ELSEVIER Journal of Crystal Growth 172 (1997) 323-336

j . . . . . . . . C R Y S T A L G R O W T H

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

A b s t r a c t

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. I n t r o d u c t i o n

Single crystal Cd 1_ ,Zn~Te ( x = 0.045) solid so- lution 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 manufactur- ers 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 dislo- cations [3,4]. In spite of many experimental efforts to investigate the relationships between material purity, the controllable growth parameters and the resulting mater ia l charac te r i s t i c s [5,6], the y ie ld of 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 liquid- solid interface during crystal growth [7,8,12]. The relationships between an eddy current sensor's fre- quency response, the electrical conductivities of the solid/liquid and the position/curvature of the liq- uid-solid interface are complex. Recent electromag- netic finite element modelling has identified several concepts to recover the interface shape during verti- cal Bridgman growth [8,12], and a companion paper [16] explores their application to Cd0.%Zn0.0aTe. The companion study has also revealed potential applica- tions 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 semicon- ductors containing volatile elements like Cd. The temperature and composition dependence of the elec- trical conductivity of equiatomic CdTe has been investigated by Glazov and coworkers using an elec- trodeless 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 1000- 1040°C temperature range. An abrupt rise in conduc- tivity commenced at about 1045°C. During this tran- sition, 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 oc- curred 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 anoma- lously low temperature where the conductivity dis- continuity was observed. Glazov et al.'s thermome- try may have been inaccurate because of the small sample size and the potentially large errors associ- ated 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 con- ductivity 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 measure- ments of material properties such as electrical con- ductivity 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 elec- tromagnetic fields are created within the test object by passing an alternating current through a nearby primary (driving) coil. These fluctuating electromag- netic fields are used to induce eddy currents in the test object. The eddy currents in turn create a sec- ondary 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) 323-336 325

1.0

'~\ " ' % , ( s = 1.2MHz

,, ...... -t(~. E 0 .9 - ~ ~.7 - (3) !

,, E o \

(..) \ \ N 0 . 8 - - , - -

~r'a'fL = " 2 M H z

IE 0 . 7 - ~ ' - /

N /

/ o / z 0 . 6 -

/ /

- - Liquid (~t = 5,873S/m) . . . . Solid (~, = 1,377S/m)

0.5 I 0.0 0.1 0.2 0 .3

N o r m a l i z e d Rea l 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 mag- netic 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 fre- quency dependent angle, c~, through

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

- 1.686 × 10 40~3 q- 7.193 × 10-70~ 4.

(2)

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. How- ever, 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 expan- sion for both materials are reasonably well estab- lished [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 coeffi- cients (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

~ 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 cur- rent was used to induce a reasonably uniform elec- tromagnetic field of variable frequency in the sam- ple. A secondary pick-up coil then sensed the pertur- bations to this field created by the sample. The main advantage of the two coil eddy current sensor ap- proach is that effects of temperature induced resis- tance changes to the coils can be minimized by using a high impedance measurement of the induced sec- ondary coil voltage, ~ , whilst simultaneously moni- toring 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 multi- frequency impedance/gain-phase analyzer by moni- toring V~ on the analyzer's test channel and I v (via the voltage drop, V R, 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

phase (g,4~) remeasured. The real and imaginary components of the normalized impedance, Z, are then given by

g Re(Z) = - - s i n ( 4~ - d~0), (5)

go g

Im(Z) = - - c o s ( ~ b - ~b0). (6) go

2.3. Sensor design for L, ertical Bridgman growth

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 heat- ing/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 plat- inum 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 ma- chined 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 ana- lyzer 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 ampli- fier 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 us- ing 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

H.N.G. Wadley, B.W. Choi / Journal of Crystal Growth 172 (1997) 323 336 327

b) Sensor~Sample Configuration

0 127mm

~-~ ~ 36mm ----~ 30mm "~1

pie Secondary

furnace

Main furnace

a) Furnace Geometry

¢ , coil

AluIT Jary p) coil

a eddy :sensor

Fig. 3. (a) A schematic diagram of the vertical Bridgman furnace; (b) detail showing the sensor configuration.

