Interband Cascade Lasers
I. Vurgaftman, W. W. Bewley, C. L. Canedy, C. S. Kim, M. Kim, J. R. Lindle, J. Abell,
and J. R. Meyer
Code 5613, Naval Research Laboratory, Washington DC 20375
Abstract
The physical principles involved in the operation and design of mid-infrared interband
cascade lasers (ICLs) are described. While the cascaded geometry is analogous to those used in
quantum cascade lasers and bipolar cascade quantum-well lasers, the implementation is unique
to the antimonide material system. Quantum confinement is used to tune the overlapping and
gapped conduction and valence-band states in neighboring electron and hole quantum wells. We
discuss the main ingredients necessary to design a high-performance room-temperature ICL, and
present some highlights from recent characterization results for narrow-ridge ICLs operating in
continuous-wave mode.
Keywords: mid-infrared semiconductor lasers, interband cascade laser, cascade geometry, typeII band alignment, ridge waveguide.
1
INTRODUCTION
Due in part to greater scientific challenges, the development of semiconductor lasers
emitting in the mid-infrared (mid-IR,  = 3-5 m) portion of the optical spectrum has lagged far
behind that in the near-infrared. The best-known and most convenient materials from a
technological standpoint, i.e., those lattice-matched to GaAs or InP substrates, have energy gaps
much wider than the mid-IR photon energies. Attaining a gap corresponding to  3 m, requires
an expensive investment in the more exotic antimonide materials (including AlSb, InAs, and a
variety of ternary and quaternary alloys) with lattice constants near the GaSb value of 6.096 Å.
Moreover, it was long suspected that the exponential wavelength dependence of the coefficient
for Auger non-radiative decay would prevent mid-IR lasers from ever operating in continuous
wave (cw) at ambient temperatures. As the mid-IR applications in chemical sensing and IR
countermeasures grew in importance since the 1990s, three parallel tracks for realizing mid-IR
lasers have been pursued: (1) conventional type-I quantum-well lasers on GaSb substrates [1-5];
(2) interband antimonide lasers with a type-II alignment of the conduction and valence bands [610]; and (3) intersubband quantum cascade lasers (QCLs), primarily using the well-studied InPbased materials [11-15]. A decade ago, few would have guessed that all three approaches would
now be producing mid-IR lasers operating in cw mode at room temperature (RT), albeit each
subject to its own limitations. Conventional quantum-well lasers have become firmly established
in the 2-3 m range, and are making inroads to mid-IR wavelengths as long as 3.4 m without
suffering significant adverse effects from the once-worrisome Auger recombination [4,5].
Single-ridge QCLs with emission wavelengths slightly shorter than 5 m [11,12] have displayed
multi-Watt output powers, and cw RT operation has been attained in a few cases for wavelengths
down to 3.8 m [13]. This article will focus on type-II antimonide materials, which have the
2
most natural match to the mid-IR region, and in particular on interband cascade lasers (ICLs)
based on these materials.
As the ICLs have advanced in recent years, numerous expositions of improving
experimental results have been published in the archival literature [9, 10, 16]. Our main purpose
in this article is to consider some of the less-frequently-discussed physical principles behind the
operation and design of ICLs. We will begin with the broad-brush device concept, and then
proceed to fill in details that are critical for any successful design. This will include a discussion
of our current understanding of the mechanisms limiting the ICL output powers for hightemperature operation, and an analysis of what can ultimately be expected from these devices.
The discussion will be aided by a brief review of experimental results from recently fabricated
devices. We emphasize that rather than being designed from scratch to have high-performance,
ICLs have developed over a number of years via numerous incremental improvements and
refinements that were introduced as the physical understanding grew. Each design modification
has then required painstaking demonstration in the laboratory, to determine whether it improves
or degrades the device characteristics. We conclude the article with some further thoughts on the
competitiveness of ICLs with other mid-IR sources.
INTERBAND CASCADE LASER CONCEPT
The basic ICL concept was introduced in 1995 by Rui Yang [17], then at the University
of Toronto. Critical improvements to the structure were shortly suggested by two co-authors of
this article in collaboration with Dr. Yang. The ICL in its present form is the product of
development efforts by several groups [18-20], with recent Naval Research Laboratory designs
achieving the highest performance to date [8, 10]. Rather than reviewing the historical
3
development of ICLs any further, the remainder of this article will follow a pedagogical
approach to the subject matter.
The total (unsaturated) gain provided by the active region of any semiconductor laser
needs to exceed the total loss, including contributions from both the laser waveguide itself and
the mirrors formed by the crystal facets. Quantum wells (QWs) have become the gain medium of
choice, since both electrons and holes are confined to the light-emitting region, and the
differential gain is enhanced by the quasi-2D densities of states near the conduction and valence
band edges [21]. At the longer emission wavelengths in the mid-IR, scaling considerations cause
the overlap of the waveguide mode with a single QW with fixed width to decrease. Furthermore,
the smaller electron and hole effective masses imply reduced densities of states and hence
smaller material gain. Broadly speaking, multiple QWs must usually be employed at longer
wavelengths to provide sufficient gain at reasonable injection currents.
We now consider the options available for connecting multiple QWs in a single lightemitting device. Since the QWs must share the same optical mode, they need to be placed within
a small fraction of a wavelength of each other. Thus it seems that the most convenient
arrangement would be to place the QWs side by side, with barriers sufficiently thick to preserve
their quasi-2D nature (typically of order 10 nm). Insofar as we expect the carrier capture into and
escape from the QWs to be much faster than electron-hole recombination, the carriers in each
QW will share common quasi-Fermi levels for electrons and holes. It is well known that the
separation of those quasi-Fermi levels must exceed the QW energy gap to produce optical gain.
