,. . . . . . . .
ELSEVIER
CRYSTAL
GROWTH
Journal of Crystal Growth 172 (1997) 337-349
Eddy current sensing of vertical Bridgman growth of
Cdo96Znoo4Te
Kumar P. Dharmasena, Haydn N.G. Wadley *
hltelligent Processing ()[Materials b~boratot T, School (~["Engineerin~ and Applied Science, University (~f Virginia, Charlottesz'ille, Virginia
22903, USA
Received 21 August 1995: accepted 17 April 1996
Abstract
An encircling two coil eddy current sensor has been integrated into the ceramic liner of a commercial six zone vertical
Bridgman furnace and used to monitor the growth of 72 mm diameter Cd0.96Zno.o4Te crystals. The sensor was maintained at
a fixed location with respect to the ampoule and monitored melt cooling/composition, detected the position of the
liquid-solid interface, measured the interface's curvature and determined the electrical resistivity of the solid during
post-solidification cooling. The study confirmed earlier predictions that a two coil, multifrequency sensor approach can
independently recover the liquid-solid interface location and provide insight about its curvature using data collected in the
50 kHz to 5 MHz frequency range. It suggests that the directional solidification of Cdo.96Zno.o4Te most probably initiates
from a Cd-depleted melt, occurs in a colder than anticipated region of the furnace and progresses with a convex interface
shape.
1. I n t r o d u c t i o n
High performance infrared focal plane arrays
(IRFPAs) for infrared imaging systems can be produced by depositing Hg I _ , C d , T e infrared detector
films on infrared transparent substrates such as CdTe
[1-4]. Recently, 3 % - 5 % atomic Zn has been added
to CdTe substrates to increase their high temperature
yield stress and provide better lattice matching with
the detector material [1,4-7]. The single crystal substrates needed for IRFPA applications are normally
" m i n e d " from large polycrystalline boules made by
the u n s e e d e d
directional
solidification
of
Cd~ ~Zn~Te melts using either a vertical [6,8-12] or
Corresponding author.
horizontal [13-16] variant of the Bridgman process.
In spite of intensive efforts by many groups [17-19]
to experimentally optimize furnace temperature profiles, ampoule geometries/materials, charge material
purity/stoichiometry and the growth (i.e. furnace
translation) rate, the ultimate yield of Cdt_~Zn,Te
suitable for large area (e.g. 4 cm × 6 cm) substrates
remains disappointingly low ( < 10%).
The reasons for yield loss are many and complex,
but amongst the most important are the polycrystalline nature of the boules, macrosegregation of Zn
[20], high dislocation densities ( > 105 cm -~) [21]
and low ( < 0.65 of theoretical) infrared transmission
due to inhomogeneities (principally Te inclusions or
precipitates greater than 10 /xm in diameter) [22].
The poor yield directly affects the affordability of
these substrates. It also results in the need for exten-
0022-0248/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved
PII S0022-0248(96)00498-8
338
K.P. Dharmasena, H.N.G. Wadley /Journal o[ Crystal Growth 172 (1997) 337-349
sive characterization and screening which further
increases the cost of substrate manufacture. Since
most of the yield loss is associated with the solidification process, intensive efforts are under way to
improve this technology.
Several groups are attempting to model the solidification process [10,12,23-28]. This requires incorporating heat transport by conduction and convective
flows within the melt, as well as addressing the
moving (liquid-solid) boundary and the segregation
of Zn. Other work seeks to model the differential
thermal contractions on cooling and predict the dislocation density and its distribution [29]. Significant
progress is being made in each of these areas [24-27]
and the ability to simulate a virtual growth process
for prescribed heat flux distributions (in space and
time) applied to the ampoule wall boundary is now
close at hand. Once fully validated, the modelling
approach may enable a scientifically directed redesign of Bridgman growth to achieve the optimal
conditions for solid nucleation/seeding, for single
crystal growth and the post-solidification cooling
that is used to homogenize the Zn distribution, control the dislocation density and reduce the concentration of inhomogeneities.
A second parallel thrust seeks to develop sensor
technologies for in situ monitoring of the Bridgman
growth process. These sensors would ideally provide
deeper insights into the growth process, aiding model
development and, perhaps, providing new technologies for on-line sensing and feedback control [30-32].
The most critical parameters of the growth process to
measure include the melt's composition and temperature, the nucleation of solid on cooling, the liquidsolid interface velocity (i.e. the interface's position
within the ampoule as a function of time), the interface's curvature (which affects the probability of
secondary grain nucleation and successful competitive growth) and the temperature within the cooling
solid.