and 5 MHz. It then calculated the gain and phase angle difference and the normalized impedance com- ponents at each frequency. The basic program acti- vated the measurement periodically during heating/cooling of the sample and stored the impedance data together with the parametric temper- atures. An error analysis methodology for this mea- surement 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 "knee" of the impedance curve, i.e. 20°< a < 60 °, where the skin depth is about a half the sample radius. For low conductivity materi- als 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 conduc- tivities 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 (mea- sured 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 measure- ments. The reference samples were also used to

328 H.N. G. Wadley. B. W. Choi / Journal o[" Crystal Growth 172 (I 997) 323 336

check the test setup in this way before and after each 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 main- tain 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 thermo- couple 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,

2.6. Preparation and precompounding of samples

The Cd~ ,Zn~Te samples were contained in 33 mm ID quartz ampoules. When Cd containing com- pounds are in contact with quartz for extended peri- ods 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 car- bon 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 am- poule 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

O

E 100

E

~ 75

e.- .

Q 50

25

Eddy current sensor

R type thermocouple

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) 323 336 329

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 tempera- ture experiments. The Cd0.955Zn0.45Te sample was prepared from a precompounded polycrystalline in- got 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 multi- zone 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 am- poule. The data from the lower thermocouple could be also used to monitor solidification through its latent heat release.

The electrical conductivity-temperature relation- ships for the samples described above were mea- sured 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 approxi- mately 0.7°C/rain, and finally furnace-cooled to reach room temperature. Gain and phase measure- ments were subsequently made during reheating from room temperature to 1150°C and then back to ambi- ent temperature. At low temperatures, the conductiv-

ity was only a weak function of temperature, and so the conductivity was measured every 10°C. How- ever, 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 in- volved holding the temperature for up to 10 h (usu- ally 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 fur- nace and by impedance contributions from test cir- cuit components, a series of calibration tests were conducted. Fig. 5 shows measured impedance data at ambient temperature for the JME-31844 (high con- ductivity) silicon calibration sample. Two sets of impedance curves are shown; one corresponded to a measurement made with considerably shorter cables

1.0

¢-. (V 0.9 ¢- O CL E o o 0.8 N

c 0.7

E (~ 0.6 .N

o 0.5 Z

=~,~OikHz I I n 50 kHz ~ 1 2 5 kHz

% 200 kHz

% 315 kHz

Q I 500 kHz

92 kHz

~ , ~ " 1.25 MHz

2 MHz JME -31844 sample

~-~"-! 3,15 MHz ~e Measured outside furnace %

\ ""-o 5 MHz ~ Measured inside furnace

0.4 I i i i 0.0 0.1 0.2 0.3 0.4 0.5

Normalized real Z component

Fig. 5. A compar i son of the impedance curves for the JME-31844

sample measured outside and inside the furnace.

330 H.N.G. Wadley, B.W. Choi / Journal q# Co'stal Growth 172 (1997) 323-336

Table l Uncertainties in the impedance components for calibration sample JME-31844

Frequency Nominal Probable Nominal Probable (kHz) Re(Z) error in Ira(Z) error in

Re(Z) Im(Z)

50.0 0.04882 0.00010 0.99215 0.00033 125.6 0.10798 0.00077 0.95683 0.00065 315.5 0.16781 0.00039 0.84679 0.00210 500.0 0.16169 0.00056 0.77378 0.00313 792.4 0.13173 0.00084 0.72250 0.00372

1990.5 0.06998 0.00156 0.64747 0.03256 5000.0 0.10406 0.63928 0.50547 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 out- side the furnace, a conventional impedance curve was obtained. However, when the sensor was con- nected 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 "hook" appeared on the impedance curve. This originated from the increasing impedance contribution of the test circuit (particu- larly 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 origi- nated from interactions with conducting components in the furnace. Data collected at these two frequen- cies 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 uncertain- ties 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 fre- quency (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 4- point 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 indepen- dent of frequency. In each case, the eddy current conductivity was within the range of values mea- sured by the 4-point probe method and it was con- cluded that no corrections to the data were necessary provided data from the region of frequency indepen- dent 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 cool- ing 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 be- low 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 # Conductivity (S /m) Frequency

4-point probe Eddy current range (kHz)

MNl-1861 1471-1149 1390_+60 800-1200 MPO-5792 6667-4000 5810 _+ 170 300-700 JME-31844 11628-11234 11700_+ 170 120-300

H.N. G. Wadle~' B. W. Choi / Journal of Co'stal Growth 172 (1997) 323-336 331

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 con- ductivity.

