Absorption spectroscopy on room- apl phys. 74,570.pdf

Journal of Applied Physics 74, 570 (1993); https://doi.org/10.1063/1.355269 74, 570
© 1993 American Institute of Physics.
Absorption spectroscopy on room
temperature excitonic transitions
in strained layer InGaAs/InGaAlAs
multiquantum-well structures
Cite as: Journal of Applied Physics 74, 570 (1993); https://doi.org/10.1063/1.355269
Submitted: 14 December 1992 • Accepted: 01 March 1993 • Published Online: 04 June 1998
Y. Hirayama, Woo-Young Choi, L. H. Peng, et al.
ARTICLES YOU MAY BE INTERESTED IN
Band parameters for III–V compound semiconductors and their alloys
Journal of Applied Physics 89, 5815 (2001); https://doi.org/10.1063/1.1368156
Material parameters of In1−xGaxAsyP1−y and related binaries
Journal of Applied Physics 53, 8775 (1982); https://doi.org/10.1063/1.330480
Compositional dependence of band-gap energy and conduction-band effective mass of
In1−x−yGaxAlyAs lattice matched to InP
Applied Physics Letters 41, 476 (1982); https://doi.org/10.1063/1.93537

Absorption spectroscopy on room temperature excitonic transitions
in strained layer InGaAs/lnGaAlAs multiquantum-well structures
Y. Hirayama,a) Woo-Young Choi, L. H. Peng,b) and C. G. Fonstad
Department of Electrical Engineering and Computer Science and Research Laboratory of Electronics,
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
(Received 14 December 1992; accepted for publication 1 March 1993)
The physical properties (transition energy, oscillator strength, linewidth, binding energy, and
reduced effective mass) of room temperature excitons in compressively strained InGaAs/
InGaAlAs multiquantum-well (MQW) structures as a function of the well width have been
investigated for the first time by both absorption measurements and photomodulated
transmittance measurements. Photomodulated transmittance spectroscopy has been successfully
applied to clearly reveal critical transition points. Measured transition energies are in good
agreement with a model which includes the heavy hole and light hole splitting due to the strain.
For well widths of 2.5-7.5 nm, oscillator strengths are smaller for the strained layer MQWs than
for the lattice-matched MQWs by 35%-45%. This is due to the larger exciton radius for the
strained MQWs resulting from smaller in-plane reduced effective masses (0.031-0.038m0),
which are 65% of those of the lattice-matched MQWs.
I. INTRODUCTION
An exciton, which is in fact a many body effect, con-
sists of an electron and a hole interacting with each other
through Coulomb attraction. It is well known in quantum
wells that exciton effects are enhanced because of the wave
function confinement perpendicular to the quantum well
plane. Strong exciton resonances in quantum wells have
been reported. l-l4 Among _ many multiquantum-well
(MQW) structures, strained layer MQW structures’
~-‘
*
have been intensively studied in recent years for their ap-
plication to high performance optical devices such as low
threshold, high-power, and high-speed lasers.‘
9-34 Espe-
cially, the strained layer InGaAsAnAlAs, InGaAs/
InGaAlAs, and InGaAs/InP material systems are attrac-
tive and important, because these materials emit or absorb
the light at around 1.55 pm wavelength, which is the op-
timal wavelength for optical communication systems.
Therefore, a systematic understanding of the behavior of
excitons in strained layer MQWs in these material systems
is very important for advanced photonic devices. Only few
results on the basic optical properties have been re-
ported,‘
3-‘
5 however, and the important physical parame-
ters of the excitons in the strained layer MQWs as a func-
tion of the well width have not yet been determined.
In this paper, the physical properties of excitons, i.e.,
transition energy, oscillator strength, linewidth, binding
energy, and reduced effective mass, in strained layer
MQWs based on long-wavelength materials are presented.
To the authors’ knowledge, this is the first systematic re-
port on the room temperature excitons in long-wavelength
strained layer MQWs. Photomodulated transmittance
spectroscopy is found to be a more effective way to reveal
the subband structures compared with conventional ab-
‘
IOn leave from Toshiba Co., Research and Development Center, Ka-
wasaki, Japan.
“Division of Applied Sciences, Harvard University, Cambridge, MA
02138.
sorption measurement. Important results which show
weaker excitonic transitions for the compressively strained
MQWs resulting from smaller reduced effective masses are
described.
II. EXPERIMENTS
A. Sample structures
Three kinds of strained layer InGaAs/InGaAlAs
MQW structures with different well thicknesses (samples
A, B, and C) were grown on (001) 1nP:Fe substrates by
molecular beam epitaxy (MBE) . For comparison, a lattice
matched InGaAs/InAlAs structure (sample D) was also
fabricated. The well thickness in each sample was precisely
determined by fitting a simulated satellite pattern to x-ray
diffraction spectra. Table I summarizes the sample
structures. Samples A, B, and C contain four 2.5 nm wells,
four 5.0 nm wells, and four 7.5 nm wells, respectively.
