RAPID COMMUNICATIONSPHYSICAL REVIEW B

VOLUME 57, NUMBER 16

15 APRIL 1998-II

Reduction of oscillator strength due to piezoelectric fields in GaN/Alx Ga12x N quantum wells
Jin Seo Im,* H. Kollmer, J. Off, A. Sohmer, F. Scholz, and A. Hangleiter
4. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany~Received 15 December 1997!
We demonstrate a dramatic reduction of the oscillator strength in GaN/Alx Ga12x N quantum wells due topiezoelectric fields. Our study using time-resolved photoluminescence spectroscopy reveals a strong increaseof the luminescence decay time of the dominating transition with increasing well width by several orders ofmagnitude in parallel to a redshift of the emission peaks. The experimental results are consistently explained bya quantitative model based on the piezoelectric fields in strained wurtzite quantum wells. We estimate thepiezoelectric constant of GaN to d 31520.9310210 cm/V. @S0163-1829~98!52016-4#

GaN-based quantum wells ~QW’s! have been successfully
applied in blue and green light emitting laser diodes as wellas in violet laser diodes.1,2 Despite the poor material qualityof epitaxial nitride layers compared to other III-V semiconductors, those devices have shown high performance andhigh reliability.
In parallel to the progress in the fabrication of opticaldevices, there have been lively discussions about the opticalproperties of quantum wells based on GaN, Alx Ga12x N, andGa12x Inx N. Particularly for Ga12x Inx N/GaN QW’s, it has
been noted for some time that there exists a large redshift ofthe optical emission spectrum as compared to the absorption.
Together with other features, such as an energy-dependent
decay time of the emission in quantum wells, this has often
been interpreted in terms of localization of excitons at composition fluctuations or even the formation of quantum dots
due to local phase separation of InN and GaN.3,4Recently, it has been proposed that piezoelectric fields
due to mismatch-induced strain in Ga12x Inx N/GaN QW’s
are the primary reason for the large redshift of theluminescence.5 In fact, the strongly polar Ga-N bond should
give rise to rather large piezoelectric charges in the wurtzite
structure when subject to elastic strain. On the other hand, inthe presence of the piezoelectric field, the electron and hole
wave functions separate spatially leading to a reduced overlap and hence a reduced recombination rate. To the best of
our knowledge, there has been no report on the recombination rate influenced by piezoelectric fields in GaN-based materials until now.
GaN/Alx Ga12x N QW’s are well suited to investigate theoptical properties of the GaN-based QW, because effects likecomposition fluctuations are not expected. Therefore, in thispaper, we have studied GaN/Alx Ga12x N QW’s using timeresolved photoluminescence ~TRPL! spectroscopy. Our
study exhibited a dramatic decrease in oscillator strength byseveral orders of magnitude with increasing well thickness,
which can only be explained by large piezoelectric fields up
to 1 MV/cm.
Our samples were grown on ~0001!-oriented sapphire
substrates using low-pressure metalorganic vapor phase epitaxy. A nucleation layer of about 10 nm AlN grown at
800 °C was employed improving the quality of the upper
nitride layers grown at 1000 °C. The layers consist of anominally undoped GaN double heterostructure that is sand0163-1829/98/57~16!/9435~4!/$15.00

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wiched between a 500 nm Alx Ga12x N buffer and a 50 nm
Alx Ga12x N cap layer. The AlN mole fraction of barrier layers was estimated as 0.15 from photoluminescence spectra.
The thickness of the GaN layers was varied between 1.3 nm
and 100 nm. In the measurements, the samples were resonantly excited with 5 ps pulses from a frequency-doubled,
cavity-dumped dye laser ~Pyridine 1!, which was pumped bya mode-locked Nd:yttrium aluminum garnet laser. The wavelength is tunable between 337 nm and 376 nm, and the repetition rate was selected between 4 MHz and 8 kHz depending on the decay time in order to avoid multiexcitation. The
luminescence is dispersed by a 0.75 m grating monochromator, detected by a Hamamatsu R3809 microchannel-plate
photomultiplier, and processed using time-correlated, singlephoton-counting electronics. An appropriate deconvolution
technique provides a time resolution of 15 ps. All measurements ~time-resolved and time-integrated photoluminescence
spectroscopy! were done at 5 K.
Time-integrated low-temperature luminescence spectra of
GaN/Alx Ga12x N QW’s under resonant excitation are shownin Fig. 1. The 100 nm double heterostructure ~DH! reveals aspectrum similar to that of bulk GaN, due to the fact thatquantum confinement effects are negligible. The emission of
excitons at about 3.5 eV dominates the spectrum of the 100
nm DH, but the peak originating from donor-acceptor-pair

FIG. 1. Time-integrated photoluminescence spectra of a seriesof GaN/Alx Ga12x N double heterostructures ~DH’s!. The dashedline indicates the position of the GaN band gap.
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JIN SEO IM et al.

