Quantum Well Infrared Detectors
Wan-Ching Hung, Jie Zhang
Department of Electrical and Computer Engineering, University of Rochester, Rochester, New York, 14627-0231
zhangj@ece.rochester.edu
Abstract: Quantum well infrared photodetectors (QWIP) have been developed very
quickly over the past twenty years and large format focal plane arrays (FPA) with low
noise equivalent temperature differences (NETD), high uniformity and operability have
been achieved. In this paper, we make brief comparison of QWIPs with HgCdTe (MCT)
detectors. Basic device physics and structures, characteristics, performance and benefits of
QWIPs were demonstrated. The state-of-the-art of the QWIP FPA technology and its
application were presented.
© Department of Electrical and Computer Engineering
I. INTRODUCTION
Infrared (IR) radiation is electromagnetic radiation of a wavelength longer than that of visible light,
shorter than that of radio wave. It spans three orders of magnitude and has wavelengths between
approximately 750 nm and 1 mm. IR detector technologies are very important nowadays both in
military and civilian applications and have been widely investigated over the past century. Commercial
applications of IR FPAs could cover astronomy, art history and archaeology, biological and medical
systems, spectroscopy, fire control, surveillance and driver’s vision enhancement. The military
applications could include night vision, rifle sight, surveillance, missile guidance, tracking, and
interceptors. Fig 1 shows the atmosphere transmittance in the IR region which indicates the prospect
applications in the astronomy, communication and military. [1-5]
Fig. 1 Plot of atmospheric transmittance in the infrared region of the electromagnetic spectrum [6]
In this paper, we focus on devices which involve IR excitation of carriers in quantum wells. A
distinguishing feature of QW infrared detectors is that they can be implemented in chemically stable
wide-band-gap materials as a result of the use of intersubband (intraband) processes. Till now, different
types of quantum well infrared detectors have been achieved, among which, the technology of
GaAs/AlGaAs multiple quantum well (MQW) detectors is the most mature. Rapid progress has been
made recently in the performance of these detectors. Infrared focal plane arrays with high sensitivity,
high uniformity, large format, and flexible wavelength are fabricated. Based on the high requirement in
surveillance sensors and interceptor seekers, quantum well infrared photodetectors (QWIP) focal plane
arrays (FPA) with lattice matched GaAs/AlGaAs material system which can provide high uniform,
multicolor and long-wavelength operation is currently a hot topic in the worldwide. Here, the
characteristics, performance and benefits of QWIP are demonstrated and discussed. The basic device
physics and detector design of QWIP structures are given. The stability, reproducibility, yield, cost,
maintenance, and manufacturability are also very important issues.
II. HISTORY: Overview of current IR detectors
The first IR photoconductor was developed by Case in 1917. Since then, many materials have been
investigated in the IR field. Observing the IR detector technology development history, a simple
theorem can be stated: All physics phenomena in the range of about 0.1-1 eV can be proposed for IR
detectors. Among these effects are: change in electrical conductivity (bolometers), gas expansion
(Golay cell), pyroelectricity (pyroelectric detectors), photon drag, Josephson effect (Josephson
junctions, SQUIDs), internal emission (PtSi Schottky barriers), fundamental absorption (intrinsic
photodetectors), impurity absorption (extrinsic photodetectors), low dimensional solids [superlattice
(SL) and quantum well (QW) detectors], different type of phase transitions, etc. Since the initial
proposal by Esaki and Tsu and the advent of molecular beam epitaxy (MBE), interest in semiconductor
superlattices (SL’s) and quantum well (QW) structures has increased continuously over the years. As a
result, a new class of materials and heterojunctions with unique electronics and optical properties has
been developed.
Fig. 2 History of the development of IR detectors [3]
Fig. 2 gives approximate dates of significant development efforts for the materials mentioned. The
modern IR detector technology started from the World War II. Till recently, photon IR detector
technology combined with semiconductor material science, photolithography technology developed for
integrated circuits and research progress in optical engineering have propelled extremely advances in
IR capabilities in just a fraction of the last century.
