956 of ELECTRONIC MATERIALS, Vol. 29, No. 7, 2000
Journal
Dutta
Special
andIssue
Miller
Paper
Engineering Phase Formation Thermo-Chemistry
for Crystal Growth of Homogeneous Ternary
and Quaternary III-V Compound
Semiconductors from Melts
P.S. DUTTA1,3 and T.R. MILLER2
1.—Rensselaer Polytechnic Institute, Department of Electrical, Computer and Systems
Engineering, Center for Integrated Electronics and Electronics Manufacturing, Troy,
New York 12180. 2.—Lockheed Martin Inc., Schenectady, New York 12301.
3.—e-mail: [email protected]
Based on intrinsic alloy phase formation chemistry and thermodynamics, a
novel and unique way of producing compositionally homogeneous multi-component (binary, ternary, quaternary) semiconductor materials is presented. A free
energy minimization computer program licensed from AEA Technology Engineering Software, Inc., has been employed to study the composition of the
solidifying phases from Ga-In-As-Sb melts at different temperatures and with
various liquid compositions. The solid phases have been identified (theoretically and experimentally) to be either ternary compounds of Ga1–xInxSb,
Ga1–xInxAs, GaAsy Sb1–y , and InAsySb1-y, or quaternary Ga1–xInx AsySb1–y depending on the melt temperature and composition. By engineering the thermochemistry of preferential phase formation in the Ga-In-As-Sb melt, compositionally uniform, single phase, crack free, large polycrystalline Ga1–xInxSb and
Ga1–xInxAs have been grown.
INTRODUCTION
Substrates of III-V compound semiconductors with
variable band gaps and lattice constants are desirable
to obtain high performance electronic and optoelectronic devices. Unfortunately, at the present time,
device grade, single crystal, substrates of only binary
compounds (such as GaAs, GaSb, InP) with discrete
energy band gaps and lattice constants are commercially available. Ternary and quaternary based devices are fabricated on thin epitaxial layers grown by
non-equilibrium techniques (from vapor or solid phase)
on binary substrates using buffer layers. The buffer
layer technology necessary to relieve misfit (lattice
mismatch) related stresses at the epilayer-substrate
interface is not optimized for all systems and often
devices exhibit large leakage currents due to poor
interfacial regions. Availability of substrates with tunable band gap and lattice constant will open up numerous possibilities of interesting band gap engineering in
homo- and hetero-epitaxial devices, and would reduce
the complexity and cost of the epitaxial technology.
Results of rigorous investigation in the area of bulk
crystal growth of ternary and quaternary compounds
over the past few decades have indicated the unfeasi(Received September 19, 1999; accepted March 30, 2000)
956
bility of large scale production of multi-component
substrates by the conventional melt growth techniques.1 Melt grown ternary and quaternary substrates are of poor quality primarily due to spatial
compositional inhomogeneity arising from the wide
separation between the liquidus and solidus curves in
the phase diagrams.1–6 Hence, new thermodynamic
approaches of preparing homogeneous semiconductor alloys from melt should be considered.
The development and optimization of materials
and processes are generally time-consuming and costly
operations. As a result, significant delays are frequently encountered before important materials advances can be introduced in technological applications. For these reasons, thermodynamic calculations
and simulations based on critically evaluated data
are now finding wide and increasing use as a basic tool
in materials and process design. Commercial software packages incorporating thermodynamic databases are already available for this purpose.7 Their
use enables the number of direct measurements to be
minimized, as information on necessary process conditions can be obtained very rapidly and inexpensively to achieve the required product with minimum
waste of energy and materials.
