RAPID COMMUNICATIONSPHYSICAL REVIEW B

VOLUME 58, NUMBER 20

15 NOVEMBER 1998-II

Quantum confined Stark effect due to built-in internal polarization fields
in „Al,Ga…N/GaN quantum wells
M. Leroux, N. Grandjean, M. Laügt, and J. Massies
CNRS-Centre de Recherche sur l’ Hétéro-Epitaxie et ses Applications, Rue B. Grégory, 06560 Valbonne, France

B. Gil and P. Lefebvre
CNRS-Groupe d’ Etude des Semiconducteurs, Université de Montpellier II, Case Courrier 074, 34095 Montpellier Cedex 5, France

P. Bigenwald
Laboratoire de Physique des Matériaux, Université d’ Avignon, 84000 Avignon, France~Received 13 May 1998; revised manuscript received 20 July 1998!
~Al,Ga!N/GaN quantum wells have been studied by temperature-dependent luminescence and reflectivity.
The samples were grown by molecular beam epitaxy on ~0001! sapphire substrates, and well widths werevaried from 3 to 15 monolayers ~ML’s! with a 2-ML increment, thus providing a reliable data set for the studyof the well width dependence of transition energies. The latter shows a strong quantum confined Stark effectfor wide wells, and an internal electric-field strength of 450 kV/cm is deduced. X-ray diffraction performed on
the same samples shows that the GaN layers are nearly unstrained, whereas the ~Al,Ga!N barriers are pseudomorphically strained on GaN. We conclude that the origin of the electric field is predominently due tospontaneous polarization effects rather than a piezoelectric effect in the well material.
@S0163-1829~98!50944-7#

The progress in the growth and electronic quality ofgroup-III nitrides has been very rapid in the last few years, as
illustrated by the realization of bright blue and green lightemitting diodes and near-UV laser diodes.1,2 The active region of these devices consists of ~Ga,In!N quantum wells~QW’s!. There is also an increasing interest for ~Al,Ga!N/GaN QW’s, in view of extending the domain of applicationof this group-III nitride family towards the UV range.
~Al,Ga!N/GaN QW’s can be grown either by metalorganic
vapor phase epitaxy3,4 ~MOVPE! or by molecular beam
epitaxy5,6 ~MBE!. A striking feature is that whatever thegrowth method, the photoluminescence ~PL! energy of sufficiently thick ~Al,Ga!N/GaN QW’s ~typically .4 nm! islower than that of the A free exciton of GaN.3,4,6,7 This was
attributed by Im et al.7 to a strong piezoelectric field present
in biaxially compressed GaN QW’s. In this paper, we discuss
the optical properties of thin Al0.1Ga0.9N/GaN quantum
wells, whose widths have been varied by a small incrementof 2 molecular monolayers ~ML’s!, 1 ML corresponding to
2.59 Å. We show that excitons are localized at low temperature, with a localization energy of 20 meV on the average.
The study of the well width dependence of the QW energies
provides evidence for a quantum confined Stark effect due toan internal electric field of about 450 kV/cm. In the light of
x-ray diffraction ~XRD! study of the samples, we conclude
that spontaneous polarization effects are highly important in
the determination of this field.
The samples were grown on ~0001! sapphire substrates bymolecular beam epitaxy using NH3 as the nitrogen precursor.
Details of the MBE growth of the GaN template on whichheterostructures are grown can be found in Ref. 8. The parameters of the heterostructures ~i.e., well width and barriercomposition! are determined in situ by using reflection highenergy electron diffraction ~RHEED! intensity oscillations.90163-1829/98/58~20!/13371~4!/$15.00