Earlier studies have indicated that eddy current
techniques may have the potential for this [33-38].
Eddy current sensors exploit the large differences in
the electrical conductivity of the solid and liquid
phases of Cd~ xZn,Te at its melting point [39], the
strong dependence of the melt's electrical conductivity upon composition (particularly the Cd:Te ratio)
[40] and the significant temperature dependence of
both the liquid and solid electrical conductivities
[39,40]. The basic idea underlying all eddy current
sensor applications to semiconductor crystal growth
is to detect perturbations to the electromagnetic field
created by an a.c. excited solenoid arising from
induced (eddy) currents in the test sample. The
intensity of these eddy currents depends on the electrical conductivity distribution within the sample (i.e.
the position of a liquid-solid interface), the distribution of electromagnetic flux within the test material
(governed by the sensor/test material geometry and
excitation frequency) and the rate of change of the
electromagnetic flux (i.e. the test frequency) [41]. If
the perturbations associated with solidification processes can be measured and if suitable signal analysis protocols are developed, then it may be possible
to non-invasively recover new information about the
growth process.
Detailed electromagnetic finite element analyses
of the interactions between various eddy current
sensor designs and solidifying semiconductors with a
cylindrical symmetry has led to proposed designs for
two encircling sensor types suitable for monitoring
the vertical Bridgman process [42]. Both use a
multi-turn primary coil to excite a reasonably uniform electromagnetic field in the region occupied by
the cylindrical sample. One design uses a single
"pickup" (or secondary) coil to sense the perturbed
flux due to the sample (a so-called "absolute" sensor); the second "differential" sensor type uses a
pair of opposingly wound coils to sense the difference in flux at axially displaced locations along the
axis of the sample. The finite element calculations
indicate that both approaches are capable of sensing
changes in interface location and shape. Benchtop
tests with silicon surrogate samples (doped and machined to create an electromagnetically equivalent
problem to that encountered in growth) have confirmed the validity of these calculations and demonstrated the potential usefulness of the eddy current
sensor [43]. Additional modelling has subsequently
led to the design of a signal analysis protocol for
separately resolving the contributions to an eddy
current sensor signal from movement of the interface
a n d / o r a change of its curvature [44].
Here the "absolute" sensor design has been incorporated into the ceramic liner of a six zone
commercial vertical Bridgman furnace and several
K.P. Dharmasena, H.N.G. Wadley / Journal of Cr3,stal Growth 172 (1997) 337-349
growth runs monitored. The resulting data are used
to determine the melt stoichiometry, to detect the
location of the liquid-solid interface, infer its curvature and to monitor the post-solidification cooling of
the solidified ingot. The study reveals that the
Cd i - x z n xTe vertical Bridgman growth process studied here probably occurs from a Cd-depleted melt
with a far from ideal liquid-solid interface shape.
cal alumina liner was placed inside the furnace to
eliminate direct radiation transport from the exposed
windings to the quartz ampoule used to contain the
Cd i - xZn ~Te charge.
The top (#1) furnace was operated as a separately
controlled, single zone furnace. The middle (#2) and
lower furnace (#3) units were set up as three and
two zone furnaces, respectively. They were equipped
with independent temperature controllers to establish
the axial temperature profile needed for crystal
growth. Six thermocouples (TC 1-6) were positioned within the heating elements of each furnace
zone and were used to control their temperatures (see
Fig. l a for their approximate locations). The temperatures of all six zones of the furnace assembly were
independently controlled by a Model 823 MicRicon
programmable process controller. The furnace was
also equipped with two additional thermocouples
(TC 7 and 8) located in the furnace wall. TC 7 was
located between zones 3 and 4 while TC 8 was
positioned between zones 5 and 6, Fig. la. The
temperatures at each thermocouple location are
shown in Fig. lb. During a growth run, the furnace
temperature at each thermocouple location was held
2. The vertical Bridgman furnace
A six zone vertical Bridgman furnace (Fig. l)
used for the commercial production of large (up to
3.5 kg) CdZnTe ingots was used for an investigation
of the eddy current sensing of vertical Bridgman
crystal growth. The furnace, shown in Fig. l a, consisted of an assembly of three modular Marshall-type
tube furnaces (outer diameter 0.36 m and assembled
height 1.32 m) manufactured by Thermcraft Inc. The
furnaces utilized resistance heating by internally exposed 0.204 inch diameter Kanthal wire elements
helically wound at three turns per inch and had a
maximum service temperature of 1316°C. A cylindri-
200
(a)
339
...................