For III-V compounds, even though thermodynamic
calculations have been widely used since 19698,9 to
Engineering Phase Formation Thermo-Chemistry for Crystal Growth of Homogeneous
Ternary and Quaternary III-V Compound Semiconductors from Melts
predict liquid or gas mixtures required to grow alloys
of various target compositions, and to predict solidsolid miscibility gaps, experimenters working with
systems of three or more components still cannot rely
exclusively on phase diagrams that have already been
published in the literature. It is impossible for a
journal article to cover all of the composition-temperature space that may be of interest. Moreover,
published liquidus and solidus curves for a fixed
temperature are often drawn on a composition plot
without tie-lines (connecting equilibrium liquid and
solid compositions). Similarly, isotherms representing the boundaries of a miscibility gap are often
shown without tie-lines (indicating pairs of solids in
equilibrium with each other). Furthermore, liquidsolid and solid-solid equilibria are rarely shown on
the same plot. This last omission tends to obscure an
important point: For some compositions that are
within a miscibility gap at one temperature, there
may be a higher temperature at which they can be
grown as single phase solids. Other compositions,
deeper within the miscibility gap, are not stable as
single phase solids at any temperature, because on
heating, they begin to melt before the solids become
miscible. The incompleteness of the information in
the literature makes it essential for any group trying
to grow multi-component solids to be able to perform
phase diagram calculations for their own conditions
of interest. Recently, based on thermodynamic calculations, Dutta and Miller10 proposed a novel method of
deriving large quantities of homogeneous ternary and
quaternary alloys from melts by monitoring the nucleation temperature and melt composition. Isothermal
phase diagram calculations in the present work concentrated on guiding efforts to grow Ga1-xInxSb,
Ga1–xInxAs, GaAsySb1–y, InAsySb1–y and Ga1–xInxAsySb1–y
from Ga-In-As-Sb melts. Results presented herein
are limited to conditions where the liquid is stoichiometric, that is, the sum of the mole fractions of the
group III components equals that of the group V
components. The calculations were undertaken using
MTDATA, the National Physical Laboratory (NPL,
UK) Database for Metallurgical Thermochemistry.
THERMODYNAMIC MODEL
Models and Data Sources
MTDATA determines equilibrium compositions by
minimizing the Gibbs free energy of the system. It
requires an input file containing free energies of pure
substances as a function of temperature, and excess
free energies of solution phases as functions of temperature and composition. Data for the pure elements
in their solid and liquid phases and for the pure solid
compounds were taken from the assessment of Ansara
et al.11 The published free energy expressions were
multiplied by two because the compounds were formulated in the present work as AB, rather than as
A0.5 B0.5 (MTDATA reads the stoichiometry of each
substance in the system from the input file and
accounts for it in the calculations).
957
The liquid was modeled as comprised only of atoms.
The strong attraction between group III elements and
group V elements in the liquid was accounted for by
negative excess free energy terms rather than by
postulating the existence of III-V compounds in the
liquid phase. The excess free energy of a solution
phase is defined as the difference between the actual
free energy of mixing and the free energy change that
would result from the entropy of mixing of an ideal
solution. The excess free energy of the liquid was
represented using a Redlich-Kister model12 having
non-zero coefficients for all of the six possible binary
interactions and for two of the four possible ternary
interactions. The contribution of an interaction to the
excess free energy is
Gexcess = W0(T)X1X2 + W1(T)X1X2 (X 1-X2)
+ W2(T)X1X2(X1-X2)2…….
for a binary interaction, and
Gexcess = W0(T)X1X2X3
for a ternary interaction, where Xn is the mole fraction
of species n.
Redlich-Kister coefficients for the binary interactions in the liquid were taken from Ansara et al.11 A
coefficient for the ternary interaction among Ga, In,
and Sb in the liquid was taken from Ref. 13.
The zincblende phase was treated using a twosublattice model, with gallium and indium occupying
one sublattice, while arsenic and antimony occupy
the other. Using YX to represent the fraction of sites on
its appropriate sublattice occupied by element X, the
free energy of the solid was calculated as:
G = YGa YAs GoGaAs + Y In YAs GoInAs
+ YGa YSb GoGaSb + YIn YSb G oInSb
+ RT (YGa ln YGa + YIn ln YIn)
+ RT (YAs ln YAs + YSb ln YSb) + Gexcess
where
Gexcess = YGa YAs YSb ao + YGa YIn YAs bo
+ YGa YIn YSb co + YIn YAs YSb do
Solid solutions of III-V compounds were not included in the Ansara et al. assessment.11 Expressions
for the ao, bo, co, and do coefficients were taken from
other literature sources.13,14 Calculations of the
pseudobinary phase diagrams of GaAs-InAs, GaAsGaSb, and GaSb-InSb agreed well with experimental
data from the literature, with the exception of the
InAs-InSb. Improved agreement for this subsystem
was achieved by addition of a ternary As, In, Sb
interaction in the liquid, and adjustment of the do
coefficient. The values for these two coefficients were
arrived at by trial-and-error rather than by a rigorous
optimization procedure. All interaction terms from
sources other than the Ansara et al.11 assessment are
listed in Table I. All interactions listed in Table I used
only the first term (W0) in the Redlich-Kister series.
