

The excitation source was the 302 nm (4.1 eV) line of an argon laser which lies below the WL emission energy at

In the same way as in other self-assembled systems, GaN QDs also present a large inhomogene-

ity in QD sizes resulting in large inhomogeneous broadening of the emission spectrum, see Fig.

7.17 . A possible strategy for reducing the dispersion in island size is the growth of vertically cor-

related QD multilayers. As already described in section 7.2, when increasing the number of layers

the vertical self-alignment is accompanied by the homogenization of the QD size distribution in

successive dot planes and an average increase of their diameter [37, 38] . The spacer layer acts like

a bandpass ﬁ lter that prevents the formation of QDs of smaller size. Figure 7.19 shows the room

temperature PL spectra of samples containing 1, 3, 5, and 10 layers of buried QDs grown by

MOCVD [38] . Besides the emission from the QDs, a higher energy peak centred at 4.7 eV is attrib-

uted to the emission of the WL. In order to evidence the effects of the stacking in the multilay-

ered samples, the PL spectrum of the reference single layer can be subtracted, see the inset of Fig.

7.19 , and it is shown that the PL from the upper layers is red shifted in energy and shows a clear

reduction of the spectral linewidth when compared to that of the single-layer sample. Another

interesting observation is that the intensity of the emission increases with the number of layers

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

PL intensity (arb. units)

345

Photon energy (eV)

10 layers

5 layers

3 layers

1 layers

3 layers

5 layers

10 layers

Photon energy (eV)

PL intensity (normalized)

Figure 7.19 PL spectra of GaN QDs samples containing an increasing number of dot layers grown by MOCVD.

The emission of the WL appears at 4.7 eV. The excitation wavelength is 193 nm (6.4 eV). The inset shows the nor-

malized PL of the multilayer samples after subtracting the single-layer spectrum [38] . With permission from AIP©

2004.

0.1

0.01

0.001

0 50 100 150 200 250 300

QW 40Å

p-GaN

20 large dots

Photoluminescence intensity (arb. units)

Temperature (K)

Figure 7.18 Comparison of the temperature dependence of the PL intensity of three different GaN systems: a 20

period GaN/AlN QD multilayer containing dots of 4.1  0.4 nm height and 17 nm diameter; a single GaN QW with

0.15

0.85

N barriers; and a p -type-doped GaN ﬁ lm [86] .

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Optical and Vibrational Properties of Self-assembled GaN Quantum Dots 251

indicating that new non-radiative recombination centres associated with structural defects are

not introduced during the stacking process. This has important technological connotations since

vertical stacking of the QDs is important to increase the total QD density and the subsequent

increase of the gain for lasing operation.

The optical emission properties are determined by the electronic energy levels and wave func-

tions of the system. Though there exist some atomistic approaches for the calculation of the

electronic structure of GaN-based heterostructures [87, 88, 44, 45, 89–93, 46] , the most com-

mon approach nowadays is the multiband envelope function approximation, which relies on the

use of a multiband k  p Hamiltonian to describe the bulk band structure in combination with

the standard envelope function theory to account for the conﬁ nement. The k  p Hamiltonian

around the Γ point, including the effects of strain, allows the characterization of the wurtzite

bandstructure in terms of a reduced number of parameters (energy gaps, effective masses,

Luttinger-like k  p parameters, deformation potentials, etc.) [94] . Unfortunately, in the case of

the III-N compounds the values of those parameters are not as well known as for other III–V

semiconductors [47, 52, 95] , and this situation hampers to some extent the comparison between

theory and experiment in the III-N systems. For deﬁ niteness, in the calculations presented below

we shall employ the same parameters used in [47] .

In the case of lattice-mismatched heterostructures, such as the GaN/AlN systems considered

here, the band-edge proﬁ les are determined by the strained band offsets, as calculated from the

electronic deformation potentials. This approach [96–98] has proved to be a convenient and reli-

able tool to describe quantum size effects in QWs [99, 100] , as well as in QD structures [47, 101,

50, 102, 54] . To illustrate the impact of the deformation on the band structure, we show in Fig.

