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Growth of CdS Platelets
Journal of Crystal Growth 19 (1973) 33—44 © North-Holland Publishing Co.
GROWTH OF CdS PLATELETS KENNETH A. JONES 3M Company, St. Paul, Minnesota 55101, U.S.A. Received 15 August 1972; revised manuscript received 7 December 1972 A mechanism for the growth of CdS platelets is hypothesized. It is suggested that platelet growth is initiated by two dimensional nucleation on the close packed prismatic planes, and that nucleation occurs when a needle growing in the c direction grows into a region where the supersaturation exceeds a critical amount. The prismatic ledge formed by the growth of these nuclei then acts as a site for another c needle on which other two dimensional nuclei form, etc. The platelet can therefore be described as a band of coherent c needles. It is further suggested that nucleation occurs only on specific crystallographically equivalent planes and that the plane of the platelet surface varies because this anisotropic growth form is produced by spacial fluctuations in the free energy gradient. It is also shown that the frequently observed surface striations are due to imperfect epitaxial growth of c oriented needles.
1. Introduction There are a number of hypotheses describing platelet growth. One of the more detailed, and seemingly most accepted, growth mechanisms is the dislocation mechanism of Chikawaand Nakayama1). They suggested that CdS platelet growth occurs when an [0001] edge dislocation slips out of a [1010]needle and then maintains itself near the (0001) surface by means of line tension. Another hypothesized dislocation mechanism is that the edge portion of a dislocation parallel to the c axis slips out of the c needle and then acts as a nucleation site for platelet growth2). Sears and Coleman3) concluded that platelets are formed when two nonparallel needles containing only screw dislocations grow together. Platelets can be formed because a two dimensional grid of screw dislocations now exists3). It has also been suggested that platelets are formed when a side whisker grows out from the primary needle forming a notch where the atoms preferentially precipitate4). Yet another theory was set forth by Volmer and Estermann5) long before the existence of dislocations was recognized. They hypothesized that platelet growth occurs when the atoms impinge on the lateral surface and diffuse to the growing edge. The growth, morphology, and defect structure of the CdS platelets were examined, and all of these observations are combined with those in the literature. Using Present address: The Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755, U.S.A. *
33
the above theories as guides, an attempt is made to develop a hypothesis that is consistent with the observations. 2. Experimental procedure The CdS platelets were grown by Dierssen and Gabor4) in a fused silica tube by a modified Frerichs method6) using argon flowing at 1 cm/sec as the carrier gas. The CdS powder was evaporated at 1100 °Cand redeposited at 900 °C. After the growth tube was cooled and opened, the specimens were removed and photographed using an optical microscope. The orientation of the platelet was determined with a Laue back reflection camera and the defect structure and the internal strain of the platelet were investigated using a Lang X-ray camera. A Mo fine focus tube with a 40 cm beam extender was used to record the transmission topographs and rocking curves, whereas a Cu fine focus tube and a 1 mil nickel foil placed in front of the 50 ).Lm Ilford nuclear emulsion film were used for those taken in the back reflection mode. The Mo tube was used for the transmission studies because it penetrates deeper into CdS (89 ~tm), and the Cu tube was used in the back reflection studies so that opposite sides of the same platelet could be studied independently (penetration depth 10 ~tm)and larger diffraction angles could be used. The beam extender was used with the Mo tube to obtain a more parallel beam and thereby increase the resolution. Also, the platelet flatness was determined using an interfe-
34
KENNETH A. JONES
(2a)
—
(la)
(Ib) Fig. 1. Micrographs of platelets growing out from needles. (a) Growth with one platelet growing out from a needle (20 x); (b) growth with two platelets growing out from a needle (60x).
rence microscope which recorded the number of interference fringes per unit length. 3. Experimental results and discussion During the initial stage of growth, needles grew out from the sides of the growth tube and after the needles had grown out a sufficient distance, a platelet nucleated and grew laterally4). There usually was only one platelet growing out from a needle as shown in fig. Ia, but in some instances two platelets 180°apart grew out from a single needle (fig. lb). The Laue patterns showed that the needles always grew out in the c direction. They also showed that a majority of the platelets had a (1 l~0)orientation, some had a (1010) orientation while still others has a (l2~0)orientation. The orientations varied about four degrees about the latter orientation,
e (2b)
whereas the scatter was much less pronounced about the other two. The crystals were more likely to have the platelet form when the growth zone was maintained two hundred degrees below the 1100 °Cevaporation temperature. It was noted that platelets were more readily formed when a carrier gas was used than when growth occurred in a static system. Most of the platelets grew at the top of the furnace tube where it was shown that most of the gas flowed by observing the flow pattern of a colored gas. The crystal structure also appears to be a critical factor as crystals with the hexagonal wurtzite structure grow in the form of a platelet but the structurally similar zincblende cubic crystals7) do not grow in the
GROWTH OF
CdS
~
— (2c)
35
PLATELETS ~0o\
(3a)
_
2Io]
__~~~~___a.__[I
tIOTO)
(1010)
(3b)
/ /4P (2d) Fig. 2. Characteristics of a smooth, thin (1120) platelet. (a) Micrograph (18 x); (b) (0002) transmission rocking curve; (c) (0002) transmission topograph (12.5 x); (d) Fizeau fringe pattern (18 x).