As a consequence of the common Fermi levels, the voltage drop at the lasing threshold,
Vth, exceeds the energy gap Eg/q by a small margin E/q that is ideally determined by the
differential gain and internal loss (and the photon energy by an even smaller margin). In the ideal
4
device, the electron current from the n contact divides into equal parts to feed each QW. Each
branch makes a separate radiative transition to the valence band, followed by a rejoining of the
electrons as they escape from each QW and then finally flow into the p contact. This scheme,
shown in Fig. 1(a), is equivalent to a parallel connection of the light-emitting QW regions. The
current density feeding each QW must be high enough to produce the optical gain needed to
overcome the losses. Denoting this value by Jm, the threshold current density is MJm, where M is
the number of QWs.
Any real device will display a nonzero resistance s in series with the QWs. For example,
the optical cladding layers contribute sc = dc/c, where dc is the total cladding thickness and c
is the cladding material’s bulk conductivity. There can also be a current-independent parasitic
voltage drop, though it appears small in state-of-the-art devices and is ignored here for
simplicity. Therefore, the total power density dissipated at threshold for the scheme of Fig. 1(a)
can be written:


Pth ( parallel )  ( E g  E ) / q  MJ m  s MJ m  ( E g  E )MJ m / q  M 2 J m  s
2
(1)
While this scheme is used in most conventional multiple QW diode lasers, as Eg decreases and M
and Jm increase with increasing wavelength (the reasons for increasing Jm are discussed in detail
below), the useful part of Pth (given by MEgJm/q) drops while the parasitic second term grows.
This suggests that the threshold power density can be reduced if the QWs are connected
in series so that the same current Jm feeds all of them. Since the useful voltage drop then scales
with QW number, Pth is given by:


Pth (series )  M ( E g  E ) / q  J m  s J m  ( E g  E )MJ m / q  J m  s
2
(2)
5
Equations (1) and (2) are equivalent only if M = 1 or s = 0, neither of which is realized in actual
mid-IR lasers to date. Otherwise Pth (parallel) > Pth (series), i.e., the series connection requires
less power to operate and devotes a larger fraction of that power to produce lasing.
The preferred series connection, illustrated schematically in Fig. 1(b), is now generally
called “cascading”, with the implication that each injected electron traverses the entire circuit
instead of only one of its branches. While a voltage of at least Eg+E must now be dropped at
each “stage” of the device, the current density can be the same as for a single QW since each
stage feeds the next. Similar considerations have driven the development of QCLs [22] and
bipolar cascade lasers [23-25]. Analogous reasoning is also used to optimize the power density in
multi-junction solar cells that stack multiple diodes in series. The total voltage is the sum of the
individual cell contributions, while the same current flows through the entire stack [26]. Multijunction devices can exhibit substantially higher conversion efficiencies (up to the current record
of 35.8% without concentrating optics [27]) than single-junction devices (typically 25% for
GaAs and Si cells), even if the latter absorb as much sunlight.
In a cascaded geometry with the band diagram shown schematically in Fig. 2, the
electron quasi-Fermi level of one stage ideally coincides with the hole quasi-Fermi level of the
preceding stage. This implies that an average electric field of F = (Eg + E)/(qd), where d is the
thickness of one stage, must develop in the intervening region, and that any electrons
transitioning optically to the valence band need to transfer back to the conduction band on a time
scale much shorter than that for recombination. Bipolar cascade lasers and multi-junction solar
cells accomplish the latter requirement by inserting tunnel junctions between individual stages.
However, deleterious side effects include the introduction of highly-doped absorbing regions in
the laser waveguide, as well as additional series resistance.
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The antimonide system comprising materials with lattice constants near the GaSb value
of 6.096 Å provides an alternative route to electron removal from the valence band. The band
offsets in an antimonide heterostructure align such that the conduction band minimum of InAs is
lower in energy than the valence band maximum in GaSb (by 0.21 eV at room temperature) and
the related ternary alloy Ga1-xInxSb [28]. Figure 3(a) illustrates a simple type-II structure
consisting of an InAs electron QW adjacent to a GaSb hole QW. In this example, quantum
confinement induces a spatially indirect bandgap of Ei. However, an applied electric field F can
re-impose a semimetallic band alignment with overlap B(V) = F(de + dh) - Ei, where de and dh are
center-of-mass distances of the electron and hole wavefunction distributions from the interface.
Assuming B >> kBT and 2D densities of states, the common Fermi level across the interface is
given by EF = mh*B/(mh* + me*) + Ec, where me* and mh* are the electron and hole effective
masses and Ec is the conduction-band minimum. In the absence of background doping and
injected carriers, the overlap-induced electron and hole densities in the two QWs are p = n =
mr*B/ħ2, where mr* = me*mh*/(mh* + me*) is the reduced effective mass, in the zerotemperature limit. Thus once the quantum-confinement gap of Ei has been overcome, the
generated carrier densities scale with electric field F and total applied bias V. Since the typical
values of the effective masses are: me* = 0.04m0 and mh* = 0.09m0, we find that at T = 300 K an
overlap of B ~ 100 meV is sufficient to produce the typical lasing threshold carrier concentration
of nth = 1.5 x 1012 cm-2.
The band overlap may be viewed as a means for “doping” each stage of the cascade with
equal electron and hole densities. Electrical injection is then required only to replenish the
carriers already available automatically, with electrons moving rapidly to the right and holes to
the left, according to our convention in Fig. 2, under bias. While in principle the ICL can operate
7
without any additional doping of the active stages, in practice the electron injector QWs (see
below) tend to be doped somewhat to provide a better balance between electrons and holes in the
active QWs.
Since any excess electrons generated near the Fermi level in the GaSb hole QW are
transferred by interband tunneling or scattering to the adjacent InAs QW on a sub-picosecond
time scale [29], the semimetallic interface also serves as a means for efficiently emptying the top
of the valence band to maintain population inversion. The electrons are then quickly removed
from the semimetallic interface via miniband transport to the right through the electron injector,
which typically consists of a sequence of InAs QWs separated by Al(In)Sb barriers. The
structure may also contain a hole injector, comprising a sequence of GaSb QWs separated by
AlSb barriers, which separates the active QWs from the electron injector. The next section
reviews design rules for the electron and hole injectors.
