In this work we analyze the relation between the interface microroughness and the full width at half maximum (FWHM) of the photoluminescence (PL) spectra for a GaAs/Ga0.7Al0.3As multiple quantum well (QW) system. We show that, in spite of the complex correlation between the microscopic interface-defects parameters and the QW optical properties, the Singh and Bajaj model [Appl. Phys. Lett. 44, 805 (1984)] provides a good quantitative description of the excitonic PL-FWHM. [S0163-1829(99)01424-1].6031519152

da Silva, ECF

de Oliveira, JBB

Meneses, EA

Repositorio da Producao Cientifica e Intelectual da Unicamp

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auru,
il
PHYSICAL REVIEW B 15 JULY 1999-IVOLUME 60, NUMBER 3Magneto-optical studies of the correlation between interface microroughness parameters and th
photoluminescence line shape in GaAs/Ga0.7Al0.3As quantum wells
J. B. B. de Oliveira
Departamento de Fı´sica, Universidade Estadual Paulista, Av. Eng. Luiz Edmundo C. Coube, s/n, Caixa Postal 473, 17033-360, B
SP, Brazil
E. A. Meneses
Instituto de Fı´sica Gleb Wataghin, Universidade Estadual de Campinas, Caixa Postal 6165, 13083-970 Campinas, SP, Braz
E. C. F. da Silva
Instituto de Fı´sica da Universidade de Sa˜o Paulo, Caixa Postal 66318, 05315-970, Sa˜o Paulo, SP, Brazil
~Received 29 October 1998!
In this work we analyze the relation between the interface microroughness and the full width at half
maximum ~FWHM! of the photoluminescence~PL! spectra for a GaAs/Ga0.7Al0.3As multiple quantum well
~QW! system. We show that, in spite of the complex correlation between the microscopic interface-defects
parameters and the QW optical properties, the Singh and Bajaj model@App . Phys. Lett.44, 805 ~1984!#
provides a good quantitative description of the excitonic PL-FWHM.@S0163-1829~99!01424-1#ll
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The interfaces structural properties in quantum we
~QW’s! have been extensively investigated, as they are
tremely important for the high performance of the electro
and optoelectronic QW-based devices.1–3
Semiconductor heterostructures interfaces have been
vestigated by means of direct or indirect characterizat
techniques. Direct investigations of the interfacial qual
have been obtained, for instance, by scanning tunneling
croscopy, atomic force microscopy, and transmission e
tron microscopy~TEM!.4 However, interfaces that are dee
inside a semiconductor heterostructure are not acces
through direct investigation methods, so optical techniq
~which indirectly probe the interfaces! have been intensively
used in semiconductor-interface characterization in QW s
tems.
One of the most efficient sensors used in the optical ch
acterization of interfacial quality, due to their sensitivity
the structural aspects of the interface on the atomic scal
the behavior of confined excitons.5 In fact, an interesting
subject of debate is the correlation between the excito
optical properties and the microscopic configurations of
interfaces.6–8
The flat island model~FIM! associates the properties
the QW emission lines with the microscopic patterns of
interfaces. According to this model, when the excitons
confined in extensive and plane islands, which have lar
dimensions than the exciton lateral dimension, the photo
minescence~PL! emission line splits. These splittings a
due to different confinement potentials, which are associa
with islands of different sizes. Moreover, each one of
split PL emission line is broadened due to confineme
potential fluctuations. These fluctuations are due to interf
microroughness~defects with smaller extension than that
the lateral dimension of the confined exciton! and to alloy
fluctuations, resulting in an inhomogeneous~Gaussian!
broadening of the PL spectrum. In addition, the emissPRB 600163-1829/99/60~3!/1519~4!/$15.00s
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spectra are also broadened due to final-state interact
~Lorentzian broadening! and due to the thermal distributio
of the carriers.
In the FIM, the QW has different widths that differ from
each other by an integer multiple of monolayers~ML !, re-
sulting in several PL peaks with corresponding differences
energy. However, more recently, splittings in the PL spec
related to noninteger ML variations in the QW width we
observed.9 The authors of Ref. 9 argued that for a realis
description of the interfaces it is necessary to use a Fou
