j. . . . . . . .
ELSEVIER
CRYSTAL
GROWTH
Journal of Crystal Growth 172 (1997) 323-336
Eddy current determination of the electrical
conductivity-temperature relation of Cdl_xZn xTe alloys
Haydn N.G. Wadley *, Bill W. Choi
Intelligent Processing of Materials Laboratory, School o["Engineering and Applied Science, Unicersity of Virginia, Charlottesville, Virginia
22903, USA
Received 21 August 1995; accepted 17 April 1996
Abstract
A multifrequency eddy current sensor has been installed in a vertical Bridgman furnace and used to measure the electrical
conductivity of Cd l_XZn,Te alloys (for x = 0, 0.045 and 0.08) as a function of temperature during heating and cooling
through the melting transition. The conductivity of the x = 0.0 and 0.08 samples increased exponentially with temperature
up to the melting point. A 4 - 6 fold increase of conductivity accompanied melting, sufficient for the proposed eddy current
sensing of liquid-solid interfaces in this materials system. Above the melting point, the liquid phase conductivity again
exponentially increased with temperature. The x = 0.045 sample exhibited similar behavior except in a ~ 30°C interval
immediately below the melting/solidification transition on heating and cooling. In this temperature interval, an "anomalous"
decrease in conductivity with an increase in temperature was repeatedly observed. Zn has been found to depress the liquid
conductivity while that of the solid (near its melting point) exhibited a weak maximum in conductivity at x = 0.045. These
observations raise the possibility of eddy current monitoring of melt composition and segregation/homogenization behaviors
during post-solidification annealing.
1.
Introduction
Single crystal Cd 1_ ,Zn~Te ( x = 0.045) solid solution alloys are used as substrates for the epitaxial
growth of Hg I - ~Cd ~Te thin film infrared focal plane
array (IRFPA) detectors [ 1]. As detector manufacturers seek to increase the size and number of IRFPAs
per substrate, a demand has been created for large
area substrates with low defect densities, uniform
distributions of Zn and high infrared transmission
coefficients. Either a vertical or horizontal variant of
the Bridgman method can be used for the growth of
this substrate quality material [1-3]. Unfortunately,
* Corresponding author.
both the seeded and unseeded growth of vertical
Bridgman grown material is usually multigrained
with significant Zn segregation (0.02 < x < 0.07), Te
precipitation and a sometimes high density of dislocations [3,4]. In spite of many experimental efforts to
investigate the relationships between material purity,
the controllable growth parameters and the resulting
m a t e r i a l c h a r a c t e r i s t i c s [5,6], the y i e l d o f
C d l _ ~ Z n , Te of a quality suitable for large area
substrates remains disappointingly low ( < 10%).
Since much of the poor yield is directly associated
with the growth process (e.g. melt stoichiometry,
solidification velocity, interface shape, temperature
gradients, cooling rate, etc.), intensive efforts are
under way to improve this technology.
0022-0248/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved
PII S0022-0248(96)00497-6
324
H.N.G. Wadley, B.W. Choi / Journal qf CP3'stal Growth 172 (1997) 323-336
One approach involves the in situ monitoring of
the growth process with multifrequency eddy current
sensors [7-13]. The potentially large difference in
electrical conductivity of many solid and liquid
semiconductors [7,14,15] has led to the proposed use
of eddy current sensors for monitoring the liquidsolid interface during crystal growth [7,8,12]. The
relationships between an eddy current sensor's frequency response, the electrical conductivities of the
solid/liquid and the position/curvature of the liquid-solid interface are complex. Recent electromagnetic finite element modelling has identified several
concepts to recover the interface shape during vertical Bridgman growth [8,12], and a companion paper
[16] explores their application to Cd0.%Zn0.0aTe. The
companion study has also revealed potential applications of eddy current sensors for monitoring the
composition of the liquid prior to solidification and
observing segregation related phenomena in the solid
during post-growth annealing. In order to realize the
potential of eddy current sensing, reliable electrical
conductivity data as a function of temperature and
Zn concentration are needed for both the solid and
liquid phases of Cdl_,Zn.,Te alloys over the range
of Zn concentrations and temperatures likely to be
encountered during vertical Bridgman growth.
Comparatively little data relating the electrical
conductivity of CdTe to temperature exist for the
elevated temperatures encountered in crystal growth,
and no data have been published concerning the role
of Zn upon the conductivity of Cd~_ ~Zn,Te alloys
at high temperature. This has arisen because of the
difficulty of making ohmic contacts with semiconductors containing volatile elements like Cd. The
temperature and composition dependence of the electrical conductivity of equiatomic CdTe has been
investigated by Glazov and coworkers using an electrodeless induction method [ 14,15].
