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Type-II quantum-well lasers for the mid-wavelength infrared
J. R. Meyer,a) C. A. Hoffman, and F. J. Bartoli
Code 5613, Naval Research Laboratory, Washington, DC 20375
L. R. Ram-Mohan
Worcester Polytechnic Institute, Worcester, Massachusettes 01609
~Received 28 March 1995; accepted for publication 24 May 1995!
We discuss an improved mid-wave infrared diode laser structure based on InAs-Ga12xInxSb-
InAs-Ga12xAlxSb Type-II multiple quantum wells. The proposed design combines strong optical
coupling, 2D dispersion for both electrons and holes, suppression of the Auger recombination rate,
and excellent electrical and optical confinement. © 1995 American Institute of Physics.
Fundamental mechanisms limiting the performance of
III-V semiconductor diode lasers1–4 operating at mid-wave
infrared ~MWIR!wavelengths beyond 3
m
m have included
inadequate electrical confinement due to small conduction
and/or valence band offsets, and the increasing predomi-
nance of Auger recombination when the energy gap is low-
ered and the temperature raised. The nonradiative decay has
tended to be dominated by the so-called CHHS Auger pro-
cess, in which the conduction-to-heavy-hole ~CH!recombi-
nation is accompanied by a heavy-to-split-off-hole ~HS!tran-
sition. In InAs-rich alloys such as InAsSb, InAsSbP, and
InGaAsSb, both momentum and energy are easily conserved
in this process because the energy gap Egis nearly equal to
the split-off gap D0.1
Type-II heterostructures employing the InAs-GaSb-AlSb
family have recently been proposed as a promising new ma-
terial system for the MWIR.5–7 The Type-II alignment effec-
tively eliminates CHHS Auger transitions by removing the
resonance between Egand D0, and also introduces large
conduction and valence band offsets for enhanced electrical
confinement. Researchers at Hughes have recently demon-
strated emission at 3.5
m
m from diode lasers with active
regions consisting of InAs-Ga12xInxSb superlattices.6
The structures considered in Refs. 5 and 6 are non-
optimal, however, in that the electrons in the superlattice
~SL!have strong energy dispersion along all three coordinate
axes ~their effective mass is nearly isotropic!. At non-
vanishing in-plane wavevectors, the holes also display a
smaller but still consequential dispersion along the growth
axis ~the miniband width is 20-30 meV for hole states within
25 meV of the valence band maximum!. It is well known that
quantum well ~QW!lasers with quasi-two-dimensional
~quasi-2D!electron and hole populations tend to significantly
outperform double heterostructure lasers with 3D bulk carri-
ers once a given fabrication technology has matured,8prima-
rily because the more concentrated 2D density of states
yields much higher gain per injected carrier at threshold.
In this work, we propose a four-constituent Type-II mul-
tiple quantum well ~InAs-Ga12xInxSb-InAs-Ga12xAlxSb!
which preserves the large optical matrix elements of the
InAs-Ga12xInxSb SL while yielding 2D dispersion relations
for both electrons and holes. An 8-band finite-element
formalism7has been used to fully incorporate the band struc-
ture, wavefunction overlap, and dispersion of the optical ma-
trix elements into calculations of the gain, threshold current,
and linewidth enhancement factor.
Figure 1 illustrates the conduction, valence, and split-off
band profiles for the proposed Type-II multiple quantum
well, along with the calculated energy levels and wavefunc-
tions. Note first that even though the electron wavefunctions
~solid curves!have their maxima in the InAs layers and the
hole wavefunctions ~dashed curves!are centered on the
Ga12xInxSb, their overlap is sufficient to yield interband op-
tical matrix elements (PCV) more than 70% as large as those
in typical Type-I heterostructures. Furthermore, the small in-
plane hole mass (mh
i
'0.072m0), which is roughly equal to
the average value in the superlattice ('0.046m0at kz50
and '0.087m0at kz5
p
/d), yields a reduced density of
states that decreases the threshold carrier density required to
achieve population inversion.5We particularly emphasize
that the electrons and holes in this structure both have 2D
dispersion due to the lack of penetration through the
Ga12xAlxSb barriers. Because of the coupled-well nature of
the conduction band profile, the electron states split into
symmetric ~E1S!and anti-symmetric ~E1A!levels. However,
only E1S will be significantly populated at T<300 K, since
the energy separation between the two is 120 meV.