7.20a the band dispersion of GaN around the Γ point both without and with the effect of a biaxial

strain (see section 7.2.2). In GaN, bands A and B are composed mostly of ( p

, p

) atomic functions,

whereas band C has dominantly p

symmetry. The coupling between the conduction and valence

bands in wide-band gap nitrides is relatively small over the energy range of interest, and can be

3.78

3.68

3.63

3.58

3.53

0.00

0.05

0.10

0.15

3.73

Energy (eV)

2.156 eV

0.459 eV

3.684 eV

6.3 eV

3.5 eV

GaN



biaxial

strain

AIN

(b)

(a)

Figure 7.20 (a) Bulk bandstructure of GaN around the Γ point, along the in-plane direction ( k

) and [0001]

direction ( k

), both without (grey line) and with (black line) the effect of a biaxial strain. (b) Band-edge proﬁ le of

a GaN/AlN heterostructure both without and with the effect of a biaxial strain. The unstrained valence band offset

between GaN and AlN has been taken to be 0.5 eV [47] .

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

0.4

0.2

0.0

3.2

3.4

3.6

10 5

51015

Depth (nm)

Energy (eV)

3.35 eV

Figure 7.21 Impact of electrical polarization on the energy band diagrams and electron and hole ground states of a

5 mm width GaN/AlN(0001) QW [106] .

safely neglected. On the other hand, due to the small spin–orbit and crystal–ﬁ eld splittings, the mix-

ing in the valence band is very important, especially in the k

dispersion, leading to a strongly non-

parabolic dispersion near the Γ point. Under deformation, the conduction band (CB) shifts to high

energies and the valence bands (VBs) shift to low energies, thus increasing the value of the funda-

mental gap. In general, the curvature of the bands of GaN is not affected by strain as much as, e.g.,

in InAs. Figure 7.20b also presents the band-edge alignment in a heterojunction GaN/AlN both

without and with the effect of a biaxial strain. As it can be seen, the combined effect of the con-

ﬁ nement and the compressive strain in a GaN/AlN QW would produce a blue shift of the emission

compared with the GaN bulk band gap larger than 200 meV. Nevertheless, we recall that the strain

in the GaN/AlN QDs is far from homogeneous and deviates from the biaxial case, and this has to be

fully taken into account for the quantitative modelling of the electronic properties of QDs.

7.4.2 Electric ﬁ eld effects: quantum-conﬁ ned Stark effect

As a matter of fact, the most distinctive characteristic of III-nitride QD optical response comes

from the existence of giant built-in electrostatic ﬁ elds. On the one hand, the wurtzite crystal-

line structure is non-centrosymmetric, and therefore exhibits piezoelectric properties, i.e. devel-

ops electrical polarization when deformed [103] . The magnitude of the piezoelectric constants

exceeds that of zinc-blende semiconductors by more than one order of magnitude [104, 52] .

In addition, the [0001] direction or c -axis of the wurtzite structure is polar, meaning that the

wurtzite crystals carry a spontaneous electrical polarization along [0001] even at equilibrium.

These spontaneous polarizations are of the same order of magnitude as those found in ferro-

electric materials [105] . Therefore, the strained heterostructures based on III-nitrides present

polarization charges arising from spatial variations of the polarization that lead to huge internal

ﬁ elds and potentials, as shown in Fig. 7.21 . The accurate values of the piezoelectric constants

and spontaneous polarizations in III-N compounds are still the object of intense investigation.

In Table 7.6 we compile the set of values used below to calculate the electric ﬁ elds.

