Journal of Crystal Growth 225 (2001) 34–44
Laser ultrasonic sensing of the melting and solidification of
cadmium telluride
Douglas T. Queheillalt*, Haydn N.G. Wadley
Department of Materials Science and Engineering, School of Engineering and Applied Science, 116 Engineers way,
University of Virginia, Charlottesville, VA 22904-4745 USA
Received 2 August 2000; accepted 21 February 2001
Communicated by M.E. Glicksman
Abstract
A noninvasive laser ultrasonic method has been used to investigate the melting and solidification of a (Cd,Zn)Te alloy
during vertical Bridgman growth. A single zone vertical Bridgman furnace was integrated with a laser ultrasonic system
and used to monitor the time-of-flight of ultrasonic pulses that propagate across an ampoule during the melting and
solidification of Cd0.96Zn0.04Te. The measurement approach is based upon the difference in the elastic stiffness of the
solid and liquid phases of Cd0.96Zn0.04Te (Queheillalt et al., J. Appl. Phys. 83 (1998) 4124) and its significant dependence
upon temperature. This results in a reduction of the longitudinal wave ultrasonic velocity as the temperature was
increased (from ambient temperature) followed by a 45% decrease upon melting. The laser ultrasonic sensor provided
a robust in-situ method for monitoring the melting and solidification of Cd0.96Zn0.04Te. The data indicated that the
melting was slow and that solidification was accompanied by a 10–158C undercooling. # 2001 Elsevier Science B.V. All
rights reserved.
Keywords: A1. Directional solidification; A1. Solidification: A2. Bridgman technique; B1. Cadmium compounds; B2. Semiconducting II–VI materials
0. Introduction
The now well documented difficulties associated
with the growth of premium quality Cd1yZnyTe
(with y ¼ 0:04) alloys [1] have stimulated an
interest in the development of ultrasonic sensor
technologies to noninvasively monitor growth
conditions during vertical Bridgman (VB) solidification. Noninvasive in-situ sensors are needed to
implement closed loop feedback control of crystal
growth processes. Here, we explore an optical
*Corresponding author.
E-mail address: [email protected] (D.T. Queheillalt).
approach (laser ultrasonics) for monitoring temperature changes and liquid–solid transformations in a
CdTe system. The principle underlying this sensing
methodology is the strong temperature dependence
of the ultrasonic velocity in the solid and liquid
phases, and the large increase in the longitudinal
wave velocity upon solidification [2]. These effects
arise from temperature dependent softening of elastic
stiffness constants and the accompanying change in
density associated with thermal expansion.
Early attempts to apply an ultrasonic approach
to solidification sensing sought to exploit the
acoustic impedance difference across a solid–liquid
interface by detecting ultrasonic reflections
0022-0248/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 0 2 2 - 0 2 4 8 ( 0 1 ) 0 1 0 2 7 - 2
D.T. Queheillalt, H.N.G. Wadley / Journal of Crystal Growth 225 (2001) 34–44
from the interface. A pulse-echo approach was
investigated by Parker et al. [3] for Si, by Jen et al.
[4] and Carter et al. [5] for Ge. For both of these
semiconductors, good solid and liquid elastic
constant and density (hence ultrasonic velocity)
data existed in the literature [6–10] and the
measured time-of-flight of signals reflected from
the solid–liquid interface was used to estimate the
interface position as solidification progressed.
However, the large usually poorly characterized
axial temperature gradient combined with a
significant temperature dependent velocity introduced uncertainties in mapping time-of-flight data
into the interface’s axial position, and little
information was inferred about interfacial curvature by this method. An alternative approach
sought to exploit the ultrasonic delay when
ultrasonic rays were transmitted through the solid
and liquid phase. Norton et al. [11] and Mauer
et al. [12] have reported measurement of the timeof-flight for rays transmitted through a solid–
liquid interface during the controlled solidification
of an aluminum alloy. Using the predictions of a
heat flow model, they were able to construct an
interface geometry model and used a simple ray
tracing code in conjunction with the temperature
dependent elastic stiffness and density data, to
compute the time-of-flight values for a fan beam
set of rays propagating from arrays of source and
receiver points on the boundary of the body. A
nonlinear least-squares reconstruction technique
was then used to fit for the unknown coefficients of
the interface geometry model and thus robustly
reconstruct the interface position and shape from a
small transmission ray path data set.