The Indium composition in the InGaAs ternary compound
is determined to be 0.652 for sample C and almost same
for samples A and B. This corresponds to 0.83% compres-
sive strain in the plane of the quantum well. The wells in
each sample are separated by 8.5 nm thick
Ino.4,0G~s,,Ab.2,sAs barriers which have 0.43% tensile
strain. Although the total well thickness for sample C is
more than a critical thickness,36 the strain is not relaxed,
partly because the growth temperature is lowered37 and
partly because the total strain is compensated by the tensile
strained barriers. The upper and lower cladding layers
have the same composition as the barriers and are 0.12 and
0.16 pm thick, respectively. They are doped with Si and Be
for n and p type, respectively, to 5 x 10” cmw3 except 0.04
pm undoped regions in each layer which cover the MQW
region. These thin undoped layers are employed to avoid
any dopant diffusion into the MQW region, which is un-
intentionally doped. This p-i-n structure is helpful for the
photomodulated transmittance measurements as will be
described later. The reference sample D consists of 40
570 J. Appl. Phys. 74 (l), 1 July 1993 0021-8979/93/74(1)/570/9/$6.00 @ 1993 American institute of Physics 570

TABLE I. Structural parameters of the samples investigated. & and Lb
are the well width and barrier width, respectively. Samples A-C have
compressively strained InGaAs quantum wells with InGaAlAs barriers.
Sample D has lattice-matched InGaAs quantum wells with InAlAs bar-
riers.
Sample No. of well L, bun) Lb (nm) In composition
A 4 2.5 8.3 0.652
B 4 5.0 8.3 0.652
c 4 7.5 8.3 0.652
D 40 7.2 7.2 0.517
lattice-matched quantum wells with 7.2 nm thickness and
InAlAs barriers with 7.2 nm thickness. The whole struc-
ture is unintentionally doped for this sample. Details of the
sample growth have been reported elsewhere.35
B. Absorption measurements
We measured the optical absorption spectra of the
samples at room temperature by conventional phase-
sensitive lock-in technique using a monochromator and a
tungsten (W) lamp. A PbS detector was used for light
detection. For these measurements, the rear side of the
samples were polished by Br-methanol to avoid light scat-
tering. A perpendicular incidence geometry was employed.
The absorption coefficient was determined by comparing
the transmitted light intensity with (II) and without (1,)
the sample. By definition of the transmission coefficient T,
we obtain the following relation between these two quan-
tities:
T==1~/1~=(1-R)2exp(-aard)/[1-R2exp(-2ad)],
(1)
where R is reflection coefficient, a is absorption coefficient,
and d is total thickness of well layer. The absorption coef-
ficient which is measured from a transparent point below
the bandgap energy takes the following form:
a,,,=a-a’
=ln(T’
/T)/d[ 1+x(a)], (2)
where a’ is the absorption value at almost transparent
point. The calibration factor x(a) is expressed as
x(a)=In{[l-R2exp(-22ad)]/
[ l-R2 exp( -2a’
d)])/(&-a’
)o!, (3)
and the value is found to be around 0.2 for our structures.
For samples A and B, more than one piece of wafer are
stacked and measured to improve the signal-to-noise ratio.
C. Photomodulated transmittance measurements
Modulation optical spectroscopy is a very attractive
technique because of its high sensitivity. The photomodu-
lated transmittance (PMT) technique38’
39 is similar to
photoreflectance (PR) spectroscopy.40-42 For structures
grown on transparent substrates, sample thinning is not
necessary, which makes the transmittance measurement
technique more attractive. Moreover, spectra can become
less complicated because the substrate contribution is al-
Monochromator
Lens PbS
FIG. 1. The photomodulated transmittance measurement setup.
Chopped Ar laser light at a power of 1 mW was used to modulated the
internal built-in field in a sample.
most completely suppressed. The photomodulated trans-
mittance is produced by a contactless electric field modu-
lation by means of a laser beam. Ar laser light at 1 mW
power was chopped and shone on the sample as shown in
Fig. 1. A strong increase in both resolution and signal-to-
noise ratio compared with the conventional room temper-
ature transmission spectroscopy was obtained by the addi-
tion of a modulated light source. It is found that this
technique is much more sensitive when it is used for the
p-i-n structure which has a relatively strong built-m elec-
tric field.
Ill. RESULTS AND DISCUSSION
A. Transition energy
Figure 2 shows the measured room temperature ab-
sorption spectra for three kinds of the strained layer
MQWs (samples A, B, and C) and the lattice matched
MQW (sample D), The arrows indicate calculated exci-
tonic transition energies. Clear transitions between el (first
subband in a conduction band) and hhl (first subband in
a heavy hole valence band) are observed for all samples.
The energy values are 0.897 (and also 0.9 13)) 0.792, 0.73 1,
and 0.835 eV for samples A-D, respectively. However,
critical points are not always clear for higher order transi-
tions.
Figure 3 shows the corresponding photomodulated
spectra. As shown in Fig. 3, PMT signals are very sensitive
at critical points. In these figures, the conventional absorp-
tion spectrum is superimposed for comparison. The arrows
indicate calculated excitonic transition energies. The PMT
signals are stronger by an order of magnitude for samples
A, B, and C, which have the p-i-n structure, compared
with those for sample D, which is unintentionally doped.
The signal level is of the order of 10B3. This is thought to
be due to the relatively strong built-in electric field in the
strained layer MQW samples.