We also find that the resonance between Eg~the separa-
tion of E1S and H1!and D0~the difference between H1 and
S1!is completely removed by the Type-II band alignment,
even though it is present in bulk InAs and GaSb, and is
potentially an issue in Ga12xInxSb. Furthermore, by analogy
to the Type-II SL considered by Grein et al.,5for these layer
thicknesses the energy gap does not resonate with any inter-
valence transitions involving H1 near its maximum ~it falls
approximately halfway between H1-H2 and H1-H3!. Hence
all multi-hole Auger processes are energetically unfavorable,
and CCCH events ~in which the CH recombination is accom-
panied by an electron transition to a higher-energy conduc-
tion state!will probably dominate the nonradiative lifetime.
Moreover, even the CCCH rate is suppressed by the small
in-plane mass for H1 holes near the band extremum. Young-
dale et al. have recently demonstrated experimentally that at
77 K, InAs-Ga12xInxSb SLs can display Auger lifetimes
which are two orders of magnitude longer than those in
Hg12xCdxTe alloys with the same energy gap, a finding that
is consistent with theoretical predictions.9The structure in
a!Electronic mail: meyer@sisyphus.nrl.navy.mil
757Appl. Phys. Lett. 67 (6), 7 August 1995 0003-6951/95/67(6)/757/3/$6.00 © 1995 American Institute of Physics
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Fig. 1 is cladded by AlSb layers, which have a low refractive
index for optical confinement as well as providing a nearly
exact match to the average lattice constant of the active QW
region. Note also that electrical confinement ceases to be an
issue, because the AlSb provides large offsets for both con-
duction and valence bands.
Assuming k-conservation, the dependence of the optical
gain on photon energy \
v
in a system with 3D dispersion is
given ~in cgs units!by10
g~\
v
!54
p
2ne2
\
k
c~\
v
!
2
~2
p
!3
E
0
2
p
/ad2k
i
E
2
p
/d
p
/ddkz
3~G/
p
!
u
PCV~k
i
,kz!
u
2~fe1fh21!
@Ee~k
i
,kz!2Eh~k
i
,kz!2\
v
#21G2,~1!
where n(
v
) is the refractive index,
k
(
v
) is the dielectric
constant, dis the period, fi@Ei(k
i
,kz)#is the Fermi distribu-
tion function and EFi the quasi-Fermi energy for carrier type
i. For the collision broadening energy, we estimate G'4
meV based on transport data for n-type and p-type
InAs-Ga12xInxSb superlattices.11 The gain for a multiple
QW with 2D dispersion may also be obtained from Eq. ~1!,
simply by taking all of the parameters appearing under the
integral to be independent of kz.
The quasi-Fermi energies depend on the electrically-
injected carrier concentration, N, which is related to the cur-
rent density through the expression10
j~N!5NeL
S
1
t
R~N!11
t
NR~N!
D
1jL.~2!
Here Lis the net thickness of the active region ~the number
of quantum wells times the total thickness per period!,
t
Ris
the radiative lifetime,
t
NR is the nonradiative lifetime ~gov-
erned primarily by Auger recombination, for which
1/
t
NR'
g
3N2with
g
3being the Auger coefficient!, and jLis
the leakage current resulting from inadequate electrical con-
finement. The radiative lifetime due to spontaneous emission
processes has the form10
1
t
R
54n3e2
\4
k
c3N
E
0
`
~\
v
!d~\
v
!2
~2
p
!3
E
0
2
p
/ad2k
i
3
E
2
p
/d
p
/ddkz
~G/
p
!
u
PCV~k
i
,kz!
u
2fefh
@Ee~k
i
,kz!2Eh~k
i
,kz!2\
v
#21G2.
~3!
Grein et al. have argued on the basis of detailed Auger
rate calculations that for a properly-engineered InAs-
Ga12xInxSb superlattice, jNR can be made much less than
jRfor all temperatures up to 300 K.5Since we can obtain
similar relations between the subbands in the four-
constituent structure, a comparable degree of Auger suppres-
sion should be possible in the multiple QW. We therefore
proceed by ignoring the non-radiative contribution to the cur-
rent density, although the consequences of taking a more
pessimistic view will be reexamined below.
Figure 2 illustrates calculated results for g(\
v
) at 300
K, where two different current densities are shown for both
the SL and QW structures. As expected, the 2D density of
states in the QW leads to a much narrower spectrum, which
has its maximum at a photon energy within Gof the energy
gap. On the other hand, the spectrum for the SL is much
broader and has its maximum approximately kBTabove
Eg. Although the radiative lifetime at fixed Nis slightly
longer in the SL ('24 ns vs '19 ns in the QW at
N51018 cm23), for a given jRthe QW nonetheless yields a
significantly larger maximum gain gmax.
Figure 3 plots the increase of the maximum gain with
current density at 77 K and 300 K. Although the carrier
concentrations required to achieve transparency in the active
region are smaller in the QW at both temperatures
(1.331017 cm23vs 1.531017 cm23at 77 K and 5.231017
cm23vs 6.731017 cm23at 300 K!, the longer
t
Rin the SL
leads to a slightly smaller jRfor transparency at low tem-
peratures ~the broadening also plays a larger role at low T!.