Calculations were performed using the
MULTIPHASE module of MTDATA. At each temperature, overall compositions (moles of each ele-
958
Dutta and Miller
Table I. Redlich-Kister Coefficients Used for Phase Diagram Calculations (Other than from Ref. 11)
Interacting
Species
Phase
Coefficient
Joule/mole, T in Kelvin
Source
As,In,Sb
Ga,In,Sb
GaAs, GaSb
GaAs, InAs
GaSb, InSb
InAs, InSb
Liquid
Liquid
Zincblende
Zincblende
Zincblende
Zincblende
Wo = –37435 + 55.6 T
Wo = –5072.76 – 10.8842 T
ao =17866
bo = 10498
co = 9093 – 2.8698 T
d0 = 20914 – 12 T
Present Work
Ref. 13
Ref. 14
Ref. 14
Ref. 13
Present Work
ment) corresponding to selected points expected to be
in the interior of two phase or three phase regions
were input. The program then calculated the compositions and amounts of the phases present at equilibrium. Each point that was within a two-phase region
generated a tie line, and each point within a three
phase region generated the three lines forming the
boundaries of the region.
Calculated Diagrams
Phase diagrams for the Ga1–xIn xAsySb1–y system
were calculated for temperatures from 200°C to
1200°C. Representative diagrams are presented in
Figs. 1–4. In these diagrams, dotted lines represent
solid-liquid tie lines, while dashed lines represent
solid-solid tie lines. Dashed-Dotted lines ending in
filled circles [in Figs. 2, 3, and 4] are the experimental
tie lines of Nakajima et al.15 Between 720°C and the
melting point of GaAs (1237°C), there is only a single
solid, which is rich in gallium and arsenic, and a liquid
which is rich in indium and antimony (shown in Figs.
1 and 2). The only change with increasing temperature in this range is a continuous shift of both the
liquidus and solidus curves toward the GaAs corner.
Below the melting point of InAs (942°C), the In-rich
ends of both curves are on the InSb-InAs axis (Figs. 1
and 2). Above the melting point of InAs, both curves
end on the GaAs-InAs axis. In the temperature range
~543–720°C, three-phase regions are predicted to
exist, where an arsenic-rich solid and an antimonyrich solid are simultaneously in equilibrium with a
liquid that is richer than either solid in indium and
antimony (Figs. 3 and 4). At 400°C and below, a threesolid region appears within the solid-solid miscibility
gap, as the arsenic-rich solid decomposes further into
separate gallium-rich and indium-rich phases.
The calculations predict that Ga0.78In 0.22As0.1Sb0.9
for example is within the miscibility gap at 500°C, but
at 600°C it is stable as a single solid in equilibrium
with a liquid of composition Ga0.25In0.75As0.004Sb0.996. In
contrast, Ga0.8In 0.2As0.2 Sb0.8 is also within the miscibility gap at 500°C, but it is not stable as a single phase
solid at any temperature. Solid with bulk composition
Ga0.8In0.2As0.2Sb0.8 does not separate from a liquid
until the liquid has been cooled to about 600°C. When
the solid does form, it will be a two phase mixture of
antimony-rich and arsenic-rich solids, because it is
already below the minimum temperature at which
the solids would be miscible if they did not melt.
Modeling of Solidification
Many models for growth of solid solutions from
melts have been developed, with varying degrees of
complexity. One of the simplest models assumes that
the actively growing zone of the solid is constantly in
quasi-equilibrium with the entire bulk liquid (not a
true equilibrium to the extent that the temperature is
non-uniform). Solid is “frozen” in composition and
cannot exchange matter with the liquid. Also, solid
phase diffusion is extremely low and hence neglected.
As the solid grows, the liquid becomes depleted in the
elements that preferentially enter the solid; so with
time, the solid also gets depleted in those elements.
