The temperature distribution in ZnWO4 crystal during growth from the melt

Journal of Crystal Growth 10 (1971) 39—44 © North-Holland Publishing Co.

THE TEMPERATURE DISTRIBUTION IN ZnWO4 CRYSTALS DURING GROWTH FROM THE MELT*

R. A. M. SCOTT Thames Polytechnic, London SE. 18, England Received 22 March 1970; revised manuscript received 12 December 1970 The temperature distribution in Czochralski pulled zinc tungstate crystals has been predicted and measured for pure and cobalt doped specimens. The results indicate a uniform temperature gradient in the crystal from the melt interface up to the ]evel of the top of the crucible walls, thereafter the temperature of the crystal drops exponentially with increasing distance from the melt interface. Only in this latter region does the temperature depend on the cobalt doping and hence radiative properties of the crystal. The temperature distribution in the melt and the surrounding air space has also been measured.

8’ 9), the results indicate that the longitudinal manium is uniform over at least the first 8 mm of the gradient crystal. In silicon1 0) the temperature falls linearly from themeltingpointalongthefirst 12—15mm of the ingot but after this point the temperature falls less sharply in a smooth curve. Measurements of the thermal distribution in a growing ZnWO 4 crystal within a few mm of the solid—liquid interface have previously been reported”) and these also indicate a uniform temperature gradient in the growing solid. This paper extends the established theoretical relationships so as to cover the previously quoted experimental work and results obtained during this investigation of the growth of ZnWO4. The effect on the temperature distribution within the growing crystal of a modification of the optical density by doping normally transparent zinc tungstate is also reported.

1. Introduction An important factor controlling the quality and perfection of any crystal grown from the melt is the temperature gradient at the growth interface. An interface formed of a concave solid will permit mis-orientated regions nucleated at the external surface to grow into the bulk of the crystal. Supercooling at the interface will produce dendritic growth and, in doped materials, microsegregation ofthe dopant. Many criteria for stable growth have been derived in terms of gradients existing at the interface~j. In addition the temperature gradient in the grown crystal affects the density and distribution of dislocations and internal strain. Thus a knowledge of the temperature distribution in both the growing crystal and the melt is highly desirable, Previous estimates of the temperature 7) havedistribution in general in pulled crystals during by growth’ been based on cooling radiation from a static crystal, one end of which is maintained at the melting point, although recently Brice8) has included in the

2. Experimental Crystals were grown in air in a fairly conventional Czochralski puller1 2) The seed crystal, which throughout this investigation was pure ZnWO 4, was held in a chuck which was both rotated and hydrauli1 3), A hollow shaft and slip ringraised system9) were cally employed to carry six insulated sets of thermocouple wires, each pair consisting of 0.5 mm diam. platinum and platinum/13% rhodium wires, down to the rotating chuck. A 5 MHz r.f. heater with constant power control up to 6 kW was used to maintain the crucible temperature constant to within ±0.25 deg C at approx.

theoretical analysis radial temperature gradients and growth velocity. Whether or thermal not this characteristics extra refinement is important depends on the of the crystal. Measurements of equilibrium thermal distributions in semiconductor crystals have been reported. In ger* Work performed on industrial secondment at Mullard Research Laboratories, Redhill, Surrey.