The other crucial part of the laser core is the active region where photon emission takes
place. While the cascading scheme described above is compatible with other configurations, here
we focus exclusively on the type-II active region [30, 31], which most commonly combines an
InAs electron QW with a GaInSb hole QW. To maximize the optical matrix element, both QWs
must be thin enough to assure a substantial overlap of the electron and hole wavefunctions
peaking in neighboring layers. However, even in optimized structures the resulting gain is nearly
a factor of 2 smaller than for type-I QWs with electron and hole wavefunctions concentrated in
the same layer. This in turn reinforces the need for the multiple active QWs discussed above.
Because the spatially-indirect bandgap is governed by quantum confinement, varying the
electron and hole QW thicknesses can tune the emission wavelength over a vast spectral range,
from 2 m when the InAs layer is only a few monolayers wide to arbitrarily long as the
8
bandgap approaches the semimetallic regime. It is important to remember, however, that thicker
QWs are required at longer wavelengths, causing reduced electron-hole wavefunction overlap to
decrease the gain while free carrier absorption losses increase. Nonetheless, wavelengths in the
3-5 m mid-IR spectral region are ideally suited to the type-II active region, since the QWs are
then thin enough to maintain substantial wavefunction overlap yet thick enough for reproducible
epitaxial growth.
Putting these pieces together, we may now describe operation of the full ICL core
illustrated in Fig. 4. Electrons are injected into each stage from the preceding one or from the
contact. On a sub-ps time scale they reach quasi-thermal equilibrium in the active electron
QW(s) followed either by the emission of a photon or non-radiative recombination on a ns or
sub-ns time scale. Having reached the valence band, the electron then travels on a ps time scale
through the GaSb hole injector QW, across the semi-metallic interface, and into the electron
injector. The applied field F then propels the electron into either the next stage or the contact.
The next section discusses the implementation of this basic concept in greater detail.
DETAILED DESIGN OF INTERBAND CASCADE LASER CORE
As discussed in the previous section, the ICL active region employs a compressively
strained Ga1-xInxSb hole QW with In fraction x approaching the limit dictated by the critical
thickness, typically 30-35%. Since the large compressive strain (>2%) pushes the top heavy-hole
subband higher in energy, a given mid-IR emission wavelength can be reached using a thinner
InAs QW than would be possible, say, with a GaSb active QW. This results in a larger electronhole wavefunction overlap. A second effect of the large compressive strain is to reduce the hole
effective mass near the top of the valence band. Theory suggests that this reduces the multielectron (CCCH) Auger recombination rate [32, 33], although the magnitude of the effect has not
9
been quantified rigorously. The active hole QW thickness and composition also determines the
positions of the lower-lying heavy- and light-hole subbands, which are thought to affect the
multi-hole Auger rate and free-hole internal loss [33-36]. However, such resonant Auger and
absorption behavior should induce a non-monotonic dependence of the threshold current density
on hole QW design, whereas the characterization data for numerous ICLs with different active
regions and hole QW parameters thus far have not shown evidence for this effect. The threshold
current densities tend to remain relatively flat over the mid-IR spectral range [10, 37]. Thus the
precise choice of GaInSb QW thickness does not appear to strongly affect Auger recombination,
although thinner hole wells do result in larger optical matrix elements as will also be discussed
below.
State-of-the-art ICLs use the so-called “W” arrangement, whereby two active InAs QWs
sandwich a single GaInSb hole QW [38] (as in Fig. 4) to enhance the optical matrix element.
Owing to the applied electric field, the gain is maximized when the two InAs wells have slightly
different widths, with typical values of 15-20 Å for the 3-4 m spectral region. However,
because the Auger coefficient presumably scales with the electron-hole overlap as well, it is not
obvious that the “W” structure should perform better than a type-II structure with a single InAs
QW. We discuss this issue further in the section on mechanisms limiting the ICL performance.
We now consider the electron and hole injector properties in greater detail, beginning
with the hole injector. Figure 5 shows band profiles and selected wavefunctions for one stage of
an ICL core plus the subsequent active region. Note that the intervening hole injector
substantially augments the potential barrier separating the active InAs electron QWs from the
electron injector [18]. In the absence of such a barrier, electrons would have a far greater
tendency to tunnel directly to the injector, possibly via mid-gap defects. Substantial leakage
10
currents may then increase the lasing threshold. While it is apparent from Fig. 5 that the
tunneling barrier becomes quite thick for a hole injector consisting of two GaSb QWs, it is
unclear at present whether a single GaSb well would suffice. Empirical studies comparing NRL
characterization data for various ICL designs appear to show some improvement when the
second GaSb QW is included, although the available data are limited.
The GaSb QWs in the hole injector should be narrow enough to ensure that relatively few
holes reside in those wells at the field corresponding to the threshold voltage [39]. However, hole
transport from the semimetallic interface with the electron injector to the GaInSb active hole QW
may be inhibited if these wells are too thin. The optimal energy separation between the
corresponding states of the active and injector hole QWs under bias should therefore be on the
order of a few kT. Recent empirical studies have found that the threshold power density for hightemperature operation is minimized when the subband splitting is near 100 meV [39]. Note also
that if two QWs are used in the hole injector, the one next to the electron injector should be
wider so as to compensate for the field-induced slope in the valence-band profile. Wavefunctions
for the highest valence subbands in the coupled hole injector QWs peak in both wells. Note that
the active-hole injector subband splitting of 100 meV does not imply an extra voltage drop of
that magnitude, since efficient hole transport appears to be maintained as long as there is semimetallic overlap between the active hole subband and the injector electron subband.
An additional concern is parasitic interband absorption that can occur at the semimetallic
interface between the electron and hole injectors. That process can be mitigated by placing a thin
AlSb barrier between the last GaSb QW of the hole injector and the first InAs QW of the
electron injector. The barrier thickness is adjusted so as to suppress the interband absorption
11
while still maintaining adequate carrier transport across the interface. Characterization data for
structures with empirically-adjusted barriers suggest an optimal thickness of 20-25 Å [40].