(b)
L
i
Quartz
ampoule
Tel
l
Rpe
thermoI couples
15o
TC7
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posit~. . . . . . . . . . . . . . . . .
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c4
501
700
• AmpouleTemperatureProfile
[] FurnaceZone Set Points (TCl-6)
• FurnaceWallTemperature('rc7o8)
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800
900
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Temperature
imensions in
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~200
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Fig, l, (a) Schematic diagram of" six zone vertical Bridgman furnace. (b) Furnace temperature profile and measured temperatures within an
empty ampoule.
K.P. Dharmasena, H.N.G. Wadley / Journal of Cr3"stal Growth 172 (1997) 337-349
340
constant while the furnace was translated vertically
through the movement of a lead screw driven by a
Compumotor Model SX-6 stepper motor. The position of the furnace was conveniently referenced by
the location of a pointer (attached to the moving
furnace) relative to a fixed measuring rule attached
to the supporting framework, Fig. l a.
Prior to each growth run, the axial temperature
profile along the furnace axis was measured with an
array of nine R-type thermocouples spaced 5.1 cm
apart along the central axis of an empty quartz
ampoule. Fig. lb shows an example of this profile
(together with the eight furnace thermocouple temperatures) for a pointer position of 14.9 cm. Obviously, the axial temperature profile within the stationary ampoule will be dependent on the position of
the furnace which varies with time during a growth
run. To characterize this, the furnace was first moved
to its start position (a pointer reading of 5.1 cm), a
R-type thermocouple was then positioned at the bottom of an empty ampoule and a temperature mea-
112o I
,,00 y ; / 7
1o2o
I
1000 "
0
Furnace
position
:
(cm)
i
i
....
i
!°
i
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2 4 6 8 1'0 1}2 14 16 1'8
Distance from inside ampoule tip (cm)
20
e ee'Le e~®
*
type thermocouple
t
,>o ~. ®~ Quartzampoule
Fig. 2. Measured temperature profiles inside an empty ampoule
for varying positions of the furnace.
surement made once thermal equilibrium had been
achieved. The thermocouple was then raised 25.4
mm to a new axial location and a new reading
obtained. This process was repeated until a distance
of 178 mm (which covers the ingot lengths typically
grown in this furnace) had been profiled. After the
measurements were completed with the furnace at its
start position, the furnace was moved upwards by
25.4 mm to a new location and a new axial temperature profile measured as before. These temperature
measurements were repeated until the full furnace
translation used for the growth runs had been covered. Fig. 2 shows these temperature profiles together with the location of the sensor relative to the
ampoule tip. This data is sufficient to characterize
the temperature within the region of an ampoule
interrogated by the sensor.
3. Sensor design, measurement methodology, and
calibration
The basic sensor design analyzed in earlier studies
consisted of a seven turn primary solenoid and a
single turn secondary of slightly smaller radius located midway along the primary's length. To minimize perturbations to the temperature profile of the
furnace, the two eddy current sensor coils were
wound on the exterior and interior surfaces of a
section of the alumina liner that is normally located
in the annular space between the furnace walls and
the ampoule containing the sample, Fig. 3. This
enabled the installation of the sensor inside the furnace without significantly perturbing the thermal environment during the growth runs. The liner assembly consisted of three separate alumina tube pieces
recessed as shown in Fig. 3 for ease of insertion and
removal of the sensor. Seven turns of 18 gauge
platinum wire with a 6.35 mm spacing were used for
the primary (driver) coil. The " p i c k u p " coil consisted of a single turn of 30 gauge platinum wire
centered on the primary coil. In order to constrain
the movement of the wires during heating/cooling, a
high temperature cement (Saureisen Cement No. 8)
was applied to both coils.
The detailed operating principle and analysis of
the two coil sensor has been reported elsewhere [42].
Briefly, a continuous signal to the primary coil was
K.P. Dharmasena, H.N.G. Wadley / Journal of Crysta I Growth 172 ( 1997) 337-349
341
127
Insule
le
)oule
Secondary
(absolute pick.
ure
Alumi
.............
lie ~- O 5018~
I~
(
~ 63.5
~ 76.2
All dimensionsin m m .
)1
)
Fig. 3. A two coil eddy current sensor integrated into the alumina liner of a Bridgman furnace,
provided by the variable frequency oscillator within
a Hewlett Packard HP4194A impedance analyzer.