In general, the absorption change, Aa, in the PMT
measurement is proportional to the change in the imagi-
nary part of the dielectric function, Aei resulting from the
change in the intensity of the pump beam P. For excitonic
transitions, A~i can be expressed as41*42
571 J. Appl. Phys., Vol. 74, No. 1, 1 July 1993 Hirayama et a/. 571

Strained InGaAs/lnGaAIAs MQW
Lz = 2.5 nm
Lz = 2.5 nm
0.8
0.8 0.85
0.85 0.9
0.9
Photon Energy (eV)
Photon Energy (eV)
x104
3
+z
-9 2.5- (b)
5
E 2-
.a,
g
-z
8 1.5-
g I-
T=
F
$ 05-
Lz = 5.0 nm el-lhl
T=300K I
g 2.5 -
c
E 2-
.a,
.Y
g 1.5-
s
5 l-
‘
G
g0.5-
O-
Cc)
-if-
2
2.5
5
E 2
.!2
.di
g 1.5
0
MQW
0.7 0.75 0.8 0.85 0.9 0.95 1
Photon Energy (eV)
0
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15
Photon Energy (eV)
0 J ..
0.7 0.75 0.8 0.85 0.9 0.95
Photon Energy (ev)
FIG. 2. Room temperature absorption spectra (solid line) and fitted Gaussian curves (dashed line). (a) Sample A has strained layer MQW with 2.5
nm well width. The arrows indicate calculated energies for el-hhl (0.882 eV) and el-lhl (0.985 eV) transitions. (b) Sample B has strained layer MQW
with 5.0 nm well width. The arrows indicate calculated energies for el-hhl (0.772 eV) and el-lhl (0.872 eV) transitions. (c) Sample C has strained layer
MQW with 7.5 nm well width. The arrows indicate calculated energies for el-hhl (0.726 eV), el-hh2 (forbidden 0.761 eV), el-lhl (0.815 eV), and
e2-hh2 (0.915 eV) transitions. (d) Sample D has lattice matched MQW with 7.2 nm well width. The arrows indicate calculated energies for el-hhl
(0.833 eV), el-lhl (0.867 eV), al-lh2 (forbidden 0.986 eV), and e2-hh2 (1.070 eV) transitions.
where Eph is the exciton energy gap, J?is a phenomenolog-
ical broadening parameter, and S is the integrated intensity
of the excitor& transition. The relative contributions to the
PMT line shape arising from the linewidth, energy gap,
and intensity modulation mechanisms are determined by
the magnitude of the bracketed coefficients in Eq. (4).
These coefficients are functions of the pump intensity and
the subband indices of the excitons. When the first term in
Eq. (4) is dominant, the line shape will be a dispersive
shape, which has both positive and negative parts, and the
zero crossing point gives the excitonic transition energy.
When the second or the third term is dominant, the line
shape will be symmetric and the peak gives the excitonic
transition energy. This relationship is schematically drawn
in Fig. 4. In actual cases, it is thought that the signal shape
is the combination of three limiting cases described above.
Therefore, the interpretation of PMT signals is not always
easy and it should be done carefully, but it gives not only
complementary information but also useful clues to reveal
critical points. Empirically, in many cases, a middle point
572 J. Appl. Phys., Vol. 74, No. 1, 1 July 1993
between a peak and a bottom in the PMT signal peak
corresponds to a critical point in the absorption spectra.
They can be attributed to excitons composed of electrons
and heavy holes, and electrons and light holes. The exci-
tonic transition energies for el-lhl are determined to be
0.99, 0.87, 0.81, and 0.86 eV for samples A-D, respec-
tively. For samples C!and D, the excitonic transitions from
hh2 to e2 are also observed. Parity forbidden transitions
between el and hh2 and between el and lh2 are also re-
vealed in samples C and D, respectively. Sample D shows
extra peaks near the band edge which we cannot yet ex-
plain.
The excitonic transition energies were calculated by
using effective-mass approximation including heavy hole
and light hole energy split at the gamma point due to
strain. The effect of strain on the band lineups was calcu-
lated in a straightforward manner based on the model solid
theory proposed by Van de Walle and Martin.43Y44The
energy shifts of an averaged valence band position E",.+"and
a conduction band position ECinduced by the hydrostatic
strain component can be expressed as
Hirayama et a/.
(5)
572

-0.5 aAs/lnGaAIAs MQW
-1
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
Photon Energy (eV)
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
Photon Energy (eV)
Strained InGaAsDnGaAIAs MQW
0.8 0.7 0.8 0.9 Eneriy 1.1 1.2 1.3
Photon (eV)
Lattice-Matched InGaAs/lnAIAs MQW
28P -3
-4
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
Photon Energy (eV)
FIG. 3. Room temperature photomodulated absorption spectra. Absorption spectra are superimposed for comparison. The arrows indicate calculated
transition energies. (a) Sample A, (b) sample B, (c) sample C, (d) sample D.
dE,=a,( An/a), (69
where a, and a, are the hydrostatic deformation potentials
for the valence and conduction bands, respectively. The
AWR is the fractional volume change which, for small
strains on (001) substrates, can be approximated by
Absorption
0
Absorption i Change i
(4 W (c)
FIG. 4. Schematic photomodulatcd transmittance line shapes for three
limiting cases: (a) dispersion like line shape due to transition energy
change, (b) symmetric line shape due to linewidth change, (c) symmetric
line shape due to transition intensity change.