We next turn attention to the electron injector. A first consideration is the advisability of
avoiding extremely high electric fields in the laser core. For mid-IR emission, an arbitrary limit
of 100 kV/cm corresponds to a minimum stage thickness of d = 300-400 Å. Since electron
transport is far less impeded by barriers, most of this thickness should occur in the electron
injector consisting of a InAs/Al(In)Sb SL with graded QW thickness.
The transparency condition dictates that the lowest possible voltage drop per stage, i.e.
the separation of the electron quasi-Fermi levels (QFLs) in two consecutive sections, must
exceed the photon energy: EFi – EFi+1 > ħ. That this requirement is analogous to the BernardDuraffourg condition in conventional lasers [41] follows from the consideration that the electron
QFL in stage (i+1) is equivalent to the hole QFL in stage i since carriers easily equilibrate across
the semi-metallic interface. The difference between the QFL differential per stage and the photon
energy depends on the total loss, but is commonly on the order of the thermal energy kT [21]. In
what follows we assume that EFi – EFi+1 = ħ + kT for an ideal design.
The band overlap at the semimetallic interface: B  (mh* + me*)ħ2nth/me*mh*, where nth
is the threshold carrier density, is ideally attained when the applied field corresponding to the
voltage drop per stage divided by the total stage thickness (ħ + kT)/ed is equal to: Fth = (B +
Ei)/(de + dh). This implies that if the first InAs QW of the electron injector (de) is too narrow, the
band overlap at the ideal threshold field is insufficient to generate enough optical gain to
overcome the losses. Additional voltage must then be applied to boost the band overlap for
higher electron and hole densities. On the other hand, too wide a first electron injector QW
would cause unnecessarily large electron and hole densities to accumulate in the injectors below
12
threshold, inducing excessive free-carrier absorption and Auger recombination. The electron
injector QWs in most early ICLs were far too thick, which resulted in high threshold current
densities [19, 42, 43]. More precise modeling of the carrier statistics at the semimetallic interface
reveals that the first electron injector QW should be 40-50 Å for total stage thicknesses near 400
Å [40]. While this QW width may be increased when the stages are much thicker, the optical
waveguide considerations discussed in the next stage favor thinner stages.
Since most of the electric field drops over the electron injector, all subsequent InAs QWs
should be successively thinner such that their lowest-subband energies line up to form a
miniband. This miniband must align properly with the active subband of the next stage, since all
of these states share a common electron QFL. If the miniband ground state is much higher than
the active subband, most of the electrons will reside in the active QWs of the next stage as
desired. However, electron transport from the semimetallic interface to those active QWs may be
obstructed by the absence of any injector states in the required energy range, possibly causing the
assumption of a common QFL to break down.
Alternatively, if the bottom state of the miniband aligns at or below the active subband
minimum, most of the electrons will reside in the injector where the density of states is higher.
This is in fact the case in a QCL, where electron densities are much lower. In the ICL we employ
a modified version of this approach, in which the miniband wavefunctions are delocalized over
several wells rather than the entire injector, with their center of mass shifting toward the active
region of the next stage with increasing energy. As illustrated in Fig. 5, this allows us to align the
injector ground state (at left) with the active subband, while the injector states closer to the active
region are higher in energy by >5 kT. Even though the latter states are unoccupied under quasiequilibrium conditions, the experimental data presented in later sections confirm that they
13
nonetheless allow effective transport between stages. The threshold current densities for this
modified miniband scheme are somewhat lower than for designs with fully delocalized miniband
states having thicker QWs adjacent to the active region [39], although the reasons are currently
unclear.
Since the electron injector’s ground state energy does not significantly exceed that of the
active subband, under quasi-equilibrium conditions the two regions will have comparable
populations. On the other hand, it seems possible to ensure that the population of the much
thinner hole injector remains much smaller than that in the active region. Given that the type-II
interface generates an equal number of electrons and holes, it follows that an undoped ICL
structure with the design outlined above will have a much higher density for holes than for
electrons. This may be a disadvantage if multielectron Auger processes do not dominate the
threshold current density. Furthermore, the hole absorption cross-sections associated with
transitions between valence subbands [44] tend to be much higher than typical electron cross
sections, since the latter are second-order processes requiring momentum transfer to phonons,
interface roughness, or defects [45]. It may be necessary to equalize the electron and hole
densities without needing to generate more carriers at the semi-metallic interface by dropping
more voltage. This can be accomplished by n-doping the electron injector region, most
conveniently with Si. It is advisable to leave the last few injector wells undoped, in order to
minimize dopant diffusion into the active QWs that could broaden the linewidth. To assure
comparable active electron and hole densities, the total doping sheet density should be
comparable to the threshold carrier density, i.e., on the order of 1012 cm-2 for operation at 25 ºC
[46]. The additional electrons will divide between the injector and active regions in a fashion
similar to those generated by the voltage across the type-II interface.
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Figure 6 illustrates the band profiles for an ICL design [39, 40] that was iteratively
improved via a combination of theoretical simulations and empirical testing. Although we make
no claim that this design is fully optimized, when grown and processed it performs better than
other ICL structures presented in the literature. The figure also shows the computed profile of the
difference between electron and hole densities at threshold for a net electron-injector sheet
doping level of 41011 cm-2.
DESIGN OF INTERBAND CASCADE LASER WAVEGUIDE
While the active core design has the most critical effect on the ICL operation, the
waveguide configuration also strongly influences the laser performance. In designing the
waveguide, one would like to simultaneously minimize both the material gain in the active
region required to reach transparency, gtr, and the internal loss of the waveguide. The core design
outlined above reduces the electron injector thickness, partly by increasing the thickness of the
hole injector [40]. This beneficially impacts the core’s average refractive index, since the
InAs/AlSb SL of the electron injector has a much lower index (in fact, it is used as the optical
cladding region) than the GaSb/AlSb QWs of the hole injector [40, 47]. Nevertheless, a
relatively large number of stages (10-15) would be needed to confine a guided optical mode if no
high-index separate confinement region is incorporated. Since a much smaller number of stages
(about 5) is strongly preferred from the thermal standpoint [40], we consider structures in which
two symmetric bulk-like GaSb separate-confinement layers (SCLs) surround the laser core.