platelet form. In addition to CdS wurtzite platelets of 8—10
11—13
‘4
ZnS ), ZnO ), and CdSe ) have been grown but zincblende CdTet 3) and GaP’ 6) crystals grown under similar conditions do not grow as platelets. The (0002) transmission topograph (fig. 2c) of the thin (10 ~tm), smooth platelet displayed in fig. 2a shows that this platelet contained no dislocations. The sharpness of the KcL 1 and KcL2 peaks of the (0002) rocking curve shown in fig. 2b also indicates that the platelet was strain free, and the lack of fringes in the Fizeau 2d shows that surfacesfringe were pattern parallel of to fig. within seconds of the arc.platelet The number of platelets that were thin and smooth was small. Most of the platelets were thicker and contamed striations that were parallel to the c axis. At this point I will discuss the growth mechanism for the thin, smooth platelets and will later attempt to explain how the striations are formed. A hypothesis that is consistent with the above experimental evidence is that a platelet is formed by growth in only one ofat least six crystallographically equivalent
(3c) Fig. 3. Schematic diagrams illustrating how platelets can be formed by two-dimensional nucleation of specific { 1 l20} and/or {1OTO} prismatic planes. (The c axis is normal to the plane of the paper.) (a) Formation of a (1120) platelet growing in the [1100] direction by nucleation of the (2110) and (1210) planes; or (b) by the (1010) and (0110) planes; (c) formation of a (1010) platelet growing in the [1210] direction by nucleation of the (1100) and (0110) planes; or (d) by the (2110) and (1120) planes; (e) formation of a (l2~0)platelet growing in the [14101 direction by nucleation of the (TOlO) and (1210) planes; or (f) by the (1120) and (0110) planes.
directions that is determined by a free energy gradient in much the same way a lead dendrite grows in one of six equivalent <100> directions’ 7). Platelet growth occurs when a needle grows into a region where the supersaturation exceeds forpacked two dimen1 8)the to value occur necessary on the close prissional nucleation matic planes. Nucleation occurs on two adjacent close packed planes which grow together and form a wedge shaped growth front (see fig. 3) that points in a basal direction determined by the free energy gradient. The ledge that is formed by this lateral growth produces a nucleation site for a new, thin needle. Two dimensional nucleation occurs on the new, thin needle; a ledge is formed; a second new, thin needle grows from this ledge; etc. Therefore a thin, smooth platelet is formed by the nucleation and growth of a band of coherent
36
KENNETH A. JONES
needles. This model has other things in common with the dendritic growth model in that the platelet (I) grows rapidly; (2) is thin so that it can dissipate the heat of sublimation; and (3) is thin because the nutrient near the face of the platelet has been depleted by the growth process. The observation that wurtzite crystals grow as platelets but zincblende crystals do not can be explained by examining their crystal structures. Wurtzite crystals have only one preferred growth direction (the [00011) whereas zincblende crystals have four crystallographically equivalent preferred growth directions (four of the eight <111>). A platelet can form when two dimensional nucleation occurs on the prismatic surfaces of a wurtzite needle because another c needle will grow out of the ledge formed by the two dimensional nuclei, However, as in the case of CdTe’ 5), a secondary dendrite will grow out from a zincblende needle because there is more than one preferred growth direction. Growth will occur in these other preferred grow directions rather than parallel to the original growth direction because it increases the surface to volume ratio and therefore the rate of dissipation of the heat of formation. Wurtzite crystals do not have this choice. The hexagonal structure of the wurtzite crystals is necessary insofar as it allows the crystals to have one strongly preferred growth direction. Other hexagonal materials such as alumina could crystallographically have a strong tendency to grow in the c direction, but they do not. It is therefore possible that flag shaped alumina platelets are not formed because growth occurs almost as readily in the a direction as it does in the c’ 9), This model requires that free energy gradients exist, Free energy gradients exist if there is an inhomogeneous distribution of the nutrient and/or a nonuniform thermal field. A gas flow would facilitate the formation of a free energy gradient when the gas is forced to flow around an obstacle, such as a CdS needle, if the rate of thermal diffusion is not significantly greater than the rate of flow of the carrier gas. Using the hard sphere model2 0) to calculate the diffusion coefficient and using the appropriate diffusion equations2’) one can show that about twice as much material would flow across a boundary when the carrier gas has a uniform velocity of! cm/sec the flow rate used to grow the platelets4) than would thermally diffuse at 900 °Cat one atmoC
—
—
sphere of pressure. Therefore using a gas flow could facilitate platelet growth by encouraging the formation of free energy gradients. The growing platelets would cause the flow pattern to continuously change and in some instances this could cause two platelets to grow out from the same needle. The flowing gas produced free energy gradients in the growth tube even before platelet growth was mitiated. As was mentioned earlier the gas had a tendency to flow to the top of the furnace tube. This should lead to an inhomogeneous distribution of the nutrient. The friction that produces the boundary layer near the tube wall should also help to create free energy gradients. The free energy gradient need not be large for growth to occur rapidly in one direction and not at all in the other crystallographically equivalent directions. Hirth and Pound1 8) have shown that no growth occurs by two dimensional nucleation until a critical supersaturation has been reached, but that the growth rate increases very rapidly with the supersaturation at supersaturations greater than the critical amount. They also showed that the greater the critical supersaturation the greater the growth rate will be at a supersaturation slightly exceeding the critical amount’ 8) This can explain why having a 200 °Ctemperature difference between the evaporation and the growth zones promotes platelet growth. It provides the large critical supersaturation necessary for two dimensional nucleation, and the large critical supersaturation accounts for the observed rapid growth’ P4). The platelets do not necessarily grow in the direction of the free energy gradient. Rather they grow in specific crystallographic directions that are most nearly parallel to the free energy gradient. These specific crystallographic directions are determined by the prismatic planes on which two dimensional nucleation occurs. According to the calculations of Wolff and Gualtieri22) and the experimental results of others [see Strehlow23) for references] the (1010) and the (1120) close packed planes have similar surface energies. Therefore growth occurs by two dimensional nucleation on either type of plane or on both types simultaneously. Thus it is possible to explain the growth of (1120) platelets by lateral growth in the [TI00] direction either by the rapid nucleation of (2110) and (1210) planes (fig. 3a) or by rapid nucleation of (1010) and (0110) planes (fig. 3b). Likewise a (1010) platelet can
GROWTH OF
CdS
37
PLATELETS
ease....
I.
