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Parameters of growth from the vapor phase of ZnS crystals
Mat. Res. Bull. Vol. 1, pp. 173-183, 1966. in the United States.
Pergamon P r e s s , Inc.
Printed
PARAMETERS OF GROWTH FROM THE VAPOR PHASE OF ZnS CRYSTALS Indradev t University of Delaware, Newark, Delaware
(Received August 17, 1966; Refereed)
ABSTRACT Large crystal~ of cm size of zinc sulfide have been grown at 1350 C by the self=sealing method. Argon, hydrogen sulfide, and helium gases at various pressures were used as ambients. AT, the initial difference in temperature between the charge and the nucleation site, dT/dz, the temperature gradient in the growth zone and the drive rate of the growth tube through the furnace were studied as parameters of thi~ method of growth. The optimum value of AT = 22 ± 3 C v gives 1.4 as the supersaturation ratio needed for initial nucleation. The rate of solid-transport has been found to be controlled by diffusion. Introduction Zinc sulfide crystals have been grown for over a decade by various workers but, cm size crystals of good quality are still rare°
Addamiano and Aven (I)
have grown zinc sulfide crystals
from melt at 1850°C under argon pressure of I0 atmospheres°
The
various methods of growth from the vapor phase need lower temperatures and the use of hlgh pressure is not necessary.
These
crystals are usually smaller than those grown from the melt. Reynolds and Czyzak (2) grew mm size rod crystals in sealed quartz*Portions of this paper were presented at the Conference on Luminescence, Hull (1964). Work supported by U.So Army Research %Office-Durham, Contract No. Da-31-124-ARO (D)-173o Present address: Department of Applied Physics, Techniche, Hochschule, Karlsruhe, Germany.
173
174
ZnS CRYSTALS FROM VAPOR PHASE
Vol. I, No. 3
ampules at I150°C Kremheller (3) grew needle and ~late type crystals at 1250°C using the flow method. Samelson (4j used the halogen transport method to grow cubic crystals of zinc sulfide at 980°C. Relatively larger crystals have been grown by Green et. al. (5) at 1550°C. Piper and Polich (6) used the self-sealing system to grow cm size crystals of ZnS. A study of the kinetics of growth of ZnS crystals from the vapor phase should reveal the relevant parameters of crystal growth which may be optimized to grow large crystals at temperatures below 1500°C. Hamilton, (7) Samelson,(4)and Patek (8) discuss the mechanism of growth of zinc sulfide crystals, but supersaturation is the only parameter they consider. Jona (9) and Jona and Mandel (I0) have considered the solid transport in the growth of zinc sulfide by the halogen transport method. Dev (II) has found that when zinc sulfide crystals are grown by the flow method, the crystal habit depends on the dissipation of the heat of condensation. The kinetics of growth of cadmium sulfide crystals in relation to the dislocation structure has been reported by Chikawa and Nakayama (12). HSschl and Konak (13) have studied the relationship between the sublimation velocity and the vapor pressure of one of the components in the growth of CdSe and CdTe crystals. The growth of crystals from the vapor phase in a sealed tube can usually be separated into three stages: (a) transport of solid, (b) initial nucleation, and (c) the subsequent growth of crystal. The transport of solid depends on the vapor pressure of the solid at the growth temperature and on the diffusion coefficient of the vapor (if the transport is controlled by diffusion). The initial nucleation depends on the difference in temperature between the charge and the nucleation site which gives rise to a difference in the vapor pressure and to supersaturation. The subsequent growth of the crystal is determined by the rate of solid transport, maintenance of supersaturation and on the dissipation of the heat of condensation. The above considerations suggest that a fast rate of growth can be achieved by working at high temperatures and by using an ambient gas with low molecular weight in order to have a high value of diffusion coefficient° The optimumvalue of supersaturation can be determined experimentally and can be maintained during crystal growth° An increase in the
Vol. 1, No. 3
ZnS CRYSTALS FROM VAPOR PHASE
175
supersaturation will lead to the formation of a large number of separate nuclei on which growth can proceed and polycrystalline growth will result. stop altogether.
At low values of supersaturation growth may
The heat of condensation raises the temperature
at the vapor-crystal interface unless it is removed at the same rate at which it is being given to the crystal. This excess heat can be removed by conduction and by radiation from the outer crystal surface.
In either case the thermal conductivity of the
crystal will determine the temperature gradient in the growth region of the furnace. The present work makes a study of the factors controlling crystal growth that have been mentioned above for the specific case of zinc sulfide.
The self-sealing growth system has been
selected because it yields large crystals at relatively lower temperatures.