Laser based ultrasonic techniques utilize a
pulsed infrared laser to generate elastic waves with
ultrasonic frequencies and a laser interferometer to
detect the surface displacements associated with
their arrival at a surface [13]. This noncontact
ultrasonic measurement approach can be utilized
at elevated temperatures where conventional
piezoelectric transducers fail. It can also function
in high or low pressure environments where the
ultrasonic couplants used with contact ultrasonic
methods may cause difficulties, and it possesses a
broad bandwidth [14,15]. First proposed in the late
1970s, laser ultrasonic approaches have since been
35
used for physical property measurements such as
elastic modulus determination, [16–20] microstructural characterization, [17,21–32] and measurement
of the crystallographic texture of bulk solids [33–37].
These methods have also been used for thickness
gauging, [38–41] and elastic property determination
[42–46] of thin films and nano-structured materials
[47–52]. More recently, this technique is beginning to
be used for in-situ measurement of internal temperature profiles, [53,54] monitoring of solid–solid
phase changes, [54,55–57] consolidation kinetics of
ZnO ceramics, [58] thickness variations of SiN films
manufactured by chemical vapor deposition (CVD)
[59] and for silicon wafer temperature measurement
during rapid thermal processing [60].
Here, a laser based ultrasonic transmission
approach has been investigated to monitor the
melting and solidification of a Cd0.96Zn0.04Te
alloy. The sensors development is based upon the
recognition that the ultrasonic velocity (and the
elastic stiffness constants and density that control
it) of the solid and liquid phases of (Cd,Zn)Te
alloys are temperature dependent and an abrupt
increase of the longitudinal wave velocity occurs
upon solidification. As a result, the time-of-flight
of rays diametrically traversing the region of
solidification exhibit a 100% increase upon
melting because the ultrasonic velocity (v) and
the time-of-flight (t) are directly related (v ¼ l=t,
where l is the propagation distance). In addition,
the experimentally measured longitudinal wave
times-of-flight were compared with simulated
time-of-flight predictions for quasi-isotropic wave
velocities evaluated from the polycrystalline average of the single crystal elastic stiffness constants.
1. Experimental procedure
1.1. Sample preparation
Cd0.96Zn0.04Te ingots were supplied by Johnson
Matthey Electronics (Spokane, WA). The polycrystalline ingot used was initially grown from the melt
using a commercial 17-zone vertical Bridgman
growth furnace. This resulted in a polycrystalline
ingot with a coarse grained microstructure possessing a linear density typically less than 5 grain
36
D.T. Queheillalt, H.N.G. Wadley / Journal of Crystal Growth 225 (2001) 34–44
diameters across the ingots diametral plane. The
material consisted of precompounded infrared focal
plane array (IRFPA) substrate purity polycrystalline
equatomic CdTe to which Zn and Te was added to
reach the target zinc concentration of 4 at% 1%.
The ingots were encapsulated in 30 mm ID (36 mm
OD) quartz ampoules with quartz plugs (to fill in the
free volume) and sealed under 106 Torr with a very
small free volume to inhibit the vaporization of Cd
during heating. The free volume was less than 2% of
the ingots total volume.
1.2. Laser ultrasonic sensor
The ultrasonic time-of-flight between precisely
positioned source and receiver points were measured using a laser ultrasonic system (see Ref. [2]
for details). Briefly, a 10 ns duration Q-switched
Nd : YAG laser pulse of 1.064-mm wavelength was
used as the ultrasonic source. The energy per pulse
was 10 mJ and the roughly Gaussian beam of the
multimode pulse was focused to an approximate
circular spot of 1 mm diameter. Thus, the source
power density was 100 MW/cm2. This was
chosen to keep the generation laser power density
below the threshold for cracking the quartz
ampoule. The quartz ampoule was transparent to
the infrared laser pulse. As a result, absorption
occurred at the CdTe-quartz interface and provided a constrained surface that enhanced the
ultrasonic signal strength [13].
A Mach–Zehnder heterodyne laser interferometer
was used for ultrasonic detection. It responded to
the sample’s out-of-plane (normal) surface displacement associated with the ultrasonic wavefront
arrivals at the receiver point. It was powered by a
5 mW HeNe laser which produced a continuous
Gaussian beam of 632.8 nm wavelength focused to a
circular spot 100 mm in diameter. The signal from
the interferometer was bandpass filtered between
10 kHz and 10 MHz and recorded with a precision
digital oscilloscope at a 2 ns sampling interval using
8-bit analog-to-digital conversion. To improve the
signal-to-noise ratio, each waveform used for a timeof-flight measurement was the average of 10 pulses
collected at a pulse repetition rate of 20 Hz. A fast
photodiode identified the origination time for the
ultrasonic signals.