Figure 7 shows the calculated optical mode profile for the waveguide of a typical 5-stage
ICL emitting at = 3.6 m. The top and bottom claddings are provided by 24.3 Å InAs/23 Å
AlSb SLs, with average lattice constant matched to the GaSb substrate. The simulation finds that
both claddings are thick enough to prevent mode interactions with the top metallization and the
15
GaSb substrate, a potential issue that will be discussed further below. Also shown in Fig. 7 are
refractive indices for the various regions, which have the values: na = 3.58 in the active region, ns
= 3.75 in the SCLs, and nc = 3.25 in the cladding layers. The thickness of the two SCLs governs
the optical confinement factors in the active region (a), both SCLs (s), and the claddings
(including various transition regions, 1 – a – s). Figure 8 plots these relationships for the same
structure as in Fig. 7, but with variable SCL thickness. One should especially avoid thicknesses
beyond  800 nm, since the third waveguide mode then dominates a, resulting in an undesired
broadening of the fast-axis far-field profile.
Taking the internal losses in the active region, GaSb, and InAs/AlSb SL to be a, s, and
c, respectively, the transparency condition can be written:
g tr   a 
s
1  s  a
s 
c
a
a
(3)
The total internal loss that determines the slope efficiency above threshold is then given by:
i  a  a  s s  (1  s  a ) c
(4)
We emphasize, however, that the quantities given by Eqs. (3) and (4) are not necessarily
minimized for the same parameters. Although the values of a, s, and c are not well known at
present, we can surmise some basic relationships among them. While the InAs/AlSb SL and
GaSb have similar energy gaps, the SL is typically doped more than an order of magnitude more
heavily and may also be affected by interface roughness. It is therefore almost certain that c >>
s. With a large hole density and narrow energy gap in the active region, we may also assume a
>> s. Thus the internal loss can be minimized by allowing s to approach unity at the expense of
a and 1 – a – s. However, from Eq. (3) the transparency gain becomes very large as a  0.
16
The value of a is determined by the thickness of the SCLs and the number of stages, M.
While a scales with M (linearly in the limit of small values), it is important to remember that the
threshold power density also scales with M. From the optical point of view only a is important,
and a given value can be achieved for various M. However, the caveat is that adequate
confinement can be obtained with low M only by reducing the SCL thickness and hence s.
Furthermore, the wall-plug efficiency above threshold decreases if Mħ becomes comparable to
sJ. Using typical values of s  1 m cm2, J ~ 1 kA/cm2, ħ~ 0.3-0.4 eV, we see that more
than 3 stages are likely to be needed in practical devices. The following analysis is based on M =
5, which is empirically known to provide a favorable balance between internal loss, threshold
current density, and threshold voltage.
Empirical optimization shows that the threshold power density for 5-stage ICLs emitting
at  = 3.7 m and operating at T > 300 K is minimized at SCL thicknesses near 500 nm [40]. For
this waveguide design, it is likely that the losses from the active region, SCLs, and claddings,
when scaled by their confinement factors, are comparable, although further work is needed to
determine the exact values. As the emission wavelength moves beyond 4 m, the SCL thickness
must increase appropriately to remain optimized.
For mid-IR emission wavelengths, the conduction-band edges of the SL cladding and the
active region differ only by tens of meV. On the other hand, the GaSb conduction band is 500600 meV higher. Abrupt connection of the various waveguide regions would therefore introduce
substantial discontinuities that would obstruct electron transport. We alleviate this problem by
introducing thin transition regions between the claddings and GaSb SCLs, as well as between the
SCLs and the active region [40]. These transition regions consist primarily of InAs/AlSb SLs
with thicknesses decreasing gradually in the direction of the bulk-like GaSb layers, which has the
17
effect of grading the conduction-band minimum. Experimental evidence confirms the
effectiveness of these transition regions in reducing the threshold voltage without significantly
contributing to the threshold current density.
We finally estimate the top and bottom cladding thicknesses that are required to keep the
increase in the internal loss, say to <<1 cm-1 in comparison to its value for infinitely-thick
cladding layers. Simulations show that for = 3.7 m, a top cladding thickness of tc 1.5 m
sufficiently reduces the overlap with the top contact metallization to accomplish this goal. An
inadequate bottom cladding thickness leads to extra wavelength-dependent losses arising from
leakage of the lasing mode into the high-index GaSb substrate [48]. The maximum value of this
loss is approximately given by exp(-2kmtc)/dm, where km = 2(nm2-nc2)/2[2nm-nc)nm]/,
nm =3.58 is the modal index, and dm  1 m is the modal diameter [49, 50]. The implication is
that the bottom cladding thickness should be at least  2.5 m. Both thicknesses scale almost
linearly with wavelength.
INTERBAND CASCADE LASER PERFORMANCE CHARACTERISTICS
The major performance characteristics of the ICLs are best judged by operating broadarea devices in pulsed mode, since then the limiting factors are not obscured by device
processing and heat management issues. We will examine the threshold current density and
threshold voltage, which can be multiplied to produce the threshold power density, the slope
efficiency, and their temperature variations. In order to extract the more physically relevant
internal efficiency i and internal loss i, the slope efficiency can be measured as a function of
cavity length or, alternatively, with and without facet coatings. With the caveat that cavity-length
studies can have a built-in bias if the internal loss depends on cavity length (shorter cavities
require more carriers at threshold, which can give more loss via free-carrier absorption), we use
18
the results of a previously published investigation that obtained i = 64% at T = 300 K [37].