Also, because the pressures inside and outside
the growth tube are equal, fused quartz can be easily used at these temperatures. Three ambient gases, helium, hydrogen sulfide, and argon at various pressures were used. The growth temperature was kept between 1300 and 1350°C.
Experimental Experimental arrangement adopted in this work is shown in Fig. I.
The starting material was pre-fired GE electronic grade
zinc sulfide powder.
About 15 gms of the powder was packed in a
quartz charge tube and was placed inside a quartz growth tube of about 1.5 cm bore.
The growth tube was open at one end and was
drawn out to bullet-shape with a pointed tip at the other end. At the tip, a quartz conduction rod was sealed to the growth tube. A gap of 3 to 5 cm(depending on temperature profile of the furnace) was kept between the charge tube and the tip of the growth tube. Behind the charge tube, another quartz tube (blocking-tube) with closed end was placed inside the growth tube. The blocking tube left a gap of about I rmm between itself and the growth tube. This gap gets sealed by the deposition of zinc sulfide when crystal-growth starts. All the quartz used in these experiments was 'Amersil' transparent fused quartz. The growth tube and its contents were placed in an alumina tube of 2 cm bore and 50 cm
176
ZnS CRYSTALS FROM VAPOR PHASE
Vol. I, No. 3
length. The alumina tube was closed at one end;at the other end it was ground to take a graded glass joint. The glass joint had outlets for evacuation and for introducing the ambient gas. The alumina tube was placed in a two-zone platinum furnace. Electric power through the main heating coil was regulated by a 'West SCR Stepless' control unit to keep temperature at the controlling thermocouple to within I C °.
Temperature in the hot zone was
kept at 1350°C and the power in the slde-coil was regulated to keep the temperature gradient in the growth-zone constant.
The
temperature gradient could be varied from I0 to 50 C ° per cm.
A
motor drive was coupled to the alumina tube which pushed it through the furnace at a rate ranging from 1.5 to 3 cm per day.
CHARGE
TIP
TUBEI CONDUCTION ROD ~ / / / / / /o/o/o~ooo V / / /.... / / / / AoJo / V / /....... / / / A / / //o /.3"/I///¢/ BLOCKING TUBE
~
GROWTH
....
i~ ___
Lo
......
/
DRIVE)
~/fflllI////llll/I/llllll~(lllllllll/~ ...............
FURNACE MUFFLE
"7 ......
ALUMINA TUBE
f 1300 TEMP. "C 1200
5
I0
15
20
DISTANCE |CM)
FIG. I Experimental Arrangement for Crystal Growth and the Temperature Profile of the Furnace ' The following procedure was adpoted to start a growth run: zinc sulfide powder was packed in the charge tube which was then placed at proper position in the growth tube with the help of the blocking tube° The growth tube was then placed in the alumina
Vol. 1, No. 3
ZnS CRYSTALS FROM VAPOR PHASE
tube which was in the furnace.
The alumina tube was evacuated
and the furnace heated to 800°C. for one hour at this temperature.
The system was vacuum baked After baking,
the alumina tube
was filled with the ambient gas at suitable pressure. step, stabilization,
177
The next
consisted of raising the temperature of the
furnace to get the desired temperature profile for that growthrun.
The tip of the growth tube was placed at the highest temp-
erature so that no nucleation may take place there during stabilization period which lasted for one hour. stabilization,
the
At the end of
the alumina tube was shifted to a position in the
furnace such that the tip of the growth tube was at the starting temperature.
The driving motor was started and the growth-run
was in progress.
During the period of stabilization and the
early part of the growth-run,
the gap between the growth tube
and the blocking tube is sealed by the condensing vapor of zinc sulfide and subsequent growth takes place in a sealed system. A growth-run usually lasted from 20 to 60 hours, after which the furnace was allowed to cool to below 300°C and the crystal was taken out by breaking the growth tube. The crystal growth experiments were done with three ambient gases:
helium, hydrogen sulfide, and argon.
The ambients were
used at pressures of I arm., 30 cm and I0 cm of mercury.
Some
growth-runs were made without any ambient in which case zinc sulfide, zinc and sulfur had to duffuse through a mixture of their own vapors. A successful growth-run depends, to a large extent, on the initiation of growth from only a few nuclei, preferably one.
It
is for this purpose that the tip of the growth tube is pointed and the temperature-difference
&T between the powder charge and
the tip at the start of the growth-run has a definite value. &T was used as one of the growth-parameters
in these experiments.