This signal was amplified with a Model 25A100,
Amplifier Research Inc. amplifier to increase the
field strength of the primary coil. Frequency dependent gain (G) and phase (4)) measurements for the
two coil system were used to calculate the real and
imaginary components of the sensor's transfer
impedance [43]. To emphasize the effects of the
sample on the transfer impedance, the impedance
was normalized by that of the empty (i.e. no sample)
sensor. These "empty sensor" gain/phase measurements (Go/eho) were made at the growth temperature since they depend on the (temperature dependent) dimensions of the sensor.
When an eddy current sensor is installed within a
crystal growth furnace, the eddy current sensor interacts with the sample and surrounding furnace. In
addition, the long lead lengths between the sensor
coils and the measurement instrumentation potentially introduce "anomalous" contributions to the
measured impedance [43]. Thus, a calibration of the
sensor was performed using a 75 mm diameter, 152
mm long silicon cylindrical sample (Lattice Materials Corporation) contained in a quartz ampoule within
the growth furnace, Fig. 4a. Four-point probe resistivity measurements performed on the silicon ingot
indicated a conductivity of 2994 S / m [45]. Standard
eddy current analysis methods [46] were applied to
an experimental multifrequency impedance curve
(Fig. 4b, obtained with the silicon ingot) and led to a
deduced electrical conductivity of 2150 S / m for a
test frequency near the knee of the normalized
impedance curve ( ~ 267 kHz).
The standard analysis technique to deduce electrical conductivity assumes infinitely long samples and
solenoids. To determine and correct for the effects of
both the finite sample (i.e. edge effects) and the
finite coil (i.e. fringe field effects) lengths, a finite
element model was created for a 75 mm diameter,
152 mm long silicon sample located in a seven turn
sensor of the geometry used here (Fig. 4a). The
342
K.P. Dharmasena, H.N.G. Wadley / Journal of Crystal Growth 172 (1997) 337-349
(a)
~102
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) )
0 92
F
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"~OOkHz
t
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Calculated
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~ 1 267kHz
0.8
,t,ook.z
1 7 500kHz
E
0.7
O~7ookHz
1MHzdt~ 850kHz
/1MHz
N
"--"~-~
0
Z
0.6
2MHzI~ 2MHz
~;3MHz
t!
l/
Alumin~
line
0.5
0.0
Mullite base
All dimensions in ram.
3MHz rt
I
I
0.1
0.2
0.3
Normalized Real Z Component
Fig. 4. Measured and calculated sensor responses for a silicon calibration sample.
transfer impedance of the sensor was calculated at 11
selected frequencies between 50 kHz and 3 MHz
with a sample electrical conductivity (specified in
the finite element model) of 2994 S / m . The standard analysis method when applied to synthesized
impedance data led to a recovered electrical conductivity of 2200 S / m very close to that measured with
the eddy current sensor. Thus, the finite lengths of
sensor/sample result in a ~ 26% underestimation of
the true conductivity when a "standard" conductivity analysis [46] is used. A correction factor was
therefore applied to the conductivities deduced during the monitored growth runs.
4. Growth experiments
Two crystal growth experiments (JME runs #862
and #869) were monitored with the eddy current
sensor. The samples were prepared from pieces of
pre-compounded CdZnTe material previously synthesized using high purity grade (99.9999% or better), elemental Cd, Zn and Te. For the first run
(#862), a charge weighing 3020 g and having a
4.0% (atomic) Zn content was used. For the second
experiment (#869), the charge weighed 2948 g and
contained 4.25% (atomic) Zn. The slight difference
in Zn concentration has a negligible effect upon the
electrical conductivity. About 3.8 g of excess Cd was
added to the charge to compensate for Cd evaporation into the ampoule's large free volume. The charge
material was contained in a 72.5 mm inner diameter
pyrolytic boron nitride (pBN) crucible (conically
shaped at one end), placed within a 76 mm inner
diameter quartz ampoule.
A seventeen segment furnace heating, translation
and cooling schedule was programmed in the Micricon process controller for each growth run. The
first six segments caused the furnace temperature to
be increased to set point values of 1137, 1133, 1133,
1020 and 800°C in zones 2 through 6 over a period
of approximately 4 h. During this period, the temperature in the cadmium overpressure region (zone # 1 )
was simultaneously increased to a set point of 825°C.