Current cooled IR detector systems use material systems, such as HgCdTe (MCT), InSb, PtSi, and
doped Si. The quantum well infrared photodetector is a relatively new technology for IR sensor
applications. Among these cooled IR detector systems, PtSi FPAs are highly uniform and
manufacturable, but have very low quantum efficiency and can only operate in the MWIR range. The
InSb FPA technology is mature with very high sensitivity, but it also can only operate in the MWIR
range. Neither PtSi nor InSb IR detectors have wavelength tunabiligty or multicolor capabilities. Doped
silicon has a wide spectral bandwidth from 0.8 to 30 um, with no wavelength tenability or multicolor
capability, and it can only operate at very low temperature (around 12 K). Both MCT and QWIPs offer
high sensitivity with wavelength flexibility in the
middle-wavelength infrared (MWIR),
long-wavelength infrared (LWIR) and very-long-wavelenth infrared (VLWIR) regions, as well as
multicolor capabilities.
Table 1. Comparison of infrared detectors [2]
Detector type
Thermal (thermopile, bolometers, pyroelectric)
Intrinsic
IV-VI
(PbS, PbSe, PbSnTe)
II-VI (HgCdTe)
III-V (InGaAs, InAs, InSb, InAsSb)
Advantages
Light, rugged, reliable, and low
cost
Room temperature operation
Easier to prepare
More stable materials
Easy band gap tailoring
Well developed theory & expiment
Multicolor detectors
Good material and dopants
Advanced technology
Possible monolithic integration
Photon
Extrinsic
(Si:Ca, Si:As, Ge:Cu, Ge:Hg)
Free carriers
(PtSi, Pt2Si, IrSi)
Type I
(GaAs/AlGaAs, InGaAs/AlGaAs)
Quantum
Wells
Type II
(InAs/InGaSb, InAs/InAsSb)
Quantum dots InAs/GaAs, InGaAs/InGaP, Ge/Si
Very-long-wavelength operation
Relatively simple technology
Low-cost, high yields
Large and close-packed 2D arrays
Matured material growth
Good uniformity over large area
Multicolor detectors
Low Auger recombination rate
Easy wavelength control
Normal incidence of light
Low thermal generation
Disadvantages
Low detectivity at high frequncey
Slow response (ms order)
Very high thermal expansion
coefficient, Large permittivity
Nonuniformity over large area
High cost in growth and processing
Surface instability
Heteroepitaxy with large
Lattice mismatch
Long wavelength cutoff limited
To 7 um (at 77K)
High thermal generation
Extremely low-temperature operation
Low quantum efficiency
Low-temperature operation
High thermal generation
Complicated design and growth
Complicated design and growth
Sensitive to the interfaces
Complicated design and growth
HCdTe (MCT) is a variable-gap semiconductor most often used in the production of IR
photodetectors. It is nearly the most perfect IR detector material in terms of fundamental properties.
But, since the conventional interband optical absorption involves photoexciting acrriers across the band
gap Eg, i.e., promoting an electron to jump from the valence band to the conduction band. These
photocarriers are then collected, in order to produce a photocurrent. This process is comparatively
simpler in the visible light or ultra violet light spectrum ranges. However, for an infrared radiation
whose wavelength ranges from 0.1 um to about 100 um, it requires an extremely small band gap which
is in the order of 100 meV. Such small-band-gap materials are well known to be more difficult to grow,
process, and fabricate into devices than are larger-band-gap semiconductors. In addition, the week
Hg-Te band resulting in bulk, surface, and interface instabilities as well as the uniformity and yield are
still unresolved issues. These difficulties thus motivate the study of novel artificial low effective
band-gap materials which use quantum wells in large-band-gap (Eg>1 eV) semiconductors. [7]
III. DEVICE PHYSICS & CHARACTERISTICS
The QWIP is a semiconductor device using intersubband transitions within either the conduction band
(n-type) or the valence band (p-type). The quantum well is formed by using an ultra thin layer of
narrow band gap semiconductor (e.g. GaAs) sandwiched between two thin wider band gap
semiconductors (e.g. AlGaAs) barrier layers. The motion of the charge carriers perpendicular to the
layers becomes quantized so that localized two-dimensional (2-D) subbands of quantized states are
formed inside the quantum well. When an optical beam is incident with an angle to the QWIP surface,
an electron in the ground state of the quantum well absorbs an infrared photon and excites to a higher
state during an intersubband optical transition.