Results The crystals grew in the shape of the growth-tube and usually consisted of two or three crystals of the size of I0 x 5 x 3 mm. crystal,
Occasionally,
the as-grown crystal was a single
15 mm long and about 12 mm in diameter.
The crystals
178
ZnS CRYSTALS FROM VAPOR PHASE
did not show large natural faces, however, narrow strips of less than I m m w i d t h crystals.
Vol. 1, No. 3
low index faces in
were found on several
The direction of growth of these crystals was along
the c-axis.
The (0001) face was always present as a circle of
about 0.5 mm
diameter at the growing end of the single crystals.
Most of the surface of the crystal at its growing end looked glassy without any sharp edges and faces. The chemical purity of the crystals was of the same order as that of the starting material. representative
The chemical analysis of a
crystal is given in Table I. TABLE I
Spectrographic Analysis of a ZnS Crystal and the Starting Material. The Numbers Represent Parts Per Million. ND = Not Detected
A5
AI
Cd
Cr
Cu
Fe
Mn
Ni
Pb
Si
Crystal
ND
7
ND<5
ND
4
i0
ND
5
ND<5
90
Powder
ND
2
ND<5
ND
3
ND
ND
ND
ND<5
15
The optimum value of AT, the initial temperature difference between the tip of the growth tube and the charge, was found to be 22 & 3 C ° . transport.
It varied only slightly with the rate of solid
The temperature gradient in the growth-zone had a
value between 25 and 30 C ° per cm for best results.
The changes
in the rate of growth of the crystals did not affect the temperature gradient but, the drive-rate of the growth tube through the furnace had to be adjusted.
The drive rate had to be in-
creased to about 3 cm per day for a fast growth e.g. in helium gas and it was 1.5 cm per day for growth in argon at atmospheric pressure, The experimental values of the transport rates are given in Table II.
These values are for an average temperature
difference of 50 C ° , the diffusion distance of about 6 cm and 2 the area of cross-section being approx. 0.8 cm .
Vol. 1, No. 3
ZnS CRYSTALS FROM VAPOR PHASE
179
Hydrogen sulfide at reduced pressure and helium at atmospheric pressure as ambient gases yielded the maximum number of large single crystals. The crystals grown in helium showed green luminescence with a long decay period while those grown in hydrogen sulfide showed a weak blue or no luminescence. TABLE II Flux of Zinc Sulfide at 1325°C
Ambient Experimental Flux Pressure (10-7mols cm-2sec "I) Gas (cm of mercury)
Argon
H2S
Theoretical Flux (10-7mols cm-2sec -I)
76 30 I0
3.5 4.5 5
1.4 3.9 12.9
76
3.9
4.3
30
5.0
10.2
76
Ii.0
3.8
30
ii
8.8
Vacuum
6
Helium
28
Discussion The theoretical calculation of solid-transport is based on the assumptions that: (a) fixed concentrations of the vapors of ZnS, Zn, and S 2 are present at the charge and at the growth site, (b) these concentrations have the equilibrium values corresponding to the temperatures at those points, and (c) the transport is according to the Fick's first law(14): c Di
dx i
Ni = i - x i dz
180
ZnS CRYSTALS FROM VAPOR PHASE
Vol. I, No. 3
where N i = gm mols of the i th component transported c = Z ci
•
CI
=--= mi
molar density
Oi and m i are density and mol. wt. of the i th component ci Pi xi =~=-c p Pi = partial pressure of the i th component p = total pressure in the system D i = effective diffusion constant of the i th component in the mixture as given by: (15) ~ i = ~ P] j Dij The individual diffusion constants Dij were calculated by the method used by Jona and Mandel (I0) with the help of the formula Di j =
3 8n°ij
[ kT(mi + mj) 2
]
2~mim j
where n is the total gas density in atoms per cm 3.
This can
be calculated from the total pressure and average temperature T which was 1598°Ko
m i and mj are the masses of the molecules
or atoms considered° oij = 1/2 (~i + oj) ~'i and ~j being the corrected "hard-sphere diameters" of molecules i and J. The value of D.. obtained from this formula was 13 0.3 corrected by multiplying by (1598/273) = 1.7. These corrections are explained in Jona and Mandel's paper. The calculated values of the diffusion constants are given in Table III. The various partial pressure in the systems ZnS = Zn + 1/2 S 2
Vol. I, No. 3
ZnS CRYSTALS FROM VAPOR PHASE
181
and H2S = H 2 + 1/2 S 2 have been obtained by extrapolating the data of Pogorelyi (16) which was measured over the range 800 to 1250°C. TABLE III Binary Diffusion Constants (cm2sec'~)- at About I Atm. Total Pressure and 1325vC
ZnS
Zn
Argon and
ZnS
0.93
1.58
Helium Systems
Zn
1.58
2.79
S2 A He
1.16 1.57 5.33
1.93 2.57 9.25
ZnS Zn
2.31 3.92
3.92 6.91
S2
2.87
4.77
H2S H2
3.38 22.2
5.39 39.5
H2S System
Table II lists the calculated rates as well.