573 J. Appl. Phys., Vol. 74, No. 1, 1 July 1993
An/O= (2e,+e,), (79
where the strain components (eif) are defined as
%p=(Gd~-l9, (89
e,=(-2cdcl19exx, (99
where a0 is the lattice constant of InP, a is the lattice
constant of the free-standing InGaAs epilayer, and C, is
the elastic stiffness constant of InGaAs. The valence band
degeneracy at the gamma point is lifted by the shear strain
component. The energy shifts for the heavy hole ( 1J,mj)
= [3/2,3/2) ) valence subband, the light hole ( 13/2,1/2) 9
subband, and the split-off band ( 1l/2,1/2)) are calculated
with respect to their weighted average and given by
dEuvhh
= Ad3 -SE&2, (109
d&,,h= -Aho/6fSEo,,1/4+sp, (119
dE,,, = - At/6 -t-SE,,/4 - sp, (129
with
s~=~/~[A;+A,SE,,+~/~(SE~,)“]“~, (139
where A0 is the spin-orbit splitting in the unstrained bulk
InGaAs, and SE,, is given by
Hirayama et a/. 573

TABLE II. Material parameters for the binary compound InAs, GaAs,
and AlAs. Lattice constant, a,; elastic modulus, C,,; shear deformation
potential, b; spin-orbit splitting, Ac; weighted average over the three up-
permost valence bands at gamma, &BY ; hydrostatic deformation potential
for the valence band, a,, and for the conduction band, a,; and the elec-
tron, heavy hole, and light hole effective massesat gamma, m, , mhh, and
ml,, , respectively. Interpolated values for ternary (InGaAs and InAlAs)
and quatemary (InGaAlAs) materials are used for calculation.
IliAr? GaAS= AIAsb
=0
Cl1
CIZ
b
Ao
E“,BY
=u
=c
mhh
mlh
me
A 6.0584 5.6533 5.65
IO” dyn/cm’ 8.329 11.88 12.5
10” dyn/cm* 4.526 5.38 5.34
eV -1.8 -1.7 - 1.5
eV 0.38 0.34 0.28
eV -6.67 - 6.92 -7.49
eV 1.00 1.16 2.47
eV -5.08 -7.17 -5.64
m0 0.41 0.45 0.409
m0 0.025 0.082 0.153
m0 0.023 0.067 0.13
“Reference 15.
bReference 43.
6Eml=2b(e,--e,,), (14)
where b is the shear deformation potential for a strain of
I tetragonal symmetry. The numerical parameters are calcu-
lated by Vegard’
s law from the binary compound data. The
parameters for binary materials are listed in Table II.15*43
Band gaps for Inr-,Ga&s (this is obtained by an inter-
polation of the band gap for GaAs, InAs, and
In,s3Gae4,As) and In, -,-,,Ga,/&As4’ at room tempera-
ture are expressed as
E,(InGaAs) =0.36+0.6212~+0.4438~~, (15)
EJInGaAlAs) =0.36+2.093x+0.629y+0.577x2
+0.436y2+ l.O13xy-2.Oxy( l--x--y),
(16)
respectively. The InGaAs/InGaAlAs band lineups used
for the calculation are shown in Fig. 5. The subband ener-
gies were calculated by an effective mass envelope function
approach. Band nonparabolicity associated with the real
wave vector in the conduction band of the well was taken
into account as follows:46
me=m&Jo(l+aE), (17)
a= ( 1-mJmo)2/Eg, (18)
where m, is electron mass at an energy E, ma is band
bottom mass, and m. is free electron mass. For simplicity,
valence band effective masses of the unstrained bulk mate-
rials were used, although the strain causes complicated
valence band nonparabolicity. Continuity of the envelope
function q(z) and of [l/m(E)]dg,(z)/dz were used as
boundary conditions. The absorption energy is given by
Eph=Ee+E/,+Eg-Ebr (19)
where E, and Eh are electron and hole subband energies in
the quantum well, Eg is the band gap of the well material,
Ev,lh -6.823
Ev,hh -6.853
Ev,so -7.015
- Ev.so -7.182
FIG. 5. The band lineups of strained InGaAs and InGaAlAs used for
calculations.
and Eb is the exciton binding energy. The calculated tran-
sition energy and experimental results were plotted in Fig.
6. Although no fitting parameter is used, they are in good
agreement, which confirms that the strain effect causes
splitting of the heavy hole band and the light hole band.
Uncertainty in material parameters such as effective mass,
band discontinuity, and bandgap especially for
InGaAlAs4’ is thought to be a cause of slight difference in
experimental and calculated values. The relatively strong
built-in field may also modify the transition energy, how-
ever, it is estimated to be less than several meV. The higher
order transitions and the parity forbidden transitions ob-
served in the PMT spectra also match the calculated tran-
sition energy very well.