Following a two hour soak period (segment #7), the
furnace was initially translated upwards using an
K.P. Dha rmasena, H.N.G. Wadley / Journal of C©'stal Growth 172 (1997) 337-349
interrupted growth strategy, adopted with the intention of controlling undercooling and to help initiating
nucleation at the early stages of the run (Figs. 5a and
6a). This consisted of two 13.3 h segments ( # 8 and
#10) at a translation rate of 1.475 r a m / b , each of
which was followed by two 6.0 h stationary periods
(segment # 9 and #11, respectively). The remaining
growth occurred in segments 12 and 13 over a period
of 76.7 h during which time the furnace was moved
by a further 113 mm.
After the growth period, segment #14 allowed
the temperature of zones 3 and 4 to initially cool to
1090°C over a 4 h period. The furnace was then
343
translated downwards (during segment #15 over a
21 h period) to an annealing position with the temperature reduced further to 1025°C. With the furnace
stationary at the end of segment # 15, a controlled
cool down to 825°C was scheduled over 20 h (segment #16), followed by a 10 h cool-down period to
625°C (segment #17) before the furnace power was
turned off for natural cool down to room temperature.
During the crystal growth experiments, eddy current sensor gain/phase data were collected (from the
beginning of segment # 8 ) at 101 logarithmically
spaced test frequencies between 50 kHz and 6 MHz.
Stationary
1.4wlF75o.o 1.444750.0~-~ TranslattonRateUp(mm/h)=
8
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0.6
E
0.4
0
1200
20
40
.
60
.
BO
.
100
120
140
160
180
.
Temperature at point A
("3
. . . . . . . . . . . . . . . . .
1100
~....
Temperature at ~dn~
fi . . . . . . . . .
1000
E
900
~1
800
0
20
I
I
I
40
60
80
100
120
140
160
180
40
60
100
120
140
160
180
"~'20,000
v
~15,000 -
~ 10,000
-
8
"~ 5000
0
"",
-
I
0
20
80
Time
(hrs)
Fig. 5. (a) Measured impedance response at four frequencies for run #862 during crystal growth and cooling. (b) Furnace temperature
variation during crystal growth and cooling. (c) The "apparent" conductivity variation during crystal growth and cooling.
344
K.P. Dharmasena, H.N.G. Wadley / Journal of Costal Growth 172 (1997) 337-349
A total of 256 samples were averaged with an integration time of 5 ms for each sweep frequency
resulting in approximately a five minute data collection period. Due to the slow furnace translation rate
(1.475 ram/h), the data were collected and downloaded to a personal computer once every 10 rain
throughout the monitored growth and cooling periods.
Post-growth analysis on the two ingots from runs
#862 and #869 were performed [47] and revealed
infrared transmission values > 60%. Te precipitates
of < 2 and < 7 /.Lm and defect density (EPD)
counts of ~ 3 × 104 and ~ l × 105 cm 2 were
obtained in ingots #862 and #869, respectively. For
ingot #862, zinc concentration values of 4.17% and
3.3% were observed near the head and tail regions.
variation deduced from the measured impedance data
was then corrected for the finite length sample/coil
effects (from the finite element modelling study) and
plotted in Fig. 5c as the "apparent" conductivity.
We use "apparent" because the conductivity observed during the time period when the sensor interacted with both solid and liquid is ill-defined.
Fig. 6a-6c show the results obtained from the
second experiment. The starting position and furnace
translation rate were the same as for the first run.
The impedance and conductivity changes and their
trends observed from this experiment were very similar to the first experiment. The growth period was
extended to 130 h to compensate for a time period
(during segment #12) when the furnace had not
translated. It was also possible to monitor the annealing segments more fully; cooling data for this run
was obtained over the longer period of 46 h.
5. Results
5.1. Melt characterization
The complex normalized impedance was calculated from the gain and phase data at each measurement frequency. Fig. 5a shows the imaginary component of impedance (normalized by that of the empty
sensor at the growth temperature) for four frequencies as a function of time for the first experiment
(run #862). The time axis began when the furnace
commenced its upward translation from its 5.1 cm
start position (i.e. the start of segment #8). For run
#862, the growth period was 115 h and was followed by a cool-down period of approximately 26 h.
Using the furnace temperatures and the profiling
data of Fig. 2, the temporal variation of the temperature near the sensor was estimated. Fig. 5b shows the
time variations of temperature near the furnace liner
(where the sensor was located) and at the center of
an empty ampoule. This latter temperature is of
course only an estimate of the exact temperatures
within the sample and depends on the thermal transport properties of the solid and liquid. For low
thermal conductivity materials like Cdi_~Zn.,Te,
significant radial temperature gradients are expected
to be present in the large diameter boules used here.