The effects of the built-in electric ﬁ elds have been widely reported in the optical properties of

GaN and InGaN QWs [107, 108] and GaN/AlGaN heterostructures [109] . These effects are to

be accounted for also in the study of the optical properties of GaN/AlN QDs, where the novelty

is the non-trivial distribution of the electric ﬁ eld as a consequence of the multifaceted QD geom-

etry and inhomogeneous strain distribution. The total potential is the sum of the piezoelectric

plus spontaneous contributions, φ

TOT

 φ

 φ

, which can be obtained by solving the Poisson

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Optical and Vibrational Properties of Self-assembled GaN Quantum Dots 253

equation with the appropriate polarization charges [47] . In Fig. 7.22a we show a map of the calcu-

lated total potential φ

TOT

for a typical QD geometry. The potential proﬁ le along the [0001] dot axis is

also displayed in Fig. 7.22b , together with the separate contributions of φ

and φ

. Quantitatively

is around one third of φ

, and both present the same polarity. Though the spontaneous contri-

bution is dominant, the piezoelectric potential contribution cannot be neglected. Thus any realistic

model of this system must include these two contributions, and therefore needs a previous evalua-

tion of the strain. Qualitatively, it is clear that the variation of the potential inside the dot is consid-

erably more pronounced along the [0001] direction than in the radial one. This fact has been used

sometimes as a justiﬁ cation to approximate the electrostatic potential in the dot as equivalent to

a parallel plate capacitor with a constant electric ﬁ eld. Figure 7.22b also displays the electric ﬁ eld

calculated from φ

TOT

, showing that it is approximately constant and can reach values as large as

5–7 MV/cm, which are nevertheless half of those found in a QW of the same height.

Table 7.6 Material parameters of bulk wurtzite GaN and

AlN used to calculate the built-in electric potentials [105] .

GaN AlN

(C/m

)

 0.49  0.6

(C/m

) 0.73 1.46

(C/m

)

 0.49  0.6

(C/m

)

 0.029  0.081

9.6 9.6

2

4

0246810

0.3

0.3

z (nm)

ρ (nm)

Potential (V)

1.5

1.0

0.5

0.0

0.5

1.0

1.5 10

5

20246

1.2

0.9

0.6

0.3

0.3

0.6

0.9

1.2

1.5

Potential (V)

Field (MV/cm)

(a)

(b)

TOT

Figure 7.22 (a) Contour map of the internal electrostatic potential φ

TOT

of a GaN/AlN QD, with the same dimen-

sions as used in Fig. 7.6 . The strain used to calculate φ

is given in Fig. 7.6 and the same piezoelectric and dielectric

constants (those of GaN) have been taken throughout the whole structure (see Table 7.6). The spontaneous polariza-

tion values used to calculate φ

are also given in Table 7.6 . (b) Values of φ

TOT

, φ

, and electric ﬁ eld E

TOT

along

the [0001] axis.

The impact of this internal ﬁ eld on the optical properties of a QD can be best substantiated by cal-

culating the electronic states and wave functions. The electric potential φ

TOT

has to be added to the

conﬁ nement potential given by the (strain-modiﬁ ed) band edge proﬁ le. In Fig. 7.23a we show the

dependence on the height of the dot of the ﬁ rst few CB and VB conﬁ ned electronic states, as calculated

with the multiband envelope function approximation [54] . It is seen that the energy of the CB states

(VB states), decreases (increases) steeply with increasing dot height, unlike in other kinds of self-

assembled QDs where the decrease is slower. This is due mostly to the presence of the huge potential

difference between the top and bottom surfaces of the dot (see Fig. 7.22 ), which exhibits a quasi-linear

dependence on the QD height. The electrons (holes) are mostly conﬁ ned in the top (bottom) region

of the dot, as is better visualized in Fig. 7.23b , where the squared envelope functions are represented.

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

Therefore, their energies follow the top (bottom) potential which decreases (increases) almost

linearly with the QD height. It must be noted that the quantitative ﬁ tting of experimental meas-

urements is at present difﬁ cult because small changes in the parameters that determine the mag-

nitude of the built-in potential (i.e. the piezoelectric constants and spontaneous polarization

values assumed for GaN and AlN) strongly modify the calculated energy levels [47] . Given the

above results for the electron and hole energy levels, their difference, i.e. the electron–hole transi-

tion energy, also decreases rapidly with increasing the QD height. This decrease can eventually

lead to an emission energy lower than the bulk GaN band gap, see Fig. 7.23c . Concomitantly,

there is a decrease in the overlap of the electron and hole wavefunctions, and therefore a drastic

reduction of the oscillator strength, as can also be seen in Fig. 7.23c . Thus, the most distinctive