I
(4a) (4c)
z
w
I
(4b)
(4d) Fig. 4. Characteristics of a (1120) platelet with narrowly separated striations. (a) Micrograph (18 x); (b) (0002) transmission rocking curve; (c) (1 TOO) transmission topograph (12.5 x); and (d) Fizeau fringe pattern (18 x).
be formed by growing laterally in the [1210] direction either by the rapid nucleation of the (1100) and the (0110) planes (fig. 3c) or by the rapid nucleation of the (2110) and the (1120) planes (fig. 3d). The (12~0)orientation and small variations about it can also be explained by this growth mechanism. It can be formed by lateral growth in the [5410] direction either by the rapid nucleation of the (1010) and the (1210) planes (fig. 3e) or by the rapid nucleation of the (1120) and the (0110) planes (fig. 3f). The probability that two dimensional nucleation will occur on the { 1 120} faces is slightly different than the probability that two dimensional nucleation will occur on the { 1OTO} faces because they have slightly different surface energies. Therefore there should be more ofone
type of platelet and the growth direction of the (l2~0) platelet should not make an equal angle of 15°with the growth directions of the (1120) and the (0110) platelets. This is what was observed as there were more platelets with the (1120) orientation, and the growth direction of the (l2~0)platelets usually made an angle slightly larger than 10.9°with the growth direction of the (1170) platelets. As was mentioned earlier almost all of the platelets contain striations on at least one of their two surfaces. The striations, which were always parallel to the c axis, can be narrowly separated (fig. 4a) or widely separated (fig. 5a) and they often appear on only one side of the platelet and this side is usually rougher. The latter observation is illustrated in fig. 5 where the side view
_________________________________________
e
-
38
KENNETH A. JONES
iiJUtL~i~ II
-
___
(5a)
(6a)
(5b) Fig. 5. Micrographs of a (1120) platelet with widely separated striations. (a) Front view (18><); (b) side view (150><).
——
FUJI -~------
—.1. —~--
(fig. Sb) shows protrusions on only one side. The front side of the aluminum coated platelet (fig. 6a) has many striations on its surface and the back side (fig. 6d) has much fewer in comparison. The micrograph of a polished and etched cross section of two striated crystals cleaved parallel to their c axis (figs. 7a, 7b) show that there are growth layers parallel to the platelet surface whereas there are no layers in the thin, smooth specimen (fig. 7c). The thickness of the platelet also tends to increase as the growth time increases, When the striations do not extend the length of the platelet they terminate where a ridge terminates in a pointed tip on the platelet surface as is shown in fig. 8a. Sometimes entire layers terminate on the platelet surface as shown in fig. 8b. In some instances the ridges
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1
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—
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(6b)
extend out over the end of the platelet and form needles as is shown in fig. 8c. The X-ray rocking curves and topographs of the striated crystals were almost always different than those of the thin, smooth platelets. By comparing the rocking curve of a thin, smooth platelet (fig. 2b) with the rocking curve of a striated platelet (fig. 4b) one sees that the striated crystal has more diffraction peaks and that the peaks are broader. The extra peaks mean that the striated crystal is an imperfect crystal, and the broader peaks mean that the striated crystal is more highly
GROWTH OF
fJA)
CdS
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39
PLATELETS
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e (6c)
8 (6f) Fig. 6. Characteristics of the opposing platelet surfaces of a thick (1120) platelet with gross striations. (a) Micrograph of the aluminum coated front surface (18 x); (1,) (1230) back reflection topograph of the front surface (12.5 x); (c) (1120) back reflection rocking curve of the front surface; (d) micrograph of the aluminum coated back surface (18 x); (e) (1230) back reflection topograph of the back surface, (12.5 x); and (f) (1120) rocking curve of the back surface.
H
______
(6d)
strained. The (1100) topograph of the striated crystal (fig. 4c) also shows that the crystal is highly strained, The Bragg reflecting center section contains stress lines, and the platelet was so warped that neither end was oriented for Bragg reflection. The fact the striated plate-
lets were more brittle than the thin, smooth platelets also indicates that the striated crystals contained more internal strain. The opposing surfaces of the striated platelet deviate more from parallelism than do the surfaces of the thin, smooth platelet. This is seen by comparing the Fizeau fringe pattern in fig. 2d with that in fig. 4d. It should be pointed out that the platelet in fig. 4a is one of the smoother striated platelets. Most of the striated platelets do not exhibit a fringe pattern because they are too rough.
40
KENNEIH
A. JONES
(7a)
(8a)
I
____
~‘-~r?-
~
1
(8b)
(7b)
(8c) Fig. 8. Micrographs of the different striation configurations. (a) Single striations terminating on the surface where a ridge terminates (100/); (b) an entire layer terminating on the platelet surface (18 ‘); (c) ridges extending out over the end of platelet (100 .).
(7c) Fig. 7. Micrographs of polished and etched cross sections contaming the c axis of: (a) a striated platelet (100’ ); (b) a striated platelet ~kith a thick layer on top of a thin layer (500 ); and (c) a smooth thin platelet (500 ~.
The back reflection topographs and rocking curves of the rough surface containing striations (fig. 6a) and the smoother Uig. 6d) surface ofa thick, striated platelet show that the two surfaces were structurally different. The (1230) topograph of the striated surface thg. ób) contains a number ofdark lines that correspond roughly to the ridges in fig. 6a. This shows that the ridges had . . . a different orientation than the rest of the platelet. That portions of the rough side of the platelet had different
GROWTH OF
CdS
orientations is seen in the (1120) rocking curve (fig. 6c) where the rocking curve has more than one Kct, and one Kct2 peaks. The (1230) topograph (fig. 6e) of the smooth surface is substantially different than the (l2~0)topograph (fig. 6b) in that it has a diffuse pattern characteristic of a highly strained crystal rather than the long narrow diffracting regions of the front side. The rocking curve for the smooth side (fig. 6f) also shows that this side of the crystal is highly strained as the rocking curve is broad. However, it indicates that this side of the crystal is single crystalline as there are only two peaks. The topographs of the thicker platelets revealed that some of them contained dislocations whereas no dislocations were observed in the thin, smooth platelets. The (1210) and (0002) transmission topographs of a (1010) platelet in figs. 9a and 9b show that there were a number of line defects lying in the basal plane. Because the defects had a much stronger contrast in the (1210) topograph it is likely that they were the 24). 30° +[12A 10] hypothesis dislocations thatobserved is consistent previously with by theMohling above ob servations is that striations are formed by the imperfect epitaxial growth of c oriented needles on the platelet surface. The striations are visible because the c needles have vicinal prismatic surfaces. Some of the layers and some of the striations terminate before they reach the end of the platelet because they do not have time to grow out to the end. The thickness of the striated platelets increases with time because new epitaxial layers have more time to nucleate and grow. The layered structure seen in the cross sections of the striated platelets indicates that the striations are formed by epitaxial growth on the platelet surface. This is particularly true of fig. 7b where there is a thick layer on a thin layer. Also, the striations often appear on only one face of the platelet because one face is more exposed to the gas flow, The X-ray topographs and rocking curves show that the striated platelets are imperfect and are highly strained. According to my hypothesis this is due to imperfect epitaxy of the c needles. The back reflection topograph of the striated face of a platelet (fig. 6b) supports this idea as some of the needles producing the striations have a slightly different orientation than the rest of the platelet, but each individual needle has the same orientation along its entire length. The internal stresses ob-
41
PLATELETS
~
_______________________________________________
(9a)
-_____________________________________________
Fig. 9. ~
(9b) Transmission X-ray topographs of a (1010) platelet con(a) (1210) topograph (100 x); (b) (0002)
served on both sides of the platelet, then, are due to the warping of the crystal that partially compensates for the lattice mismatch generated by the imperfect epitaxy. The dislocations observed in some of the platelets are also produced by the imperfect epitaxy.