Fig. 1. Schematic illustration of the vertical Bridgman sensing
configuration with an integrated laser ultrasonic sensing system.
1.3. Integrated growth furnace
The ingots were heated with a single zone
programmable tubular furnace (12008C max, 6 in
diameter). The furnace was equipped with a
temperature controller that was able to maintain
the temperature to within 18C. The Cd0.96Zn0.04Te
samples were supported by an alumino–silicate
machinable ceramic and quartz support tube
assembly. The laser source and receiver gained
access into the furnace through small (4 mm) slits
along the diametral plane of the furnace. The
sample temperature was measured with two type R
thermocouples affixed to the quartz growth
ampoule with tungsten wire. In both cases, the
thermocouples were in physical contact with the
outer surface of the quartz support tube assembly.
Variations of the temperature in the region of the
sample were better than 28C. Scanning was
accomplished using mirrors attached to translation
stages which were controlled using stepper motors.
The screw driven translation stages had a movement resolution of 1.27 mm/step with a repeatability of 1.175 mm per 5.08 mm of linear travel.
Fig. 1 shows a schematic illustration of the
experimental configuration.
2. Polycrystalline elastic properties
The single crystal elastic stiffness constants (C11 ,
C12 and C44 ) for solid and the adiabatic bulk
modulus (KS ) for liquid Cd0.96Zn0.04Te have been
37
D.T. Queheillalt, H.N.G. Wadley / Journal of Crystal Growth 225 (2001) 34–44
previously investigated [2]. They were evaluated
from simple inversion techniques of the temperature dependent ultrasonic velocity obtained in
primary h1 0 0i, h1 1 0i and h1 1 1i orientations
and the temperature dependence of the density in
both the solid and liquid phases. The elastic
stiffness constants exhibited a monotonically
decreasing function with increasing temperature
in both the solid and liquid phases.
However, CdTe and its alloys rarely solidify as a
single crystal. Therefore, methods for averaging
the single crystal elastic stiffness constants (C11 ,
C12 , C44 for cubic materials) to obtain effective
values for polycrystalline elastic moduli have been
used to predict the ultrasonic behavior of the
polycrystalline material. The isotropic polycrystalline elastic constants include Young’s modulus
(E), the bulk modulus (K), the shear modulus (G),
Lame’ constants (l; m) and Poisson’s ratio (n).
Several authors [61–65] have proposed methods to
estimate the polycrystalline moduli and several
thorough reviews have been published by Ledbetter [66], Hearmon [67] and Hashin [68].
The elastic properties of polycrystalline bodies
depend on the macroscopic behavior of a polycrystalline body’s individual single crystals (crystallites or grains). In principle, the averaging
problem can be solved by considering simultaneously the elastic equilibrium equations for each
grain together with the boundary conditions at
grain interfaces; in practice, this approach poses
insurmountable problems [69].
Most averaging methods assume, either explicitly or implicitly, certain conditions in the
polycrystalline body [69]:
*
*
*
*
*
*
The number of grains composing the body is
sufficiently large.
Grains are randomly oriented; that is preferred
orientations are absent.
Grains sizes do not vary so much that a few
orientations contribute dominantly.
Grains are not so small that their crystallinity is
lost.
Elastic stiffnesses are homogeneous within a
grain and between crystallites.
Grain boundaries per se contribute nothing to
the body’s elastic properties.
For materials with a cubic symmetry, the
averaging problem consists of reducing the three
independent elastic stiffness coefficients to two
independent constants that describe completely the
elastic behavior of quasi-isotropic solids (i.e. those
solids whose properties are anisotropic locally but
isotropic macroscopically) [69]. The bulk modulus
is a scalar invariant of the elastic stiffness tensor
and is represented by
K ¼ 13ðC11 þ 2C12 Þ:
ð1Þ
It is assumed that the polycrystal and single crystal
bulk moduli are equal and therefore the grain
boundaries contribute nothing to the polycrystalline elastic properties.