The interface temperature is assumed to decrease as
the liquid becomes richer in the lower melting components. Quantitative treatment of such a model usually begins by defining effective solid-liquid distribution coefficients, ki, for the components i. The distribution coefficients are often assumed to remain constant, and may or may not be assumed to be the same
as the equilibrium distribution coefficients. Experimentally, it is usually found that attempts to grow
pseudo-binary solid solutions such as Ga1–xIn xAs or
Ga1–xInxSb from a ternary liquid produce solids with
a gradation in composition that conforms to a model
of this first type.
The crystal growth experiments described herein
more nearly followed a second type of model. In this
model, the interface solid is in equilibrium only with
a thin zone of liquid at the liquid-solid interface. The
temperature at the liquid-solid interface is assumed
to be constant, but lower than the bulk liquid temperature. The interface liquid exchanges matter with
the bulk liquid on a time scale that is slow compared
to the equilibration between solid and interface liquid. As the solid grows, the interface liquid becomes
depleted in the elements that preferentially enter the
solid, but they are continuously replenished by exchange with the bulk liquid. As the process continues,
the solid composition remains uniform, and the interface liquid composition remains constant, but the
composition of the bulk liquid gradually approaches
that of the interface liquid. When the composition of
the bulk liquid becomes the same as the interface
liquid, the growth of solid stops unless the temperature decreases (in which case the composition of the
solid will change), or the bulk liquid is replenished by
adding the elements that have become depleted.
The second type of model can be represented by
Engineering Phase Formation Thermo-Chemistry for Crystal Growth of Homogeneous
Ternary and Quaternary III-V Compound Semiconductors from Melts
Fig. 1. Calculated phase diagram of Ga-In-As-Sb system at T = 900°C.
959
Fig. 3. Calculated phase diagram of Ga-In-As-Sb system at T = 700°C.
Dashed-Dotted lines ending in filled circles are the experimental tie
lines of Nakajima et al.15
Fig. 2. Calculated phase diagram of Ga-In-As-Sb system at T = 800°C.
Dashed-Dotted lines ending in filled circles are the experimental tie
lines of Nakajima et al.15
Fig. 4. Calculated phase diagram of Ga-In-As-Sb system at T = 600°C.
three points on an isothermal phase diagram for the
growth temperature. In Figs. 1 and 4, point A represents an initial bulk liquid composition. Point B is the
composition of the solid, and point A* is the composition of the interface liquid. As the growth continues,
the solid composition remains at point B, and the
interface liquid composition remains at point A*, but
the bulk liquid composition moves along the tie line
from point A toward point A*. The theoretical maximum fraction of the original liquid charge that can be
solidified at constant temperature is equal to the
ratio of the length of line segment AA* to that of
segment BA*.
While the model predicts that yield can be maximized by starting with a liquid composition as close as
possible to the desired solid composition, that in-
creases the risk of nucleation within the bulk liquid.
For example, a bulk liquid corresponding to point A1
on Fig. 1 has a calculated liquidus temperature of
950°C. Random nucleation could occur in the bulk if
the bulk liquid temperature is any less than 50°C
above the interface temperature (900°C) at the start
of the experiment. While the model predicts that the
same solid could be grown at a theoretical yield of 70%
by starting with a bulk composition close to point A1′,
the calculated liquidus temperature for composition
A1′ is 1000°C. Hence, to increase the maximum yield
of the uniform composition region in the crystal using
the present approach, the temperature gradient in
the melt needs to be increased.
It was theoretically predicted that alloy concentra-
960
Dutta and Miller
a
Fig. 5. Experimentally grown uniform Ga0.88 In0.12Sb polycrystal (growth
temperature ~630°C; melt composition: 75 mol.% Ga, 25 mol.% In, 98
mol.% Sb, and 2 mol.% As).
tions in the solid should remain constant, provided
the growth temperature was constant, in spite of the
fact that the segregation coefficients of individual
elements were all much different than unity. Figure
1 above demonstrated the growth of uniform Ga-InAs from a Ga-In-As-Sb melt. A similar concept can be
applied for the growth of uniform Ga-In-Sb, In-As-Sb
and Ga-As-Sb from Ga-In-As-Sb by choosing appropriate melt compositions and growth temperatures.
The results presented here on uniform ternary solids
from quaternary melts are in accordance with the
second type of model.