Glazov et al. observed the electrical conductivity
of the solid to gradually increase with temperature
up to a value of a few hundred S / m in the 10001040°C temperature range. An abrupt rise in conductivity commenced at about 1045°C. During this transition, the conductivity increased by about one order
of magnitude and was then followed by a non-linear
variation of conductivity with temperature between
1045 and l l00°C. In other semiconductors [15], the
abrupt rise in conductivity normally accompanied
melting, but in the Glazov et al. experiment it occurred more than 40°C below the accepted melting
point of 1092 _+ I°C for equiatomic CdTe [16,17].
Several factors may have contributed to the anomalously low temperature where the conductivity discontinuity was observed. Glazov et al.'s thermometry may have been inaccurate because of the small
sample size and the potentially large errors associated with contact thermocouple measurements. A
second possibility is that the composition tested may
not have been that of equiatomic CdTe due to the
high vapor pressure of Cd near the melting point and
the significant free volume present in their ampoules
[18]. It is also unclear if the trends in conductivity
reported by Glazov et al. [14,15] on heating would
also occur during cooling.
In this study, the electrical conductivities for both
solid and liquid CdTe, Cd095sZn004sTe and
Cd092Zn00sTe contained in quartz ampoules with
very small free volumes have been deduced from
multifrequency eddy current sensor data collected in
a multi-zone furnace assembly. The temperature and
Zn concentration dependence of the electrical conductivity has been obtained for the solid and liquid
phases between ~ 650 and 1150°C.
2. Experimental procedures
2.1. Eddy current measurement technique
Eddy current testing has become a widely used
method for non-destructive materials evaluation and
inspection [19-21]. |t enables quantitative measurements of material properties such as electrical conductivity or magnetic permeability, the dimensions
of conducting samples via lift-off effects, as well as
the detection of crack-like discontinuities in metals.
The principle underlying the eddy current method is
electromagnetic induction [20,21]. Fluctuating electromagnetic fields are created within the test object
by passing an alternating current through a nearby
primary (driving) coil. These fluctuating electromagnetic fields are used to induce eddy currents in the
test object. The eddy currents in turn create a secondary electromagnetic field which perturbs that of
the primary coil. This can be sensed either as a
change in the impedance of the primary coil (the
H.N.G. Wadley. B. W. Choi / Journal qf Co'stal Growth 172 (1997) 323-336
1.0
'~\
E
(3)
"'%,(s
= 1.2MHz
,,
0.9 -
......-t(~.
~ ~.7
!
-
,,
E
o
\
(..)
N
\\
,
0.8--
--
~r'a'fL = " 2 M H z
IE
0.7-
-
~'
325
where X(c~) is a reference number that has been
published in tabulated form [19,20]. Best precision is
obtained for intermediate values of o~ (19°_< a_<
770), where the electromagnetic skin depth is about
half the sample radius. Values of X(o~) for an
infinite cylindrical sample contained in the uniform
field of a long solenoid are also well fitted by a
polynomial expression:
X(oe) = 12.083 - 0.5944c~ + 1.460 × 10 2oe2
/
N
o
z
- 1.686 × 10 40~3 q- 7.193 × 10-70~ 4.
/
/
0.6-
(2)
/
//
- ....
0.5
0.0
Liquid (~t = 5,873S/m)
Solid (~, = 1,377S/m)
I
0.1
0.2
0.3
N o r m a l i z e d Real Z C o m p o n e n t
Fig. 1. Typical normalized impedance diagram for an eddy current
sensor containing a solid or liquid semiconducting cylinder whose
conductivity increases upon melting. If the angle o~ is measured at
a specific frequency, f, then provided the sample radius, a~ and
magnetic permeability, #, are known, the electrical conductivity,
o-, can be obtained using precalculated values of X(o~).
basis of single coil test methods, e.g. Ref. [13]) or by
monitoring the emf induced in a nearby secondary
coil (the two coil method analyzed in Ref. [8]). The
eddy current magnitude is directly affected by the
test material's electrical conductivity, its magnetic
permeability, and the test frequency. The non-contact
measurement of impedance of the eddy current test
coil at frequencies where the electromagnetic skin
depth is about one-half the sample's radius then
enables the sample's electrical conductivity or magnetic permeability to be deduced with relatively good
accuracy [20,21 ].
Work by Libby [20] and Forster [21] showed that
if a long cylindrical sample is contained in a long
solenoid (i.e. in an axially uniform field), an
impedance curve of the type shown in Fig. 1 is
obtained. The sample's electrical conductivity, o', its
magnetic permeability, #, the sample radius, a, and
the angular test frequency, o), are related to a frequency dependent angle, c~, through
To compute a precise conductivity using Eqs. (1) and
(2) requires the measurement of the angle, c~, at
known frequencies, together with knowledge of the
sample radius, a, and its magnetic permeability, p,.