values of the transport
The agreement between the two sets of values is
good enough to conclude that the growth of zinc sulfide crystals in this study was transport-controlled and that the solid is transported by diffusion. However, the nature of the ambient probably influences the crystal growth through adsorbed layers at the vapor-solid interface. The assumption made in the above calculations that the vapor pressure of zinc sulfide at the growth site is the equilibrium vapor pressure, points to the difficulty in obtaining any estimate of supersaturation in front of the growing crystal 18)." " Since the crystal growth has been found to be transport-controlled, the supersaturation should be very small°
182
ZnS CRYSTALS FROM VAPOR PHASE
Vol. 1, No. 3
However, a definite value of AT suggests the existence of a maximum value of supersaturation necessary to initiate the crystal growth. of 1.4.
AT ffi 22 ± 3 C ° would mean a supersaturation ratio
This value is slightly lower than that obtained by
Samelson(17)which was between 2 and 3 for growth of zinc sulfide crystals in sealed ampules. But, Samelson hadnot considered the influence of transport rate (which is limited by diffusion) on the value of actual vapor pressure at the growth site. The dissipation of the heat of condensation is another important factor which determines the growth of large single crystals.
The heat generated at the growing face must travel
through the crystal to its cooler end from where it is lost mainly by radiation to the surrounding alumina tube.
The con-
duction rod merely fixes the separation and hence the temperature difference between the tip of the growth tube and the closed end of the alumina tube.
The dissipation of the heat of
condensation depends on the thermal conductivity of the crystal and the temperature gradient in which it is situated.
The direc-
tion of growth in these experiments has been found to be along the c-axis. This is interpreted to mean that hexagonal zinc sulfide has maximum thermal conductivity along c-axis(ll)o Moreover, the growing surfaces of the crystals are convex indicating that this value of thermal conductivity is higher than that of fused quartz at this temperature (1300°C) (18). Conclusion Large single crystals of zinc sulfide can be grown by the self-sealing method if suitable values of parameters such as AT and temperature gradient are selected. The exact values of these parameters depend on the ambient gas used and on its pressure. These parameters can be interpreted to give a better understanding of the supersaturation during crystal growth and of the thermal conductivity of the crystals at the temperature of growth. Further work is needed to determine the exact role of the ambient gas in the growth process.
Vol. I, No. 3
ZnS CRYSTALS FROM VAPOR PHASE
183
References I. 2. 3. 4. 5. 6. 7. 8. 9. I0. Ii. 12. 13. 14. 15. 16. 17. 18.
A. Addamiano and M. Aven, J. Appl. Phys. 31, 36 (1960). D. C. Reynolds and S. J. Czyzak, Phys. Rev. 79, 543 (1950). A. Kremheller, Sylvania Technologist 8, ii (1955). H. Samelson, J. Appl. Phys. 33, 1779 (1962). L. C. Greene, D. Co Reynolds, S. J. Czyzak and W. M. Baker, J. Chem. Phys. 29, 1375 (1958). W. W. Piper and S. J. Polich, J. Applo Phys. 32, 1278 (1961). D. R. Hamilton, Brit. J. Appl. Phys. 9, 103 (1958). K. Patek, Czch. J. Phys. BI2, 216 (1962). F. Jona, J. Phys. Chem. Solids 23, 1719 (1962). F. Jona and Go Mandel, J. Chem. Phys. 38, 346 (1963). Indra Dev, Brit. J. Appl. Phys. 17, 761 (1966). J. Chikawa and T. Nakayama, Jo Appl. Phys. 35, 2493 (1964). P. HSschl and Co Konak, physo status sol. 9, 167 (1965). R. B. Bird, W. E. Stewart, and Eo N. Lightfoot, Transport Phenomena, p. 523, John Wiley and Sons, Inc. New York (1965). C. F. Curtiss and Jo O. Hirschfelder, J. Chem. Phys. 17, 550 (1949). A. Do Pogorelyi, Zhur. Fiz. Khim. 22, 731 (1948). H. Samelson, J. Appl. Phys. 32, 309 (1961). Ho H. Soonpa and J. W. Dunning, J. Applo Phys. 37, 454 (1966).