EXPERIMENTAL RESULTS
Charge Synthesis and Crystal Growth
The quaternary melts were synthesized by either
(a) melting Ga, In, Sb and InAs, or GaAs or (b) by
mixing pre-synthesized binary compounds GaSb, InSb,
GaAs, and InAs. Synthesis was performed in silica
crucibles by keeping the melt in a linear temperature
gradient zone of the furnace to promote mixing through
natural convection for 12–15 hours. The maximum
temperature in the melt was approximately 50°C
above the liquidus temperature. The bottom of the
crucible where solidification (nucleation) initiates was
monitored carefully and was decided based on the
MTDATA simulations.10 Melt was encapsulated by
boric oxide or alkali halide salt. Inert argon gas up to
1.5 atmospheres was used to pressure the melt to
avoid volatilization of the group V components during
synthesis. After synthesis, crystal growth was performed by the conventional vertical Bridgman method.
The crucible lowering rate was in the range of 2–3
mm/hr. Typical temperature gradients of the furnace
near the melt-solid interface used in this work ranged
between 20–50°C/cm.
Growth of Ga1–xInx Sb
By using the above described procedure, we were
able to produce compositionally uniform polycrystalline Ga1–xIn xSb (shown in Fig. 5) from Ga-In-As-Sb
melts. Melt composition and growth temperature is
b
Fig. 6. Radial indium profiles for the two wafers “A” and “B” (from the
crystal shown in Fig. 5) as measured using EPMA technique.
indicated in the figure caption. Due to spatial compositional homogeneity, cracks usually seen in ternary
boules are absent in this crystal. The elemental concentrations in the solid obtained in these crystals are
close to the predicted values from MTDATA calculations (simulations performed at the respective growth
temperatures with the experimental melt compositions). Using electron micro-probe x-ray analysis
(EPMA), the radial and axial indium concentration in
the grown crystals was evaluated. Figure 6 shows the
radial indium profile of two wafers “A” and “B” taken
from two axial positions of the grown ingot. The radial
position 0 mm represents the edge of the crystal and
the position 10 mm corresponds to the center of the
crystal. As clearly seen in the two plots, the axial as
well as the radial indium concentration is very uniform and close to 12 mol.%. The compositional homogeneity of the crystal is also evident from the Fourier
transform infrared transmission plots of the two wafers (Fig. 7). Both the transmission spectra show a
band edge of ~0.6 eV.
Growth of Ga1–xInx As
By using the procedure similar to that above, we
were also able to produce homogeneous polycrystalline Ga1–xIn xAs from Ga-In-As-Sb melts. As in the
earlier case, no cracks were observed due to spatial
alloy homogeneity of the crystals. Figure 8a shows an
experimentally grown Ga0.2In 0.8As polycrystal at a
growth temperature of ~900°C from a melt (A1) comprising of 10 mol.% Ga, 90 mol.% In, 20 mol.% Sb, and
Engineering Phase Formation Thermo-Chemistry for Crystal Growth of Homogeneous
Ternary and Quaternary III-V Compound Semiconductors from Melts
961
a
a
b
Fig. 8. (a) Experimentally grown Ga0.2In 0.8As polycrystal (Growth
temperature ~900°C; melt composition: 10 mol.% Ga, 90 mol.% In, 20
mol.% Sb, and 80 mol.% As). The axial compositional profile of indium
in the first to freeze 18 mm of the crystal (the uniform region) is shown
in Fig. 8b.
b
Fig. 7. (a) and (b) Room temperature Fourier transform infrared
transmission plots for wafers “A” and “B” respectively of the crystal
shown in Fig. 5. The band gap evaluated from the two plots is ~0.6 eV.
80 mol.% As. From the MTDATA predictions in Fig. 1,
the solid composition (B1) should be close to 20 mol.%
Ga, 80 mol.% In, negligible amount of Sb, and nearly
100% As. The total length of the uniform region of the
crystal expected is ~40% of the total melt volume
(proportional to the length of the tie line A1-A1* with
respect to the length of B1-A1*), which is experimentally verified using the axial EPMA measurements
for the first to freeze 18 mm of the crystal as shown in
Fig. 8b. Figure 9a and b are room temperature Fourier transform infrared transmission plots for wafers
“A” and “B” respectively of the crystal shown in Fig.
8a. The transmission cut-off edge lies at the same
point in the two wafers, indicating the axial compositional homogeneity in the crystal (in the first to freeze
one-third portion). The band gap evaluated from the
two plots is ~0.5 eV.