4.6

3.53.02.52.01.5

4.4

3.6

4.2

3.8

4.0

Dot height (nm) Dot height (nm)

1.4

1.5 3.53.02.0 2.5

1.6

1.5

1.7

1.9

1.8

1

(b)

(a)

804626842

h  1.5 nm

h  3.375 nm

x (nm)

z (nm)z (nm)

4.0

1

2

5

3

4

3.8

2.6

2.4

3.5

4.0

3.0

2.51.5 2.0

2.8

3.0

3.2

3.4

3.6

Dot height (nm)

Oscillator strength

(c)

Energy (eV)

Conduction band

levels

Valence band

levels

|M|  1/2

|M|  3/2

GaN

gap

0.5

0.1

Figure 7.23 (a) Three lowest CB and VB energy levels of GaN/AlN QDs as calculated within the multiband enve-

lope function approximation [54] . The same aspect ratio as in Figs 7.6 and 7.22 has been employed. The coupling

between the bulk CB and the VB is neglected, and the same band parameters (those of GaN [47] ) have been taken

throughout the whole structure. The zero of energy is taken on the VB top of unstrained AlN. (b) Probability density

distribution for the electron (dashed line) and hole (solid line) ground states. The points indicate the maxima of the

distributions, which have been scaled to unity. (c) Electron–hole transition energy and oscillator strength as a func-

tion of the QD height.

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Optical and Vibrational Properties of Self-assembled GaN Quantum Dots 255

characteristic of III-nitride QD optical response derived from the intrinsic ﬁ elds is a sizeable red

shift of the ground-level transitions for increasing well width (quantum conﬁ ned Stark effect,

QCSE) accompanied by the reduction of the oscillator strength.

The theoretical picture presented in the above paragraphs is essentially consistent with the

experimental ﬁ ndings on all types of polar GaN dots. For example, in Fig. 7.24 , it is evidenced by

the remarkable red shift experienced by the maximum of the QD PL spectrum (depicted by tri-

angles) with increasing dot height [112] . As a matter of fact, the QD emission energy falls more

than 1 eV below the strained GaN bulk band gap energy for heights higher than 4 nm. This is

very different to the energy calculated assuming a vanishing internal ﬁ eld (see dotted line) and

to the dependence of the emission of GaN/AlN QDs with zinc-blende structure (depicted by

squares). The behaviour of cubic QDs will be analysed in more detail in section 7.4.5. The experi-

mental results of Fig. 7.24 were in agreement with the theoretical calculations of Widmann et al.

[110] for an electric ﬁ eld strength F  7 MV/cm in good agreement with the theoretical predic-

tions of Fig. 7.22 .

1000

500

10 20 30 40 50 60

500

1000

1500

2000

QD hei

ht (Å)

 E

gap (meV)

WZ QD

ZB QD

F  0 MV/cm

F  6

F  7

F  8

Figure 7.24 Energy shift of QD emission with respect to the GaN band gap energy as a function of the QD height.

The GaN band gap energy has been corrected to take into account the biaxial compression of the dot material due to

Several authors have determined the strength of the built-in electric ﬁ eld in self-assembled GaN/

AlN QDs employing a variety of experimental techniques and theoretical models. Table 7.7 sum-

marizes some of the values published to date and shows a clear disagreement of the quoted ﬁ g-

ures. Uncertainties in the determination of the dot size, especially of the dot height often measured

from AFM images and therefore subjected to considerable error, can explain partly the wide range

Table 7.7 Estimated value of the built-in electric ﬁ eld in self-assembled

GaN/AlN QDs.

F (MV/cm) As determined by: Ref.

5.5 PL energy versus QD height [110]

7 PL energy and radiative lifetime versus QD height [112]

9 PL decay time versus PL energy [113]

  5

PL Stark shift induced by an external electric ﬁ eld

[114]

6 Calculation of the strain distribution with a Green’s

function technique

[47]

3.8 Self-consistent tight-binding calculations [89]

[114] predicts a 50% reduction in the AlN/GaN spontaneous polarization disagreement

as compared to that calculated by Bernardini et al. [105] (see Table 7.2 ).