A typical GaAs/AlGaAs QWIP consists of 30-50 quantum well periods. Using GaAs as the well region
and AlGaAs as the barrier region, confined quantum well structures can be formed when the well width
is small (less than an electron’s de Broglie wavelength). The thickness of the GaAs layer determines
the well width, and the x value in AlxGa1-xAs determines the barrier height. The well region has one
bound ground state and one or more excited states, depending on the barrier structure.
A. Classification
Fig. 3 Energy Band Diagram for the type-I, type-II staggered, type-II misaligned, and type-III. [8]
A majority of the studies on quantum well infrared photodetectors (QWIPs) have been focused on
GaAs/AlGaAs. However, other material such as n-type InGaAs/InAlAs, GaAs/GaInP, InGaAsP/InP,
type II AlAs/Al0.5Ga0.5As, and SiGe/Si have also been investigated for QWIPs applications. In general,
the hetero-interface quantum well structures may be classified into four categories: type-I, type-II
staggered, type-II misaligned, and type-III, as shown in Fig. 3
Fig. 3 Type-I is the most used structure for QWIPs, which maybe fabricated from n-type GaAs/AlGaAs,
InGaAs/InAlAs, GaSb/AlSb, GaAs/GaInP material. In a type-II quantum well structure, electrons and
holes are confined in different semiconductor layers at their heterojunctions and super lattices. The
type-III QWIPs involve the use of a zero band gap material such as HgCdTe.
B. Working principle
(1) Intersubband absorption
Fig. 4 is a typical figure for single well of type I. For instance, the low-band-gap material in the
quantum well is GaAs and the high-band-gap material is AlGaAs. The intersubband transition energy
3 2 2
between the lowest and first excited state is E 2  E1 
2m * L2w
(1)
where Lw is the width of the quantum well, m* is the effective mass in the well.
Fig. 4 Band structure of quantum-well (depths Ec, and Ev. Intersubband absorption between electron levels E, and E2 or hole
levels HI to H2 is schematically shown. [1]
Furthermore this transition has a large dipole matrix element (z) = 16L/92~0.18 L, and an
integrated absorption strength of
  c N w hf
 a(v)dv   4 m*cn
0
r
 o

 sin 2  ' 


 cos ' 


Where c=NDLW is the two-dimensional density of carriers in the well, ND is the three-dimensional
carrier density, LW is the number of doped well, nr is the index of refraction, θ’ is the angle between the
direction of the optical beam and the surface normal, and f is the oscillator strength. This oscillator
strength is very large and is given for this quantum well with infinitely high barriers as
f 
2m*
( E2  E1 )  z  2  0.96
2
(where z is the direction normal to the quantum well). By changing the quantum-well width L, this
Intersubband transition energy can be varied over a wide range from the short wave infrared SWIR
(A-2 pm), the medium wave infrared MWIR (n-4 pm>, through long-wave LWIR (n-10 pm) and into
the very long-wave VWIR spectral regions (A > 14 pm). Since the oscillator strength only has a
component along z, the optical electric field must also have a component parallel to z in order to induce
an intersubband absorption; thus, normal incidence radiation will not be absorbed. Based on the above
limitation, several optical coupling methods are adopted, such as gratings, random scattering and
microlenses.
(2) Sequential resonant tunneling
Consider the application of electric fields to a multiquantum-well structure, and the tunneling escape
and subsequent transport of these photoexcited electrons. The infrared absorption due to the
intersubband transition from the bound ground state to the bound excited state is followed by the
photoexcited electrons tunneling out of the well (as shown in Fig. 5). These photocarriers, which
escape from the well, are transported by the electric field in the continuum above the barriers for an
excited-state lifetime τL during which they travel a distance L (which is the mean free path for
recapture back into the quantum wells) and thereby produce a photocurrent. The total current I can be
written as I=Ist+Ith+Ipt, where Ist is the sequential resonant tunneling contribution, Ith is due to
thermionic emission, and Ipt is phonon assisted tunneling.
In principle, due to the two-dimensional (2D) nature of the electron gas in the well, resonant tunneling
is possible only when the energy levels in each well coincide. The presence of acoustic phonons and
impurity scattering within each well, conservation of energy and momentum is possible provided that
eV p  2 , where Vp is the potential difference per period between the adjacent wells and τ 1 is the

ground-state scattering time. Therefore, at small bias the electrons are able to conduct by ground-state
resonant tunneling through the ground states of each well.