Pergamon P r e s s , Inc.
Printed
PARAMETERS OF GROWTH FROM THE VAPOR PHASE OF ZnS CRYSTALS Indradev t University of Delaware, Newark, Delaware
(Received August 17, 1966; Refereed)
ABSTRACT Large crystal~ of cm size of zinc sulfide have been grown at 1350 C by the self=sealing method. Argon, hydrogen sulfide, and helium gases at various pressures were used as ambients. AT, the initial difference in temperature between the charge and the nucleation site, dT/dz, the temperature gradient in the growth zone and the drive rate of the growth tube through the furnace were studied as parameters of thi~ method of growth. The optimum value of AT = 22 ± 3 C v gives 1.4 as the supersaturation ratio needed for initial nucleation. The rate of solid-transport has been found to be controlled by diffusion. Introduction Zinc sulfide crystals have been grown for over a decade by various workers but, cm size crystals of good quality are still rare°
Addamiano and Aven (I)
have grown zinc sulfide crystals
from melt at 1850°C under argon pressure of I0 atmospheres°
The
various methods of growth from the vapor phase need lower temperatures and the use of hlgh pressure is not necessary.
These
crystals are usually smaller than those grown from the melt. Reynolds and Czyzak (2) grew mm size rod crystals in sealed quartz*Portions of this paper were presented at the Conference on Luminescence, Hull (1964). Work supported by U.So Army Research %Office-Durham, Contract No. Da-31-124-ARO (D)-173o Present address: Department of Applied Physics, Techniche, Hochschule, Karlsruhe, Germany.
173
174
ZnS CRYSTALS FROM VAPOR PHASE
Vol. I, No. 3
ampules at I150°C Kremheller (3) grew needle and ~late type crystals at 1250°C using the flow method. Samelson (4j used the halogen transport method to grow cubic crystals of zinc sulfide at 980°C. Relatively larger crystals have been grown by Green et. al. (5) at 1550°C. Piper and Polich (6) used the self-sealing system to grow cm size crystals of ZnS. A study of the kinetics of growth of ZnS crystals from the vapor phase should reveal the relevant parameters of crystal growth which may be optimized to grow large crystals at temperatures below 1500°C. Hamilton, (7) Samelson,(4)and Patek (8) discuss the mechanism of growth of zinc sulfide crystals, but supersaturation is the only parameter they consider. Jona (9) and Jona and Mandel (I0) have considered the solid transport in the growth of zinc sulfide by the halogen transport method. Dev (II) has found that when zinc sulfide crystals are grown by the flow method, the crystal habit depends on the dissipation of the heat of condensation. The kinetics of growth of cadmium sulfide crystals in relation to the dislocation structure has been reported by Chikawa and Nakayama (12). HSschl and Konak (13) have studied the relationship between the sublimation velocity and the vapor pressure of one of the components in the growth of CdSe and CdTe crystals. The growth of crystals from the vapor phase in a sealed tube can usually be separated into three stages: (a) transport of solid, (b) initial nucleation, and (c) the subsequent growth of crystal. The transport of solid depends on the vapor pressure of the solid at the growth temperature and on the diffusion coefficient of the vapor (if the transport is controlled by diffusion). The initial nucleation depends on the difference in temperature between the charge and the nucleation site which gives rise to a difference in the vapor pressure and to supersaturation. The subsequent growth of the crystal is determined by the rate of solid transport, maintenance of supersaturation and on the dissipation of the heat of condensation. The above considerations suggest that a fast rate of growth can be achieved by working at high temperatures and by using an ambient gas with low molecular weight in order to have a high value of diffusion coefficient° The optimumvalue of supersaturation can be determined experimentally and can be maintained during crystal growth° An increase in the
Vol. 1, No. 3
ZnS CRYSTALS FROM VAPOR PHASE
175
supersaturation will lead to the formation of a large number of separate nuclei on which growth can proceed and polycrystalline growth will result. stop altogether.
At low values of supersaturation growth may
The heat of condensation raises the temperature
at the vapor-crystal interface unless it is removed at the same rate at which it is being given to the crystal. This excess heat can be removed by conduction and by radiation from the outer crystal surface.
In either case the thermal conductivity of the
crystal will determine the temperature gradient in the growth region of the furnace. The present work makes a study of the factors controlling crystal growth that have been mentioned above for the specific case of zinc sulfide.
The self-sealing growth system has been
selected because it yields large crystals at relatively lower temperatures.