The problem remains, to determine a second
polycrystalline elastic stiffness constant. The second constant cannot be chosen uniquely. Generally, Young’s modulus and the shear modulus are
often calculated. The most straight forward of the
averaged quantities are the Voigt (EV and GV ,
homogeneous strain) [61,62] and the Reuss (ER
and GR , homogeneous stress) [63] averages given
by
ER ¼
5C44 ðC11 C12 ÞðC11 þ 2C12 Þ
;
2 þ C C 2C 2 þ 3C C þ C C
C11
11 12
44 11
44 12
12
ð2Þ
GR ¼
5C44 ðC11 C12 Þ
;
4C44 þ 3ðC11 C12 Þ
ð3Þ
EV ¼
ðC11 C12 þ 3C44 ÞðC11 þ 2C12 Þ
;
2C11 þ 3C12 þ C44
ð4Þ
C11 C12 þ 3C44
:
ð5Þ
5
Hill [70] states the (EV and ER ) and (GV and GR )
are upper and lower bounds for the polycrystalline
moduli obtained from the single crystal elastic
stiffness constants and suggests two approximations:
GV ¼
EVRa ¼ 12ðEV þ ER Þ;
pffiffiffiffiffiffiffiffiffiffiffiffi
EVRg ¼ EV ER ;
ð6Þ
ð7Þ
where EVRa and EVRg represent the arithmetic
and geometric averages. The same arithmetic and
geometric averaging can be applied to the shear
38
D.T. Queheillalt, H.N.G. Wadley / Journal of Crystal Growth 225 (2001) 34–44
Fig. 2. Temperature dependence of the Voigt and Reuss
polycrystalline elastic moduli for solid Cd0.96Zn0.04Te.
Table 1
Temperature dependent polynomial fits of the polycrystalline
elastic moduli data of Cd0.96Zn0.04Te
Elastic moduli
Temperature dependent
elastic property (GPa) T=8C
K
E
G
42.905–7.304 103 T–3.249 106 T2
39.669–5.481 102 T–3.231 106 T2
14.745–1.985 103 T–1.204 106 T2
modulus (GVRa and GVRg ):
GVRa ¼ 12ðGV þ GR Þ;
GVRg ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffi
GV GR :
ð8Þ
ð9Þ
Now, the polycrystalline elastic moduli can be
calculated from the single crystal elastic stiffness
constants for solid Cd0.96Zn0.04Te. The calculated
temperature dependent polycrystalline elastic stiffness moduli for Young’s and the shear moduli
(Eqs. (2)–(9)) are shown in Fig. 2. In Fig. 2, the
arithmetic and geometric means of the Voigt and
Reuss models are sufficiently equivalent that only the
arithmetic mean is shown. Table 1 shows polynomial
fits for the temperature dependence of the polycrystalline elastic moduli of solid Cd0.96Zn0.04Te.
3. Quasi-isotropic wave propagation
The propagation of high frequency elastic waves
(ultrasound) in isotropic polycrystalline bodies is
Fig. 3. Temperature dependence quasi-isotropic wave velocities
(polycrystalline average) for solid Cd0.96Zn0.04Te.
directly related to the (dynamic) elastic moduli of
the body. In the long wavelength limit, the
longitudinal and shear wave velocities can be
expressed in terms of the low frequency limit
(static) elastic constants and the density [71].
The thermal expansion characteristics of
Cd0.96Zn0.04Te have been previously evaluated [2]
and not reported here. The longitudinal (v‘ ) and
shear (vs ) wave velocities were computed from well
known relationships
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E
1n
v‘ ¼
;
r ð1 þ nÞð1 2nÞ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffi
E 1n
G
vs ¼
¼
r 2ð1 þ nÞ
r
ð10Þ
ð11Þ
where E is Young’s modulus, G is the shear
modulus, r is the density and Poisson’s ratio
(n) can be expressed as n ¼ E=2G 1 and the
data of Table 1. The calculated temperature
dependent quasi-isotropic longitudinal and shear
wave velocities (Eqs. (10)–(11)) are shown in
Fig. 3. Table 2 shows polynomial fits for the
temperature dependence of the quasi-isotropic
wave velocities of solid Cd0.96Zn0.04Te. In addition, the temperature dependent longitudinal wave
velocity for liquid Cd0.96Zn0.04Te is also shown in
Table 2.