PRB 58Three samples are discussed. The first two contain single
Al0.11Ga0.89N ~50 Å!/GaN QW’s of width 5, 9, and 13 ML’sin sample A, and 3, 7, 11, and 15 ML’s in sample B. Sample
C is a 17-ML-wide QW embedded in Al0.09Ga0.91N barriers. PL was excited with the 325-nm line of an HeCd
laser, and reflectivity was recorded by shining white lightfrom a halogen lamp onto the sample. XRD mapping was
performed using a high-resolution diffractometer using narrow slits in front of the detector.
Figure 1 displays the photoluminescence spectra at 9 K of
samples A and B. The first point to be noted is that PLenergies of the 5-, 9-, and 13-ML-wide wells are well intercalated with those of the 3-, 7-, 11-, and 15-ML-wide ones.
This is a clear demonstration of the monolayer control ofthicknesses achievable in the MBE growth of nitrides. The
PL linewidths in Fig. 1 are 20–30 meV. As also shown in
Fig. 1, the samples exhibit well resolved reflectivity structures, due to each individual quantum well, providing a reliable data set for the study of the well width dependence of
QW transition energies. The free exciton energies are obtained by assigning a Drude-Lorentz oscillator to each transition, and the dotted line in Fig. 1 shows such a calculated
reflectivity spectrum. Figure 1 indicates that the luminescence at 9 K originates from localized excitons, with binding
energy of the order of 20 meV for wide wells, increasing to
46 meV for the 5-ML-wide well. Another way of estimating
localization energies is to study temperature-dependent PL.
As shown in Fig. 2, when the temperature increases, the QW
PL energy first increases for T,100 K and decreases forhigher temperatures. This is assigned to a thermal delocalization of QW excitons. The solid lines through the data,
including the GaN buffer luminescence, correspond to thetemperature dependence of the A excitonic gap of GaN,
which we determined previously from typical GaN/Al2O3
samples of similar thickness:
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M. LEROUX et al.

FIG. 1. Luminescence spectra at 9 K of two Al0.11Ga0.89N/GaN
quantum well samples ~samples A and B!. The well widths are
given in ML units (1 ML52.59 Å). Also shown is the reflectivity
spectrum of sample A with a calculated spectrum ~dotted line!.

E ~ T ! 5E ~ 0 ! 28.8731024 T 2 / ~ T1874!

~1!

~this expression is in very good agreement with that given in
Ref. 10!. The difference between the extrapolated lowtemperature free exciton energy and the PL energy gives an
independent estimation of the excitonic localization energy.
The squares in Fig. 2 correspond to transition energies obtained from reflectivity. We find a rather good agreement
between the two determinations of localization energy, whenboth are available, for well widths larger than 5 ML’s ~seeFIG. 2. Temperature dependence of the PL energies of sample
A. The closed squares are free exciton energies deduced from reflectivity.

PRB 58

FIG. 3. Well width dependence of Al0.11Ga0.89N/GaN quantum
well energies ~samples A, B, and C!. Closed squares are luminescence energies, open circles and open squares are free exciton energies deduced from reflectivity or temperature-dependent PL, respectively.

also Fig. 3 below!. For narrower wells, the discrepancy between the two determinations of the free exciton energies
could be due to incomplete thermal detrapping of these
deeply localized excitons.
Figure 3 displays the QW transition energies at 9 K of
GaN QW’s with an Al barrier composition of 0.11, forwidths ranging from 3 ~8 Å! up to 15 ML’s ~39 Å!. Dark
squares are PL energies, circles and open squares are free
exciton energies obtained from reflectivity and temperaturedependent PL, respectively. A first remark regards localization energies ~Stokes shift! in our samples. As Fig. 3 shows,
it is nearly constant with a value of 2265 meV for widths
larger than 5 ML, and higher for narrower wells. If excitons
are localized due to QW thickness fluctuations, for a given
corrugation, the Stokes shift is expected to be proportional to
the slope of the energy versus width curve.11 This is what we
observe, with a nearly constant Stokes shift in a well width
range where the transition energy varies linearly with width
due to the Stark effect discussed below. Such a localization
scheme is in good agreement with the results of the time
resolved PL study of Al0.07Ga0.93N/GaN QW’s by Lefebvre
et al.12
As shown in Figs. 1 and 3, a 15-ML-wide well emits at anenergy slightly lower than the excitonic energy of the GaN
buffer. As mentioned in the Introduction, this has alreadybeen reported3,4,6,7 for wide GaN QW’s. Figure 4 emphasizes
this effect, by displaying the PL spectrum of a 17-ML-wide
Al0.09Ga0.91N/GaN quantum well. The luminescence energy
is indeed 85 meV lower than that of GaN. This is the signature of the quantum confined Stark effect, the physical originof which is now discussed.
In Fig. 3 are given the results of different calculations. A
difficulty arises from the fact that, as Fig. 1 shows, no signal
from the barrier has been observed either in PL or in reflectivity in our samples with Al0.11Ga0.89N barriers. This testifies to a very efficient capture of carriers by the wells. By