For non-magnetic semiconductors, the free space
permeability (4~-x 10 7 H / m ) can be used for ~,
and a can be obtained by a combination of an
ambient temperature physical measurement coupled
with a calculation of thermal expansion. In the solid
state, the sample's diameter will be governed by the
thermal expansion of the Cd I ~Zn, Te sample. However, in the liquid state the diameter will be defined
by the internal diameter of the quartz ampoule used
to contain the charge. Coefficients of thermal expansion for both materials are reasonably well established [22]:
~CT = 4.865 + 1.85537 × 10 3T,
(3)
sCo = 0.403 + 5.466 × 10-4T - 4.623 X 10 7 T 2 ,
(4)
where ~CT and ~Q are the thermal expansion coefficients (in units of 10 6 K - l ) for CdTe and quartz
respectively and T is the absolute temperature. The
sample diameter can also be obtained from high
frequency eddy current measurements provided the
measurement system can attain skin depths that are
small in comparison with the sample radius, a [16];
but this is unlikely for poorly conducting solid
Cd t ,Zn ,.Te alloys. The CdTe sample's diameter for
the data shown in Fig. 1 was 28.5 mm and so the
deduced conductivity of the solid was o-~ = 1377
S / m , while that of the liquid was o-/= 5873 S/re.
326
H.N.G. Wadley, B. W. Choi / Journal of Co'sml Growth 172 (1997) 323-336
phase (g,4~) remeasured. The real and imaginary
components of the normalized impedance, Z, are
then given by
g
R e ( Z ) = - - s i n ( 4~ - d~0),
go
g
I m ( Z ) = - - c o s ( ~ b - ~b0).
go
(5)
(6)
2.3. Sensor design for L,ertical Bridgman growth
~
Sample
Electrical conductivity, c
Magnetic permeability, I.,t
Fig. 2. A schematic circuit diagram of the two coil impedance
measurement system.
2.2. Sensor approach
A two coil sensor technique, Fig. 2, has been used
to obtain impedance curves suitable for determining
the electrical conductivity of Cdl_~ZnxTe alloys. A
primary coil excited by a sinusoidally varying current was used to induce a reasonably uniform electromagnetic field of variable frequency in the sample. A secondary pick-up coil then sensed the perturbations to this field created by the sample. The main
advantage of the two coil eddy current sensor approach is that effects of temperature induced resistance changes to the coils can be minimized by using
a high impedance measurement of the induced secondary coil voltage, ~ , whilst simultaneously monitoring the current flow, 1t,, in the primary coil [16,19].
The gain ( g ) and the phase (4~) of the two coil
system can be conveniently measured with a multifrequency impedance/gain-phase analyzer by monitoring V~ on the analyzer's test channel and I v (via
the voltage drop, VR, across a precision resistor
connected in series with the primary coil) on the
analyzer's reference channel as shown in Fig. 2. To
obtain a normalized impedance curve suitable for
deducing the conductivity via Eq. (1), the gain and
phase difference of these two voltages is obtained for
the empty coil condition, (go and d~0) at each test
frequency for each of the test temperatures. The test
object is then placed in the sensor and the gain and
A schematic design of the encircling two coil
eddy current sensor is shown in Fig. 3 along with a
detail of the furnace geometry in which it was
installed. The sensor windings were wound on a high
machinable alumina ceramic mandrel. Grooves were
machined on this mandrel with the same dimensions
(depth and width) as the winding wires in order to
limit movement of individual coil turns during heating/cooling. 1.02 mm diameter platinum wire was
used for the eight-turn, 50.8 mm long (i.e. four turns
per 25.4 ram) primary coil. 0.25 mm diameter platinum wire was used to wind a four-turn 12.5 mm
long secondary coil. To maximize the potential fill
factor (i.e. the ratio of the sample and secondary coil
areas), the grooves for the secondary coil were machined on the inner surface of the primary coil
mandrel, Fig. 3b. Approximately 0.6 m long Nextel
sleeved platinum lead wires were used to connect the
sensor to two pairs of terminals located at the bottom
of the furnace. Connections to an impedance analyzer were made with a pair of 1.2 m long 50
coaxial cables.
Multifrequency impedance measurements were
performed using a Hewlett Packard 4194A
impedance/gain-phase analyzer. A RF power amplifier was used to increase the primary current Ip and
thus to enhance the voltage signal monitored across a
1 f~ precision resistance in the primary test circuit.
An attenuator was used in the line to the test channel
to prevent overloading of the secondary coil signal.
The multifrequency measurement was automated using a basic program on a personal computer in
conjunction with a program installed in the
impedance analyzer. The program on the analyzer
recorded test and reference channel voltages for 101
logarithmically spaced frequencies between 50 kHz
327
H.N.G. Wadley, B.W. Choi / Journal of Crystal Growth 172 (1997) 323 336
a) Furnace Geometry
b) Sensor~SampleConfiguration
0 127mm
~-~ ~ 36mm----~
30mm "~1
pie
Secondary
furnace
Main
furnace
AluIT
Jary
p) coil
¢
, coil
a eddy
:sensor
Fig. 3. (a) A schematicdiagram of the verticalBridgmanfurnace; (b) detail showingthe sensor configuration.
and 5 MHz. It then calculated the gain and phase
angle difference and the normalized impedance components at each frequency. The basic program activated the m e a s u r e m e n t periodically during
heating/cooling of the sample and stored the
impedance data together with the parametric temperatures. An error analysis methodology for this measurement approach is developed in Ref. [11].