From the time-varying complex impedance data,
the variation in the "nominal" conductivity was
calculated using a standard (infinite length
sample/infinite length sensor) eddy current data
analysis [46]. The "nominal" electrical conductivity
The results of Figs. 5 and 6 show that the change
of state from a liquid to a solid causes an attendant
decrease in electrical conductivity and results in an
increase in the imaginary impedance component towards unity (the empty sensor's value) for all of the
test frequencies. During the first 60 h of furnace
translation, the high frequency imaginary impedance
component was around 0.6 for both samples, consistent with the sensor's interrogation of a relatively
good electrical conductor. The changes in impedance
throughout this first 60 h were relatively small,
suggesting that the liquid's conductivity changed
only moderately and the liquid-solid interface was
too distant from the sensor to be detected. Finite
element modelling results also indicated that the
sensor interacted only with the liquid in this configuration. Thus, we conclude that the sensor "sampled"
only the liquid state and the data can therefore be
used to infer the liquid's electrical conductivity.
The liquid conductivity of the charge at the starting furnace location was found to be around ~ 18 000
S / m for both of the growth runs. This value of
conductivity is significantly higher than that expected (7200-8000 S / m ) for a stoichiometric
Cd0.96Zn0.04Te melt even if it has been heated 3 0 40°C above its melting temperature [39]. Investigations of the effects of melt stoichiometry upon the
K.P. Dha rmasena, H.N.G. Wadley / Journal of Crystal Growth 172 (1997) 337-349
345
Stationary
1.475 0.0 1.475
Translation Rate Up (mm/'h) = 1.475
0
|14|
Segment Number= 12,13
CL
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CL
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20
40
60
80
100
120
140
160
180
1200
....
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|~ ~
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O
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1000 ~
r',
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,~'-------
A
.
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.........
U !
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900 :
t'-
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800
20
40
60
80
100
120
20
L
40
I
60
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80
t
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[
120
140
160
180
140
160
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"~ 20,000
03
~
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~
10,000
o
eo
5000
'~
0
0
Time
=~'~
(hrs)
Measured impedance response at four frequencies for run #869 during crystal growth and cooling. (b) Furnace temperature
variation during crystal growth and cooling. (c) The "apparent" conductivity variation during crystal growth and cooling.
Fig. 6. (a)
electrical conductivity of binary Cd-Te and ternary
Cdj_~Zn~Te alloys have indicated significant increases in conductivity for both Cd-rich and Cd-depleted melts [39,40]• The observation of an initially
high conductivity here strongly suggests the existence of a non-stoichiometric melt but the data alone
cannot distinguish between either Cd rich or Cd
depleted. However, observations of tellurium precipitates after growth [47] in material grown in this
furnace using similar growth run histories is consistent with a Cd-depleted melt.
The melt appeared to remain non-stoichiometric
for much of the growth. For example, after about 60
h, the electrical conductivity had only decreased to
~ 12000 S/re. It is therefore concluded that the
liquid was significantly depleted in Cd from the start
of furnace translation until at least the time when the
solidification front reached the sensor.
5.2. Interface characterization
As the liquid-solid interface approached the sensor (after ~ 6 0 h for run # 8 6 2 and ~ 7 5 h f o r r u n
#869), a gradually increasing fraction of the low
conductivity solid appeared in the sensor's "field of
view" and the imaginary impedance was observed to
346
K.P. Dharmasena, H.N.G. Wadley / Journal of Crystal Growth 172 (1997) 337-349
rise for all of the frequencies measured, Figs. 5a and
6a. This was consistent with the behavior predicted
using finite element modelling in which the greatest
change of impedance occurs when the interface
passes roughly through the center of the sensor [44].
The impedance data exhibited inflection points
around 84 h after the start of furnace translation for
run #862 and therefore roughly indicated the time of
passage of the solid-liquid interface through the
central region of the sensor. A time delay in the
occurrence of the inflection point was observed in
the second experiment (run #869). This was caused
in part by the unintended time interval during which
the furnace had not translated in segment #12. As a
result, the interface appeared to have passed through
the sensor after about 92 h (Fig. 6a). As the interface
moved upwards away from the sensor, a decreasing
fraction of the liquid and an increasing fraction of
the solid were sampled, and the impedance approached an asymptote determined by the conductivity of the solid material.
The time at which the inflection point was observed has been predicted to depend on the interface
location (relative to the sensor, h), its curvature
(defined by a convexity parameter, 0 = Z/D, where
Z is the axial displacement of the interface at the
center relative to its position near the crucible wall,
and D is the crucible diameter), and the test frequency [44]. The modelling study indicated that for
intermediate frequencies, the time at which the inflection point would be observed increases as the
curvature changes from convex to flat, to concave.