4. Further discussion 4.1. THIN, SMOOTH PLATELETS There is much evidence in the literature that supports the observation that platelets grow out laterally from a c needle. Ibuki2 5) observed that CdS platelets grow laterally out from a c needle while Dev8) made a similar observation for zinc sulfide. Also all those who have
42
KENNETH
studied CdS platelets have found that at least some of them have a (1120) orientation, most investigators have detected a (1010) orientation, whereas only one other group of investigators has found platelets which had neither a (1170) nor a (1010) orientation26). However, all of the orientations observed by them contained the c axis, It has been suggested that two dimensional nucleation does occur on the prismatic planes of some needles at a critical supersaturation when they grow into a region of higher supersaturation. Devries and Sears2 7) have attributed the fattening and subsequent decrease of the growth rate in the direction of the needle axis of A1 2O3 needles to the onset of two dimensional 28) nucleation on the prismatic faces. Dittmar and Kohler observed the same growth behavior in sodium needles and they, too, attributed it to two dimensional flucleation. Observations made by Hildisch29) can be interpreted to mean that smooth, thin platelets nucleate and grow at a critical supersaturation. He noted that all of the smooth, thin platelets taken from the same section of the growth zone contained the same amount of excess cadmium, but the amount ofexcess varied from section to section. According to my hypothesis the platelets from the same section contained the same amount of excess cadmium because they nucleated and grew at the same critical supersaturation. The amount ofexcess varied from section to section because the temperature and therefore the critical supersaturation varied, There is evidence in the literature that a large supersaturation promotes platelet growth. Ibuki25) and Sears30) observed that CdS needles grow at small supersaturations and that platelets appear when the supersaturation is increased. Park and Reynolds’2) noted that ZnO platelets were likely to grow at the cooler end of the growth tube, and Sears31) observed that the number of mercury platelets was increased three orders of magnitude when the supersaturation was doubled, There is also evidence in the literature that small amounts of impurities can impede or facilitate platelet growth. This can be interpreted to mean that the impurities affect the critical supersaturation. Chickawa and Nakayama’) observed that the growth forms of the CdS crystals were altered by intentionally introducing different impurities. Also, Park and Reynolds’2)
A. JONES
observed ZnO platelet growth when oxygen was reacted with ZnS, but no platelet growth occurred when oxygen was reacted with ZnSe. The studies on how the temperature gradient affects the growth form of CdS32) and ZnS9) crystals indicate that the free energy gradient is a critical parameter. In both studies it was found that steep gradients favor the growth of platelets whereas needles were formed when the gradients were smaller. Fochs32) observed that platelet growth was favored when the temperature difference between the evaporation and the growth zones was changed rapidly, and needle growth was favored when the temperature difference was changed slowly and uniformly. He also noted gas thatwas platelets were when more likely to form when a carrier used than growth took place in a closed tube. According to the hypothesis the surface energy of the close packed planes as well as the free energy gradient determine the platelet orientation. That the surface energy influences the orientation of CdS platelets has been suggested or implied by Caveny1 0) MohIing33), and Tang34). It was suggested that hexagonal wurtzite crystals grow in the form ofplatelets and cubic zincblende crystals do not because the cubic crystals have more than one crystallographically equivalent preferred growth direction. This also appears to be the case for metals as the metals that grow in the platelet form cadmium3 5) (hcp), zinc3 6) (hcp), and mercury3 1) (rhombohedral) do not have a cubic crystal structure. As mentioned in the introduction some of the theories of platelet growth involve a dislocation mechanism. The primary reason that this mechanism has been rejected is that I and many others”33’3739) have not observed any dislocations in the smooth, thin CdS platelets. Dislocation free cadmium3640), zinc36) and mercury31) platelets have also been grown. It has been suggested that the dislocations responsible for platelet growth slip out of the crystal’), but this possibility has been mathematically justified only for a single dislocation in a very thin needle2). Another objection to the dislocation mechanism is that it is difficult to envisage how it can explain the growth of (12~0)platelets. There is another objection to Chickawa and Nakayama’s’) growth mechanism. They claim that the original needle grows in the [1010] direction, but all of the other investigators believe that it grows in the [0001] —
—
GROWTH OF
CdS
direction. If it did grow in the [1010] direction it would be difficult to explain how the (1010) and the (12~0) platelets are formed and why all of the platelets that were examined contained the c axis, It has also been suggested that platelets are formed when a side whisker grows out from the primary needle forming a notch where the atoms preferentially precipitate4). The major objection to this growth mechanism is that I did not see any X-ray evidence of a side needle inside of a platelet. It was suggested that the side whisker was annealed out4), but this is difficult to accept as my annealing of some striated crystals did not noticeably reduce the imperfection or the internal strain of some striated platelets. If platelet growth were caused by the growth of a side whisker, it is more likely that the side whisker would remain and be visible as it is in the case of the ZnO fourling4’).