Other studies reported somewhat lower values for the internal efficiency, so this issue may need
to be revisited in future investigations. Using calculated gain properties, we can also extract the
carrier lifetime at threshold c = qnth/(iJth). If all of the recombination at threshold at room
temperature is due to Auger processes, the Auger coefficient is 3 = 10-12/(cnth2) cm6/s. Because
electron degeneracy effects are ignored, the Auger coefficients at threshold obtained by this
procedure may disagree by roughly a factor of 2 with low-density values [33].
The peak emission wavelength of the representative ICL under consideration varied from
3.05 m at T = 78 K to 3.45 m at 300 K. For a 2 mm cavity with uncoated facets, the pulsed
threshold current density at room temperature was 482 A/cm2, which combined with the
threshold voltage of 2.46 V yielded a threshold power density of Pth = 1.19 kW/cm2. In other
ICL samples, Jth as low as 370 A/cm2 and Pth  0.9 kW/cm2 have been realized. In the
thermoelectric-cooler range 250 K < T < 340 K, the characteristic temperatures associated with
Jth and Pth were T0 = 47 K and T0P = 40 K, respectively. However, both quantities deviated from
a strictly exponential fit, with both characteristic temperatures decreasing markedly at the highest
operating temperatures. The external differential slope efficiencies were dP/dI = 601 and 188
mW/A per facet at 78 and 300 K, respectively, which correspond to external differential quantum
efficiencies (from two facets) of 59% and 21% per stage. The latter result implies an internal loss
of 9.2 cm-1 at 300 K. Other ICL samples have exhibited external quantum efficiencies as high as
27% at room temperature, which corresponds to i = 5.9 cm-1.
Combining the experimental threshold current density at room temperature with the
deduced internal loss and calculated gain properties, derived by applying an 8-band kp algorithm
to the type-II active medium, yields a carrier lifetime of c = 0.7 ns, and Auger coefficient of 3 =
19
2.8x10-27 cm6/s. Using our measurements of 60 different ICLs, the room-temperature threshold
current densities are nearly independent of the emission wavelength in the 2.9-4.5 m
wavelength range. Following the procedure described earlier, we deduce that they exhibit 300 K
Auger coefficients in the low-to-mid 10-27 cm6/s range. Furthermore, the ICL 3 values show no
obvious correlation with the thickness or composition of the hole QW, or with any other design
parameter. These Auger coefficients are smaller than those reported for bulk mid-IR materials, in
part because of the reduced electron-hole wavefunction overlap.
Narrow ridges with varying widths were also fabricated from the same wafer. Owing to
the trade-off between sidewall defects and lateral heat dissipation, the cw Jth at 300 K exhibits a
minimum at w = 11.1 m, where the threshold of 582 A/cm2 is only 21% higher than the pulsed
result for the broad stripe. However, the threshold current density for the 3.2-m-wide ridge
increased by nearly a factor of two, owing to recombination and leakage at defects in the
processed sidewalls as well as possibly to increased optical losses due to roughness scattering.
The differential resistance-area product extracted from the current-voltage characteristics of the
narrow ridges saturates ats  0.2 mcm2 at the highest measured current densities. The
corresponding value for wide ridges running in pulsed mode is higher by a factor of 3-4, possibly
because of the extra contributions from the one-dimensional current flow in the substrate (as well
as in the bottom cladding and SCL).
Because wide ridges exhibit high thermal impedance per unit power density while narrow
ridges suffer from excessive leakage currents and optical losses at the sidewalls, the output
power and wallplug efficiency tend to peak at intermediate ridge widths. Figure 9 shows
dependences of the cw L-I characteristics and wall-plug efficiencies on injection current for the
w = 11.1 and 13.0m ridges with uncoated facets at T = 20 oC. Both devices reached similar
20
maximum cw output powers of 44-45 mW per facet, and nearly the same maximum wall-plug
efficiencies of 3.5%.
Since the performance penalty due to sidewall damage remains modest for ridges with w
 5.1 m, we expect that narrow ridges with enhanced lateral heat dissipation should achieve the
highest cw operating temperatures. Confirming this expectation, a device with w = 5.1 m, Lcav =
3 mm, and uncoated facets operated up to Tmaxcw = 345 K (72 oC), which is a record value for
interband semiconductor lasers emitting in the mid-IR spectral range.
PERFORMANCE-LIMITING MECHANISMS
We now consider the mechanisms that currently limit the ICL performance, and what
future improvements can be expected. As mentioned in the previous section, Auger
recombination is believed to strongly dominate the threshold current density at higher
temperatures. While calculated radiative lifetimes are 30-40 ns, the lifetimes derived as discussed
above from combining the measured threshold current densities with calculated threshold carrier
densities approach 1 ns. Another alternative is Shockley-Read (SR) nonradiative recombination,
but its influence at thermoelectric-cooler (TEC) temperatures can be ruled out for two reasons.
While typical carrier lifetimes at T = 78 K are 10-20 ns [37], it is uncertain whether these are due
mostly to SR recombination or another mechanism such as defect-assisted Auger recombination
(the wide variation observed in similar samples probably rules out regular Auger processes). The
projected SR lifetime at T = 300 K is nearly an order of magnitude too long if the capture crosssection is constant and the carrier thermal velocity varies as T1/2. Secondly, preliminary studies
of spontaneous emission at high temperatures demonstrate a sublinear increase with current, as is
typically associated with the Auger process [51].