However, at the thin Lrequired for minimization of the
threshold current density (L51400 Å has been assumed in
these calculations, which corresponds to 12 periods of the
QW or 27 periods of the SL!, the optical confinement factor
is small and a relatively large gain is required to overcome
parasitic losses due to free carrier absorption in the cladding
layers, reflection, etc. We estimate that gmax on the order of
500 cm21will be required to achieve optimized laser opera-
tion, for which the QW with its much steeper slope has a
clear advantage at all temperatures. The larger
]
g/
]
Nin the
QW also leads to a significantly smaller linewidth enhance-
ment factor ('1.7, vs '4.2 in the SL for gmax5500 cm21at
300 K!and hence reduced filamentation.
Even using a conservative value for the required gain
(gmax5500 cm21), we obtain extremely attractive threshold
FIG. 1. Conduction, valence ~heavy-hole!, and split-off band profiles for the
four-constituent, Type-II multiple quantum wells. Also shown are electron
~solid!and hole ~dashed!wavefunctions, along with subband energy ex-
trema.
758 Appl. Phys. Lett., Vol. 67, No. 6, 7 August 1995 Meyer
et al.
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currents at 300 K ~71 A/cm2for the QW and 162 A/cm2for
the SL!and characteristic temperatures T0~350 K for the
QW and 250 K for the SL!. The analysis thus predicts per-
formance comparable to GaAs- AlxGa12xAs QW lasers. By
comparison, there have thus far been no reports of stimulated
emission at 300 K for other III-V diode lasers emitting at
wavelengths beyond 3
m
m, and to our knowledge the highest
T0for T.150 K has been 28 K.3
However, it must be remembered that up to this point we
have employed the theoretical prediction by Grein et al.5that
optimized InAs-Ga12xInxSb structures are radiative-
recombination-limited up to 300 K. While it has been con-
firmed experimentally that the Auger rate at 77 K can be
suppressed by orders-of-magnitude,9there has thus far been
no definitive testing of the predictions for higher T.Itis
therefore useful to examine the opposite ‘‘worst-case’’ limit,
in which we take the Auger coefficient to be no better than
what has already been observed at 300 K:
g
355310227
cm6/s, as recently measured12 for a non-optimized three-
constituent InAs-Ga12xInxSb-Ga12xAlxSb multiple quantum
well with photoluminescence emission at 4.8
m
m. This upper
bound for
g
3leads to jNR'4000 A/cm2for g5500 cm21at
300 K, which is much less attractive than the jRfrom Fig. 3
but is nonetheless more than an order of magnitude lower
than values extrapolated from the best current MWIR
(l>3
m
m!thresholds.3Combination of this result with that
calculated at 77 K using the observed
g
3at that temperature,
we obtain T0559 K, which is a factor of two higher than any
observed to date for diode pumping at l>3
m
m.
While the ultimate prospects for high-efficiency am-
bient-temperature operation remain unproven, we expect the
proposed Type-II multiple quantum wells to perform at least
as well and potentially far better than any of the other
narrow-gap III-V systems now under consideration. Even if
the Auger mechanism never becomes altogether negligible at
300 K, InAs-Ga12xInxSb heterostructures have the most fa-
vorable prospects for its significant suppression. Further-
more, the large offsets effectively eliminate the electrical
confinement difficulties that currently limit many of the other
systems now being studied. These advantages naturally apply
to both the QW and the SL configurations. We finally note
that as in the case of the intersubband quantum cascade
laser,13 the emission photon energy is controlled almost en-
tirely by quantum confinement rather than the energy gaps of
the constituents, and can in principle be tuned from zero to
more than 1 eV.
This research was supported by Air Force/Phillips Labo-
ratory. We thank Greg Dente, Mike Prairie, Mike Tilton, and
Richard Miles for valuable discussions, and Quantum Semi-
conductor Algorithms for use of the finite-element band
structure software.
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FIG. 2. Gain vs photon energy ~relative to the energy gap!for the superlat-
tice ~dashed curves!and multiple quantum well ~solid curves!at 300 K.
FIG. 3. Maximum gain vs current density at 77 K and 300 K for the super-
lattice ~dashed curves!and multiple quantum well ~solid curves!, assuming
L51400 Å and j5jR.
759Appl. Phys. Lett., Vol. 67, No. 6, 7 August 1995 Meyer
et al.
Downloaded¬23¬Apr¬2001¬to¬132.250.152.193.¬Redistribution¬subject¬to¬AIP¬copyright,¬see¬http://ojps.aip.org/aplo/aplcr.jsp