39

40

R. A. M. SCOTT

1300 °C. The crucible was thermally insulated from the r.f. coil by 1 cm of alumina wool filling and a pulling enclosure was formed by a large diameter concentric silica tube, All the crystals were grown in air parallel to the C-axis from a pure platinum crucible using Johnson Matthey and Co. “Specpure” reagents. Initially a stoichiometric melt of zinc oxide and tungstic oxide was made up; if it was required to alter the thermal properties of the crystal, a measured quantity of cobalt oxide was added as dopant. Cobalt is a particularly suitable dopant in this respect as it was found to have a broad absorption band from 1.0 J.tm to 2.2 l.tm when incorporated in a matrix ofZnWO4, so that at temperatures down to at least 1000 °Cthe wavelength of maximum emission of a black body radiator is covered by the cobalt absorption band. The doped crystal is however not an idealized black body and will in fact radiate predominately within precisely the wavelength range at which its maximum absorption occurs, so that cobalt doping should appreciably modify the thermal characteristics of the crystal. The experimental technique utilized for obtaining the temperature distribution in a growing crystal is as follows: appropriate melt was made1.5upcmin diathe crucible andAna crystal of approximately meter was grown on to the seed. Growth was generally performed at a rotation rate of 24 r.p.m. and a pulling speed of 8 mm/hr. The crystal was allowed to grow uniformly until it reached approximately 5 cm in length at which point the melt temperature was raised at 1 deg C/mm causing the crystal to taper rapidly to a

crystal was dipped and melted back at the usual pulling rate until the lowest thermojunctions were 1—2 mm from the melt interface. Pulling was re-commenced and the temperature from all six thermocouples was read as a function of distance which the crystal had been pulled. The location of the exact zero point of distance was later determined by measurement of the “melt-back” mark on the crystal surface when it had cooled. The temperature distribution in the melt was determined by means of a 0.5 mm diarn. platinum and platinurn/l3~ rhodium thermocouple mounted in alumina sleeving with its tip exposed and located in position with a micromanipulator. Relative temperatures of both melt and crystal could be read to 0.1 °Calthough the absolute temperature measurement was probably no better than ±2°C. 3. Results and interpretation 3. 1.

TEMPERATURE DISTRIBUTION IN

THE

GROWING

CRYSTAL

In his theoretical approach to the steady state heatflow problem8)inbased a cylindrically symmetrical his calculations on thegrowing equilicrystal,equation Brice brium ~2O

~~

point. The crystal was then removed from the puller with chuck stillinto attached and aunder set ofwater six 0.5 mma holes the were drilled the crystal with high speed rotary drill. The holes were located in three pairs, spaced 5 mm apart along the growth axis and drilled to a depth equal to half the thickness of the

+ = 0 (I) r or oz where 0 is the difference between the actual temperature T and the ambient temperature of the pulling system T 0, and r and z are radial and axial co-ordinates respectively. Assuming a crystal of radius a, a simpli8) as fled solution to this equation has been suggested 2 /1—hr ~2a~ I /2h 1 0 = Om (~—j— ) exp [—k-—(2) ia a where 0m is the telative melting point (Om = —T

crystal. The crystal and chuck were then replaced in the puller and thermojunctions made from 50 ~tmdiam. platinum and platinum/l3% rhodium wires were welded to similar 0.5 mm diam. wires running through the pulling shaft. The thermojunctions were placed in the drilled holes as near as possible to the centre of the crystal. The crystal andwere meltestablished were re-heated slowly until growth conditions and then the

and h = a/k, where a is the energy emission pcr unit area of surface per unit temperature excess over ambient and k is the thermal conductivity of the crystal. This indicates an exponential drop in temperature along the length of the crystal. Axial and radial gradients are thus 2/2a\~exp zl (3) ~ = 0 (2h~(1_hr l~z m ~a / \ 1— ~ha / L \aI i

-~

~+

-~-~

oi

zj

~

0)

F—

(—~

IHE TEMPERATURE DISTRIBUTION IN

ZnWO4

thus

CRYSTALS DURING GROWTH FROM THE MELT

41

expression similar to eq. (2) would be expected so that =

—

—

(—~0,

(4)

\aJ

from eq. ~~4) 0z

and also --

/2h\~

-

hr (2h\* 1 exp 1— z], a(1—~ha) ~ a

=

~--

_-~

(5)

—(1

(T-T0).