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

of electric ﬁ eld values. Also, as analysed in section 7.2.2, the piezoelectric contribution of QD mul-

tilayer stacks signiﬁ cantly differs from that of a single QD layer (see Fig. 7.7 ). Furthermore, there

is an ongoing controversy about the magnitude of the difference in the spontaneous polarization

between AlN and GaN that affects strongly the value of the internal ﬁ elds [105, 111] .

A side effect of the size dependence of the QD emission energy described above is the ampliﬁ ca-

tion of inhomogeneous broadening of the PL due to ﬂ uctuations in the QD size. Typical FWHM

of GaN/AlN QDs fall in the 200–400 meV range much above the 60–80 meV of other non-polar

self-assembled nanostructures.

Although the red shift of the QD emission is an undesired effect from the point of view of

obtaining UV operating devices, this can also be used commercially for white light emission. It

has been demonstrated that by controlling the QD size the emission can be continuously tuned

from blue to orange. Figure 7.25 shows the room temperature PL of four GaN/AlN QD samples

grown by MBE on Si(111). Three of them contain a single QD layer grown after the deposition of

7, 10, and 12 ML of GaN at a growth temperature of 800°C and the fourth one corresponds to a

stacking of four dot planes of different deposition thickness [15] . As a consequence of the QCSE

the addition of 1 ML of GaN induces a red shift of 150 meV in the emission energy. A proper

combination of QD sizes can be used to obtain white light emission. Alternatively, rare earth-

doped nitride QDs are being investigated as white light sources [115–117] . Vertically coupled

GaN QDs have also been proposed as the material support for quantum computation by exploit-

ing the existence of strong built-in electric ﬁ elds to generate entangled states [118] .

1000 400 200600800

Wavelength (nm)

Stacked QDs

T  300 k

(a)

(d)

(c)

(b)

Luminescence intensity (arb. units)

0.8

0.6

0.4

0.2

0 0.60.40.2

Figure 7.25 Emission of a single plane of GaN/AlN QDs grown on Si(111) by MBE for a GaN growth deposition

of (a) 7; (b) 10; and (c) 12 MLs. Spectrum (d) corresponds to a four QD plane stack. All spectra present Fabry–

Another clear manifestation of the QCSE is observed when studying the dependence of the

emission upon excitation power [110, 119, 120] . In this case a blue shift of the emission energy

occurs for increasing excitation density, as shown in Fig. 7.26 for three different GaN QD sam-

ples grown by MBE on Si(111). Samples 1, 2, and 3 contained 86, 40, and 10 periods of GaN/

AlN QDs and the average dot height was 3.7, 5, and 4.3 nm, respectively. More details on the

sample growth are reported in [120] . The reported energy shifts are now understood as the

result of the partial screening of the internal electric ﬁ eld by the ﬁ eld induced by the photogen-

erated electron–hole dipoles. These screening effects are larger for higher dots due to the ampliﬁ -

cation of the QCSE for increasing dot height, note that sample 2 presents the largest blue shift in

the emission energy. The effect of screening by photogenerated carriers has been discussed

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Optical and Vibrational Properties of Self-assembled GaN Quantum Dots 257

theoretically by Rajan et al. [89] . A linear blue shift of the emission energy with increasing

electron–hole pair density is predicted. The calculated screening energy, deﬁ ned as the energy

shift per electron–hole pair, increases with the QD height as observed experimentally. The emis-

sion broadening is also affected by the excitation density but in a less straightforward manner.

An increase in the FWHM for higher excitation powers can be attributed to the population of

the excited states of the dots. However, a reduction of the emission width has been observed in

some GaN QD multilayer stacks [120] . Kalliakos et al . pointed out that differences in the photo-

generated carrier densities between different dot planes in QDs stacks could explain the observed

reduction in the FWHM.