Also, because the pressures inside and outside
the growth tube are equal, fused quartz can be easily used at these temperatures. Three ambient gases, helium, hydrogen sulfide, and argon at various pressures were used. The growth temperature was kept between 1300 and 1350°C.
Experimental Experimental arrangement adopted in this work is shown in Fig. I.
The starting material was pre-fired GE electronic grade
zinc sulfide powder.
About 15 gms of the powder was packed in a
quartz charge tube and was placed inside a quartz growth tube of about 1.5 cm bore.
The growth tube was open at one end and was
drawn out to bullet-shape with a pointed tip at the other end. At the tip, a quartz conduction rod was sealed to the growth tube. A gap of 3 to 5 cm(depending on temperature profile of the furnace) was kept between the charge tube and the tip of the growth tube. Behind the charge tube, another quartz tube (blocking-tube) with closed end was placed inside the growth tube. The blocking tube left a gap of about I rmm between itself and the growth tube. This gap gets sealed by the deposition of zinc sulfide when crystal-growth starts. All the quartz used in these experiments was 'Amersil' transparent fused quartz. The growth tube and its contents were placed in an alumina tube of 2 cm bore and 50 cm
176
ZnS CRYSTALS FROM VAPOR PHASE
Vol. I, No. 3
length. The alumina tube was closed at one end;at the other end it was ground to take a graded glass joint. The glass joint had outlets for evacuation and for introducing the ambient gas. The alumina tube was placed in a two-zone platinum furnace. Electric power through the main heating coil was regulated by a 'West SCR Stepless' control unit to keep temperature at the controlling thermocouple to within I C °.
Temperature in the hot zone was
kept at 1350°C and the power in the slde-coil was regulated to keep the temperature gradient in the growth-zone constant.
The
temperature gradient could be varied from I0 to 50 C ° per cm.
A
motor drive was coupled to the alumina tube which pushed it through the furnace at a rate ranging from 1.5 to 3 cm per day.
CHARGE
TIP
TUBEI CONDUCTION ROD ~ / / / / / /o/o/o~ooo V / / /.... / / / / AoJo / V / /....... / / / A / / //o /.3"/I///¢/ BLOCKING TUBE
~
GROWTH
....
i~ ___
Lo
......
/
DRIVE)
~/fflllI////llll/I/llllll~(lllllllll/~ ...............
FURNACE MUFFLE
"7 ......
ALUMINA TUBE
f 1300 TEMP. "C 1200
5
I0
15
20
DISTANCE |CM)
FIG. I Experimental Arrangement for Crystal Growth and the Temperature Profile of the Furnace ' The following procedure was adpoted to start a growth run: zinc sulfide powder was packed in the charge tube which was then placed at proper position in the growth tube with the help of the blocking tube° The growth tube was then placed in the alumina
Vol. 1, No. 3
ZnS CRYSTALS FROM VAPOR PHASE
tube which was in the furnace.
The alumina tube was evacuated
and the furnace heated to 800°C. for one hour at this temperature.
The system was vacuum baked After baking,
the alumina tube
was filled with the ambient gas at suitable pressure. step, stabilization,
177
The next
consisted of raising the temperature of the
furnace to get the desired temperature profile for that growthrun.
The tip of the growth tube was placed at the highest temp-
erature so that no nucleation may take place there during stabilization period which lasted for one hour. stabilization,
the
At the end of
the alumina tube was shifted to a position in the
furnace such that the tip of the growth tube was at the starting temperature.
The driving motor was started and the growth-run
was in progress.
During the period of stabilization and the
early part of the growth-run,
the gap between the growth tube
and the blocking tube is sealed by the condensing vapor of zinc sulfide and subsequent growth takes place in a sealed system. A growth-run usually lasted from 20 to 60 hours, after which the furnace was allowed to cool to below 300°C and the crystal was taken out by breaking the growth tube. The crystal growth experiments were done with three ambient gases:
helium, hydrogen sulfide, and argon.
The ambients were
used at pressures of I arm., 30 cm and I0 cm of mercury.
Some
growth-runs were made without any ambient in which case zinc sulfide, zinc and sulfur had to duffuse through a mixture of their own vapors. A successful growth-run depends, to a large extent, on the initiation of growth from only a few nuclei, preferably one.
It
is for this purpose that the tip of the growth tube is pointed and the temperature-difference
&T between the powder charge and
the tip at the start of the growth-run has a definite value. &T was used as one of the growth-parameters
in these experiments.