B. Oscillator strength
It is well known that the excitonic transition is well
fitted by a Gaussian distribution function.‘
*‘
2 By fitting the
data using the Gaussian line shape, the integrated intensity
S was obtained. Nonlinear least square method was used
1.05
I-
g 0.95 -
6 0.9-
5
w” 0.85 -
0’
:E 0.8-
2
,m 0.75-
l-
0.7
t
el-hhl Transition
0.651 . . . s . . s . . 1
0 1 2 3 4 5 6 7 8 9 10
Well Width (nm)
FIG. 6. Excitonic transition energies for et-hhl (circle) and el-lhl
(cross) as a function of well width. Solid and dashed curves show calcu-
lated values for el-hhl and el-lhl, respectively.

TABLE III. Fitted values of Gaussian fitting {a(@=~ exp[-(E
-EP,J2/(21?)3} for absorption spectra; a nonlinear least square method
was used in the fitting. For Sample A, a mixture of two Gaussian curves
was fit to the spectrum.
Sample
A
B
C
D
0, (cm-‘
)
9 550
12 320
13 840
7200
12 170
Eph (W
0.897
0.913
0.792
0.731
0.835
r (meV)
7.9
7.1
6.9
6.5
7.0
for the data fitting. In Fig. 2, the fitted curves are plotted.
For samples A-G, the built-in field may cause slight
changes in the absorption spectra. However, the change in
an absorption area is negligibly small according to the sum
rule.5 The integrated intensity is proportional to an oscil-
lator strength divided by the well width L,. For sample A,
two mixed Gaussian shapes are used for the fitting because
both the absorption spectrum and the PMT spectrum show
double peaks at the absorption edge. The fitted values are
listed in Table III. The absorption coefficients for el-hhl
excitonic transition are 9550 (and also 12 320), 13 840,
7200, and 12 170 cm-’ for samples A-D, respectively. Fig-
ure 7 shows the integrated intensity as a function of the
well width. The data for lattice-matched MQWs from
Refs. 8 and 12 are also plotted. In Ref. 8, the data are taken
at low temperature, however, it is reported that the tem-
perature dependence of oscillator strength is very small.12
It is found that S is smaller by 35%-45% for the strained
layer MQWs than those for the lattice-matched MQWs at
the same well width. At the same wavelength, however, S
is almost same for both strain and lattice-matched MQW
structures. It seems that the well width dependence of S is
l/L: for both strained and lattice-matched MQWs when
L, is more than 5 nm, 48,49
while it is less dependent on the
well width for narrower well widths.
It is very important to know the spatial extent of the
exciton, /2,, in the quantum well because this information
is useful in understanding the broadening of the exciton
600 SbJz et al. 4
t
Stolz et al.
Lattice-Matched MQW
Sugawara et al.
2
I
4 6 8 IO 12
Well Width (nm)
FIG. 7. Integrated intensity as a function of well width for strained (open
circle) and lattice-matched (closed circle) quantum wells. The data from
Refs. 8 and 12 are also included (cross). The lines are a guide to the eye.
Sugawara et al. -
/
6”
’
Lattice-Matched MQW
-0 2 4
Well W&h (nmj8
IO 12
FIG. 8. Exciton radius as a function of well width for strained (open
circle) and lattice-matched (closed circle) quantum wells. Cross is from
Ref. 12. The lines are a guide to the eye.
linewidth due to structural fluctuations in the quantum
well. It is also important in calculating the light intensity at
which excitons start overlapping with each other and caus-
ing very strong optical nonlinearities. The integrated inten-
sity of the exciton spectrum based on the effective-mass
approximation is given byt2
S=Je’
fiI (Pcv> I2l G144.4I97hW > I2/(~~c~~3ph&Gh
(20)
where e is the electron charge, Pcv is the optical matrix
element, qp,(z> is the electron envelope wave function,
q~(z) is the ho e envelope wave function, e. is the permit-
1
tivity in vacuum, c is the speed of the light, and n is the
refractive index. The exciton radii were obtained using E!q.
(20) by substituting experimental S values, which are 406,
240, 116, and 2 13 eV/cm for samples A-D, respectively.
As shown in Fig. 8, the values are 13.1, 13.8, 17.2, and 12.2
nm for samples A-D, respectively. The increase of exciton
radii is the main reason for small S values in the strained
MQW structures.
C. Linewidth
The exciton spectrum broadening at low temperatures
is primarily due to the spatial inhomogeneity of the exciton
energy level caused by structural imperfections in the
quantum wells,5o such as interface roughness, composition
fluctuations in constituent alloys, and nonperiodicity in
multiple quantum wells. At high temperatures, the exci-
tons are ionized to free electron-hole plasma by phonon
scattering. The increase of phonons reduces the exciton
lifetime, and broadens the excitonic transition spectrum
according to the uncertainty principle. Figure 9 shows the
room temperature PWHM (full width at half-maximum)
of the heavy hole exciton peaks as a function of the well
width. The data from Refs, 2, 11, 12, and 46 are also
plotted. Reference 46 includes a FWHM value for a
strained MQW. The dashed line is a guide to the eye. The
values are in the range of 10-15 meV for both strained and
lattice-matched MQW structures except at, narrow well
width. For the 2.5 nm well, the strained MQW structure

9
g 3o c
0 VAsai et al. (Strained)
i Asai et al.