At high bias, eV p  2
 , ground-state resonant tunneling is not possible and as a result negative
differential resistance occurs. As each period breaks off from the resonant condition, the resistance
across this period becomes much larger and a high-field domain forms. Any subsequent increase in the
bias will appear across this domain until the ground level rises to within 2
E2 in the next well whereupon the resonant tunneling condition is restored.
 of the first excited level
(3)Bound-to-bound State
All QWIPs are based on ‘‘band gap engineering’’ of layered structures of wide-band-gap (relative to
thermal IR energies) materials. These structures are designed in such a way that the energy separation
between two selected states in the structure matches the energy of the infrared photons to be detected.
By using different well widths and barrier heights, several QWIP configurations have been reported
based on transitions from bound-to-bound, bound-to-continuum states, bound-to-quasibound states, and
bound-to-miniband states.
Fig. 5 Schematic energy band diagram [9]
For Fig. 5 (a) after absorption of the infrared photon, the photoexcited carrier can either be transported
along the quantum well direction (with an applied parallel bias voltage), or perpendicular to the wells
(with an applied field along the growth direction). However, as far as detection is concerned,
perpendicular transport is superior to parallel transporting since the difference between the
excited-state and ground-state mobilities is much larger in the latter case, and thus the photo response is
substantially greater. The photocurrent from this detector arises solely from the high-field domain,
since only from this region can the photoexcited carriers tunnel out of the well and escape. But the
escape probability by tunneling is not high due to the confinement of the excited level. We can thus
express the photocurrent Ip as
I p  n p ev
(2)
where np is the number of photo generated carriers/cm3 and v is the transport velocity along the super
lattice. Furthermore, the dark current is much lower since the heterobarriers effectively block the
transport of the carriers in the doped quantum-well ground state. For this reason QWIPs based on the
escape and perpendicular transport of photoexcited carriers are to be preferred.
(4)Bound-to-Continuum State
By decreasing the size of the quantum well, the strong oscillator strength of the excited bound state can
be pushed up into the continuum resulting in a strong bound-to-continuum state absorption. This
extended state structure has the major advantage that the photoexcited electron can escape from the
quantum well without tunneling through the energy barrier. Thus, the bias voltage required for the
photoelectron to efficiently escape from the well can be dramatically reduced, strongly lowering the
dark current. In addition, the barrier thickness can now be substantially increased thereby further
reducing the ground-state sequential tunneling by many orders of magnitude.
C. Characteristics and performance
(1) Quantum efficiency η
Fig. 6. Quantum efficiency versus wavelength for a HgCdTe photodiode and GaAs/AlGaAs QWIP detector with similar cutoffs.
[2]
The quantum efficiency value describes how well the detector is coupled to the radiation to be detected.
It is usually defined as the number of electron-hole pairs generated per incident photon. Due to the
intersubband transition in the conduction band, the n-typed QWIP detection mechanism requires
photons with a non-normal angle of incidence to provide proper polarization for photon absorption.
The absorption quantum efficiency of QWIP is relatively small with a 2D grating. Fig. 6 compares the
spectral η of a HgCdTe photodiode to that of a QWIP. A higher bias voltage is used to boost η.
However, an increase in the reverse bias voltage also causes an increase of the leakage current. This
limits any potential improvement in the system performance. New grating designs are under study to
improve η, such as an enhanced QWIP, antenna gratings, and corrugated gratings. [10, 11] It is well
known that using a smaller number of quantum wells and bound-to-continuum structures, increased
optical gain and improved detector performance at low temperatures are possible. Tidrow presented [12]
a high performance QWIP consisting of only three quantum wells with the conversion efficiencies up
to 29% at a bias voltage of 20.8 V and a peak wavelength of 8.5 mm.
(2) Dark current
In ideal photodiodes the diffusion current is dominant, therefore their leakage current is very low and
insensitive to the detector bias. Leakage current is the primary contribution of unwanted noise. Figure 7
shows the I–V characteristics for temperatures ranging from 35 to 77 K, measured in a device at the
9.6-mm spectral peak. It shows typical operation at 2 V applied bias in the slowly varying region of
current with bias between the initial rise in current at low voltage and the later rise at high bias. Typical
LWIR QWIP dark current is about 10-4 A/cm2 at 77 K. Thus, the same current in a 24×24 µm2 pixel will
be in the nanoampere range. In comparison with other photodiodes, the behavior of dark current of
QWIP’s is understood better. At low temperatures (T<40 K, λc=10 µm), the dark current is mostly
caused by defect-related direct tunneling. In the medium operating range between 40 and 70 K (λ c =10
µm), thermally assisted tunneling dominates. In this case, electrons are thermally excited and tunnel
through the barriers with assistance from defects and the triangle part of the barrier at high bias.