transform of the two-dimensional interfaces, which provid
a full specification of the roughness spectrum. This is
so-called bimodal model. The observation of microroughn
on top of the macroscopically flat islands gives support
this model.10 Additionally, PL with spatial resolution11,12and
near-field spectroscopy13 showed that the PL line shape
composed by the superposition of many very narrow lin
~somemeV wide! that are associated with excitons localiz
tion by different lateral-potential fluctuations. Then, the fa
field spectrum, i.e., the traditionally observed PL spectru
is interpreted as an envelope of the very narrow lines as
ciated with defects of different sizes.4
In this work we add a contribution to this interesting di
cussion by showing that the FWHM of the emission spec
obtained by standard PL spectroscopy, can be quantitati
correlated with the structural parameters of the microrou
ness localized at QW interfaces. Our conclusion is based
the comparison between the FWHM measured directly fr
our magneto-optical PL spectra and the theoretical FWH
obtained from the Singh and Bajaj model, which is based
the flat island picture and on thermodynam
arguments.1,14,15
The sample investigated in this work was one multip
quantum well structure grown by molecular beam epita
~MBE! on top of a GaAs~100! substrate. The structure star
with a 1.0-mm-thick undoped GaAs buffer layer followed b
the active region, composed by 20 GaAs/Ga0.7Al0.3As quan-1519 ©1999 The American Physical Society
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1520 PRB 60BRIEF REPORTStum wells. The wells and barriers are 80 and 300 Å wi
respectively. The PL measurements were performed usin
Ar1-ion laser as light source (hnexc52.41 eV). The lumi-
nescence was dispersed by a 0.8-m double monochrom
and detected by a GaAs-cooled detector and a typical ph
counter system. Magneto-optical measurements were ca
out using the Faraday configuration within a 13 T superc
ducting magnet. Optical fibers coupled to a lens were use
transmit the laser beam to the sample and to collect the e
ted light. The dimension of the laser spot on the sample
maintained constant with a diameter of approximat
200 mm.
Figures 1~a!–1~c! show a line-shape analysis of the P
spectrum of our sample measured at 2 K with low excitation
density (18 mW/cm2). PL and PLE spectra~not shown
here! show a small Stokes shift of only 0.7 meV indicatin
the good quality of the sample. In addition to the free exci
~FE! emission at 1.564 eV, another peak localized 1.5 m
below the FE peak can also be observed in the spectrum
Fig. 1. Results of detailed PL and PLE measurements i
cated that the low-energy peak was a photoinduced emis
associated with excitons bound to defects localized at
QW interfaces, i.e., a bound exciton~BE!.6,16,17
In order to analyze the line shape associated with the
emission line, we decomposed the observed PL spect
into its constituents using two Lorentzian curves@Fig. 1~a!#,
FIG. 1. Decomposition of the PL spectrum using:~a! two
Lorentzian curves~dashed lines!, ~b! two Gaussian curves~dotted
lines!, ~c! one Lorentzian and one Gaussian curve for the BE
the FE peaks, respectively. The open circles are the experim
data and the solid line represents the linear superposition of
fitted peaks.,
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two Gaussian curves@Fig. 1~b!#, and one Lorentzian and on
Gaussian curve@Fig. 1~c!# to fit the BE and the FE emis
sions, respectively. It can be observed in Fig. 1~a! that the
resulting curve~solid line! obtained by using the linear su
perposition of two Lorentzian curves does not fit the hig
energy region of the experimental spectrum~open circles!.
On the other hand, the resulting curve obtained using
Gaussian curves@Fig. 1~b!# does not fit the low-energy re
gion of the experimental spectrum. However, we can a
observe in Fig. 1~c! that the linear superposition of a Loren
zian curve for the BE emission and a Gaussian curve for
FE emission provides a perfect adjust to the experime
data. This result indicates that the structural patterns of
interfaces dominate the FE emission, so the Lorentz
broadening can be neglected.
Using the Lifshitz treatment to study the excitation spe
tra of disordered alloys, Singh and Bajaj developed theo
ical expressions correlating the dimensions of the mic
roughness localized at the QW interfaces and the a