As a boundary condition we can say that at z = c5 the temperature is Te and the longitudinal gradient is represented by both expressions, i.e.

th us

TmTe

hr 0. a(1-hr~2~

O0 ---— -

—

—

(6)

crystal as shown in fig. Ia is rarely achieved. Usually hot crucible walls exist above the surface of the melt and these in turn both radiate and reflect heat back to the first centimetre or so of the growing crystal. Fig. lb shows this situation, a

~

(~)atT=T~=

In practice, however, the situation of uniform heat loss throughout the whole length of the growing

a

(9)

\aJ

1~

(2h~+ aJ (I~—T0).

—i

(10)

This enables the various coefficients to be determined from experimental results. 3.2.

TEMPERATURE DISTRIBUTION MEASUREMENTS

Crystals of pure ZnWO4, ZnWO4 + 1.9 molar °/~ cobalt doping and ZnWO4 + 2.9 molar °/~ cobalt doping were grown and the temperature distribution measured during growth. The accurate measurement of dopant concentration was later performed by chemical analysis. The measured temperatures plotted against distance

for b and each c. of the three materials are shown in figs. 2a,

Crystal

t ______

z~

~

~

y1ea

______

interface gradient linearly with temperature In fig. the 3 is plottedvaries the longitudinal gradient 8T/0 against temperature. Far from the high temperatures, gradientnear is a constant 240 °C/cm according to eq. (9)thewhereas to the interface at for each material thus corresponding to eq. (7). T

_____ Heat ‘~Crucible waI~0~

0 Fig. 1. (a) Radiation from a crystal grown from an infinite melt. (b) Radiation from a crystal grown within a limiting crucible.

is given by the temperature at which äT/äz = 0. Further, a plot of log (T— T0) against z for each

crystal enables a value of (2h/a)~to be obtained in If ö is the distance over which the heat loss is solely each case since from eq. (2). axial due to the crystal being situated within the crucible and Te is the temperature from which the exlog (T— T0) = log 0 = log Om + log (i — -2---) ponential drop in temperature with distance com4 mences, then the lowerform part would of the becrystal, an 2h’ z. expression of over the following expected — log(l —+ha) — (11)

(~)

-

TmTe --

=

constant,

(7)

so that (TTm)

(Tm~Te) =

—

‘5

(8)

From these figures, a value of ~ and Te may be determined for each crystal using eq. (10). These results are tabulated in table I. Note that for each crystal +ha <0.03 and also hr2/2a < 0.03, so that eq. (2) may be simplified to

where T 5~is the actual melting point. Over the upper part of the crystal an exponential

0

r

= Omexp

/2h\+

1

zl. LI— (—) \ a / j

(12)

42

R. A. M. SCOTT 1200

1200

1100 1000

1000~

N

~7o0 0

c700

a

0

~~—8

E600

0

~

500~

2a

0

~

2b 0

04

08

12

16

20

Z (cm)

24

28

32

36

40 44

Z (cm)

1200

1100

Using values of the various parameters listed in table I, a relationship can be obtained to represent the temperature as a function of distance measured from the

N

.

0

1000

interface for each of the three different types of crystals. The equations are listed in table 2 and are shown as

900 3.800

2

solid curves in figs. 2a, b and c. The close agreement between the experimental points

700~-

~600

and the curves from therole equations of crucible table 2, illustrates clearlyplotted the important which the

%-~

500

2c

4000

-

.

04

0812

16

20

242832

36

.

wall and rim play in determining the thermal conditions in a pulled crystal immediately after it has solidified. It may be noted that the thermal gradient in this region is independent of the dopant concentration in the material. The extent of the region of linear temperature gradient is determined primarily by the level of the melt in the crucible and so is necessarily somewhat time-dependent as the crystal is growing.

40 -~T

0,

2 (cm)

Fig. 2. (a) Longitudinal temperature distribution in a pure ZnWO4 crystal during growth; curve corresponds to eqs. (13) and (14). (b) Longitudinal temperature distribution in a 1.9% cobalt doped ZnWO4 crystal during growth; curve corresponds to eqs. (15) and (16). (c) Longitudinal temperature distribution in a 2.9 /~cobalt doped ZnWO4 crystal during growth; curve corresponds to eqs. (17) and (18).