The electrical conductivity was deduced for each

test frequency using the procedures described above. Fig. 8a shows the resulting conductivity versus fre- quency 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~ 87 ° 86 ° 84 ° 80 ° 73 ° 66 ° 53 °

10,000 ~ , ~ ~ ~ ~ ~

(a) M N I - 1 8 6 1

8OOO

E

8000

>

= 4000 " (3 E O L)

2000

6 8 1 0 s 2 4 6 8106

Frequency (Hz)

42 °

10,000

80O0 !

E

oooo

.~ 4000 Q

2000

4 6 8 1 0 5

Angle 79 ° 74 ° 65 ° 54 ° 41 °

(b) M P O - 5 7 9 2

2 4 6 8 1 0 6

Frequency (Hz)

30 ° 20 ~ 1 4 °

20,000

17,000

E

~v14,000

._~ >

11,000 "O E O (O

8000

5000

Angle 68 ° 59 ° 48 ° 36 ° 25 ° 18 °

I I I I I

(c) J M E - 3 1 8 4 4

1 1 ° 8 o

, , , 1 1 , i i , , , L J l

8 1 0 s 2 4 6 8 1 0 6

Frequency (Hz)

I I

2

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 inde- pendent 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

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

1.0

E 0.9

E O t-~ E O o 0.8 a

e3 ._c 0.7

E -o 0.6 o ._N

o 0.5 Z

0.4 0.0

Hz I

25 MHz

°°,2 MHz o o%

• 3.15 MHz

(a) CdTe Heating 1094°C i I I I

0.1 0.2 0.3 0.4

Normalized real Z component

1.o

0.5

0.9 t - O O.. E o ° 0.8 N b ._~ 0.7

E ,m

-~ 0.6

E ~ O.5 z

0.4 0.0

kHz i 1

~ 15 kHz

X 500 kHz

792 kHz

g

] .25 MHz

o o o ~ MHz

o 3.15 MHz

(b) CdTe Heating 1095°C I I I J

0.1 0.2 0.3 0.4

Normalized real Z component

0.5

1.0

t - 0.9

E O O. E O o 0.8 U

c:: 0.7

E "O

0.6 N

o 0.5 Z

180 kHz I 50 kHz " ~ = ~ 2 5 kHz

- % , 00 kHz

~ 315 kHz 8

~ 500 kHz

792 kHz

~ 1 . 2 5 MHz

° ~o~2° MHz

~P3.15 MHz

(c) CdTe Heating 1150°C 0.4 i i i i

0.0 0.1 0.2 0.3 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.

H.N.G. Wadley, B.W. Choi / Journal of Crystal Growth 172 (1997) 323-336 333

higher inductance of the more conductive test mate- rial. Nevertheless, for intermediate frequencies be- tween 200 kHz and ~ 1 MHz, frequency indepen- dent conductivities were observed. The average con- ductivity 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 contin- ued rise in conductivity. The variation of conductiv- ity with frequency at 1150°C is shown in Fig. 8c.

A n g l e

89 ° 86 ° 84 ° 82 ° 79 ° 72 ° 65 ° 52 ° 39 ° 35 ° 10,000 ~ , , , , ~ , , ,

(a) CdTeHeating 1094°C

8O0O

E

8000

O 4000

0 0

2000

, , , , 1 , , , , , , , , ] ,

8105 2 4 6 8106 2

F r e q u e n c y (Hz)

Angle 83 ° 79 ° 74 ° 66 ° 55 ° 42 ° 30 ° 19 ° 12 °

10 ,000 ~ , ~ , , , , ~

(b) C d T e Heating 1095°C

8 O O O

E

6000

O 4000

0 0

2000

/

, , , , I , , , , , , , , I ,

elO 5 2 4 6 8 1 0 6 2

F r e q u e n c y (Hz)

15,000

13,000

E

~,~ 11,000

" 0

C 0 0

9O0O

7000 I

5000 . . . . i 6 8105

Angle cc 77 ° 71 ° 62 ° 51 ° 39 ° 28 °

I I I I I L

(c) C d T e Heating 1150°C

20 ° 13 ° 9 o

I I [

:i / i¢ #

h , , , , , , , I

2 4 6 8 106

Frequency (Hz)