FIG. 7. Current-voltage characteristics of a QWIP detector having a peak response of 9.6 mm at various temperatures, along with
the 300 K background window current measured at 30 K with an 180° FOV. [2]
(3) Detectivity
Figure 8 compares the detectivities of p-on-n HgCdTe photodiodes with those of GaAs/AlGaAs
QWIP’s. The theoretical curves corresponding to HgCdTe photodiodes are calculated on the
assumption of constant cutoff wavelengths of 10 µm and 11 µm. The VLWIR results for HgCdTe
~14.8 µm at 80 K and 16.2 µm at 40 K! and QWIP at 16 µm show the intrinsic superiority of HgCdTe
photodiodes. The detectivity of HgCdTe is roughly an order of magnitude higher, though the advantage
decreases as the temperature is reduced. The best example of a region where QWIP’s could have a
performance advantage is low temperatures. As we can see from Fig. 8, the comparison of detectivity is
more advantageous for GaAs/AlGaAs QWIP’s in the spectral region below 14 µm and at temperatures
below 50 K.
FIG. 8. LWIR detector detectivity versus temperature for GaAs/AlGaAs QWIP’s and p–on–n HgCdTe photodiodes. [2]
IV. Focal plane array
The combination of existing high-performance arrays and highly developed silicon integrated circuits
in hybrid IR array/silicon planes have proved to be useful for thermal imaging systems with the thermal
and spatial resolution unmatched by any competing technologies at present. In hybrid FPA’s, detectors
and multiplexers are fabricated on different substrates and mated with each other by flip-chip bonding
(as shown in Fig. 9). In this case the detector material and the multiplexer may be optimized
independently. Other advantages of hybrid FPA’s are the near 100% fill factor and the increased
signal-processing area on the multiplexer chip. The detector array can be illuminated either from the
front side (with the photons passing through the transparent silicon multiplexer) or from the backside
(with photons passing through the transparent detector array substrate). The relatively new QWIP
technology has been developed very quickly in the last decade. Large-size LWIR GaAs/AlGaAs FPA’s
with up to 640×480 (640×512) pixels have been demonstrated with excellent uniformity and
operability.
Fig. 9 Hybrid IR FPA interconnects technique between a detector array and silicon multiplexer: (a) indium bump technique, (b)
loophole technique, and (c) scanning electronic microscopy photo FPA
A. Uniformity & NEDT
FPA uniformity influences the complexity of an IR system. Uniformity is important for accurate
temperature measurements, background subtraction, and threshold testing. The admissible
nonuniformity depends on the requirements of the operability. The nonuniformity value is usually
calculated using the standard deviation over the mean, counting the number of operable pixels in an
array. FPA performance is uniformity limited and thus essentially independent of detectivity. An
improvement in nonuniformity from 0.1% to 0.01% after correction could lower the NEDT from 63 to
6.3 mK. FPA uniformity influences the complexity of an IR system. Uniformity is important for
accurate temperature measurements, background subtraction, and threshold testing. A typical
uncorrected-response nonuniformity in QWIP FPA’s is 1%–3% with the operability (the fraction of
good pixels) higher than 99.9%. For a 128×128 15-μm array fabricated by Jet Propulsion Laboratory,
the uncorrected standard deviation is 2.4% and the corrected nonuniformity is 0.05%. For a large
640×486 9-μm FPA the uncorrected noise nonuniformity is about 6%, and after a two-point correction
improves to an impressive 0.04%. [13] For an FPA of the the same format demonstrated by Lockheed
Martin, operability higher than 99.98% was described. [14] It is very hard for HgCdTe to compete with
QWIP’s in the area of high uniformity and operability of large-array formats, especially at low
temperatures and in the VLWIR region. High uniformity and high operability, as shown in the above
examples, demonstrate the maturity of GaAs growth and processing technology.