RAPID COMMUNICATIONSPRB 58QUANTUM CONFINED STARK EFFECT DUE TO BUILT- . . .

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FIG. 4. Luminescence spectrum at 9 K of a 17-ML-wide
Al0.09Ga0.91N/GaN quantum well ~sample C!.

using the bowing parameter for ~Al,Ga!N proposed by
Amano et al.,13 we estimate the barrier excitonic gap to be
3.75 eV. On the other hand, reflectivity performed on sample
C places the excitonic gap of Al0.09Ga0.91N at 3.731 eV, alinear interpolation leading then to an excitonic gap of 3.788
eV for Al0.11Ga0.89N. A value of 3.76 eV has been used in
the following calculation. The valence-band offset is assumed to vary linearly with the Al barrier composition, avalue of about 800 meV for the AlN/GaN heterostructure has
been used.14,15 First, the dashed line in Fig. 3 shows that thelinear decrease with well width of the QW energies forwidths higher than 5 ML’s cannot be explained by assuming
square QW potential profiles. In order to include the electricfield effect, we first use the approximate band to band, but
analytical, model of Singh.16 This model is known to fail forvery narrow wells ~as Fig. 3 shows!, but is valid for wide
ones. The results of this model for electric fields F of 0 and
400 kV/cm are shown as dotted lines in Fig. 3. In the case ofF50, this model reproduces the previous square well calculation only for wide wells, as expected. Now, it can be seenthat an electric field of 400 kV/cm is necessary to reproduce
the linear decrease of QW energies with well width. Finally,
the solid line in Fig. 3 gives the results of a self-consistentenvelope function calculation, including excitonic effects
and the modification of the band lineups produced by thepresence of the excitonic dipole.17 A good agreement withthe experiment is obtained for the whole range of wellwidths investigated, assuming a field strength of 450 kV/cm,
50 kV/cm higher than the value obtained with a less sophisticated calculation. It is important to note that this value
compares well also with that determined by Im et al.,7 who
determined a piezoelectric field of 420 kV/cm for MOVPEgrown Al0.15Ga0.85N/GaN QW’s, and with the value of 450
kV/cm used by Honda et al.18 for Al0.1Ga0.9N/GaN QW’s.
We now discuss the possible origins of this field. The
piezoelectric field magnitude for ~0001! biaxial strain isgiven by13,15,19,20
F pz 52 P pz /«« 0 52 ~ 2e 31P xx 1e 33P zz ! /«« 052 ~ 2e 3122c 13e 33 /c 33! P xx /«« 0 ,~2!

FIG. 5. X-ray map of sample A around the 2105 reciprocallattice point. The abscissa leads to the in-plane a lattice parameterand the ordinate to the on-axis c one.