Cathodoluminescence has also been used in many investigations of the optical properties of

III-N and their heterostructures. This technique is in many ways equivalent to PL but it allows a

better control over the depth of the emission and, on the downside, it induces signiﬁ cantly higher

excitation densities [78, 117] . Thus, in CL experiments the internal electric ﬁ eld is partly screened

by the excitonic dipoles and the spectra appear blue shifted in energy. The CL and PL spectra of a

GaN/AlN QD multi-stack are compared in Fig. 7.27 . Both of them were recorded from the lateral

section of the sample in order to prevent Fabry–Perot interference fringes as those observed in

2.6

2.9

2.5

2.4

2.7

2.8

1 10 100 1000

Power density (W/cm

)

Peak energy (eV)

T  300 K

Sample 1

Sample 2

Sample 3

Figure 7.26 Evolution of the maximum energy of the PL spectra corresponding to three different GaN/AlN QD

samples. The excitation source was the 266 nm fourth harmonic of an Nd:YAG laser which produced 5 ns pulses at a

20 000

15 000

10 000

5000

2.0 3.2 3.62.82.4

Energy (eV)

2.6 eV

2.4 eV

2.9 eV

S40

Intensity (arb. units)

(20 000)

Figure 7.27 Comparison between the cross-sectional PL and CL of a sample containing 40 periods of GaN/AlN QDs

grown on Si(111) by MBE. Measurements were carried out at room temperature and CL spectrum was recorded under

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

Fig. 7.25 . The higher injection conditions not only give rise to the 200 meV blue shift but also

to the higher intensities of the CL in comparison to the PL peaks. The screening of the internal

ﬁ eld yields a strong increase of the oscillator strength and a more efﬁ cient absorption due to an

increased overlap of the electron and hole wavefunctions.

The excited states of semiconductor nanostructures are often investigated by means of PLE.

This technique has not been very much exploited in the study of group III nitrides due to the

lack of tunable lasers in the UV range. One of the very few published PLE studies of a GaN/AlN

QD sample is depicted in Fig. 7.28 together with the PL of the sample for two different excitation

energies. The sample was grown by plasma-assisted MBE on 6H-SiC and consisted of ﬁ ve periods

of GaN QDs separated by Al

0.25

0.75

N spacers grown in between two 45 nm thick Al

0.25

0.75

optical waveguide layers. Several peaks appear in the PL spectrum of the sample excited at

4.7 eV (266 nm): the QD emission centred at 3.57 eV; the emission from the WL at 3.87 eV;

and the emission from the AlGaN waveguide layers at 4.07 eV. The PLE maxima for the WL and

the AlGaN layers is blue shifted by 100 meV, approximately, with respect to the emission maxima

due to alloy potential ﬂ uctuations. Figure 7.28 also shows three PLE spectra of the GaN QDs

measured for three detection energies within the emission peak. A maximum is observed in each

PLE spectra, pointed by arrows, which appears more than 200 meV blue shifted with respect

to the PL maximum, the so-called Stokes shift between the PL and PLE maxima. This increases

for decreasing detection energy and therefore for increasing dot height. The severe reduction of

the resonant absorption observed experimentally is attributed to a drop in the exciton oscillator

strength as electrons and holes are separated spatially by the internal electric ﬁ eld.

360 300320 280340

Wavelength (nm)

10 K

GaN QDs

3.4 3.6 4.24.0 4.64.43.8

Photon energy (eV)

PLE intensity (arb. units)

PL intensity (arb. units)

(iv)

(v)

(iii)

(i)

(ii)

4.06 eV

3.54 eV

3.44 eV

3.87 eV

3.65 eV

PLE detection

Figure 7.28 PLE spectra of GaN/AlGaN QDs measured at 10 K for different detection energies. A xenon lamp was

used as excitation source in the PLE experiment. The detection energies from (i) to (v) are indicated on the PL spec-

trum excited at 266 nm (solid line). The dotted line corresponds to the PL spectrum excited at a lower energy of

7.4.3 Electric ﬁ eld effects on the exciton dynamics

The spatial separation of electrons and holes inside nitride QDs reduces the overlap between the

electron and the hole wavefunctions and the magnitude of the exciton oscillator strength, as dis-

cussed in the previous section and shown in Fig. 7.23b and c . In the time domain, the exciton

radiative decay time is related to its oscillator strength f by:

πε

ne f



(7.6)

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