f 25-
z
5
20-
‘
a 15-
Lu
$ IO-
c 5-
!z
I
01 I
0 2 4 10 12
Well
W&h (nm)8
FIG. 9. Heavy hole exciton linewidth at room temperature as a function
of well width for strained (open circle) and lattice-matched (closed cir-
cle) quantum wells. The data from Refs. 2, 11, 12, and 46 are also plotted
(cross). The dashed line is a guide to the eye. The solid curve shows the
calculated energy shift due to monolayer Buctuation.
shows strong broadening as wide as 31 meV. To investigate
this broadening, the theoretical subband energy change due
to one monolayer fluctuation is also plotted in Fig. 9. It is
reasonable to think that strong enhancement in the line-
width is partly due to the monolayer fluctuation of the
quantum well which has comparable island size to the ex-
citon radius. Statistical composition fluctuations may be
another cause for this strong linewidth broadening.
The data in this study show narrower FWHM values
than those of reported values.“p46 The smaller number of
quantum wells in our MQWs is thought to be one of the
reasons. To reveal linewidth broadening mechanisms, low
temperature measurements are also needed and are now
under study. The PMT spectrum widths are also useful in
studying el-hhl exciton linewidth. The broadening for 2.5
nm well is also observed in the PMT spectrum.
D. Binding energy and reduced effective mass
The two-dimensional exciton radius can be determined
by a variational method by minimizing the exciton binding
energy,51’
52
E&yJ = -fi2/(2j.&J +e2(Q>J l/p1@‘
)/(4?7e), (21)
where y is the reduced effective mass parallel to the quan-
tum well layers (l/p= l/m,,, + l/m,hll ) and p= [?+ (z,
-z*)2]“2, where z, and zh are the coordinates perpendic-
ular to the plane of the layer of the electron and hole,
respectively. The r is the relative position of electron and
hole in the plane of the layer. The first term in the right-
hand side in Eq. (21) is the kinetic energy of relative
electron-hole motion in the quantum well plane. The sec-
ond term is the Coulomb potential energy of the electron-
hole relative motion. We know that a simple trial wave
function of the ground state is
~=(P,wph(zhb&~~~
with
(22)
q=(r) = (2/r)” exp( -P/?L&/&~, (23)
$ 8.5-
2 a-
LLI
0) 7.5-
$
.g 7-
5
6.5 -
.E 6-
w” 5.5-
51
0
Lattice-Matched MQW
Strained MQW
2 4
Well W&h (nm)8
IO 12
FIG. 10. Binding energy as a function of well width for strained (open
circle) and lattice-matched (closed circle) quantum wells. The data from
Refs. 8 and 12 are included (cross). The lines are a guide to the eye.
where /2,x is the effective Bohr radius of the quasi bidimen-
sional exciton. As we know the values of the exciton radii
experimentally, the reduced effective mass and the binding
energy can be calculated based on Eq. (21). The effective
well widths were used for the calculation. Figure 10 shows
the exciton binding energy as a function of the well width.
Figure 10 includes the data for lattice-matched MQWs
from Ref. 8, in which the values are determined by mag-
netoabsorption measurements and from Ref. 12. The Eb
increases with decreasing well width and a value of 7.8
meV is obtained for a 2.5 nm strained layer MQW. The Eb
seems to saturate in the narrow well width region for both
lattice-matched and strained layer MQWs. The Eb is
smaller for the strained MQWs than those for the lattice-
matched MQWs by l-2 meV,
Figure 11 shows the reduced effective mass as a func-
tion of the well width. Data for lattice-matched MQWs
taken from Refs. 9 and 12 are also plotted. In Ref. 9, the
values are determined by magnetoabsorption measure-
ments. Small reduced effective massesfor the strained layer
MQWs are obtained. The values are in the range of 0.03 l-
E*.**1
f2
r”
0.07
.; 0.06
4
= 0.05
B
z 0.04
f 0.03
h
2 0.02
0
Lattice-Matched MQW
2 4 6 8 IO 12
Well Width (nm)
FIG. 11. In-plane reduced effective mass as a function of well width for
strained [open circle) and lattice-matched (closed circle) quantum wells.
The data from Refs. 9 and 12 are included (cross). The lines are a guide
to the eye.
576 J. Appl. Phys., Vol. 74, No. 1, 1 July 1993 Hirayama et al. 576

0.038mo, which are 65% of those of the lattice-matched
MQWs. It is well known that the heavy hole mass in the
quantum well plane decreaseswith compressive strain. Our
results reflect this strain effect as well as both the electron
and hole effective mass changes due to a composition
change in the well material. The calculations were carried
out using simple models.53”4 For well widths of 2.5-7.5
nm, the calculated reduced effective masses are 0.027-
0.032me for the strained structures, compared to 0.031-
0.039~2~for the lattice-matched structures. In spite of us-
ing simple models, the calculation results explain the
decrease of the reduced effective masses qualitatively. This
reduction of the reduced effective mass is the main reason
for the large exciton radius and therefore the small inte-
grated intensity for the strained layer MQW structures. In
a sense, these results are negative for the application of the
compressively strained MQWs in advanced devices which
use excitonic effects such as quantum confined Stark effect’
and optical Stark effect,55’
56however, tensile strain may
enhance the excitonic effect. The use of InGaAlAs for the
well material is also promising, because the electron mass
will be increased by the addition of Al. Femtosecond dy-
namics of excitons of these strained samples are also inter-
esting properties, and will be studied.