D.T. Queheillalt, H.N.G. Wadley / Journal of Crystal Growth 225 (2001) 34–44
39
Table 2
Temperature dependent polynomial fits of the quasi-isotropic
wave velocities of Cd0.96Zn0.04Te
Type of wave
Temperature dependent
wave velocities (mm/ms) T=8C
v‘
vs
vliq
3.2612–2.1161 104 T–1.7585 107 T2
1.5857–8.5394 104 T–8.3713 108 T2
1.898–5.080 104 T
4. Results
The laser ultrasonic sensors response has been
evaluated for two sensor configurations. In one
case the growth furnace was held stationary, while
the sensor recorded data for the longitudinal wave
time-of-flight during melting and solidification. In
a second type of experiment, the sensor’s response
was monitored while the molten ingot was
directionally solidified through the sensor’s region
of interrogation.
Fig. 4. Longitudinal wave time-of-flight measured during the
heating portion of the process cycle (stationary growth
furnace).
4.1. Stationary furnace
4.1.1. Heating
The longitudinal wave time-of-flight measured
during heating is shown in Fig. 4(a) as a function
of process cycle time. The ingot was heated at a
rate of 58C/min to 10508C, then 18C/min to
11408C and held for 15 min, Fig. 4(b). Also shown
in Fig. 4(a) is the simulated quasi-isotropic longitudinal wave time-of-flight calculated from the
polycrystalline averaged moduli. The simulated
data corresponds to the arrival time-of-flight of a
quasi-isotropic longitudinal wave at the sensor’s
plane of interrogation using the data in Table 2
and the reference thermocouple temperature.
The experimental data show a gradual increase
in the time-of-flight as the ingot was heated and a
discontinuous (100%) increase near the melting
temperature indicated by the thermocouple. This
discontinuous increase in the longitudinal wave
time-of-flight indicates the beginning of melting.
The deviation between the experimental and
simulated time-of-flight near the melting point
indicate that a 10–158C superheating was necessary for the ultrasonic velocity to equilibrate to the
quiescent reference velocity. It should also be
noted, Fig. 4(a), that the longitudinal wave timeof-flight in the solid phase fell below the simulated
data for the quasi-isotropic polycrystalline average
wave velocity. This arises from the initial coarse
grain size of the ingot (only 3–5 grains diameters).
The limited number of grain orientations resulted
in a sample that was not truly isotropic.
4.1.2. Cooling
The longitudinal wave time-of-flight measured
during cooling is shown in Fig. 5(a) as a function
of process cycle time. The ingot was cooled from
11408C at 18C/min to 10508C, then 58C/min to
room temperature, Fig. 5(b). Also shown in
Fig. 5(a) is the simulated quasi-isotropic longitudinal wave time-of-flight. Again, the simulated
time-of-flight was calculated from the isotropic
polycrystalline elastic constants at the temperature
measured by the reference thermocouple.
The experimental data show a gradual decrease
of the time-of-flight as the sample was cooled
and exhibited a discontinuous decrease (50%
40
D.T. Queheillalt, H.N.G. Wadley / Journal of Crystal Growth 225 (2001) 34–44
Fig. 5. Longitudinal wave time-of-flight measured during the
cooling portion of the process cycle (stationary growth
furnace).
decrease) at a temperature of 10858C. The
discontinuous decrease in the longitudinal wave
time-of-flight is indicative of the solidification of
the ingot. However, a significant amount of
supercooling was observed with the ultrasonic
sensor, revealing that solidification occurred between 10908 and 10858C. Once the ingot solidified,
the time-of-flight compared well with that predicted by the isotropic polycrystalline elastic
moduli (unlike during the heating cycle). The
grain size after solidification was comparable to
the initial diameter. However, the average grain
orientation sampled by the ultrasonic ray path
during solidification was obviously different.
4.2. Directional solidification
The ultrasonic technique was used to monitor
the directional solidification of Cd0.96Zn0.04Te as
the furnace was translated at a rate of 1.67 mm/
min (i.e. 100 mm/h). During the furnace translation segment, the temperature of the single zone
furnace was held constant at 11408C and the
Fig. 6. Longitudinal wave time-of-flight measured during the
heating and soak portion of process cycle prior to furnace
translation (directional solidification).
insulation zone at the bottom of the furnace
provided the necessary cooling to promote directional solidification.