Besides using nonuniformity to evaluate FPA’s performance, the other criterion is NEDT. This
parameter represents the temperature change, for incident radiation, that gives an output signal equal to
the rms noise level. The NEDT for QWIP is equal to
NEDT 
2kTB 
hc
g
Nw
(3)
where λ=(λ1+λ2)/2 is the average wavelength of the spectral band and g is the photoconductive gain.
NEDT value for charge-limited HgCdTe photodiodes can be determined by equation
NEDT 
2kTB 
(4)
hc 2w
If one assumes a typical storage capacity of 2×107 electrons, λ= 10 μm, TB =300 K, and g=0.4, The
value of Eq (3) NEDT of 19.8 mK. The value of Eq (4) is 17.7mK. Thus, a low photoconductive gain
actually increases the S/N ratio and a QWIP FPA can have a better NEDT than an HgCdTe FPA with a
similar storage capacity.
B. Fabrication
Fig. 10 is the steps to fabricate a detector array. The first step is to grow the QWIP structure by
MOVPE (Metal Organic Vapor Phase Epitaxy) starting with a semi-insulating GaAs wafer. A typical
QWIP structure consists of 50 quantum wells, each of width 5.0 nm surrounded AlGaAs layers (x =
0.28) of width 35 nm. On either side of the QW structure is a contact layer consisting of highly n-doped
GaAs. The next step is to lithographically define and etch a two dimensional grating into the uppermost
part of the mesa. Then detector mesas are fabricated by etching down to the lower contact layer. Finally
metal contacts are made and a layer of gold deposited over the grating.
Fig. 10 Production steps of a QWIP array [21]
1. Epitaxial growth of QWIP structure
2. Processing of the QWIP array
3. Fabrication of ROIC (readout integrated circuit)
4. Processing of indium bumps
5. Hybridization flip-chip bonding
6. Mounting and wire bonding
C. Cost
The cost of a FPA depends strongly on the maturity of the technology and varies with the production
quantity in different companies. In comparison with HgCdTe FPA’s, the industry has much less
experience in QWIP FPA’s; therefore, improvements can be expected, especially since this technology
is at an earlier stage of development. Because of the maturity of GaAs growth technology and the
stability of the material system, no investment is needed for developing QWIP substrates, MBE growth,
and processing technology. So far, more efforts have been put in the improvement of the device
performance by means of tuning the device and gratings designs. It is estimated that the cost of the
development QWIP technology and QWIP production will be much less than the other IR detecting
systems.
V. APPLICATIONS
Since the initial demonstration of QWIP FPA’s in the late 1980s, there has been a worldwide sustained
effort in developing the detector into a mainstream IR technology. So far, lots of efforts have been done
to bring this technology into the commercial market and QWIP technology is accepted as the
commercial standard for high-performance and large-format LWIR detection. Gunapala et al. [11]
presented large-format QWIP cameras holding forth a promise for many applications in the 6–18 mm
wavelength range in science, medicine, defense, and industry. Possible applications are medical
imaging, firefighting, monitoring, IR astronomy, defense and surveillance. [15, 16, 17]
VI. Conclusion
The main drawback of LWIR QWIP FPA technology is that the device performance is limited to long
integration time applications and low operation temperature. The main advantages are linked to the
performance uniformity and to the easy fabrication of large size arrays due to the mature fabrication
process of GaAs. Such large industrial infrastructure on III-V material/device growth, processing, and
packaging gives QWIP’s a potential advantage in producibility and cost.
QWIP FPAs using B-C, B-M and B-QB transition schems have been reported in the literature [18,
19, 20]. These QWIP FPAs have shown excellent imagery in the 8 – 12 um LWIR atmospheric spectral
window. Till now, efforts in the area of QWIP technology have been limited to increase the operation
temperature for tactical applications.
In summary, QWIP technology has been developed very quickly in the past 12 years and
impressive progress has been made with high performance, large format FPAs. QWIPs have special
advantage for IR detection in VLWIR and multicolor detection. QWIP manufacturing leverages the
rapidly evolving III-V GaAs industry and has the potential to be very low cost and give high
production yield. Improvements are expected in device design and performance with continuing
research and development effort.
Acknowledgement
Jie Zhang and Wan-Ching Hung would like to thank Professor Philippe M. Fauchet and all the
ECE580 students for their help and support with our paper.
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