I I

2 4

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 be- tween 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 con- ductivity 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/solidi- fication transitions were accompanied by abrupt

10,000

8000

E

6000

._~"

.2

4 0 0 0 c- O O

2000

o l - 70O

r i i r | i a) CdTe

o Heating

1 0 9 3 °

1 0 9 2 ° ,

~ 1 0 9 6 °

, 1 0 9 5 ° I

1091 ° ,

! 1 0 9 4 °

i I J I I I I I

800 900 1000 1100

Temperature (°C)

&-

.> "5

0 0

10,000

8000

6000

4000

2000

I I r ~ I I I I |

b) Cd0.955 Zno.045 Te

o Heating

• C o o l i n g / J

1 0 9 3 ° 1 1 0 0

1099 '

0 I I I I I I I I

700 800 900 1000 1100

Temperature (°C)

10,000

8O00

E

6000

>

0 4000

0 c)

2000

I i I I

c) Cd0.92 Zno.08 Te

° Heating

• Cooling

0 I I I I I I

700 800 900 1000

1 0 9 9 °

ij ' 1104~

Temperature (°C)

1098 °

1 0 9 7 ° '

10960 1 1 0 3 ° ~ . , J 1102°-

I I 1100

Fig. 9. The temperature dependence of electrical conductivity for: (a) CdTe; (b) Cdo.955Zno o45Te; (c) Cdo 92Zno.osTe.

H.N.G. Wadley, B.W. Choi / Journal q[ Co'stal Growth 172 (1997) 323-336 335

changes in conductivity. The solid just prior to melt- lO,000 / ing or immediately after solidification had a conduc- L tivity of ~ 1050 s / m while the liquid conductivity / was ~ 6200 S /m. With the exception of a small 0000~ ( ~ 3°C) temperature hysteresis during the melting/solidification region, the electrical conduc- ~ 8000 tivity at each measurement temperature was the same during heating and cooling. ~ 700o

O 3.3. Cdo.955Zno.o45Te sample

Fig. 9b shows the temperature dependence of the electrical conductivity for the Cd0.955Zn0045Te sam- ple. 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 be- havior 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 ob- served during heating. The conductivity then gradu- ally decreased as the temperature was lowered.

3.4. Cdo.92Zno.o~Te sample

The variation of electrical conductivity with tem- perature 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 heat- ing, and solidification began at 1099°C on cooling. There was 6.45-fold increase in conductivity upon melting. This sample also exhibited semiconductor- semiconductor behavior during the melting/solidifi- cation transitions.

Fig. 10 summarizes the dependence of conductiv- ity on composition and temperature near the melting points for Cdl_xZnxTe alloys. Zn significantly re- duces the melt conductivity. However, a weak maxi- mum 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 temper- ature. The origin of this reproducibly observed phe- nomenon in unclear.

6 0 0 0

, , , T: (a) liquid

5000 0.00 0.02 0.04 0.06 0.08

X 2000 l i ~ , ~ , , , ,

(b) solid

1 oBo,c ~ lO7O'(; ~ " 1 5 0 0 l o ~ , c ~ooo.c

1050"C

1ooo ._>

500

o i i i ] i i i i i 0 . 0 0 0 . 0 2 0 . 0 4 0 . 0 6 0 . 0 8

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 solidi- fication of Cd L xZn,Te alloys. The melt is found to be 4-6 times more conductive than the solid. Semi- conducting behavior (exponential conductivity-tem- perature relationship) is found in the solid and liquid phases. These solid ( ~ ) and liquid (o-/) conductivi- ties 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 com- position and recently reported ambient temperature resistivity measurements for CdZnTe alloys as func- tion 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 per- haps 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 semi- conducting behavior with an exponential conductiv- ity-temperature dependence. When the samples were heated through the melting point under quasi-equi- librium conditions (heating/cooling rates of < 0.1°C/min) a large 4 - 6 fold discontinuity in con- ductivity 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 sen- sors to monitor the liquid-solid interface during vertical Bridgman growth. The significant depen- dence of conductivity upon composition also sug- gests 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 Pro- gram conducted by a consortium that includes John- son 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 or- ganizations and in particular to the staff of JME for their assistance in preparing the samples. The consor- tium 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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