21
Taking it for granted that Auger recombination limits the lifetime at TEC temperatures,
we next address whether the entire temperature dependence of Jth can be explained in this
fashion. While the Auger coefficients in bulk materials tend to be exponentially activated in
temperature, we first assume 3 is constant. The optical gain can be approximated using the wellknown logarithmic form: ag = ag0ln(n/nt), where nt is the transparency carrier density, and g0 ≡
ntdg/dn|n=nt can also be taken as independent of T. For a total loss (T) = i(T) + M, where M is
the mirror loss at the facets, and using the Auger model without any degeneracy effects, we
obtain:
 3 (T ) 
q 3 nt3 (T )

J th (T ) 
exp 
 i (T )

g
 a 0 
(5)
With symmetric 2D densities of states for electrons and holes, the transparency carrier density is
approximately proportional to T. We consider the temperature range 250-340 K and take into
account the fact that possible lattice and carrier heating effects can raise the actual carrier
temperature to T  365 K for pulsed measurements performed at a heat-sink temperature of 340
K. A full calculation using the realistic electron and hole dispersions yields an increase by a
somewhat larger factor of 1.76 ( T3/2, usually associated with 3D densities of states), which
translates into approximately a factor of 5.5 increase in Jth. The temperature dependences of 
and i are determined by the measured external efficiency, which decreases by a factor of 3.8
over this temperature range. A reduction in the internal efficiency with constant loss would yield
nearly an extra factor of 4 in Jth, whereas a constant i and increasing loss gives a corresponding
factor of 5. Multiplying the nt3 and efficiency-related factors leads to a total projected Jth increase
by a factor of 22-27, which is much higher than the observed increase of  7 over this
22
temperature range! Even if we assume that electrons are degenerate so that Jth  nt2exp(2/ag0),
the projected increase is a factor of 9-12.
The preceding calculation derives an unrealistic increase in Jth if the observed efficiency
decrease is due to an increasing internal loss. However, if the efficiency decreases as a
consequence of carrier heating, the agreement between the theoretical and experimental
thresholds becomes much better. The results will be reported elsewhere using refined cavitylength measurements [37, 52]. Our conclusion that Auger recombination in these type-II
structures is not strongly thermally activated holds in that study.
The Auger coefficient should depend on the overlap of the electron and hole
wavefunction in a manner similar, though not identical, to optical gain. Since the modal gain is
controlled by the active-region confinement factor as well as the electron-hole overlap, it may
appear that the latter can be reduced to obtain a lower Auger coefficient without a corresponding
gain reduction. However, so far the attempts to do so by employing an InAs/GaInSb active
region with single electron QW rather than the InAs/GaInSb/InAs “W” structure have resulted in
much poorer performance. The electron-hole overlap can also be reduced by increasing the
thickness of the hole well.
One possible source of non-ideality may be that the active hole density substantially
exceeds the electron density in nearly all ICL structures grown to date [46]. This scenario will be
explored in detail elsewhere. Alternatively, it is conceivable that the injected carriers accumulate
in regions other than the active wells, thereby contributing to loss but not gain.
Although, the internal loss in ICLs is not fully understood at present, it appears likely that
in optimized structures at room temperature the contributions from the separate-confinement
layers, claddings, and laser core are comparable (i.e. with typical total losses of 6-9 cm-1, about
23
2-3 cm-1 comes from each region). Were the contribution from one of these regions strongly
dominant, our empirical search for the optimum SCL thickness and number of stages should
have produced much more dramatic differences in performance. On the other hand, at this
juncture it is difficult to account for the relatively low internal efficiency. A naïve view would
hold that the strong electrical confinement of both electrons and holes, combined with the large
barrier to electron tunneling escape to the injector, should keep the value of i very close to
unity. Regardless of the ultimate physical explanation, the observed strong temperature
dependence of the external efficiency appears to be an important clue.
CONCLUDING THOUGHTS
We have shown that cascade lasers allow lower power dissipation at the expense of
increased structural complexity and a higher voltage drop. Above-room-temperature cw
operation of ICLs has been demonstrated, and the samples already in hand should allow it to be
extended over the 3.0-4.6 m spectral range once the appropriate narrow ridges are processed.
The external efficiency is lower at T = 300 K for devices emitting at even long wavelengths,
possibly representing a higher internal loss. In combination with the reduced electron-hole
overlap and optical gain at longer wavelengths, this makes room-temperature cw operation more
difficult to achieve. Nevertheless, it still seems likely that ICLs operating cw at TEC
temperatures will soon be available at any mid-IR wavelength. The development of single-mode
devices is ongoing and does not seem to pose any fundamental obstacles. Further performance
improvements may occur as some of the issues discussed in the previous section become better
understood. Therefore, it seems timely to consider how optimized ICLs would compare with
other lasers operating cw in the mid-IR range.
24
As mentioned in the Introduction, two other semiconductor laser types are of interest for
the mid-IR: (1) intersubband QCLs and (2) conventional antimonide type-I QW lasers. QCLs
and ICLs share the cascade geometry, which permits one to maximize the useful voltage drop.
The biggest difference is that while the room-temperature carrier lifetime in ICLs is limited by
Auger recombination and approaches 1 ns at threshold, the QCL lifetime determined by
intersubband phonon and interface roughness scattering is typically three orders of magnitude
shorter. The gain spectrum for the intersubband transition also differs from the interband case,
since it is controlled by interface roughness scattering [53, 54]. The practical implication is that
the calculated differential gain for a state-of-the-art QCL emitting at  = 4.6 m [11, 12] is a
factor of 6 larger than in an ICL (9.3  10-15 vs. 1.5  10-15 cm2). Since the optical confinement
factors per stage a/M are similar for the two laser classes, the modal gain per unit current
density per stage agJ/M is about two orders of magnitude smaller in the QCL.
Were the internal losses in QCLs and ICLs the same, one would expect the QCL to have
a two-orders-of-magnitude higher threshold power density Pth. However, the actual i tends to be
lower by a factor of 3-10 [12, 55], owing to the absence of holes, the lower electron densities
required to reach threshold, and the higher differential gain. Thus in practice the typical Pth in
QCLs are higher by 10-30. This quick analysis sidesteps the consideration that QCLs tend to use
many more stages: 30-40 rather than  5 in optimized ICLs. QCLs with fewer stages would have
such high Jth = i/agJ, and hence such a high Jth2s term in Eq. (2), that room-temperature cw
operation would be prohibitive [56].