IV. CONCLUSIONS
The physical properties of the room temperature exci-
tons (transition energy, oscillator strength, linewidth,
binding energy and reduced effective mass) in the compres-
sively strained InGaAs/InGaAlAs multiquantum-well as a
function of the well width were investigated by both ab-
sorption measurements and photomodulated transmittance
(PMT) measurements. The PMT technique for the sam-
ples with a p-i-n structure is found to be very effective for
revealing subband structures. Measured transition energies
are in good agreement with the calculation which includes
the heavy hole and light hole splitting due to strain. The
oscillator strength for the same well width is smaller for
the strained layer MQWs than those for the lattice-
matched MQWs. This is due to the larger exciton radius
for the strained layer MQWs resulting from the smaller
in-plane reduced effective mass. The employment of tensile
strain and the addition of Al to InGaAs well are proposed
to increase the excitonic transition intensity. This new in-
formation is very important for application of strained
layer MQWs to advanced photonic devices which use ex-
citonic effects in MQW such as quantum confined Stark
effect and optical Stark effect.
ACKNOWLEDGMENTS
Gne of the authors (Y.H.) would like to thank Pro-
fessor E. P. Ippen for his continuous encouragement and
useful discussions. This research was supported in part by
the National Science Foundation, Contract No. ECS-
9008485, and by the Army Research Office, Contract No.
DAAL03-91-G-0051.
‘
D. S. Chemla, D. A. B. Miller, P. S. Smith, A. C. Gossard, and W.
Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
‘
5. S. Weiner, D. S. Chemla, D. A. B. Miller, T. H. Wood, D. Sivco, and
A. Y. Cho, Appl. Phys. Lett. 46, 619 (1985).
‘
D. A. B. Miller, D. D. Chemla, T. C. Damen, A. C. Gossard, W.
Wiegmann, T. H. Wood, and C. A. Burrus, Phys. Rev. B 32, 1043
(1985).
‘
K. Wakita, Y. Kawamura, Y. Yoshikuni, H. Asahi, and S. Uehara,
IEEE J. Quantum Electron. QE-22, 1831 (1986).
5D. A. B. Miller, J. S. Weiner, and D. S. Chemla, IEEE J. Quantum
Electron. QE-22, 1816 (1986).
6H. Temkin, M. B. Panish, and S. N. G. Chu, Appl. Phys. Lett. 49, 859
(1986).
‘
M. Razeghi, J. Nagle, P. Maurel, F. Omnes, and J. P. Pocholle, Appl.
Phys. Lett. 49, 1110 (1986).
*W. Stolz, J. C. Maan, M. Altarelli, L. Tapfer, and K. Ploog, Phys. Rev.
B 36, 4301 (1987).
sW Stolz, J C. Maan, M. Altarelli, L. Tapfer, and K. Ploog, Phys. Rev.
B 36, 4310’(1987).
“D. J. Westland, A. M. Fox, A. C. Maciel, J. F. Ryan, M. D. Scott, J. I.
Davies, and J. R. Riffat, Appl. Phys. Lett. 50, 839 (1987).
“Y. Kawaguchi and H. Asahi, Appl. Phys. Lett. 50, 1243 (1987).
‘
*M Sugawara, T. Fujii, S. Yamazaki, and K. Nakajima, Phys. Rev. B
42; 9587 (1990).
13D Gershoni H. Temkin, M. B. Panish, and R. A. Hamm, Phys. Rev.
B39, 5531 (1989).
14N. Yokouchi, T. Uchida, T. Uchida, T. Miyamoto, F. Koyama, and K.
Iga, Jpn. J. Appl. Phys. 30, L885 ( 1991).
“T. Y. Wang and G. B. Stringfellow, J. Appl. Phys. 67, 344 (1990).
“A. R. Adams, Electron. Lett. 22, 249 ( 1986).
“E Yablonovitch and E. 0. Kane, IEEE J. Lightwave Technol. LT-4,
504, 961E (1986).
‘
*E. Yablonovitch and E. 0. Kane, IEEE J. Lightwave Technol. LT-6,
1292 (1988).
“I. Suemune, L. A. Coldren, M. Yamanishi, and Y. Kan, Appl. Phys.
Lett. 53, 1378 (1988).
“P J A. Thijs, L. F. Tiemeijer, P. I. Kuindersma, J. J. M. Binsma, and
T: V. Dongen, IEEE J. Quantum Electron. QE-27, 1426 (1991).
“J. S. Osinski, P. Grodzinski, Y. Zou, and P. D. Dapkus, Electron. Lett.
27, 469 (1991).
=IJ. Karen, M. Oron, M. G. Young, B. I. Miller, J. L. De Miguel, G.
Raybon, and M. Chien, Electron. Lett. 26, 465 (1990).