The longitudinal wave times-of-flight measured
during the heating and the soak segments of the
process cycle are shown in Fig. 6(a). The ingot was
heated at a rate of 108C/min up to 10908C, then
18C/min up to 11408C, held for 60 min to
equilibrate at which point the furnace translation
was begun, Fig. 6(b). Fig. 6(a) also shows the
simulated data for the quasi-isotropic longitudinal
wave time-of-flight determined from the reference
thermocouple. The data show a gradual increase in
the time-of-flight as the ingot was heated, a
discontinuous increase near the melting point
indicating the beginning of the melting process
followed by another gradual increase in the timeof-flight.
After the ingot was allowed to equilibrate at
11408C for 60 min the furnace translation was
begun. The longitudinal wave times-of-flight measured during the soak and furnace translation
segment of the process cycle are shown in Fig. 7.
D.T. Queheillalt, H.N.G. Wadley / Journal of Crystal Growth 225 (2001) 34–44
41
is attributed to the anisotropic nature of the
solidifying ingot.
4.3. Summary of observations
Fig. 7. Longitudinal wave time-of-flight measured during the
soak and growth portion of the process cycle (directional
solidification).
Fig. 8. Deduced and measured temperature in the plane of the
sensor during the soak and growth portion of the process cycle.
Fig. 7 shows a uniform time-of-flight during the
isothermal soak, a gradual decrease followed by an
abrupt decrease (50%) in the time-of-flight. The
gradual decrease was due to a decrease in the
melt’s temperature as the insulation zone approached the sensors region. After the insulation
zone passed the sensor, the liquid–solid interface
propagated through the sensors plane of interrogation and the time-of-flight abruptly decreased
indicating the passage of the liquid–solid interface.
Fig. 8 shows the measured and deduced temperature in the plane of the sensor for the soak and
growth portion of the process cycle. The data show
good agreement for measurement taken in the
liquid state and some scatter in the solid state. This
During the melting–solidification experiments,
the longitudinal wave time-of-flight data exhibited
a gradual increase as the ingot was heated and a
discontinuous increase near the melting point. This
discontinuous increase in the longitudinal wave
time-of-flight indicated the beginning of the
melting process for the Cd0.96Zn0.04Te alloy. The
data indicated slow melting characteristics as the
alloy was not fully molten until the reference
thermocouple reached a temperature of 11158C.
Cadmium telluride possesses a low thermal conductivity (k 1 102 W/cm K) and high heat
capacity (Cp 150 J/g K) [72,73]. This, coupled
with a low thermal gradient resulted in a small
heat flux and slow melting. The measured data
also exhibited a gradual decrease in the time-offlight as the sample was cooled and a discontinuous decrease at a temperature of about 10858C.
The discontinuous decrease in the longitudinal
wave indicated ingot solidification. However, the
temperature of the ingot was cooled well below the
melting point before solidification was observed
with the ultrasonic sensor, indicating that solidification occurred between 10908 and 10858C.
During directional solidification, the laser ultrasonic data exhibited a gradual increase in the timeof-flight as the ingot was heated, a discontinuous
increase near the melting point followed by
another gradual increase indicating the ingot
began melting at 11008C and was not fully
molten until the temperature reached 11208C.
During the soak and furnace translation portion
of the process cycle, the sensor indicated a
relatively constant time-of-flight followed by an
abrupt decrease indicating the solid–liquid interface passed through the sensor region. The timeof-flight in the liquid state was constant up to
252 min (Fig. 7) at which point it began to
gradually decrease until 260 min. This gradual
decrease was attributed to a decrease in the melt’s
temperature as the insulation zone approached the
sensor. As the insulation zone passed the sensor
the sensor and the longitudinal wave time-of-flight
42
D.T. Queheillalt, H.N.G. Wadley / Journal of Crystal Growth 225 (2001) 34–44
decreased abruptly indicating the passage of the
liquid–solid interface. Again, the deviation between the sensors data and the simulated data has
been attributed to the low thermal conductivity,
high heat capacity of CdTe alloys in addition to
constitutional supercooling effects.
5. Discussion
The melting behavior of CdTe follows a solid
semiconductor ! liquid semiconductor transition,
i.e. its electrical conductivity increases with temperature. The early work of Glazov [10] suggested
that a considerable amount of the covalent
contribution of the cohesive energy is retained in
the melt and a three-dimensional arrangement of
the associated tetrahedra are retained in the
superheated melt. As the superheating is increased,
these tetrahedra are dissociated into two-dimensional associated (rings and chains) molecules and
separate atoms. This behavior has been experimentally examined by investigating the superheating/supercooling behavior of CdTe by
differential thermal analysis (DTA) and direct
temperature measurement at the tip of a growth
ampoule [74–77]. It was shown that at small values
of superheating (5108C), no supercooling was
observed, where at values higher than 108C,
supercoolings up to 208–308C occurred. This
behavior is indicative of the observance of a
structural transition in the molten state. These
associated complexes in the melt (tetrahedrons,
chains and rings) are likely to reduce the free
energy for nucleation and promote the phase
transition near thermodynamic equilibrium. On
the other hand, at higher superheating levels, the
thermal destruction of the associated complexes
takes place and a higher driving force (supercooling) is required for solid nucleation.