2.4. Calibration procedure
To ensure conductivity values obtained with this
approach are accurate, it is necessary to use values of
obtained near the " k n e e " of the impedance curve,
i.e. 2 0 ° < a < 60 °, where the skin depth is about a
half the sample radius. For low conductivity materials like solid CdTe, this could require the use of high
test frequencies extending to 10 MHz or above.
However, this can introduce other "test circuit"
contributions to the measured impedance and result
in erroneous conductivity values. The finite lengths
of both the sample and the sensor can also perturb
the axial uniformity of the excitation field assumed
for the calculation of X ( a ) . The field can also be
perturbed by conducting components of the furnace
used for high temperature measurements. It is thus
advisable to calibrate the measurement methodology
using standard reference samples of known conductivities spanning the range of values expected for the
test material.
Since the electrical conductivity of solid ( ~ 1000
S / m ) and liquid ( ~ 8000 S / m ) CdTe at the melting
point are relatively low [ 14,15], three ( 111 ) oriented
doped silicon bars with known conductivities (measured by a four-point probe technique) similar to
those of solid and liquid CdTe were used for the
calibrations. The three reference samples (designated
MNl-1861, MPO-5792, JME-31844) consisted of
152 mm long, 28.5 mm diameter mirror grade silicon
cylinders provided by Lattice Materials Co. The
conductivities of these reference samples were then
calculated using the eddy current methodology above,
and compared with the four-point probe measurements. The reference samples were also used to
H.N. G. Wadley. B. W. Choi / Journal o[" Crystal Growth 172 (I 997) 323 336
328
check the test setup in this way before and after each
2.6. Preparation and precompounding of samples
run.
2.5. Temperature profile in furnace
A two-zone 75 mm diameter furnace was used for
the experiments, Fig. 3. The furnace was equipped
with temperature controllers that were able to maintain the temperature set points to better than 0.5°C.
The axial temperature profile of the main furnace
assembly was measured from the tip of an empty
quartz ampoule (of identical diameter to that used
later to contain Cd~ xZn~Te specimens) to the top
of the furnace using a single probe R-type thermocouple as shown in Fig. 4. Temperature profile data
as a function of distance from the ampoule tip were
obtained over the complete range of furnace set point
temperatures used in subsequent experiments. The
maximum axial temperature variation of the region
interrogated by the sensor was + I°C,
The Cd~ ,Zn~Te samples were contained in 33
mm ID quartz ampoules. When Cd containing compounds are in contact with quartz for extended periods of time at high temperature, cadmium meta
silicate (CdSiO~) can form [23]. This can create
defects in the quartz walls and breakage of the
ampoules. To avoid this problem, a thin glassy carbon layer was deposited on the inner surface of the
quartz ampoule. The quartz ampoule was first cleaned
with a 20% HF solution for 10 rain and then etched
in a 70% HCI and 30% H N Q solution for 1 h. It
was rinsed with distilled water, evacuated to below
10 - 4 TOIT and held at 900°C for 4 b. The outside of
the ampoule was subsequently heated with H z/argon
torches and 2-propanol vapor injected into the ampoule until an opaque carbon deposit had formed on
the inner surface. This was finally followed by a
high temperature anneal to vitrify the carbon coating.
200
175
150
E
e',,
125
Eddy current
sensor
O
E 100
E
~
75
e.-.
Q
50
R type
thermocouple
25
Fig. 4. The axial temperature profile within a quartz ampoule near the eddy current sensor location.
H.N.G. Wadley, B.W. Choi/Journal o/Crystal Growth 172 (1997) 323 336
The equiatomic CdTe source material consisted of
a precompounded polycrystal cast ingot grown by
Johnson Matthey Electronics. This was broken into
pieces small enough to fit into the quartz ampoule.
These material pieces were cleaned by sandblasting
(to remove gross surface contamination) followed by
immersion in a solution of 5% bromine in methanol
for 2 rain and then five consecutive rinses in methanol
baths. A total of 600 g of CdTe were loaded into the
carbon coated quartz ampoule and sealed under 10 6
Tort with a very small free volume to reduce the
evaporation of Cd during subsequent high temperature experiments. The Cd0.955Zn0.45Te sample was
prepared from a precompounded polycrystalline ingot using similar procedures to the equiatomic CdTe
sample. The Cd0.92Zn00sTe sample was synthesized
by recycling the equiatomic CdTe sample to which
was added sufficient 99.99995% purity Zn and Te to
reach the target composition.