QCLs can tolerate much higher Pth for the simple reason that while intersubband
scattering is fast, it is not strongly temperature dependent. Thus the upper state lifetime in a QCL
does not change rapidly with temperature. For example, it decreases by 10% between 250 and
25
340 K, whereas the ICL lifetime decreases by 2.5 over the same temperature range. While the
ultimate limits of the QCL’s temperature sensitivity remain under investigation, and depend on
such factors as the thermal linewidth broadening and leakage via upper subbands [57, 58],
clearly the high T0P in a QCL more than compensates for the higher Pth in determining the
maximum achievable cw operating temperature. The weak temperature sensitivity also enables
QCLs to generate much higher output powers than ICLs with the same ridge widths.
Nevertheless, the ICL’s lower Pth is of interest when low power consumption is desired for a
long battery lifetime, e.g. in field applications that do not require high output powers.
It is less clear is whether the high performance levels achieved by QCLs at  ≥ 4.6 m
can be matched throughout the mid-IR range. As the QCL wavelength decreases, more strain is
required to induce the larger conduction band offset needed to limit leakage [13, 14]. The greater
strain may lead to broader lines, less gain, and higher threshold power densities. Although
considerable advances have been made recently for wavelengths as short as 3.8 m [13], the
reproducibility and short-wavelength limit for high performance remain unresolved.
Conventional type-I QW lasers based on the antimonide material family do not currently
employ a cascade geometry. Since their InGaAsSb/AlGaInAsSb QWs localize both the electron
and hole wavefunctions in the same well, the ICL scheme that relies on the high valence band
energy of GaInSb is not directly applicable. Other cascading configurations may be possible
[18], although the device complexity would increase. The higher gains characteristic of the typeI band alignment also imply that fewer QWs may be needed, which limits any advantage
obtained from cascading.
The threshold current densities per well [Jm in Eq. (1)] for type-I QW lasers operating
near = 3.0 m are somewhat lower than those for ICLs [4, 5]. Since similar threshold carrier
26
densities are expected, this implies that the Auger suppression discussed above is not exclusive
to type-II QWs. While a theoretical understanding of this observation lags currently, it appears
that both type-I and type-II structures with large built-in strains exhibit lower Auger coefficients
than bulk materials with the same energy gap [59]. This is in spite of the fact that only type-II
active regions feature reduced electron-hole wavefunction overlap as compared to bulk materials.
The relatively low Jth, in combination with the effectively-parallel connection, leads to excellent
Pth values in these devices.
The main challenge for type-I QW devices appears to be the relatively weak hole
confinement by the shallow valence-band offset [4]. While this issue has been mostly overcome
near = 3 m, it becomes increasingly severe at longer wavelengths. Although it is unlikely that
type-I QW lasers will be able to cover the entire mid-IR spectral region without a radical revision
to the approach; the opportunities for significant inroads from the short-wavelength side are quite
good. A more comprehensive analysis of the long-term prospects relative to ICLs must await a
deeper understanding of the factors limiting the high-temperature external efficiencies in both
device classes.
27
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Figure Captions
Figure 1. Schematic illustrations of (a) parallel and (b) series connections of semiconductor
lasers with multiple QWs.
Figure 2. Schematic band diagram of the interband cascade laser geometry.
Figure 3. Simple type-II InAs/GaSb quantum well with an energy gap imposed by quantum
confinement in the absence of an applied electric field (a) and a semimetallic alignment with
overlap-induced electrons and holes in the presence of a field (b).
Figure 4. Schematic conduction and valence band profiles for one stage of an ICL under bias.
Figure 5. Band profiles for one ICL stage with the succeeding active region. Some of the more
important electron and hole wavefunctions are plotted at energies corresponding to their
respective subband extrema under bias.
35
Figure 6. Band profiles for one stage of an optimized ICL design. Also shown is the calculated
profile for the difference between the electron and hole densities at room temperature, assuming
a net sheet doping level of 41011 cm-2.
Figure 7. Optical intensity of the lasing mode along the growth direction in a typical 5-stage ICL
structure emitting at  = 3.6 m. The refractive index profile is also shown.
Figure 8. Optical confinement factors for the active region a, SCLs s, and cladding/transition
regions 1 – a – s for the same structure as in Fig. 7 but with variable SCL thickness.
Figure 9. CW output powers and wall-plug efficiencies per uncoated facet vs. current density for
the
11.1-
and
13.0-m-wide
ridges
with
2-mm-long
cavities.
36
Jth/M
Jth
Jth/M
(a)
Jth/M
Vth
Jth
Vth/M
Vth/M
Vth/M
(b)
Figure 1.
37
CB
VB
Figure 2.
38
GaSb
GaSb
Ei
B(V)
InAs
InAs
(b) F > 0
(a) F = 0
Figure 3.
39
“W” Active
CB
InAs
AlSb
InAs/Al(In)Sb SL Injector
GaSb
VB
GaInSb
Figure 4.
40
2.5
2.0
CB
Energy (eV)
1.5
1.0
EF i-1
0.5
EA
EF i EI1
EA
EF i+1
0.0
HI
HA
-0.5
HA
-1.0
0
100
200
300
400
VB
500
Distance (Å)
Figure 5.
41
-3
2.0
19
Energy (eV), n - p (10 cm )
2.5
1.5
CB
1.0
0.5
0.0
n-p
-0.5
VB
-1.0
0
100
200
300
400
500
Distance (Å)
Figure 6.
42
Mode Intensity (a.u.), Refractive Index
4
SCL SCL
Top
Clad
Bottom
Clad
GaSb
Substrate
ICL
Core
3
2
nr
|E|2
1
0
0
2
4
6
8
Distance (m)
Figure 7.
43
90
Confinement factor
80
70
s
60
50
40
s-a
30
20
a
10
0
200
400
600
800
Thickness of each SCL (nm)
Figure 8.
44
4
Power ( W / facet )
0.04
3
0.03
2
o
0.02
T = 20 C
Lcav = 2 mm
0.01
11.1 m
13.0 m
0.00
0.0
1
0
0.1
0.2
0.3
0.4
Wall-plug efficiency per facet (%)
0.05
0.5
Current ( A )
Figure 9.
45
46