Recent measurements of the electrical conductivity during heating and cooling have been used to
characterize the superheating-supercooling behavior of CdTe and (Cd,Zn)Te alloys. The work of
Shcherbak [78,79] and Choi and Wadley [80,81]
indicated that the electrical conductivity of CdTe
and its solid solution alloys undergo a discontinuous increase by an order of magnitude during
melting and remains semiconducting in the liquid
state (i.e. its electrical conductivity increases with
temperature). These experiments confirm the
superheating/supercooling behavior observed by
differential thermal analysis (DTA) and direct
temperature measurement at the tip of the growth
ampoule. The ultrasonic measurements reported
here indicated that significant superheating was
necessary to fully melt the ingot (melting had
begun at 11008C and was not fully complete
until the temperature reached 11208C). In addition, a significant amount of supercooling (up to
158C) was observed with the laser ultrasonic
sensor. This appears to be a result of the
combination of low thermal conductivity and high
heat capacity of CdTe alloys. In addition, Singh
et al. [82] have used an ultrasonic technique to
investigate the temperature dependence of the
ultrasonic velocity for molten CdxTe1x alloys
(where 04x41 in 0.1 increments). Their data
indicated that the adiabatic compressibility of
stoichiometric CdTe exhibited the largest temperature dependence and observed degree of supercooling. Their work speculates that the large
temperature dependence of the ultrasonic velocity
in molten stoichiometric CdTe can be correlated to
the dissociation of the retained covalent bond in the
molten state with increasing temperature. This large
temperature dependence of the ultrasonic velocity
in molten Cd0.96Zn.0.04Te has also been observed in
Queheillalt et al. [2] and the present work.
6. Conclusions
The difference in the ultrasonic velocity of a
longitudinal wave propagating in solid and liquid
(Cd,Zn)Te has led to an interest in the use of
ultrasonic time-of-flight measurements as a potential noninvasive sensing methodology to monitor
the solid–liquid interface during vertical Bridgman
crystal growth provided the temperature dependence of the ultrasonic velocities (which depend on
the elastic stiffness constants and the density) for
both the solid and the liquid phases are known
a priori. The longitudinal and shear waves
exhibited a monotonically decreasing velocity with
temperature in the solid phase. When the alloy was
D.T. Queheillalt, H.N.G. Wadley / Journal of Crystal Growth 225 (2001) 34–44
heated through the melting point under quasiequilibrium conditions a 100% decrease was
observed in the longitudinal wave velocity, due to
the absence of the shear modulus in the liquid
phase. These results suggest that the ultrasonic
velocity ratio (vs =v‘ ) between the solid and liquid
phases is sufficient for the implementation of this
sensing technology to monitor the liquid–solid
interface during vertical Bridgman growth.
The laser ultrasonic sensor also provided a
robust method for in-situ monitoring of the
liquid–solid interface as it passed through the
sensor during directional solidification. Therefore
this laser ultrasonic approach exhibits the potential for providing critical information during the
vertical Bridgman growth process. The integration
of robust laser interferometers into vertical Bridgman growth furnaces may provide useful information to the crystal grower in efforts to obtain
higher yields of premium quality semiconductors.
It is believed that due to the fact that laser
ultrasonic sensors may provide ‘‘real time’’ data,
they offer the possibility of new sensor based
process control technologies for in-situ monitoring
and direct feedback control of vertical Bridgman
growth technologies.
Acknowledgements
We are grateful to Brent Bollong and Art Sochia
of Johnson Matthey Electronics for helpful
discussions concerning crystal growth. This work
has been performed as part of the Infrared
Materials Producibility Program (IRMP) managed by Duane Fletcher (JME) 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. The IRMP consortium work,
and our work within it, has been supported by
ARPA/CMO under contract MD A972-91-C-0046
monitored by Raymond Balcerak.
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