Results The crystals grew in the shape of the growth-tube and usually consisted of two or three crystals of the size of I0 x 5 x 3 mm. crystal,
Occasionally,
the as-grown crystal was a single
15 mm long and about 12 mm in diameter.
The crystals
178
ZnS CRYSTALS FROM VAPOR PHASE
did not show large natural faces, however, narrow strips of less than I m m w i d t h crystals.
Vol. 1, No. 3
low index faces in
were found on several
The direction of growth of these crystals was along
the c-axis.
The (0001) face was always present as a circle of
about 0.5 mm
diameter at the growing end of the single crystals.
Most of the surface of the crystal at its growing end looked glassy without any sharp edges and faces. The chemical purity of the crystals was of the same order as that of the starting material. representative
The chemical analysis of a
crystal is given in Table I. TABLE I
Spectrographic Analysis of a ZnS Crystal and the Starting Material. The Numbers Represent Parts Per Million. ND = Not Detected
A5
AI
Cd
Cr
Cu
Fe
Mn
Ni
Pb
Si
Crystal
ND
7
ND<5
ND
4
i0
ND
5
ND<5
90
Powder
ND
2
ND<5
ND
3
ND
ND
ND
ND<5
15
The optimum value of AT, the initial temperature difference between the tip of the growth tube and the charge, was found to be 22 & 3 C ° . transport.
It varied only slightly with the rate of solid
The temperature gradient in the growth-zone had a
value between 25 and 30 C ° per cm for best results.
The changes
in the rate of growth of the crystals did not affect the temperature gradient but, the drive-rate of the growth tube through the furnace had to be adjusted.
The drive rate had to be in-
creased to about 3 cm per day for a fast growth e.g. in helium gas and it was 1.5 cm per day for growth in argon at atmospheric pressure, The experimental values of the transport rates are given in Table II.
These values are for an average temperature
difference of 50 C ° , the diffusion distance of about 6 cm and 2 the area of cross-section being approx. 0.8 cm .
Vol. 1, No. 3
ZnS CRYSTALS FROM VAPOR PHASE
179
Hydrogen sulfide at reduced pressure and helium at atmospheric pressure as ambient gases yielded the maximum number of large single crystals. The crystals grown in helium showed green luminescence with a long decay period while those grown in hydrogen sulfide showed a weak blue or no luminescence. TABLE II Flux of Zinc Sulfide at 1325°C
Ambient Experimental Flux Pressure (10-7mols cm-2sec "I) Gas (cm of mercury)
Argon
H2S
Theoretical Flux (10-7mols cm-2sec -I)
76 30 I0
3.5 4.5 5
1.4 3.9 12.9
76
3.9
4.3
30
5.0
10.2
76
Ii.0
3.8
30
ii
8.8
Vacuum
6
Helium
28
Discussion The theoretical calculation of solid-transport is based on the assumptions that: (a) fixed concentrations of the vapors of ZnS, Zn, and S 2 are present at the charge and at the growth site, (b) these concentrations have the equilibrium values corresponding to the temperatures at those points, and (c) the transport is according to the Fick's first law(14): c Di
dx i
Ni = i - x i dz
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ZnS CRYSTALS FROM VAPOR PHASE
Vol. I, No. 3
where N i = gm mols of the i th component transported c = Z ci
•
CI
=--= mi
molar density
Oi and m i are density and mol. wt. of the i th component ci Pi xi =~=-c p Pi = partial pressure of the i th component p = total pressure in the system D i = effective diffusion constant of the i th component in the mixture as given by: (15) ~ i = ~ P] j Dij The individual diffusion constants Dij were calculated by the method used by Jona and Mandel (I0) with the help of the formula Di j =
3 8n°ij
[ kT(mi + mj) 2
]
2~mim j
where n is the total gas density in atoms per cm 3.
This can
be calculated from the total pressure and average temperature T which was 1598°Ko
m i and mj are the masses of the molecules
or atoms considered° oij = 1/2 (~i + oj) ~'i and ~j being the corrected "hard-sphere diameters" of molecules i and J. The value of D.. obtained from this formula was 13 0.3 corrected by multiplying by (1598/273) = 1.7. These corrections are explained in Jona and Mandel's paper. The calculated values of the diffusion constants are given in Table III. The various partial pressure in the systems ZnS = Zn + 1/2 S 2
Vol. I, No. 3
ZnS CRYSTALS FROM VAPOR PHASE
181
and H2S = H 2 + 1/2 S 2 have been obtained by extrapolating the data of Pogorelyi (16) which was measured over the range 800 to 1250°C. TABLE III Binary Diffusion Constants (cm2sec'~)- at About I Atm. Total Pressure and 1325vC
ZnS
Zn
Argon and
ZnS
0.93
1.58
Helium Systems
Zn
1.58
2.79
S2 A He
1.16 1.57 5.33
1.93 2.57 9.25
ZnS Zn
2.31 3.92
3.92 6.91
S2
2.87
4.77
H2S H2
3.38 22.2
5.39 39.5
H2S System
Table II lists the calculated rates as well.