where « and « 0 are the dielectric constant of GaN and thepermittivity of free space, c i j are the material elastic
constants,21 and P are the strain components. We use thepiezoelectric constants e i j of Bernardini, Fiorentini, andVanderbilt,20 linearly interpolating for the alloy between thevalues of GaN and AlN. The in-plane lattice constants of
GaN and AlN are about 3.1891 and 3.112 Å, respectively. It
can be verified that if one assumes that the GaN wells are
strained by relaxed ~Al,Ga!N barriers, a correct value for the
piezoelectric field is obtained. However this does not correspond to the situation of our samples. Figure 5 shows an
XRD reciprocal space map of sample A. It shows that
~Al,Ga!N barriers are in-plane lattice matched to the GaN
buffer layer. ~This is in agreement with the work of Takeuchi
et al.,22 showing that up to 6000-Å Al0.1Ga0.9N can be grownlattice matched to GaN.! The in-plane lattice parameter ofthe whole sample A structure is a53.1892 Å, i.e., the GaN
is nearly relaxed ~the buffer A exciton energy in this sample
is 3.474 eV!. This means that there is a negligible piezoelectric field in the wells. Note that the value of 3.1891 Å for thein-plane lattice parameter of relaxed GaN ~Refs. 23 and 24!
can be questioned. Recently, Skromme et al.25 suggested that
this value could be as high as 3.1912 Å ~corresponding to an
A exciton energy of 3.468 eV!. However, even using this lastvalue, a piezoelectric field of about 100 kV/cm is deduced,
much lower than the field present in our QW’s. ~The inclusion of the additional 2.931024 compressive strain25 that
occurs when cooling GaN on sapphire samples from 300–9
K increases this value to only 140 kV/cm.! We then attributethe quantum confined Stark effect that we observe to thedifference in polarization (piezoelectric1spontaneous) between wells and barriers, following the works of Bernardini,
Fiorentini, and Vanderbilt.20,26 In their work, the electricRAPID COMMUNICATIONS

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M. LEROUX et al.

field is due to interface charge accumulation due to thechange in polarization between two materials. In a well with
infinite barriers, this field is given by26
F w 5 ~ P b 2 P w ! /«« 0 ,~3!

where P b ( P w ) is the total polarization in the barrier ~well!
material. For a superlattice, it is given by ~assuming a samevalue of « for well and barrier material!
F w 5l b ~ P b 2 P w ! / ~ l b 1l w ! «« 0 ,~4!

where l b (l w ) is the barrier ~well! thickness. Using the valuesof spontaneous polarization computed in Ref. 20 and Eq. ~3!,
we obtain a field of 1.1 MV/cm in the infinite barrier case,with the largest contribution coming from the difference inspontaneous polarization rather than from the piezoelectricfield in the barrier ~640 kV/cm and 440 kV/cm, respectively!.
On another hand, in our samples, the barriers are not infinite(l b 550 Å), and noting that the quantum confined Stark effect is noticeable in Fig. 4 for wells of thickness 9–15 ML’s(l w 523– 39 Å), the use of Eq. ~4! gives fields in the 750–
620 kV/cm range. This is larger, but of the order of magnitude of the value deduced from Fig. 4. The origin of theremaining discrepancy could be due to the fact that GaN on

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1

PRB 58sapphire heterostructures are highly defective crystals, as
shown in particular on the reciprocal space map in Fig. 5,
where the GaN large peak width in the horizontal direction isdue to diffraction by these defects.27 These defects may influence the internal field value.
In conclusion, from the study of the quantum well energies as a function of well width with an increment of 2 ML’sfor a series of ~Al,Ga!N/GaN QW’s grown by MBE ~a technique that allows a control of widths at the monolayer scale!,a quantum confined Stark effect is revealed, and we deduced
an internal electric-field strength of 450 kV/cm for
Al0.11Ga0.89N/GaN QW’s. On the other hand, reciprocal
space maps show that in our structures the barriers are lattice
matched to nearly strain-free GaN. As such, the origin of thisfield is not a piezoelectric effect in the well material, butrather the difference in polarization between well and barriermaterials, while the piezoelectric effect is mainly present in
the barriers.
We are highly indebted to F. Bernardini and V. Fiorentini~Università di Cagliari, Italy! for clarifying discussions onpolarization effects in wurtzite semiconductors. This work
was supported in part by Brite Euram E. C. Contract No.
BPR-CT96-0334 ANISET.

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