Quantum confined Stark effect due to built-in internal polarizationfields
in…Al,Ga…N/GaN quantum wells
M.Leroux,N.Grandjean,M.Lau¨gt,and J.Massies
CNRS-Centre de Recherche sur l’He´te´ro-Epitaxie et s Applications,Rue B.Gre´gory,06560Valbonne,France
B.Gil and P.Lefebvre
CNRS-Groupe d’Etude des Semiconducteurs,Universite´de Montpellier II,Ca Courrier074,34095Montpellier Cedex5,France
P.Bigenwald
Laboratoire de Physique des Mate´riaux,Universite´d’Avignon,84000Avignon,France
͑Received13May1998;revid manuscript received20July1998͒
͑Al,Ga͒N/GaN quantum wells have been studied by temperature-dependent luminescence and reflectivit
y.
The samples were grown by molecular beam epitaxy on͑0001͒sapphire substrates,and well widths were
varied from3to15monolayers͑ML’s͒with a2-ML increment,thus providing a reliable data t for the study
of the well width dependence of transition energies.The latter shows a strong quantum confined Stark effect
for wide wells,and an internal electric-field strength of450kV/cm is deduced.X-ray diffraction performed on
the same samples shows that the GaN layers are nearly unstrained,whereas the͑Al,Ga͒N barriers are pudo-波弗特海
morphically strained on GaN.We conclude that the origin of the electricfield is predominently due to
spontaneous polarization effects rather than a piezoelectric effect in the well material.
͓S0163-1829͑98͒50944-7͔蒂格
cad绘图基础The progress in the growth and electronic quality of group-III nitrides has been very rapid in the last few years,as
illustrated by the realization of bright blue and green light-
emitting diodes and near-UV lar diodes.1,2The active re-
gion of the devices consists of͑Ga,In͒N quantum wells ͑QW’s͒.There is also an increasing interest for͑Al,Ga͒N/ GaN QW’s,in view of extending the domain of application
主的手歌谱
of this group-III nitride family towards the UV range.͑Al,Ga͒N/GaN QW’s can be grown either by metalorganic vapor pha epitaxy3,4͑MOVPE͒or by molecular beam epitaxy5,6͑MBE͒.A striking feature is that whatever the growth method,the photoluminescence͑PL͒energy of suf-ficiently thick͑Al,Ga͒N/GaN QW’s͑typicallyϾ4nm͒is lower than that of the A free exciton of GaN.3,4,6,7This was attributed by Im et al.7to a strong piezoelectricfield prent in biaxially compresd GaN QW’s.In this paper,we discuss the optical properties of thin Al0.1Ga0.9N/GaN quantum wells,who widths have been varied by a small increment of2molecular monolayers͑ML’s͒,1ML corresponding to 2.59Å.We sh
ow that excitons are localized at low tempera-ture,with a localization energy of20meV on the average. The study of the well width dependence of the QW energies provides evidence for a quantum confined Stark effect due to an internal electricfield of about450kV/cm.In the light of x-ray diffraction͑XRD͒study of the samples,we conclude that spontaneous polarization effects are highly important in the determination of thisfield.
The samples were grown on͑0001͒sapphire substrates by molecular beam epitaxy using NH3as the nitrogen precursor. Details of the MBE growth of the GaN template on which heterostructures are grown can be found in Ref.8.The pa-rameters of the heterostructures͑i.e.,well width and barrier composition͒are determined in situ by using reflection high-energy electron diffraction͑RHEED͒intensity oscillations.9Three samples are discusd.Thefirst two contain single Al0.11Ga0.89N͑50Å͒/GaN QW’s of width5,9,and13ML’s in sample A,and3,7,11,and15ML’s in sample B.Sample C is a17-ML-wide QW embedded in Al0.09Ga0.91N bar-riers.PL was excited with the325-nm line of an HeCd lar,and reflectivity was recorded by shining white light from a halogen lamp onto the sample.XRD mapping was performed using a high-resolution diffractometer using nar-row slits in front of the detector.