fluctuations with the FWHM of the excitonic emission line
Following the description of Aksenovet al.,7 when the
broadening of the PL emission is determined by the qua
of only one interface~in our case the interface formed by th
growth of GaAs on top of the Ga0.7Al0.3As layer! and one
considers an infinitely high barrier, the PL-FWHM asso
ated with the microroughness at the interface (s int) is de-
scribed as
s int50.59
d1d2
mLz
3Rex
2
, ~1!
whered1 andd2 are, respectively, the height and the late
dimension of the interface islands,Lz is the QW width,m is
the reduced exciton mass in the direction perpendicula
the QW layer, andRex is the exciton lateral dimension (Rex
5A^Cux21y2uC&). Here it was considered that the ave
aged coverage of the interface assumed the most prob
value of 0.5.7
Also, the Singh and Bajaj model describes the PL-FWH
associated with alloy fluctuation (salloy) as
salloy52S 1.4x~12x!r c3
Rex
3 P0
ex D 1/2S dEexdx D
x5x0
, ~2!
wherer c is the radius associated with the volume per cat
~aproximately 2.5 Å ),Eex is the excitonic transition energy
x is the Al concentration,x0 is the nominal Al concentration
~0.3 in our sample!, and P0
ex is the fraction of the exciton
volume that penetrates in the barrier.
The total FWHM of the excitonic emission lines tot is
written as
s tot5As int2 1salloy2 , ~3!
where boths int and salloy depend on the exciton lateral d
mensionRex. Since the value ofRex can be modified by the
application of an external magnetic field parallel to t
growth direction, it is possible to probe the QW interfac
changing the intensity of the applied magnetic fieldB.
When an increasing magnetic field is applied along
growth direction of the QW sample, it leads to a decrease
d
tal
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ift
e-
PRB 60 1521BRIEF REPORTSRex due to an additional confinement induced byB. More-
over, the excitonic emission undergoes a diamagnetic s
@DE(1S)#, which can be written as DE(1S)
5(e2B2/8mxy)Rex
2 , for the fundamental excitonic stat
(1S).18 Here, e is the elementary charge andmxy is
the exciton in-plane mass (mxy50.041m0 for our
GaAs/Ga0.7Al0.3As QW!.
We performed magneto-PL measurements from 0 up
12 T in the Faraday configuration as described earlier.
PL spectra obtained by applying different magnetic fie
were decomposed using a Lorentzian and a Gaussian c
to simulate the BE and FE emission peak, respectively.
inset of Fig. 2 shows the diamagnetic shift as a function oB
obtained from our experimental data. From these resu
keeping the zero magnetic field value ofmxy and using the
equation forDE(1S) we calculated the exciton lateral d
mension (Rex) as a function of the magnetic field. The resu
are plotted in Fig. 2. As it was expected,Rex decreases for
increasing magnetic field as a consequence of the additi
magnetic confinement. In Fig. 2 we note that the extrapo
tion down to zero magnetic field indicates a value of a
proximately 91 Å forRex at B50. This value of the exciton
dimension is in agreement with others obtained in
literature.19
Also, from the data of Fig. 2 we observe thatRex, and
consequently the optical probe, assumes its maximun v
at low magnetic field. Under that experimental condition,
excitonic PL-FWHM can be very sensitive to the alloy flu
tuation due to the larger penetration of the excitonic wa
FIG. 2. Lateral exciton dimensionRex as a function of the per-
pendicular magnetic fieldB. The inset shows the diamagnetic sh
@DE(1S)# as a function ofB.ift
to
e
s
rve
e
s,
al
-
-
e
ue
e
e
function into the barrier. Therefore, before investigating t
dependence of the PL-FWHM onB, we have estimated the
maximum value thatsalloy assumes, i.e., atB50.
In Eq. ~2! we considered that the exciton fraction in th
barrier atB50 could be estimated asP0
ex512Lz
3/Rex
3 , with
Lz580 Å andRex591 Å , which givesP
ex50.32. On the
other hand, we have calculated the dependence ofEex on x
and obtained 0.034 meV for (dEex/dx)x50.3.
20 With these
values we foundsalloy50.29 meV. Since we have measure
s tot51.60 meV@from the PL spectrum in Fig. 1~c!# we ob-
taineds int51.57 meV using Eq.~3!. As a consequence, ou
calculations show that the alloy fluctuations have a min
influence on the broadening of the PL spectra of our sam
i.e., s tot>s int as it was expected. Thus, for wider QW th
amplitude of the excitonic wave function in the barrier w
b negligible and the alloy-fluctuation effects can genera
be discarded.