.

.

.

.

TABLE

I

Growth parameters of zinc tungstate crystals doped with various quantities of cobalt Material ZnWO4 ZnWO4-)-1.9% Co ZnWO4—)-2.9% Co

T0. (C)

T, (C)

T0 (C)

1190 1190 1190

1010 905 920

435 255 175

(cm) 0.75 1.2 .2

a (cm)

(26/u)’

0.7 0.55 0.55

0.41 0.37 0.34

TABLE 2 Equations relating crystal temperature to distance from melt interface

Material ZnWO4 ZnWO4-F1.9% Co ZnWO4+2.9°~Co

Range of validity for z (cm) 0—0.75 0.75—m 0—1.2 I.2—m 0—1.2

Equation (Tin C and z in

Cm)

T = 1190—240 z T ~- 585 exp {— 0.41(z-—0.75)}-(-425 T= 1l90—240z T = 650 exp { —0.37(z—- l.2)}+255 T = l 190—240 z T = 745 exp {—0.34(z-— l.2)}-f- 175

6

(cm

(13) (14) (IS) (16) (17) (18)

—

0.060 0.038 0.032

THE TEMPERATURE DISTRIBUTION IN

0

ZnWO4

Tomparatura (OC) 100 200 300 400 500 600 700 800 900 1000 1100

~

1 90/0

pad crystal crystal

-80

0

~ -160

a

-200 -240

a

-280

Fig. 3.

Plot of dT/dz against T for each crystal.

ature Theoftemperature the pulling T0 system, represents and this the ambient appears to temperdrop linearly as the cobalt concentration of the crystal rises. This is shown in fig. 4 which also shows that the value of h( = a/k) depends reciprocally upon cobalt concentration. A possible explanation for the latter relationship is that increased doping results in a considerable increase in the effective thermal conductivity

its heat solely by contact with the crucible walls. It looses heat only from its free surface by radiation, gas convection and conduction along the growing crystal.

each °C/cm;ZnWO4+ of the materials 1.9% Co,These were: pure 7±4°C/cm; andZnWO4+ 18±5 +2.9°/~ Co,three 1±4°C/cm. resultsZnWO4, also support the suggestion that increased doping increases the effective thermal conductivity of the material. 3.3. TEMPERATURE DISTRIBUTION IN THE LIQUID ZnWO4 is an insulator. The melt, therefore, gains

3.4. TEMPERATURE DISTRIBUTION IN THE AMBIENT GAS It has been seen previously that T 0 represents the

-5

I 6

(cm)

\\

Crystal

1

\

-

“

\

6’o’-~““ ~ -o67jc~ ~o’ ~

I-

- 2 ~1

___

1

2

3

Molecular ~ of Co

Fig. 4.

Plot of T 0 and I/h against dopant concentration.

“~

\

~ __C~~~.~,N0s\

\

\

d/

1~ 9oo’c

I

~

—

—

\Q0

i1~o~c

~ 200 100 0

\\

7OO~C ~ 2-

400 (cm) - 3

Sihco ~ tube

\~

~d~ij8OOC 9O0~C

a I—

LI

shown in fig. 5, which is a cross section through the complete pulling system with isotherms marked in the crystal, melt and gas space, for a 2.9 molar% cobalt doped specimen. The presence of large temperature gradients and the associated differences in liquid density cause strong convection currents to be set up producing relatively well established temperature oscillations8)indo thehave melt. a maximum These oscillations, amplitudewhilst whichappearing depends erratic on the location at which the temperature is measured. Oscillations detected ranged from ±2 deg C near the surface of the melt to ±0.4 deg C at 1.0 cm below the surface.