2.7. Test methodology
The eddy current sensor was installed in a multizone vertical furnace, Fig. 3a. The sensor and test
sample were placed on top of a cylindrical mullite
insulator support assembly. The sample temperature
was measured with two type R thermocouples; one
was located in the annular gap between the quartz
ampoule wall and the inner ceramic preform of the
sensor (thereby shielding it from the direct heat
source); the other was located at the top of the
ampoule. In both cases, the thermocouple was in
physical contact with the outer surface of the ampoule. The data from the lower thermocouple could
be also used to monitor solidification through its
latent heat release.
The electrical conductivity-temperature relationships for the samples described above were measured by first preheating the samples beyond their
melting point to form a single cylindrical sample.
The charged ampoule was then raised to 1122°C,
held at this temperature for 1000 rain to homogenize
the melt, cooled down to 600°C at a rate of approximately 0.7°C/rain, and finally furnace-cooled to
reach room temperature. Gain and phase measurements were subsequently made during reheating from
room temperature to 1150°C and then back to ambient temperature. At low temperatures, the conductiv-
329
ity was only a weak function of temperature, and so
the conductivity was measured every 10°C. However, close to and above the melting point, the
conductivity was measured at I°C intervals. Great
care was taken to ensure that thermal equilibrium
was reached (and maintained) at each measurement
temperature. The ingot was maintained at each test
temperature until the eddy current sensor indicated a
quiescent impedance response. This sometimes involved holding the temperature for up to 10 h (usually during the melting/freezing transition).
3. Results
3.1. Calibration experiments
Since the measured impedance (and therefore the
deduced conductivity) can be affected by the sensor's
interaction with conducting components of the furnace and by impedance contributions from test circuit components, a series of calibration tests were
conducted. Fig. 5 shows measured impedance data at
ambient temperature for the JME-31844 (high conductivity) silicon calibration sample. Two sets of
impedance curves are shown; one corresponded to a
measurement made with considerably shorter cables
1.0
¢-.
(V
¢O
CL
=~,~OikHz
50 kHz ~ 1 2 5
0.9
%
I
n
200 kHz
%
315 kHz
E
o
I
kHz
o
N
0.8
c
0.7
Q
I
92 kHz
~,~"
E
500 kHz
1.25 MHz
2 MHz
(~
.N
0.6
o
Z
0.5
0.4
0.0
JME -31844 sample
~-~"-! 3,15 MHz
%
\
""-o 5 MHz
~ e Measured outside furnace
~
Measured inside furnace
I
i
i
i
0.1
0.2
0.3
0.4
0.5
Normalized real Z component
Fig. 5. A c o m p a r i s o n of the impedance curves for the J M E - 3 1 8 4 4
sample m e a s u r e d outside and inside the furnace.
H.N.G. Wadley, B.W. Choi / Journal q# Co'stal Growth 172 (1997) 323-336
330
Table l
Uncertainties in the impedance components for calibration sample
JME-31844
Frequency
(kHz)
Nominal
Re(Z)
Probable
error in
Re(Z)
Nominal
Ira(Z)
Probable
error in
Im(Z)
50.0
125.6
315.5
500.0
792.4
1990.5
5000.0
0.04882
0.10798
0.16781
0.16169
0.13173
0.06998
0.10406
0.00010
0.00077
0.00039
0.00056
0.00084
0.00156
0.63928
0.99215
0.95683
0.84679
0.77378
0.72250
0.64747
0.50547
0.00033
0.00065
0.00210
0.00313
0.00372
0.03256
5.75525
whilst the sensor was located outside the furnace.
The second corresponded to the situation used for
the high temperature tests with the sensor positioned
in the furnace and connected to the test equipment
with 1.2 m coaxial connecting leads. Fig. 5 shows
that when the sensor and sample were located outside the furnace, a conventional impedance curve
was obtained. However, when the sensor was connected to the analyzer with 1.2 m coaxial cables, a
non-standard impedance curve was obtained. Two
primary differences were seen. At high frequencies
(above 2 MHz), a " h o o k " appeared on the
impedance curve. This originated from the increasing
impedance contribution of the test circuit (particularly its 1.2 m long coaxial cables). Thus, the most
significant consequence of the long leads necessary
for use of the sensor in the furnace is an effective
limit to the upper measurement frequency. At 792
kHz and 2.2 MHz small perturbations to the
impedance response were also observed. These originated from interactions with conducting components
in the furnace. Data collected at these two frequencies were therefore excluded from the subsequent
conductivity analysis.
The gain and phase measurement accuracies for
the empty and sample filled sensor were used in the
error analysis developed in Ref. [11 ] to calculate the
uncertainties in the computed real and imaginary
components. Table 1 shows the calculated uncertainties in the 50 kHz-5 MHz frequency range for the
high conductivity silicon sample and indicates that
the error rapidly increased above 2 MHz. However,
if the operating frequency range is restricted between
50 kHz and 1.2 MHz, the incurred error is approxi-
mately 0.41% of the nominal real impedance and
0.24% of the nominal imaginary impedance. These
errors in impedance were then used to estimate the
uncertainty in the conductivities obtained with the
calibration samples in the test furnace. Fig. 6 shows
plots of the apparent conductivity versus test frequency (and angle c~).