Figure1displays the photoluminescence spectra at9K of samples A and B.Thefirst point to be noted is that PL energies of the5-,9-,and13-ML-wide wells are well inter-calated with tho of the3-,7-,11-,a
nd15-ML-wide ones. This is a clear demonstration of the monolayer control of thickness achievable in the MBE growth of nitrides.The PL linewidths in Fig.1are20–30meV.As also shown in Fig.1,the samples exhibit well resolved reflectivity struc-tures,due to each individual quantum well,providing a reli-able data t for the study of the well width dependence of QW transition energies.The free exciton energies are ob-tained by assigning a Drude-Lorentz oscillator to each tran-sition,and the dotted line in Fig.1shows such a calculated reflectivity spectrum.Figure1indicates that the lumines-cence at9K originates from localized excitons,with binding energy of the order of20meV for wide wells,increasing to 46meV for the5-ML-wide well.Another way of estimating localization energies is to study temperature-dependent PL. As shown in Fig.2,when the temperature increas,the QW PL energyfirst increas for TϽ100K and decreas for higher temperatures.This is assigned to a thermal delocal-ization of QW excitons.The solid lines through the data, including the GaN buffer luminescence,correspond to the temperature dependence of the A excitonic gap of GaN, which we determined previously from typical GaN/Al2O3 samples of similar thickness:
朱文龙PHYSICAL REVIEW B15NOVEMBER1998-II
VOLUME58,NUMBER20
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E ͑T ͒ϭE ͑0͒Ϫ8.87ϫ10Ϫ4T 2/͑T ϩ874͒
͑1͒
͑this expression is in very good agreement with that given in Ref.10͒.The difference between the extrapolated low-temperature free exciton energy and the PL energy gives an independent estimation of the excitonic localization energy.The squares in Fig.2correspond to transition energies ob-tained from reflectivity.We find a rather good agreement between the two determinations of localization energy,when both are available,for well widths larger than 5ML’s ͑e
also Fig.3below ͒.For narrower wells,the discrepancy be-tween the two determinations of the free exciton energies could be due to incomplete thermal detrapping of the deeply localized excitons.
Figure 3displays the QW transition energies at 9K of GaN QW’s with an Al barrier composition of 0.11,for widths ranging from 3͑8Å͒up to 15ML’s ͑39Å͒.Dark squares are PL energies,circles and open squares are free exciton energies obtained from reflectivity and temperature-dependent PL,respectively.A first remark regards localiza-tion energies ͑Stokes shift ͒in our samples.As Fig.3sho
ws,it is nearly constant with a value of 22Ϯ5meV for widths larger than 5ML,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.11This is what we obrve,with a nearly constant Stokes shift in a well width range where the transition energy varies linearly with width due to the Stark effect discusd below.Such a localization scheme is in good agreement with the results of the time resolved PL study of Al 0.07Ga 0.93N/GaN QW’s by Lefebvre et al.12
As shown in Figs.1and 3,a 15-ML-wide well emits at an energy slightly lower than the excitonic energy of the GaN buffer.As mentioned in the Introduction,this has already been reported 3,4,6,7for wide GaN QW’s.Figure 4emphasizes this effect,by displaying the PL spectrum of a 17-ML-wide Al 0.09Ga 0.91N/GaN quantum well.The luminescence energy is indeed 85meV lower than that of GaN.This is the signa-ture of the quantum confined Stark effect,the physical origin of which is now discusd.
In Fig.3are given the results of different calculations.A difficulty aris from the fact that,as Fig.1shows,no signal from the barrier has been obrved either in PL or in reflec-tivity in our samples with Al 0.11Ga 0.89N barriers.This testi-fies to a very efficient capture of carriers by the well
s.
By
FIG.1.Luminescence spectra at 9K of two Al 0.11Ga 0.89N/GaN quantum well samples ͑samples A and B ͒.The well widths are given in ML units (1ML ϭ2.59Å).Also shown is the reflectivity spectrum of sample A with a calculated spectrum ͑dotted line ͒
.
FIG.2.Temperature dependence of the PL energies of sample A.The clod squares are free exciton energies deduced from re-
flectivity.
FIG.3.Well width dependence of Al 0.11Ga 0.89N/GaN quantum well energies ͑samples A,B,and C ͒.Clod squares are lumines-cence energies,open circles and open squares are free exciton en-ergies deduced from reflectivity or temperature-dependent PL,re-spectively.
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M.LEROUX et al.