PLATELETS
43
observed that by increasing the cadmium pressure he increased the platelet thickness. This could be due to an increase in the rate of nucleation of new epitaxial layers because the sticking coefficient of sulfur is much larger in the presence of excess cadmium46). It is also known that reducing the amount of hydrogen present in the carrier gas reduces the number of striations. This could be due to the fact that the presence of hydrogen gas encourages growth in the c direction4 7), Some chemical analyses indicate that the striations are formed by epitaxial growth as it has been shown that the striated platelets contain more impurities48), and striated platelets taken from the same section of the growth zone contain varying amounts of excess cadmium2 9), According to my hypothesis this is due to the longer time over which epitaxial growth occurs so that growth takes place under varying growth conditions. Chickawa and Nakayama1) have suggested that the 4.2. STRIATED PLATELETS striations are produced by 4- [1010] partial dislocations. Optical studies by many investigators indicate that This does not appear to be the case because partial disthe striations are produced by the imperfect epitaxial locations have been observed only in doped plategrowth of c oriented needles. Fochs3 2) observed that lets49’5 0). It was thought that doping impurities had the platelets grown over a shorter period of time had to be present to pin the dislocation in the platelet and fewer striations. This can be interpreted to mean that not allow it to slip out’). However, it now appears that fewer striations were formed because there was less time the impurities created the partial dislocations rather for epitaxial growth to occur. Others noted that the than pinned them because studies of 4- [1120] dislocastriations often appear on only one side of the plate- tions in undoped CdS platelets showed that they do not let”37), and Caveny37) observed that the striated sur- break up into partial dislocations24’50). Their inability face was the surface that faced the gas flow. The simil- to break up into partial dislocations has been attributed arity in the morphology of wurtzite films and the to the high stacking fault energy of CdS50’5’). striated platelets also suggests that the striations are It has also been suggested that platelets grow by a due to the epitaxial growth of c needles. The optical filling in process between needles4). Using this mechamicrographs of (1120) ZnO42) and (1013) CdS43) hete- nism it would be difficult to explain why the platelet is roepitaxial films are similar to fig. 8a in that they show more misoriented on the more striated surface. If the needles terminating on the surface and pointing in the smooth surface were formed by growth over the needles c direction. it should not be more perfectly oriented than the side Another study showed that the striations do not containing the needles because the orientation of an penetrate through the entire crystal but are confined to epitaxial layer is not better than the orientation of the a layer. It was shown that many striations disappeared substrate. It also is more difficult to explain the obwhen one side of a striated CdS platelet was etched44). servations that smooth, thin platelets from the same The X-ray results of Caveny3 7) also confirm our ob- growth area have the same amount of excess cadmium servation that the striated platelets are usually imper- whereas the striated platelets do not, and that striated feet as he noted that the striated platelets contained platelets contain more chemical impurities. misorientations up to 1°. Some changes in the platelet structure brought about 5. Conclusions by changes in the growth chemistry can be interpreted It has been hypothesized that the growth of a thin, to show that epitaxial growth takes place. Woods4 5) smooth platelet occurs when a needle growing in the
44
KENNETH
c direction grows into a region where the supersaturation is greater than a critical amount. At this point two dimensional nucleation occurs on the close packed prismatic planes. A ledge formed by the nuclei then acts as a site for a new c needle, new two dimensional nuclei form on the new needle, etc. It can therefore be said that the platelet is made up of a parallel band of coherent c needles. It is further suggested that the platelet grows in only one of at least six crystallographically equivalent directions because free energy gradients are produced by the carrier gas flow patterns. The platelet will then grow out in a basal direction that is determined by a cornbination of the free energy gradient and the crystallographically possible growth directions. It is also shown that the striations frequently observed on the surface of a CdS platelet are due to the imperfect epitaxial growth of c oriented needles. It is shown that, in addition to producing a rough surface, the c needles can produce growth defects and internal strains when they are not coherent with the substrate and with each other. Acknowledgements It is a pleasure to thank 0. N. Salmon, G. H. Dierssen, T. Gabor, R. A. Hatch, W. H. Strehlow, and R. L. Weiher for their many stimulating comments. I would also like to thank G. H. Dierssen for supplying the platelets and am grateful for the technical assistance of A. L. Cowles, R. B. Yougquist, and J. M. Magnusson. References I) J. Chickawa and T. Nakayama, J. AppI. Phys. 35(1964)2493. 2) J. P. Hirth and F. C. Frank, Phil. Mag. 3(1958)1110. 3) G. W. Sears and R. V. Coleman, J. Chem. Phys. 25 (1956) 635. 4) G. H. Dierssen and T. Gabor, to be published. 5) M. Volmer and I. Estermann, Z. Physik 7 (1921) 13. 6) R. Frerichs, Phys. Rev. 72(1946) 594. 7) E. P. Warekois, M. C. Lavine, A. N. Mariano and H. C. Gatos, J. AppI. Phys. 33 (1962) 690. 8) I. Dcv, Brit. J. App). Phys. 17 (1966) 769. 9) H. Samelson, J. AppI. Phys. 32 (1961) 309. 10) R. J. Caveny, J. Phys. Chem. Solids 29 (1968) 851. 11) R. B. Sharma, Indian I. Pure AppI. Phys. 7(1969) 736.