values of the transport
The agreement between the two sets of values is
good enough to conclude that the growth of zinc sulfide crystals in this study was transport-controlled and that the solid is transported by diffusion. However, the nature of the ambient probably influences the crystal growth through adsorbed layers at the vapor-solid interface. The assumption made in the above calculations that the vapor pressure of zinc sulfide at the growth site is the equilibrium vapor pressure, points to the difficulty in obtaining any estimate of supersaturation in front of the growing crystal 18)." " Since the crystal growth has been found to be transport-controlled, the supersaturation should be very small°
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ZnS CRYSTALS FROM VAPOR PHASE
Vol. 1, No. 3
However, a definite value of AT suggests the existence of a maximum value of supersaturation necessary to initiate the crystal growth. of 1.4.
AT ffi 22 ± 3 C ° would mean a supersaturation ratio
This value is slightly lower than that obtained by
Samelson(17)which was between 2 and 3 for growth of zinc sulfide crystals in sealed ampules. But, Samelson hadnot considered the influence of transport rate (which is limited by diffusion) on the value of actual vapor pressure at the growth site. The dissipation of the heat of condensation is another important factor which determines the growth of large single crystals.
The heat generated at the growing face must travel
through the crystal to its cooler end from where it is lost mainly by radiation to the surrounding alumina tube.
The con-
duction rod merely fixes the separation and hence the temperature difference between the tip of the growth tube and the closed end of the alumina tube.
The dissipation of the heat of
condensation depends on the thermal conductivity of the crystal and the temperature gradient in which it is situated.
The direc-
tion of growth in these experiments has been found to be along the c-axis. This is interpreted to mean that hexagonal zinc sulfide has maximum thermal conductivity along c-axis(ll)o Moreover, the growing surfaces of the crystals are convex indicating that this value of thermal conductivity is higher than that of fused quartz at this temperature (1300°C) (18). Conclusion Large single crystals of zinc sulfide can be grown by the self-sealing method if suitable values of parameters such as AT and temperature gradient are selected. The exact values of these parameters depend on the ambient gas used and on its pressure. These parameters can be interpreted to give a better understanding of the supersaturation during crystal growth and of the thermal conductivity of the crystals at the temperature of growth. Further work is needed to determine the exact role of the ambient gas in the growth process.
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ZnS CRYSTALS FROM VAPOR PHASE
183
References I. 2. 3. 4. 5. 6. 7. 8. 9. I0. Ii. 12. 13. 14. 15. 16. 17. 18.
A. Addamiano and M. Aven, J. Appl. Phys. 31, 36 (1960). D. C. Reynolds and S. J. Czyzak, Phys. Rev. 79, 543 (1950). A. Kremheller, Sylvania Technologist 8, ii (1955). H. Samelson, J. Appl. Phys. 33, 1779 (1962). L. C. Greene, D. Co Reynolds, S. J. Czyzak and W. M. Baker, J. Chem. Phys. 29, 1375 (1958). W. W. Piper and S. J. Polich, J. Applo Phys. 32, 1278 (1961). D. R. Hamilton, Brit. J. Appl. Phys. 9, 103 (1958). K. Patek, Czch. J. Phys. BI2, 216 (1962). F. Jona, J. Phys. Chem. Solids 23, 1719 (1962). F. Jona and Go Mandel, J. Chem. Phys. 38, 346 (1963). Indra Dev, Brit. J. Appl. Phys. 17, 761 (1966). J. Chikawa and T. Nakayama, Jo Appl. Phys. 35, 2493 (1964). P. HSschl and Co Konak, physo status sol. 9, 167 (1965). R. B. Bird, W. E. Stewart, and Eo N. Lightfoot, Transport Phenomena, p. 523, John Wiley and Sons, Inc. New York (1965). C. F. Curtiss and Jo O. Hirschfelder, J. Chem. Phys. 17, 550 (1949). A. Do Pogorelyi, Zhur. Fiz. Khim. 22, 731 (1948). H. Samelson, J. Appl. Phys. 32, 309 (1961). Ho H. Soonpa and J. W. Dunning, J. Applo Phys. 37, 454 (1966).