using the bowing parameter for ͑Al,Ga ͒N propod by Amano et al.,13we estimate the barrier excitonic gap to be 3.75eV.On the other hand,reflectivity performed on sample C places the excitonic gap of Al 0.09Ga 0.91N at 3.731eV,a linear interpolation leading then to an excitonic gap of 3.788eV for Al 0.11Ga 0.89N.A value of 3.76eV has been ud in the following calculation.The valence-band offt is as-sumed to vary linearly with the Al barrier composition,a value of about 800meV for the AlN/GaN heterostructure has been ud.14,15First,the dashed line in Fig.3shows that the linear decrea with well width of the QW energies for widths higher than 5ML’s cannot be explained by assuming square QW potential profiles.In order to include the electric-field effect,we first u the approximate band to band,but analytical,model of Singh.16This model is known to fail for very narro
w wells ͑as Fig.3shows ͒,but is valid for wide ones.The results of this model for electric fields F of 0and 400kV/cm are shown as dotted lines in Fig.3.In the ca of F ϭ0,this model reproduces the previous square well calcu-lation only for wide wells,as expected.Now,it can be en that an electric field of 400kV/cm is necessary to reproduce the linear decrea of QW energies with well width.Finally,the solid line in Fig.3gives the results of a lf-consistent envelope function calculation,including excitonic effects and the modification of the band lineups produced by the prence of the excitonic dipole.17A good agreement with the experiment is obtained for the whole range of well widths investigated,assuming a field strength of 450kV/cm,50kV/cm higher than the value obtained with a less sophis-ticated calculation.It is important to note that this value compares well also with that determined by Im et al.,7who determined a piezoelectric field of 420kV/cm for MOVPE-grown Al 0.15Ga 0.85N/GaN QW’s,and with the value of 450kV/cm ud by Honda et al.18for Al 0.1Ga 0.9N/GaN QW’s.We now discuss the possible origins of this field.The piezoelectric field magnitude for ͑0001͒biaxial strain is given by 13,15,19,20
优秀团员推荐表F pz ϭϪP pz /0ϭϪ͑2e 31xx ϩe 33zz ͒/0
ϭϪ͑2e 31Ϫ2c 13e 33/c 33͒xx /0,
͑2͒
where and 0are the dielectric constant of GaN and the permittivity of free space,c i j are the material elastic constants,21and are the strain components.We u the piezoelectric constants e i j of Bernardini,Fiorentini,and Vanderbilt,20linearly interpolating for the alloy between the values of GaN and AlN.The in-plane lattice constants of GaN and AlN are about 3.1891and 3.112Å,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 corre-spond to the situation of our samples.Figure 5shows 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.,22showing that up to 6000-ÅAl 0.1Ga 0.9N can be grown lattice matched to GaN.͒The in-plane lattice parameter of the whole sample A structure is a ϭ3.1892Å,i.e.,the GaN is nearly relaxed ͑the buffer A exciton energy in this sample is 3.474eV ͒.This means that there is a negligible piezoelec-tric field in the wells.Note that the value of 3.1891Åfor the in-plane lattice parameter of relaxed GaN ͑Refs.23and 24͒can be questioned.Recently,Skromme et al.25suggested that this value could be as high as 3.1912Å͑corresponding to an A exciton energy of 3.468eV ͒.However,even using this last value,a piezoelectric field of about 100kV/cm is deduced,much lower than the field prent in our QW’s.͑The inclu-sion of the additional 2.9ϫ10Ϫ4compressive strain 25that occurs when cooling GaN on sapphire samples from 300–9K inc
reas this value to only 140kV/cm.͒We then attribute the quantum confined Stark effect that we obrve to the difference in polarization (piezoelectric ϩspontaneous)be-tween wells and barriers,following the works of Bernardini,Fiorentini,and Vanderbilt.20,26In their work,the
electric
FIG. 4.Luminescence spectrum at 9K of a 17-ML-wide Al 0.09Ga 0.91N/GaN quantum well ͑sample C ͒
.
FIG.5.X-ray map of sample A around the Ϫ105reciprocal lattice point.The abscissa leads to the in-plane a lattice parameter and the ordinate to the on-axis c one.
PRB 58R13373
QUANTUM CONFINED STARK EFFECT DUE
field is due to interface charge accumulation due to the change in polarization between two materials.In a well with infinite barriers,thisfield is given by26
F wϭ͑P bϪP w͒/0,͑3͒where P b(P w)is the total polarization in the barrier͑well͒material.For a superlattice,it is given by͑assuming a same value offor well and barrier material͒
F wϭl b͑P bϪP w͒/͑l bϩl w͒0,͑4͒where l b(l w)is the barrier͑well͒thickness.Using the values of spontaneous polarization computed in Ref.20and Eq.͑3͒, we obtain afield of1.1MV/cm in the infinite barrier ca, with the largest contribution coming from the difference in spontaneous polarization rather than from the piezoelectric field in the barrier͑640kV/cm and440kV/cm,respectively͒. On another hand,in our samples,the barriers are not infinite (l bϭ50Å),and noting that the quantum confined Star
k ef-fect is noticeable in Fig.4for wells of thickness9–15ML’s (l wϭ23–39Å),the u of Eq.͑4͒givesfields in the750–
620kV/cm range.This is larger,but of the order of magni-tude of the value deduced from Fig.4.The origin of the remaining discrepancy could be due to the fact that GaN on sapphire 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 is due to diffraction by the defects.27The defects may in-fluence the internalfield value.
In conclusion,from the study of the quantum well ener-gies as a function of well width with an increment of2ML’s for a ries of͑Al,Ga͒N/GaN QW’s grown by MBE͑a tech-nique that allows a control of widths at the monolayer scale͒, a quantum confined Stark effect is revealed,and we deduced an internal electric-field strength of450kV/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 this field is not a piezoelectric effect in the well material,but rather the difference in polarization between well and barrier materials,while the piezoelectric effect is mainly prent in the barriers.研究课题
We are highly indebted to F.Bernardini and V.Fiorentini ͑Universita`di Cagliari,Italy͒for clarifying discussions on polarization effects in wurtzite miconductors.This work was supported in part by Brite Euram E.C.Contract No. BPR-CT96-0334ANISET.
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