Table 2 shows the conductivities (and standard
deviations) deduced from the results shown in Fig. 6.
Good agreement between the eddy current and 4point probe conductivities was observed when test
data with intermediate a values were used. For each
sample, a range of frequencies (values of ol) was
always present where the conductivity was independent of frequency. In each case, the eddy current
conductivity was within the range of values measured by the 4-point probe method and it was concluded that no corrections to the data were necessary
provided data from the region of frequency independent conductivity were used.
3.2. CdTe sample
Eddy current measurements with an equiatomic
CdTe sample were performed systematically under
near thermal equilibrium conditions during heating
from room temperature up to 1150°C and then cooling down to 600°C. At low temperatures ( < 700°C),
the conductivity of equiatomic CdTe was too low to
obtain an impedance curve with the present setup
(measurements above 10 MHz would have been
needed). However, once the temperature exceeded
~ 700°C, the conductivity increased to the point
where usable impedance curves could be measured
and, as the temperature was further increased, a more
complete impedance curve developed. Fig. 7 shows
representative impedance curves measured just below and just above the melting point and at the
Table 2
Comparisons of conductivities obtained by an encircling eddy
current sensor technique with 4-point probe measurements
Ingot #
MNl-1861
MPO-5792
JME-31844
Conductivity ( S / m )
Frequency
4-point probe
Eddy current
range (kHz)
1471-1149
6667-4000
11628-11234
1390_+60
5810 _+ 170
11700_+ 170
800-1200
300-700
120-300
H.N. G. Wadle~' B. W. Choi / Journal of Co'stal Growth 172 (1997) 323-336
highest test temperature of ll50°C. It can be seen
that the frequency points abruptly moved clockwise
along the impedance during the melting transition
consistent with a rapid, significant increase in conductivity.
The electrical conductivity was deduced for each
test frequency using the procedures described above.
Fig. 8a shows the resulting conductivity versus frequency relationship for data collected at 1094°C (just
below the point where thermocouple data indicated
melting). A significant variation in conductivity was
observed at low frequency (between 50 kHz and 600
Angle o~
10,000
87 °
86 °
84 °
80 °
~
,
~
~
~
(a)
MNI
73 °
331
Angle
66 °
~
53 °
42 °
79 °
10,000
~
(b)
- 1861
74 °
MPO
65 °
54 °
41 °
30 °
20 ~
14 °
- 5792
80O0 !
8OOO
E
E
8000
oooo
>
=
"(3
E
O
4000
.~
4000
Q
L)
2000
2000
6
810 s
2
4
6
8106
4
6
8105
2
Frequency (Hz)
4
6
8106
Frequency (Hz)
Angle
20,000
68 °
59 °
48 °
36 °
I
I
I
I
I
(c)
JME
25 °
18 °
11 °
8 o
- 31844
17,000
E
~v14,000
._~
>
"O
E
O
11,000
(O
8000
5000
,,
,11
810 s
,
2
i
i
4
,
,,
6
LJl
8106
I
I
2
Frequency (Hz)
Fig. 6. The frequency dependence of the electrical conductivity for calibration samples: (a) MN 1-1861 ; (b) MP0-5792; (c) JME-31844.
332
H.N.G. Wadlev B. W. Choi / Journal qf Crystal Growth 172 (1997) 323-336
kHz). However, in this frequency region the angle,
oz, exceeded 77 ° and Eq. (1) was no longer valid
because the electromagnetic skin depth exceeded the
sample radius. As the frequency approached 800
kHz, the conductivity converged to a frequency independent value of 1320 _+ 60 S / m that could be used
to characterize the sample.
Increasing the sample temperature by I°C to
1095°C (and holding for 8 b) resulted in melting of
1.0
Hz
the sample. Using Eq. (2) and assuming the liquid
sample radius, a, was now governed by the thermal
expansion of the quartz ampoule, the conductivity
versus frequency relation was obtained and is plotted
in Fig. 8b. Once again, low frequency data are
invalid because of too large a skin depth, whilst data
above 1.5 MHz were adversely affected by the onset
of a test circuit resonance. This resonance occurred
at a lower frequency than before because of the
1.o
I
E
E
O
t-~
0.9
O
o
tO
O..
°°,2 MHz
o
o%
E
°
o
N
• 3.15 MHz
~
15 kHz
X
e3
._~
500 kHz
0.8
792 kHz
b
._c 0.7
g
0.7
] .25 MHz
E
E
-o
o
._N
0.9
E
0.8
a
kHz i
1
25 MHz
,m
0.6
-~
0.5
E
~ O.5
o o o~
0.6
MHz
o 3.15 MHz
o
Z
z
(a)
0.4
0.0
CdTe
(b)
Heating 1094°C
i
I
I
I
0.1
0.2
0.3
0.4
0.4
0.0
0.5
CdTe
I
I
J
0.1
0.2
0.3
0.4
Normalized real Z component
Normalized real Z component
1.0
t-
E
O
O.