A. JONES
12) Y. S. Park and D. C. Reynolds, J. Appl. Phys. 38(1967) 756. 13) H. Iwanaga and N. Shibata, Japan. J. AppI. Phys. 11 (1972) 121. 14) C. Paorici, J. Mater. Sci. 5 (1970) 918. 15) 1. Teramoto, Phil. Mag. 8 (1963) 357. 16) J. Crystal GrowthCan. 9 (1971) 346.29 (1951) 382. 17) E. F. Schonherr, Weinberg and B. Chalmers, J. Phys. 18) J. P. Hirth and G. M. Pound, in: Progress in Materials Science, Vol. 11 (Pergamon) ch. D. 19) I. L. Gelles and W. P. Binnie, Mater. Sci. Eng. 5 (1970) 71. 20) E. H. Kennard, Kinetic Theory of Gases (McGraw-Hill, New York, 1938) ch. IV. 21) L. S. Darken and R. W. Gurry, Physical Chemistry of Metals (McGraw-Hill, New York, 1953) ch. 18. 22) G. A. Wolff and J. G. Gualtieri, J. Am. Mineralogist 47 (1962) 562. 23) W. H. Strehlow, J. AppI. Phys. 41 (1970) 1810. 24) W. Mohling, J. Crystal Growth 1 (1967) 115. 25) 5. Ibuki, J. Phys. Soc. Japan 14(1959)1181. 26) Zh. G. Pisarenko and M. K. Sheinkman, Soviet Phys.-Solid State 3 (1960) 1158. 27) R. C. Devries and G. W. Sears, J. Chem. Phys. 31 (1959) 1256. 28) 29) 30) 31)
W. Dittmar and A. Kohier, J. Crystal Growth 2 (1968) 271. L. Hildisch, J. Crystal Growth 3/4 (1968) 131. G. W. Sears, Acta Met. 3 (1955) 367. G. W. Sears, J. Chem. Phys. 25 (1956) 637.
32) 33) 34) 35) 36)
P. D. Fochs, J. AppI. Phys. 31 (1960) 1733. W. Mohling, J. Crystal Growth 1 (1967) 115. Tang Ting-Yuan, Acta Phys. Sinica 18 (1962) 207. P. B. Price, Phil. Mag. 5 (1960) 473. P. B. Price, Phil. Mag. 5 (1960) 417.
37) R. J. Caveny, Phil. Mag. 12 (1965) 423. 38) W. Mohling, H. Peipst and L. Hildisch, Phys. Status Solidi 5 (1964) 101. 39) W. Mohling and J. Heydenreich, Phys. Status Solidi 7 (1964) 155. 40) P. B. Price, J. Appi. Phys. 32 (1961) 1747. 41) J. M. Cowley, A. L. G. Rees and J. A. Spink, Proc. Phys. Soc. (London) B 64 (1951) 638. 42) G. Galli and J. E. Coker, Appl. Phys. Letters 16 (1970) 439. 43) B. J. Curtis and H. Brunner, J. Crystal Growth 6 (1970) 269. 44) M. Ya. Skorokhod and L. I. Datsenko, Soviet Phys.-Cryst. 11 (1966) 272. 45) J. Woods, Brit. J. Appl. Phys. 10(1959) 529. 46) M. H. Christmann, K. A. Jones and K. H. Olsen, to be published. 47) L. van den Berg, Gov. Res. Rpts., AD688903 (1969). 48) Zh. G. Pisarenko and M. K. Sheinkman, Soviet Phys.-Solid State 3 (1960) 1158. 49) J. Chikawa, Japan. J. App). Phys. 3 (1964) 229. 50) B. N. Das and M. Weinstein, in: Proc. Intern. Conf. Il—VI Semiconductor Compounds (Benjamin, New York, 1967) p. 147. 51) B. N. Das, M. Weinstein and A. A. Menna, Mater. Res. Bull. 5(1970) 751.
GROWTH OF CdS PLATELETS KENNETH A. JONES 3M Company, St. Paul, Minnesota 55101, U.S.A. Received 15 August 1972; revised manuscript received 7 December 1972 A mechanism for the growth of CdS platelets is hypothesized. It is suggested that platelet growth is initiated by two dimensional nucleation on the close packed prismatic planes, and that nucleation occurs when a needle growing in the c direction grows into a region where the supersaturation exceeds a critical amount. The prismatic ledge formed by the growth of these nuclei then acts as a site for another c needle on which other two dimensional nuclei form, etc. The platelet can therefore be described as a band of coherent c needles. It is further suggested that nucleation occurs only on specific crystallographically equivalent planes and that the plane of the platelet surface varies because this anisotropic growth form is produced by spacial fluctuations in the free energy gradient. It is also shown that the frequently observed surface striations are due to imperfect epitaxial growth of c oriented needles.
1. Introduction There are a number of hypotheses describing platelet growth. One of the more detailed, and seemingly most accepted, growth mechanisms is the dislocation mechanism of Chikawaand Nakayama1). They suggested that CdS platelet growth occurs when an [0001] edge dislocation slips out of a [1010]needle and then maintains itself near the (0001) surface by means of line tension. Another hypothesized dislocation mechanism is that the edge portion of a dislocation parallel to the c axis slips out of the c needle and then acts as a nucleation site for platelet growth2). Sears and Coleman3) concluded that platelets are formed when two nonparallel needles containing only screw dislocations grow together. Platelets can be formed because a two dimensional grid of screw dislocations now exists3). It has also been suggested that platelets are formed when a side whisker grows out from the primary needle forming a notch where the atoms preferentially precipitate4). Yet another theory was set forth by Volmer and Estermann5) long before the existence of dislocations was recognized. They hypothesized that platelet growth occurs when the atoms impinge on the lateral surface and diffuse to the growing edge. The growth, morphology, and defect structure of the CdS platelets were examined, and all of these observations are combined with those in the literature. Using Present address: The Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755, U.S.A. *
33
the above theories as guides, an attempt is made to develop a hypothesis that is consistent with the observations. 2. Experimental procedure The CdS platelets were grown by Dierssen and Gabor4) in a fused silica tube by a modified Frerichs method6) using argon flowing at 1 cm/sec as the carrier gas. The CdS powder was evaporated at 1100 °Cand redeposited at 900 °C. After the growth tube was cooled and opened, the specimens were removed and photographed using an optical microscope. The orientation of the platelet was determined with a Laue back reflection camera and the defect structure and the internal strain of the platelet were investigated using a Lang X-ray camera. A Mo fine focus tube with a 40 cm beam extender was used to record the transmission topographs and rocking curves, whereas a Cu fine focus tube and a 1 mil nickel foil placed in front of the 50 ).Lm Ilford nuclear emulsion film were used for those taken in the back reflection mode. The Mo tube was used for the transmission studies because it penetrates deeper into CdS (89 ~tm), and the Cu tube was used in the back reflection studies so that opposite sides of the same platelet could be studied independently (penetration depth 10 ~tm)and larger diffraction angles could be used. The beam extender was used with the Mo tube to obtain a more parallel beam and thereby increase the resolution. Also, the platelet flatness was determined using an interfe-
34
KENNETH A. JONES
(2a)
—
(la)
(Ib) Fig. 1. Micrographs of platelets growing out from needles. (a) Growth with one platelet growing out from a needle (20 x); (b) growth with two platelets growing out from a needle (60x).