If we now assume in Eq.~1! that the island height isd1
52.83 Å ~one GaAs ML!, the reduced excitonic mass
m50.056m0 ~value determined from the Luttinger param
eters for GaAs!, s int>1.6 meV, Lz580 Å , and Rex
591 Å ~for B50), thus we obtaind2533 Å for the lat-
eral dimension of the microroughness. This value is in go
greement with the one determined by TEM f
GaAs/Ga0.7Al0.3As QW.
9
Using d2533 Å and the values ofRex plotted in Fig. 2,
we can calculates int for each value ofB from the same Eq.
~1!, as shown in Fig. 3. In this figure we also plotted t
values of the experimental FWHM that were obtained
rectly from the decomposition of our experiment
magneto-PL spectra~solid circles!. It can be seen that both
experimental and theoretical data are in good agreemen
It is important to stress that the main aspect of the res
of Fig. 3 is the ability of the model to correctly describe th
FIG. 3. PL-FWHM of the FE emission obtained from the d
composition of our magneto-optical data~solid circles! and values
of s int obtained from the Singh and Bajaj model~open circles!.
b
am
p
al
te
iz
he
r-
ent,
nti-
ue
De-
1522 PRB 60BRIEF REPORTSincrease of the PL-FWHM when the size of the optical pro
is reduced with the increasing magnetic field.
In a standard PL measurement, where the light-spot di
eter is large, i.e., without spatial resolution~as in our experi-
ment!, the measured PL spectrum represents a linear su
position of very narrow lines associated with the later
potential fluctuations.11 In this sense the lateral dimensiond2
extracted from the Singh and Bajaj equation has to be in
preted as an effective lateral-interface-microroughness s
In conclusion, we showed in this work that in spite of tE
B
Y
ple
-
er-
-
r-
e.
complexity of the structural characteristics of the QW inte
faces, where defects with different length scales are pres
the theoretical model of Singh and Bajaj provides a qua
tative description of the broadening of the emission line d
to the microroughness localized at the AlxGa12xAs/GaAs
interface.
The authors acknowledge the Conselho Nacional de
senvolvimento Cientı´fico e Tecnolo´gico ~CNPq! and the
Fundac¸ão de Amparo a` Pesquisa de Sa˜o Paulo~FAPESP! for
financial support.g,
.
B
un.
ys.
.
. B1J. Singh and K. K. Bajaj, J. Appl. Phys.57, 5433~1985!.
2P. Borri, M. Gurioli, C. Colocci, F. Martelli, M. Capizzi, A.
Patene`, and A. Polimeni, J. Appl. Phys.80, 3011~1996!.
3K. Fujiwara, K. Kanamoto, and N. Tsukada, Phys. Rev. B40,
9698 ~1989!.
4U. Jahn, S. H. Kwok, M. Ramsteiner, R. Hey, H. T. Grahn, and
Runge, Phys. Rev. B54, 2733~1996!.
5J. Christen and D. Bimberg, Phys. Rev. B42, 7213~1990!.
6F. Martelli, A. Polimeni, A. Patane`, M. Capizzi, P. Borri, M.
Gurioli, M. Colocci, A. Bosacchi, and S. Franchi, Phys. Rev.
53, 7421~1996!.
7I. Aksenov, J. Kusano, Y. Aoyagi, T. Sugano, T. Yasuda, and
Segawa, Phys. Rev. B51, 4278~1995!.
8R. F. Kopf, E. F. Schubert, T. D. Harris, and R. S. Becker, Ap
Phys. Lett.58, 631 ~1991!.
9C. Warwick and R. F. Kopf, Appl. Phys. Lett.60, 386 ~1992!.
10K. Fujiwara, R. Cingolani, and K. Ploog, J. Phys. IV3, 307
~1993!.
11K. Bruner, G. Abstreiter, G. Bo¨hm, G. Träkle, and G. Weimann,.
.
.
Appl. Phys. Lett.64, 3320~1994!.
12J. B. Zhu, H. I. Jeon, E.-K. Suh, H. J. Lee, and Y. G. Hwan
Phys. Rev. B52, 16 353~1995!.
13H. F. Hess, E. Betzig, T. D. Harris, L. N. Pfeiffer, and K. W
West, Science264, 1740~1994!.
14J. Singh, K. K. Bajaj, and S. Chaudhuri, Appl. Phys. Lett.44, 805
~1984!.
15A. Patane`, A. Polimani, M. Capizzi, and F. Martelli, Phys. Rev.
52, 2784~1995!.
16V. Srinivas, Y. J. Chen, and E. C. C. Wood, Solid State Comm
89, 611 ~1994!.
17J. B. B. Oliveira, E. A. Meneses, and E. C. F. Silva, Braz. J. Ph
27/A, 193 ~1997!.
18W. Ossau, B. Jakel, E. Bangert, and G. Landwehr, Surf. Sci.174,
188 ~1986!.
19R. Zimmerman and E. Runge, J. Lumin.60-61, 320 ~1994!.
20G. Olegart, M. Proctor, D. Martin, F. Morier-Geraud, F.-K
Reinhart, B. Orschel, L. C. Andreani, and H. Rhan, Phys. Rev
49, 10 456~1994!.


Magneto-optical studies of the correlation between interface microroughness parameters and the photoluminescence line shape in GaAs/Ga0.7Al0.3As quantum wells

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Magneto-optical studies of the correlation between interface microroughness parameters and the photoluminescence line shape in GaAs/Ga0.7Al0.3As quantum wells

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