The modelling study revealed that the inflection
points at higher frequencies became more independent of the interface shape and converged to a
position that corresponded to near alignment of the
outer edge of the interface with the sensor's midpoint. This phenomenon potentially enables the (interface shape independent) determination of the location and thus the growth rate of the interface. Once
the time at which the interface was located at the
center of the sensor was determined (h = 0), the
relative large shifting of the inflection points at
lower frequencies could then be used to estimate the
shape of the interface (convex, concave or flat).
Fig. 7a and 7b show the frequency dependence of
the inflection point time for runs #862 and #869,
respectively. From the high frequency data, the time
100
. . . . . . . .
(8)
Run
I
. . . . . . . .
I
. . . . . . . .
#862
90
-ff
{D
80
I--
7°t
_.
Timeestimated
from
_ . . . . . . . . . .
f u r n a c e t r a n s l a t i o n rate
60
,
100
,
,
, ....
. . . . . . . .
(b)
Run
I
,
I
. . . . . . . .
,
,
, , ,,,I
,
I
,
,
.....
. . . . . . .
#869
Time, interface
90 -~o~t,,d ;t ;
r-
;
,
,
/
~
Time estimated from
v
80
- f-umace translationrate
. . . . . . . . . . . . . . . . . .
.E
I--
70
60
10
i
i
i
i r iJi]
i
i
i
i
i Jill
105
106
i
b
i
i
i ,,i
10
Frequency (Hz)
Fig. 7. (a) Frequency dependence of the time appearance of the
inflection point for run #862. (b) Frequency dependence of the
time appearance of the inflection point for run #869.
at which the interface was located at the center of the
sensor was found to be ~ 8 4 and ~ 9 2 h for run
#862 and #869, respectively. If it is assumed that
there is no delay in nucleation upon the start of
translation, that the interface was flat, and that the
movement of the interface (i.e. the growth rate)
equalled the furnace translation rate, the time taken
for the interface to reach the position of the sensor
would be 66 h for the first experiment (run #862)
and 81 h for the second (run #869). These are
K.P. Dharmasena, H.N.G. Wadley / Journal of Crystal Growth 172 (1997) 337-349
significantly less than those measured (84 and 92 h
respectively). The difference in the estimated and
actual times could be due to (1) a growth rate not
equal to the furnace translation rate, (2) a non-planar
interface shape and (3) a delay in the onset of
nucleation as a result of liquid supercooling. If the
third possibility is discounted and we assume a shape
with the convexity deduced below, the eddy current
observed times for the passage of the interface
through the sensor imply actual growth rates of
1.105 m m / h for the first experiment and 1.244
m m / h for the second. In previous experimental work
with CdTe, growth rates of less than 35% of the
translation rate have been reported [48]. The rates of
1.105 and 1.244 m m / h are less than the furnace
translation rate (1.475 r a m / h ) and so solidification
occurred lower in the furnace than anticipated.
Having determined the moment when the interface was located at the sensor's center, it is possible
to use the result from the previous modelling study
[44], to determine the interfacial curvature. Fig. 8
plots the position of the inflection point (relative to
the interface location) against frequency for the two
experiments, compared with the calculations done
for the three interfaces in the modelling study [44]. It
is apparent from this data that the interface curvature
lay between the convex and flat cases modelled. The
low frequency data for both growth runs was similar
15.0
........
J
........
I
100
8 = - 0.333
~
5.0
R u n #869
347
indicating a convexity of about 0.167. Small differences in the high frequency (small skin depth) eddy
current behavior of the samples are indicative of a
greater flattening of the interface near the ampoule
wall for run #869. The recovery of a more exact
shape of the interface requires a detailed multifrequency inverse analysis of the impedance data.
Previous modelling work has shown that for material systems with liquid : solid thermal conductivity
ratios (kJk~) greater than one, the interface shape is
concave in the presence of a uniform temperature
gradient. However, the interface could be made convex by reducing the temperature gradient above the
interface a n d / o r increasing the temperature gradient
below the interface [48-50]. Evidence here of a
non-stoichiometric melt suggests solidification occurs at a lower temperature than the 1099-1100°C
associated with the liquidus of stoichiometric
Cdo.095Zn0.045Te. The drop in melt temperature must
move the interface upwards within the furnace into
the region of shallower temperature gradients and
therefore tends to make the interface more convex
[51,52]. The lower than expected solidification temperature and the convex interface shape should have
resulted in the interface moving past the sensor
sooner than was assumed in our initial estimation of
the growth rate (based on a flat interface propagating
at the furnace translation rate). However, the multifrequency inflection point analysis, Fig. 7, indicated
a longer than expected time for the interface to reach
the sensor. The most likely explanation for this is an
initial delay in the onset of nucleation associated
with liquid supercooling. An eddy current sensor
placed at the ampoule tip could resolve this important issue [53].