180 kHz
I
50 kHz " ~ = ~ 2 5
kHz
- % ,
00 kHz
0.9
~ 315 kHz
E
O
o
8
0.8
~
U
c::
0.7
500 kHz
792 kHz
E
"O
Heating 1095°C
I
~ 1 . 2 5 MHz
0.6
° ~o~2° MHz
N
~P3.15 MHz
o
Z
0.5
(c)
0.4
0.0
CdTe
i
0.1
Heating 1150°C
i
0.2
i
0.3
i
0.4
0.5
Normalized real Z component
Fig. 7. Normalized impedance diagrams for CdTe at different temperatures of: (a) 1094°C; (b) 1095°C; (c) 1150°C.
0.5
333
H.N.G. Wadley, B.W. Choi / Journal of Crystal Growth 172 (1997) 323-336
higher inductance of the more conductive test material. Nevertheless, for intermediate frequencies between 200 kHz and ~ 1 MHz, frequency independent conductivities were observed. The average conductivity measured in this region was 4830_+ 80
S/re.
As the temperature of the liquid was gradually
increased to l l50°C, each frequency point on the
impedance plane diagram moved further clockwise
around the impedance curve consistent with a continued rise in conductivity. The variation of conductivity with frequency at 1150°C is shown in Fig. 8c.
Angle
Angle
10,000
89 °
86 °
84 °
82 °
79 °
72 °
65 °
52 °
39 °
~
,
,
,
,
~
,
,
,
35 °
83 °
~
10,000
(b)
(a) CdTeHeating 1094°C
74 °
~
66 °
,
55 °
,
42 °
,
30 °
,
19 °
~
12 °
Heating 1095°C
CdTe
8OOO
8O0O
/
E
E
6000
8000
O
79 °
,
O
4000
4000
0
0
0
0
2000
2000
,,
,,1
,
8105
2
,
,
4
,
,,
,,]
,
6
8106
2
,,
,,I
,
elO 5
2
(Hz)
Frequency
,
,
4
Frequency
, , ,
6
,,I
,
8106
2
(Hz)
Angle cc
15,000
77 °
71 °
62 °
51 °
39 °
28 °
20 °
13 °
9o
I
I
I
I
I
L
I
I
[
(c)
CdTe
Heating 1150°C
13,000
E
~,~ 11,000
:i
/
i¢
"0
#
9O0O
C
0
0
7000 I
5000
.... i
8105
6
h
2
,
,
4
,
,
6
, , ,I
8 106
I
I
2
4
Frequency (Hz)
Fig. 8. The frequency dependence of the electrical conductivity of CdTe at temperatures of: (a) 1094°C; (b) 1095°C; (c) 1150°C.
334
H.N.G. Wadlev B.W. Choi/Journal of Co'stal Growth 172 (1997) 323-336
Again low frequency data had a frequency dependent
conductivity while the high frequency data were
affected by the test circuit's resonance. This latter
effect manifested itself at even lower frequency than
before because the test material's inductance had
further increased. The conductivity measured between 126 and 315 kHz was 9010_+55 S / m at
1150°C.
Fig. 9a shows the temperature dependence of the
electrical conductivity for equiatomic CdTe during
both heating and cooling. Repeated heating/cooling
cycles resulted in almost identical results. The conductivity increased exponentially with temperature
during heating in either the liquid or solid state. This
implies semiconducting behavior in both phases. By
monitoring the ampoule temperature during heating,
melting was observed to initiate at about 1094°C and
during further heating appeared complete by 1097°C.
Similar observations during cooling indicated that
solid nucleated (after a small undercooling) at 1093°C
and was complete by 1090°C. These melting/solidification transitions were accompanied by abrupt
10,000
10,000
a)r
8000
o
i
CdTe
i
r |i
I
I
r
~
I
I
I
|
b) Cd0.955Zno.045Te
8000
Heating
&-
E
Heating
o
• Cooling
/ J
1093 °
1093 °
6000
6000
._~"
I
1100
~1096 °
.2
.>
1092 ° , ,1095 °
I
"5
4000
4000
cO
0
O
0
1091 ° ,
2000
1099'
2000
!1094 °
ol
70O
-
i
I
800
J
I
I
900
I
I
I
1000
0
1100
I
I
700
I
900
I
I
1000
I
I
1100
ij
Temperature (°C)
Temperature (°C)
10,000
I
i
I
I
c) Cd0.92Zno.08Te
8O00
I
800
°
Heating
•
Cooling
E
1099 °
'1104~
6000
>
0
4000
1098 °
0
c)
1097 °'
2000
10960
1103 °
~.,J
0
700
I
I
800
I
I
900
I
I
1000
I
1102°I
1100
Temperature (°C)
Fig. 9. The temperature dependence of electrical conductivity for: (a) CdTe; (b) Cdo.955Znoo45Te;(c) Cdo 92Zno.osTe.