FIG. 2. Double-logarithmic plot of the luminescence decay for a
2.5 nm, a 5 nm, and a 10 nm GaN/Alx Ga12x N single quantum well.
The thickest layer shows a decay on a ms time scale.

recombination and its phonon replicas are also recognizable.
On the other hand, the luminescence spectra of
GaN/Alx Ga12x N QW’s exhibit a fairly complex behavior.
We observe two emission lines from thick QW’s but only asingle line from thin QW’s. Thin QW’s ~1 nm and 2 nm!
show a clear blueshift of their emission due to size quantization. In thicker layers ~5 nm and 10 nm!, the higher-energy
emission line lies about 70 meV above the GaN band gap,
whereas the lower-energy line shifts to energies well below
the GaN band gap with increasing thickness.
The luminescence decay time was measured at the emission peaks in the spectra, and the typical decay traces are
depicted in Fig. 2. The single emission line in thin QW’s ~1.3
nm and 2.5 nm! as well as the higher-energy line in thicker
QW’s ~5 nm and 10 nm! have decay times of 200–300 ps. In
contrast, the lower-energy emission lines in thicker layers ~5
nm and 10 nm! show a strongly nonexponential decay, andtheir decay time scale extends into the ms range. For the 10
nm QW, the decay time obtained at a long delay time after
pulsed excitation reaches 3 m s.
The temporal behavior of the spectrum of the lowerenergy line was studied by TRPL spectroscopy. Timeresolved spectra of the 10 nm QW, observed at various
times, are shown in Fig. 3. The spectra were integrated ateach time interval, and their intensity was normalized. The

FIG. 3. Time-resolved spectra of the lower-energy line of a 10
nm GaN/Alx Ga12x N single quantum well.

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FIG. 4. Schematic picture of the energies and wave functions ofelectrons and holes in a strained quantum well with a piezoelectricfield.

emission peaks in these spectra shift towards lower energy astime evolves. The redshift of the emission peak for a long
delay time after pulsed excitation was obtained as 27 meV.
The shape and linewidth of these spectra are not subject tochange with increasing delay time.
In order to explain the origin of the emission peaks well
below the GaN band gap, one might consider donoracceptor-pair ~DAP! recombination. The strongly nonexponential time decay and the redshift of the emission peaks
with evolving time would comply with this model. But DAP
transitions can be excluded since the peak energy and decay
time is dependent on the well width. The emission peak below the GaN band gap in the 10 nm QW shifts to lower
energy by about 150 meV as compared to the peak energy of
the 5 nm QW, and the emission peak of the the 10 nm QW
decays more slowly than that of the 5 nm QW. A DAP
transition model cannot explain this behavior.
Another possible model would be localized states, e.g.,
due to fluctuations of the well width. This model is also
confronted with a problem since such transitions could not
be below the bulk GaN band gap. In addition, the localization energy of about 200 meV and a decay time on ms timescale would require a strong localization to a radius of lessthan 1 Å, which is clearly not feasible.
Let us now consider the consequences of piezoelectricfields. A qualitative picture is shown in Fig. 4. The
Alx Ga12x N barriers are assumed unstrained and have no piezoelectric field, while the GaN QW is under a biaxial compressive strain perpendicular to ~0001!, which induces a piezoelectric field. The broken line and solid curve in thevalence and the conduction band indicate the energy level ofthe ground state and the wave function involved. Due to thepiezoelectric field, energy levels of quantum wells shift towards lower energy with increasing well width. At the sametime, the electron and hole ground-state wave functions are
spatially separated leading to a dramatic reduction in oscillator strength. This behavior is in good agreement with our
results from PL and TRPL spectra. For a quantitative calculation, we solved an effective-mass Schrödinger equation forthe conduction and valence band using a spatially linearlyvarying potential energy in the quantum well. In this simple
model, the quantization energy, the wave function, and thematrix elements were calculated at various well widths. The
matrix elements are proportional to the square of the overlap

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REDUCTION OF OSCILLATOR STRENGTH DUE TO . . .