5.3. Solid state annealing/cooling
0.0
Run #862
9=0.0
o.
~"
-5.0 -
~10~0
8 = +0.333
-0.333 ! "So[~d
I
-15.0 ~
10
10 5
Frequency
10 6
10 7
(Hz)
Fig. 8. Comparisons of experimental and calculated variations of
the inflection point position with frequency.
Proper post-growth annealing/cooling assists in
the homogenization of the Zn distribution and controls the dislocation density and the concentration of
Te precipitates. The dislocation density and number
of precipitates in a grown boule are affected by the
cooling rate and the overall cooling period. During
cool down, the impedance data collected from the
eddy current sensor can be used to evaluate the
conductivity of the cooling crystal and assess its
potential for characterizing some aspects of postgrowth phenomena.
348
K.P. Dharmasena, H.N.G. Wadley/Journal ~['Co,stal Growth 172 (1997) 337 349
For the first experiment, a solid conductivity of
923 S / m was observed at the end of growth (segment #13), which further decreased to 791 S / m
during a four hour stationary furnace segment ( # 14)
when the furnace zone temperatures in zones 2
through 4 were reduced by approximately 48°C. In
the next segment (#15), the furnace was moved
down to an annealing position, while the temperatures in zones 2 through 5 were decreased further by
approximately 53°C. During these two segments, the
temperatures in zones 1, 5 and 6 were maintained at
825, 1020 and 800°C, respectively. Data analyzed
from the second experiment (run #869) revealed
similar results. In this case, a post-growth conductivity of 839 S / m was observed, which decreased to
712 S / m during the initial four hour cooling period
(segment # 14).
An anomalous increase in sample conductivity
has been detected during segment #15 when the
furnace was moved to its annealing position. In
conductivity experiments performed with samples
having different Zn contents in a quasi-steady state
furnace, a slight anomalous increase in conductivity
after solidification was initially detected (i.e. within
40°C of solidification) for Cd0.%Zn0.04Te and was
then followed by a gradual decrease in conductivity
with temperature during the remaining cool down
[39]. Modelling studies of the Zn segregation has
revealed concentrations varying from ~ 5.8% (near
the first to freeze region) to 2.8% (near the top of the
boule) [25]. One possible explanation for the rise in
conductivity during post-growth cool down is the
homogenization of Zn by diffusion, which results in
a more uniform concentration closer to 4% with an
increased conductivity. In run #869, with the furnace stationary, segment #16 allowed a controlled
furnace cool down to 825°C during which time a
gradual decrease in conductivity was observed consistent with the decrease in temperature.
6. Summary
Detailed experiments have been conducted with
an eddy current sensor in a vertical Bridgman furnace to better understand the CdZnTe growth process and to obtain information about the solid-liquid
interface. From the measured impedance data, the
sensor has demonstrated the capability of providing
significant new information about the melt composition and has revealed that growth occurred from a
non-stoichiometric (probably) Cd-depleted melt. An
analysis of the high frequency data has enabled the
interface's location to be deduced and has revealed
that the growth rates were lower than the furnace
translation rate so that solidification occurred in a
colder section of the furnace where the temperature
gradient was steeper than anticipated. Lower frequency data revealed that growth occurred with a
less than ideal convex interface shape. Post-growth
monitoring of the cooling process has enabled the
electrical conductivity data of the solid to be monitored. An "anomalous" increase in conductivity was
observed as the temperature was decreased from the
solidification temperature.
Acknowledgements
This work has been performed as a part of the
research of the Infrared Materials Producibility Program conducted by a consortium that includes Johnson Matthey Electronics, Texas Instruments, I I - V I
Inc., Loral, the University of Minnesota and the
University of Virginia. We are grateful for the many
helpful discussions with our colleagues in these organizations. We would also like to thank Art Socha
of Johnson Matthey Electronics for providing data
from the post-growth characterization of the ingots.
The consortium work has been supported by
A R P A / C M O under contract MDA972-91-C-0046
monitored by Raymond Balcerak.
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