rence microscope which recorded the number of interference fringes per unit length. 3. Experimental results and discussion During the initial stage of growth, needles grew out from the sides of the growth tube and after the needles had grown out a sufficient distance, a platelet nucleated and grew laterally4). There usually was only one platelet growing out from a needle as shown in fig. Ia, but in some instances two platelets 180°apart grew out from a single needle (fig. lb). The Laue patterns showed that the needles always grew out in the c direction. They also showed that a majority of the platelets had a (1 l~0)orientation, some had a (1010) orientation while still others has a (l2~0)orientation. The orientations varied about four degrees about the latter orientation,
e (2b)
whereas the scatter was much less pronounced about the other two. The crystals were more likely to have the platelet form when the growth zone was maintained two hundred degrees below the 1100 °Cevaporation temperature. It was noted that platelets were more readily formed when a carrier gas was used than when growth occurred in a static system. Most of the platelets grew at the top of the furnace tube where it was shown that most of the gas flowed by observing the flow pattern of a colored gas. The crystal structure also appears to be a critical factor as crystals with the hexagonal wurtzite structure grow in the form of a platelet but the structurally similar zincblende cubic crystals7) do not grow in the
GROWTH OF
CdS
~
— (2c)
35
PLATELETS ~0o\
(3a)
_
2Io]
__~~~~___a.__[I
tIOTO)
(1010)
(3b)
/ /4P (2d) Fig. 2. Characteristics of a smooth, thin (1120) platelet. (a) Micrograph (18 x); (b) (0002) transmission rocking curve; (c) (0002) transmission topograph (12.5 x); (d) Fizeau fringe pattern (18 x).
platelet form. In addition to CdS wurtzite platelets of 8—10
11—13
‘4
ZnS ), ZnO ), and CdSe ) have been grown but zincblende CdTet 3) and GaP’ 6) crystals grown under similar conditions do not grow as platelets. The (0002) transmission topograph (fig. 2c) of the thin (10 ~tm), smooth platelet displayed in fig. 2a shows that this platelet contained no dislocations. The sharpness of the KcL 1 and KcL2 peaks of the (0002) rocking curve shown in fig. 2b also indicates that the platelet was strain free, and the lack of fringes in the Fizeau 2d shows that surfacesfringe were pattern parallel of to fig. within seconds of the arc.platelet The number of platelets that were thin and smooth was small. Most of the platelets were thicker and contamed striations that were parallel to the c axis. At this point I will discuss the growth mechanism for the thin, smooth platelets and will later attempt to explain how the striations are formed. A hypothesis that is consistent with the above experimental evidence is that a platelet is formed by growth in only one ofat least six crystallographically equivalent
(3c) Fig. 3. Schematic diagrams illustrating how platelets can be formed by two-dimensional nucleation of specific { 1 l20} and/or {1OTO} prismatic planes. (The c axis is normal to the plane of the paper.) (a) Formation of a (1120) platelet growing in the [1100] direction by nucleation of the (2110) and (1210) planes; or (b) by the (1010) and (0110) planes; (c) formation of a (1010) platelet growing in the [1210] direction by nucleation of the (1100) and (0110) planes; or (d) by the (2110) and (1120) planes; (e) formation of a (l2~0)platelet growing in the [14101 direction by nucleation of the (TOlO) and (1210) planes; or (f) by the (1120) and (0110) planes.
directions that is determined by a free energy gradient in much the same way a lead dendrite grows in one of six equivalent <100> directions’ 7). Platelet growth occurs when a needle grows into a region where the supersaturation exceeds forpacked two dimen1 8)the to value occur necessary on the close prissional nucleation matic planes. Nucleation occurs on two adjacent close packed planes which grow together and form a wedge shaped growth front (see fig. 3) that points in a basal direction determined by the free energy gradient. The ledge that is formed by this lateral growth produces a nucleation site for a new, thin needle. Two dimensional nucleation occurs on the new, thin needle; a ledge is formed; a second new, thin needle grows from this ledge; etc. Therefore a thin, smooth platelet is formed by the nucleation and growth of a band of coherent
36
KENNETH A. JONES
needles. This model has other things in common with the dendritic growth model in that the platelet (I) grows rapidly; (2) is thin so that it can dissipate the heat of sublimation; and (3) is thin because the nutrient near the face of the platelet has been depleted by the growth process. The observation that wurtzite crystals grow as platelets but zincblende crystals do not can be explained by examining their crystal structures. Wurtzite crystals have only one preferred growth direction (the [00011) whereas zincblende crystals have four crystallographically equivalent preferred growth directions (four of the eight <111>). A platelet can form when two dimensional nucleation occurs on the prismatic surfaces of a wurtzite needle because another c needle will grow out of the ledge formed by the two dimensional nuclei, However, as in the case of CdTe’ 5), a secondary dendrite will grow out from a zincblende needle because there is more than one preferred growth direction. Growth will occur in these other preferred grow directions rather than parallel to the original growth direction because it increases the surface to volume ratio and therefore the rate of dissipation of the heat of formation. Wurtzite crystals do not have this choice. The hexagonal structure of the wurtzite crystals is necessary insofar as it allows the crystals to have one strongly preferred growth direction. Other hexagonal materials such as alumina could crystallographically have a strong tendency to grow in the c direction, but they do not. It is therefore possible that flag shaped alumina platelets are not formed because growth occurs almost as readily in the a direction as it does in the c’ 9), This model requires that free energy gradients exist, Free energy gradients exist if there is an inhomogeneous distribution of the nutrient and/or a nonuniform thermal field. A gas flow would facilitate the formation of a free energy gradient when the gas is forced to flow around an obstacle, such as a CdS needle, if the rate of thermal diffusion is not significantly greater than the rate of flow of the carrier gas. Using the hard sphere model2 0) to calculate the diffusion coefficient and using the appropriate diffusion equations2’) one can show that about twice as much material would flow across a boundary when the carrier gas has a uniform velocity of! cm/sec the flow rate used to grow the platelets4) than would thermally diffuse at 900 °Cat one atmoC