of the crystal, which must include radiative transfer. The radial temperature gradient appeared to vary erratically along the length of the crystal and no variation of the type expected from eq. (5) could be detected. The mean values of the radial gradient for

500-

43

gradients in the melt and these do indeed occur as This would lead one to expect marked tempelature

O~\

doped c ~ -120

CRYSTALS DURING GROWTH FROM THE MELT

~iumino \wool\ insulation

— \\ \ ~Crucible _____ -10 --~-~-~ fi300’C — Melt N the \ Fig. 5. Temperature distribution in whole pulling system during growth of a 2.9% cobalt doped crystal. Isotherms are

broken lines marked in °C.

44

R. A. M. SCOTT

ambient temperature of the pulling system and it was considered important to relate this to the temperature distribution in the gas surrounding the growing crystal. The temperature distribution in the gas phase was determined using a platinum and platinuni/13 % rhodium thermocouple in alumina sleeving and located in position with a micromanipulator. There are considerable experimental difficulties associated with the gas temperature measurements due to the existence of considerable convection currents which give temperature oscillations similar to, but much larger than, those occurring in the melt. The magnitude of these oscillations ranged from ±20deg C just above the lip of the crucible to ±4 deg C near the outer silica tube. It would appear that T 0, which is 175 °C,represents the seed temperature at infinity so that although it arises from the temperature distribution equation within the crystal it cannot necessarily be said to represent the temperature at any real point within the system.

4. Conclusions Equations determined primarily by an exponential function have been derived for the temperature distribution within a growing crystal and experimentally these are shown to be applicable over the length of the crystal outside the crucible containing the melt. The exponential decay term which in turn depends ott the thermal conductivity and surface emissivity of the crystal decreases as the ZnWO4 is doped with cobalt. The temperature gradient over the part of the crystal from the melt interface to the top of the crucible is uniform and is independent of the optical characteristics of the crystal. This conclusion is of importance when considering optimum conditions for the growth

of Czochralski pulled crystals from the melt since it is the thermal gradient at the growth interface which governs growth stability and crystal quality. This gradient is determined in practice primarily by the melt temperature and the temperature of the upper walls of the crucible. These general conclusions are in agreement with previous experimental work on temperature distributions during growth of semiconductor8~°)and zinc tungstate1 i) crystals. Acknowledgement The author is grateful to Dr. J. C. Brice and his colleagues at the Mullard Research Laboratories for invaluable advice and assistance during this work. References I) W. A. Tiller, K. A. Jackson, J. W. Rutter and B. Chalmers, Acta. Met. 1 (1953), 428. 2) W. W. Mullins and R. F. Sekerka, J. AppI. Phys. 35 (1964) 444. 3) R. F. Sekerka, J. Crystal Growth 3,4(1968) 71. 4) R. T. Delves, J. Crystal Growth 3, 4 (1968) 562. 5) F. Billig, Proc. Roy. Soc. (London) A 229 (1955) 346. 6) D. T. J. Hurle, in: Progress in Materials Science, Vol. 10, Ed. B. Chalmers (Pergamon, Oxford, 1962) p. 139. 7) T. B. Reed, in: Crystal Growth, Ed. H. Peiser (Pergamon, Oxford, 1967) p. 39. 8) J. C. Brice, J. Crystal Growth 2 (1968) 395. 9) J. C. Brice and P. A. C. Whiffin, Solid State Electron. 7 (1964) 183. 10) B. M. Turovskii and K. D. Cheremin, morgan. Mater. 4 (1968) 712. II) J. C. Brice and P. A. C. Whiffin, Brit. J. AppI. Phys. 18 (1967) 581. 12) J. C. Brice, The Growth of Crystals from the Melt (North-

Holland, Amsterdam, 1965) pp. 140—1. 13) J. C. Brice, G. W. Lelievre and P. A. C. Whiffin, J. Phys. F. 2 (1969) 1063.