DISCUSSION
As mentioned above, multi-component alloys ex-
hibit miscibility gaps in solid phases. This is due to
differences in chemical interaction between the constituent elements in the melt, which leads to multiple
compounds or phase formation. Multi-phase semiconductor alloys are not suitable for any applications.
However, it is possible to obtain a single phase homogeneous alloy, if the chemistry and thermodynamics
of phase formation is well understood and carefully
monitored during experimental synthesis. Recently,
an innovative way for preparing homogeneous quaternary compounds with variable band gaps, but
discrete lattice constants termed as “quasi-binary”
was demonstrated by Dutta and Ostrogorsky.16 Quasibinary (GaSb)1–x(InAs)x could be grown in the GaSb
rich side. However, as the growth temperature increases with the increase in InAs content, the melt
tends to decompose to form a quaternary Ga-In-As-Sb
solution and multi-phase formation takes place. Hence
the composition (and band gap tuning) in QuasiBinary compounds is limited by the solubility of the
higher melting binary (such as InAs in GaSb) at
growth temperatures slightly above the lower melting one (GaSb) due to a stringent requirement of melt
association. In the present work, a unique approach is
presented through which compositionally homoge-
962
Dutta and Miller
a
quaternary melts is also applicable if one chooses
melt composition from the solid+liquid region of the
pseudobinary phase diagram such as GaAs-InAs. The
important experimental parameters are the temperature gradient above the solid-liquid interface, the
interface temperature and the temperature of the
bulk melt. With the present approach, at least a
portion of the bulk melt should be higher than the
liquidus temperature. This will avoid any random
nucleation in the melt. Any randomly precipitated
solid will float to the top of the melt due to density
difference and melt back into the liquid. The key thing
in achieving uniform composition is the solid-liquid
interface temperature. Any fluctuation in the solidliquid temperature will change the alloy concentration in the solid. Conceptually, the approach used in
this study is different from the conventional normal
solidification. During normal solidification (with a
fully mixed melt), the alloy concentration changes
continuously due to segregation.1 Hence no two wafers sliced from two different axial positions in the
crystal will have the same composition. By adopting
the present approach, a perfectly uniform alloy composition is achieved in the first to freeze certain region
and then the composition changes drastically. Thus,
two wafers taken from the uniform region will be
identically the same. The length of the uniform region
in the crystal depends on growth and melt temperatures, and melt composition as discussed above. In
general, the addition of the fourth component in the
ternary melt allows one to vary the growth temperature and provide seeding with the binary compounds.
For example, the addition of antimony to the Ga-InAs solution provides an additional degree of freedom
by lowering the growth temperatures; as a result
GaInAs can be easily grown using InAs single crystalline seed, which is not possible using a GaAs-InAs
psuedobinary melt (due to InAs melting point). Similarly, by adding arsenic to the Ga-In-Sb melt, the
liquidus and solidus temperatures can be varied,
which is useful in seeding with GaSb.
b
SUMMARY
Fig. 9. (a) and (b) Room temperature Fourier transform infrared
transmission plots for wafers “A” and “B” respectively of the crystal
shown in Fig. 8a. The band gap evaluated from the two plots is ~0.5 eV.
neous ternary and quaternary semiconductors can be
synthesized and grown from a multi-component melt.
This new alloy growth process is thermodynamically
driven and based on preferential alloy phase formation chemistry. The methodology presented in this
work is universal for all III-V, II-VI, and IV-IV alloys.
Homogeneous compounds can be grown in the entire
band gap-lattice constant plane by properly selecting
the melt compositions and nucleation temperatures.10
It is worth mentioning that single phase, stable alloys
can be synthesized and grown from melts only for
those compositions lying outside the solid-solid miscibility gaps.
The approach of growing ternary crystals from
An innovative method for the melt growth of compositionally uniform ternary and quaternary alloys is
presented. A thermo-chemistry simulation code
“MTDATA” has been employed to study the solidification of homogeneous ternary GaInSb, GaInAs, InAsSb
and GaAsSb from Ga-In-As-Sb melt. This approach is
applicable to other III-V, II-VI, IV-IV compound semiconductor alloys as well. Using this scheme, crack
free, polycrystals of compositionally homogeneous
GaInSb and GaInAs have been grown by the vertical
Bridgman method.
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