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spatially direct transition could take place, especially at low
temperatures where an extremely low mobility can be expected. On the other hand, excited carriers could be localized
as excitons bound to donors or acceptors. The bound excitons would allow spatially direct transitions prior to a spatial
separation due to the piezoelectric field.
It is interesting to use our data to estimate the piezoelectric constant of GaN. The piezoelectric field E 3 along the~0001! axis is expressed via the piezoelectric constant d 31
as10
E 35

FIG. 5. Comparison of the measured energy positions ~dots! anddecay times ~squares! of the low-energy lines in GaN/Alx Ga12x N
QW’s with a calculation based on piezoelectric fields.

integral between electron and hole wave function. We used
an effective electron mass of 0.2m 0 ,6 and a hole mass of
2.2m 0 ,7,8 assuming no difference between the effective
masses of charge carriers in the QW and the barrier layers.
The applied ratio between conduction and valence band discontinuity is 75:25.9 A comparison of the calculated energies
and oscillator strengths with the experimental data is shownin Fig. 5. For this figure, the energetic positions were takenfrom TRPL spectra at the longest possible delay time after
excitation, i.e., with screening of the field being as small as
possible. For the same reason, the decay time in the strongly
nonexponential decay was also determined at a long delay
time. The calculated curves include only a single adjustableparameter, which is the magnitude of the piezoelectric field.
In the present case, a field of 350 kV/cm consistently explains both the redshift of the emission peaks and the dramatic increase of the decay time with increasing well width.
Moreover, Fig. 5 indicates that the higher-energy line in
the thick layers is obviously associated with spatially directtransitions in the strained GaN well layer, since its transitionenergy coincides with the band gap of GaN under 0.4% compressive strain ~dashed-dotted line!. This is the strain expected for GaN embedded between Al0.15Ga0.85N layers. Of
course, these transitions can occur only directly after excitation. Optically excited carriers drift under the piezoelectricfield, and they are being separated spatially with increasing
time. The low mobility of carriers, particularly of holes, results in a large drift time leading to a long delay before
establishing a spatial separation. During this process, the*Electronic address: j.s.im@physik.uni-stuttgart.de
1

S. Nakamura, M. Senoh, S.-I. Nagahama, N. Iwasa, T. Yamada,T. Matsushita, Y. Sugimoto, and H. Kiyoku, Jpn. J. Appl. Phys.,
Part 2 36, L1059 ~1997!.

SD

2 c 2132 d 31
c 111c 122e ,e 0e rc 33 xx~1!

where e 0 and e r are the permittivity of the vacuum and thestatic dielectric constant of the material, respectively. e xx is
the in-plain strain, and c i j are the elastic constants. Recently,
the GaN elastic constants have been determined by using aresonance ultrasound method as c 115377 GPa, c 125160
GPa, c 135114 GPa, and c 335209 GPa.11 Using e r 59.5,12
we find d 31520.9310-10 cm/V, which is somewhat smaller
than the value of 21.7310210 cm/V estimated by Martin
et al.9
Let us now discuss the consequences of our results on
device operation. A strong piezoelectric field is also expectedin strained Ga12x Inx N-based quantum wells. In this case, theenergetic position of the emission is not only related to the In
fraction in the active Ga12x Inx N layer, but also to the piezoelectric field and the well thickness. Green light-emitting diodes ~LED’s! based on Ga12x Inx N, for instance, are likely tohave a much lower In content than previously thought, withthe piezoelectric shift being of the order 0.5 eV. On the other
hand, the dramatic decrease of the oscillator strength withincreasing strain and well thickness will also influence device performance. While for LED’s, a long radiative lifetime
may not be important within some limits, the small oscillator
strength will definitely be detrimental for laser operation.
This may in fact be the reason why it has proven to bedifficult to extend the lasing wavelength of a nitride-basedlaser to beyond 440 nm.13
In conclusion, the effects of piezoelectric fields on thestatic and dynamic optical properties of GaN/Alx Ga12x N
single quantum wells were studied by time-resolved photoluminescence. We found a strong increase of the luminescence decay time of the dominating transition with increasing well thickness by several orders of magnitude in parallel
to a redshift of the emission peaks. Our experimental findings are consistently explained by a quantitative model basedon the piezoelectric fields in strained wurtzite quantum wells.
We would like to thank O. Gfrörer for helpful discussions. J.S.I. acknowledges support by the Deutscher Akademischer Austauschdienst. Financial support of this work by
the Deutsche Forschungsgemeinschaft is gratefully acknowledged.

2

S. Nakamura, M. Senoh, N. Iwasa, and S.-I. Nagahama, Appl.
Phys. Lett. 67, 1868 ~1995!.
3
S. Chichibu, T. Azuhata, T. Sota, and S. Nakamura, Appl. Phys.
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