H.N.G. Wadley, B.W. Choi / Journal q[ Co'stal Growth 172 (1997) 323-336
changes in conductivity. The solid just prior to melting or immediately after solidification had a conductivity of ~ 1050 s / m while the liquid conductivity
was ~ 6200 S / m . With the exception of a small
( ~ 3°C) temperature hysteresis during the
melting/solidification region, the electrical conductivity at each measurement temperature was the same
during heating and cooling.
3.3.
Cdo.955Zno.o45Te
sample
335
T:
lO,000/
L (a) liquid
,
,
,
/
0000~
~
8000
~
700o
O
6000
Fig. 9b shows the temperature dependence of the
electrical conductivity for the Cd0.955Zn0045Te sample. At low temperatures, the solid's conductivity
again increased slowly with temperature until the
temperature reached about 1080°C, whereupon the
conductivity started decreasing. This anomalous behavior was repeatedly observed, but did not occur
with the equiatomic CdTe sample. During cooling,
solidification occurred in the 1092-1093°C range.
Further cooling resulted in an initial (anomalous)
increase in conductivity, similar to the behavior observed during heating. The conductivity then gradually decreased as the temperature was lowered.
5000
0.00
0.04
0.06
0.08
X
2000
l
(b)
i
~
,
~
1oBo,c
~"
._>
,
,
,
,
i
0.06
i
i
0.08
solid
1500
~
lO7O'(;
lo~,c
~ooo.c
1050"C
1ooo
500
o
i
0.00
3.4. Cdo.92Zno.o~Te sample
The variation of electrical conductivity with temperature for the Cd0.ezZn008Te sample is shown in
Fig. 9c as a function of the temperature up to
1150°C. The conductivity variations in the solid and
liquid showed trends similar to the equiatomic CdTe
experiment. Melting occurred at 1102°C during heating, and solidification began at 1099°C on cooling.
There was 6.45-fold increase in conductivity upon
melting. This sample also exhibited semiconductorsemiconductor behavior during the melting/solidification transitions.
Fig. 10 summarizes the dependence of conductivity on composition and temperature near the melting
points for Cdl_xZnxTe alloys. Zn significantly reduces the melt conductivity. However, a weak maximum in conductivity is seen for the solid near the
melting point at x = 0.04. For this composition, an
anomalous conductivity-temperature behavior was
also observed about 30°C below the melting temperature. The origin of this reproducibly observed phenomenon in unclear.
0.02
i
i
0.02
]
i
0.04
i
X
Fig. 10. Summary of the temperature dependence of conductivity
for (a) liquid and (b) solid Cd I_.~Zn,Te alloys as a function of
zinc concentration.
The large electrical conductivity changes upon the
melting of CdTe reported by Glazov et al. [14,15] are
confirmed and similar changes accompany the solidification of Cd L xZn,Te alloys. The melt is found to
be 4 - 6 times more conductive than the solid. Semiconducting behavior (exponential conductivity-temperature relationship) is found in the solid and liquid
phases. These solid ( ~ ) and liquid (o-/) conductivities and the relatively high c r / / ~ ratios appear
sufficient for implementation of eddy current sensor
concepts for monitoring the solidification interface
during vertical Bridgman growth of Cd~ xZn,Te
alloys as proposed in Ref. [8,11]. The observation of
a significant dependence of conductivity upon composition and recently reported ambient temperature
resistivity measurements for CdZnTe alloys as function of zinc concentration [24] suggests that eddy
current sensing might provide insight into the corn-
336
H.N.G. Wadley, B.W. Choi /Journal of Co'sta I Growth 172 (1997) 323-336
position of the melt prior to solidification and perhaps provide some insight into Zn segregation and
its redistribution during post-solidification annealing.
4. Conclusions
A multifrequency eddy current methodology has
been used to determine the conductivity of
Cd 1 ,Zn~Te alloys with x = 0, 0.045 and 0.08 in
the 700-1150°C temperature range. The solid and
liquid states of these alloys usually exhibited semiconducting behavior with an exponential conductivity-temperature dependence. When the samples were
heated through the melting point under quasi-equilibrium conditions (heating/cooling rates of <
0.1°C/min) a large 4 - 6 fold discontinuity in conductivity occurred within a degree or two of the
accepted melting point. Zn was shown to depress the
melt's electrical conductivity, but that of the solid
exhibited a weak maximum conductivity near x =
0.045 near the melting point. The results suggest that
the conductivity differences between the melt and
solid are sufficient for the use of eddy current sensors to monitor the liquid-solid interface during
vertical Bridgman growth. The significant dependence of conductivity upon composition also suggests the potential use of a sensor approach for
monitoring melt composition, segregation and solid
state composition homogenization phenomena.
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, II-VI
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 and in particular to the staff of JME for
their assistance in preparing the samples. 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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