23H. Yamada, M. Kitamura, and I. Mito, presented at the Device Re-
search Conference, 1990 (unpublished), Paper IVB-2.
s4T. Tanbun-Ek, R. A. Logan, N. A. Olsson, H. Temkin, A. M. Sergent,
and K. W. Wecht, in Technical Digest of the 12th IEEE International
Semiconductor Laser Conference, Davos, 1990 (unpublished), p. 46.
=M. Okamoto, K. Sato, H. Mawatari, F. Kano, K. Magari, Y. Kondo,
and Y. Itaya, IEEE J. Quantum Electron. QE-27, 1463 (1991).
26M. C. Tatham, C. P. Seltzer, S. D. Perrin, and D. M. Cooper, Electron.
Lett. 27, 1278 (1991).
“C. E. Zah, R. Bhat, B. Pathak, C. Caneau, F. J. Favire, N. C. An-
dreadakis, D. M. Hwang, M. A. Koza, C. Y. Chen, and T. P. Lee,
Electron. Lett. 27, 1414 (1991).
z8C. E. Zah, R. Bhat, F. J. Favire, Jr., S. G. Menocal. N. C. Andreadakis,
K. W. Cheung, D. M. D. Hwang, M. A. Koza, and T. P. Lee, IEEE J.
Quantum Electron. QE-27, 1440 (1991).
*‘
N. K. Dutta, H. Temkin, T. Tanbun-Ek, and R. Logan, Appl. Phys.
Lett. 57, 1390 (1990).
3oY. Hirayama, M. Morinaga, M. Tanimura, M. Onomura, M. Funem-
izu, M. Kushibe, N. Suzuki, and M. Nakamura, Electron. Lett. 27, 241
(1991).
“Y. Hirayama, M. Morinaga, N. Suzuki, and M. Nakamura, Electron.
Lett. 27, 875 (1991).
32Y. Hirayama, M. Morinaga, M. Onomura, M. Tanimura, M. Tohyama,
M. Funemizu, M. Kushibe, N. Suzuki, and M. Nakamura, IEEE J.
Lightwave Technol. LT-10, 1272 (1992).
33H. Yasaka, R. Iga, Y. Noguchi, and Y. Yoshikuni, IEEE Photon. Tech-
1101.
Lett. PTL-4, 826 ( 1992).
34J. D. Evans, T. Makino, N. Puetz, J. G. Simmons, and D. A. Thomp-
son, IEEE Photon. Technol. Lett. PTL-4, 299 (1992).
“‘W.-Y. Choi and C. G. Fonstad, J. Cryst. Growth 127, 559 (1993).
36
J. W. Matthews and A. E. Blakeslee, J. Cryst. Growth 27, 118 (1974).

37M. Gendry, V. Drouot, C. Santinelli, and G. Hollinger, Appl. Phys. 47J. I. Davies, A. C Marshall, M. D. Scott, and R. J. M. Griffiths, Appl.
Lett. 60, 2249 (1992); Phys. Lett. 53, 276 (1988).
38A. Frova, P. Handler, F. A. Germano, and D. E. Aspnes, Phys. Rev.
145, 575 (1966).
3gC. V. Hoof, D. J. Arent, K. Deneffe, J. De Boeck, and G. Borghs, J.
Appl. Phys. 644233 (1988).
a J. L. Shay, Phys. Rev. B 2, 803 (1970).
‘
t B. V. Shanabrook, 0. J. Glembocki, and W. T. Beard, Phys. Rev. B 35,
2540 (1987).
42W. M. Theis, G. D. Sanders, C. E. Leak, K. K. Bajaj, and H. Morkog,
Phys. Rev. B 37, 3042 (1988).
“C. G. Van de Walle, Phys. Rev. B 39, 1871 (1989).
4$C. G. Van de Walle, Phys. Rev. B 35, 8154 (1987).
45D. Olego, T. Y. Chang, E. Silberg, E. A. Caridi, and A. Pinczuk, Appl.
Phys. Lett. 41, 476 (1982).
46H. Asai and Y. Kawamura, Appl. Phys. Lett. 56, 746 (1990).
48W. T. Masselink, P. J. Pearah, J. Klem, C. K. Peng, H. Morkop, G. D.
Sanders, and Y.-C. Chang, Phys. Rev. B 32, 8027 (1985).
49J. M. Rorison and D. C. Herbert, Superlatt. Microstruct. 1,423 (1985).
5oS.Hong and J. Singh, J. Appl. Phys. 62, 1994 (1987).
“G. Bastard, E. E. Mendez, L. L. Chang, and L. Esaki, Phys. Rev. B 26,
1974 (1982).
52G Bastard, E E. Mendez, L. L. Chang, and L. Esaki, Phys. Rev. B 28,
3241 (1983).
“U. Ekenberg, Phys. Rev. B 40, 7714 (1989).
54B. K. Ridley, J. Appl. Phys. 68, 4667 (1990).
55A. Von Lehmen, D. S. Chemla, J. E. Zucker, and J. P. Heritage, Optics
L&t. 11, 609 (1986).
56A. Mysyrowicz, D. Hulin, A. Antonetti, A. Migus, W. T. Masselink,
and H. Morko9, Phys. Rev. Lett. 56, 2748 (1986).

Absorption spectroscopy on room- apl phys. 74,570.pdf

More Related Content

Absorption spectroscopy on room- apl phys. 74,570.pdf