—
—
sphere of pressure. Therefore using a gas flow could facilitate platelet growth by encouraging the formation of free energy gradients. The growing platelets would cause the flow pattern to continuously change and in some instances this could cause two platelets to grow out from the same needle. The flowing gas produced free energy gradients in the growth tube even before platelet growth was mitiated. As was mentioned earlier the gas had a tendency to flow to the top of the furnace tube. This should lead to an inhomogeneous distribution of the nutrient. The friction that produces the boundary layer near the tube wall should also help to create free energy gradients. The free energy gradient need not be large for growth to occur rapidly in one direction and not at all in the other crystallographically equivalent directions. Hirth and Pound1 8) have shown that no growth occurs by two dimensional nucleation until a critical supersaturation has been reached, but that the growth rate increases very rapidly with the supersaturation at supersaturations greater than the critical amount. They also showed that the greater the critical supersaturation the greater the growth rate will be at a supersaturation slightly exceeding the critical amount’ 8) This can explain why having a 200 °Ctemperature difference between the evaporation and the growth zones promotes platelet growth. It provides the large critical supersaturation necessary for two dimensional nucleation, and the large critical supersaturation accounts for the observed rapid growth’ P4). The platelets do not necessarily grow in the direction of the free energy gradient. Rather they grow in specific crystallographic directions that are most nearly parallel to the free energy gradient. These specific crystallographic directions are determined by the prismatic planes on which two dimensional nucleation occurs. According to the calculations of Wolff and Gualtieri22) and the experimental results of others [see Strehlow23) for references] the (1010) and the (1120) close packed planes have similar surface energies. Therefore growth occurs by two dimensional nucleation on either type of plane or on both types simultaneously. Thus it is possible to explain the growth of (1120) platelets by lateral growth in the [TI00] direction either by the rapid nucleation of (2110) and (1210) planes (fig. 3a) or by rapid nucleation of (1010) and (0110) planes (fig. 3b). Likewise a (1010) platelet can
GROWTH OF
CdS
37
PLATELETS
ease....
I.
I
(4a) (4c)
z
w
I
(4b)
(4d) Fig. 4. Characteristics of a (1120) platelet with narrowly separated striations. (a) Micrograph (18 x); (b) (0002) transmission rocking curve; (c) (1 TOO) transmission topograph (12.5 x); and (d) Fizeau fringe pattern (18 x).
be formed by growing laterally in the [1210] direction either by the rapid nucleation of the (1100) and the (0110) planes (fig. 3c) or by the rapid nucleation of the (2110) and the (1120) planes (fig. 3d). The (12~0)orientation and small variations about it can also be explained by this growth mechanism. It can be formed by lateral growth in the [5410] direction either by the rapid nucleation of the (1010) and the (1210) planes (fig. 3e) or by the rapid nucleation of the (1120) and the (0110) planes (fig. 3f). The probability that two dimensional nucleation will occur on the { 1 120} faces is slightly different than the probability that two dimensional nucleation will occur on the { 1OTO} faces because they have slightly different surface energies. Therefore there should be more ofone
type of platelet and the growth direction of the (l2~0) platelet should not make an equal angle of 15°with the growth directions of the (1120) and the (0110) platelets. This is what was observed as there were more platelets with the (1120) orientation, and the growth direction of the (l2~0)platelets usually made an angle slightly larger than 10.9°with the growth direction of the (1170) platelets. As was mentioned earlier almost all of the platelets contain striations on at least one of their two surfaces. The striations, which were always parallel to the c axis, can be narrowly separated (fig. 4a) or widely separated (fig. 5a) and they often appear on only one side of the platelet and this side is usually rougher. The latter observation is illustrated in fig. 5 where the side view
_________________________________________
e
-
38
KENNETH A. JONES
iiJUtL~i~ II
-
___
(5a)
(6a)
(5b) Fig. 5. Micrographs of a (1120) platelet with widely separated striations. (a) Front view (18><); (b) side view (150><).
——
FUJI -~------
—.1. —~--
(fig. Sb) shows protrusions on only one side. The front side of the aluminum coated platelet (fig. 6a) has many striations on its surface and the back side (fig. 6d) has much fewer in comparison. The micrograph of a polished and etched cross section of two striated crystals cleaved parallel to their c axis (figs. 7a, 7b) show that there are growth layers parallel to the platelet surface whereas there are no layers in the thin, smooth specimen (fig. 7c). The thickness of the platelet also tends to increase as the growth time increases, When the striations do not extend the length of the platelet they terminate where a ridge terminates in a pointed tip on the platelet surface as is shown in fig. 8a. Sometimes entire layers terminate on the platelet surface as shown in fig. 8b. In some instances the ridges
J.
~
1
~
I.
~—
—
‘
(6b)
extend out over the end of the platelet and form needles as is shown in fig. 8c. The X-ray rocking curves and topographs of the striated crystals were almost always different than those of the thin, smooth platelets. By comparing the rocking curve of a thin, smooth platelet (fig. 2b) with the rocking curve of a striated platelet (fig. 4b) one sees that the striated crystal has more diffraction peaks and that the peaks are broader. The extra peaks mean that the striated crystal is an imperfect crystal, and the broader peaks mean that the striated crystal is more highly
GROWTH OF
fJA)
CdS
~J\
39
PLATELETS
(6~
e (6c)
8 (6f) Fig. 6. Characteristics of the opposing platelet surfaces of a thick (1120) platelet with gross striations. (a) Micrograph of the aluminum coated front surface (18 x); (1,) (1230) back reflection topograph of the front surface (12.5 x); (c) (1120) back reflection rocking curve of the front surface; (d) micrograph of the aluminum coated back surface (18 x); (e) (1230) back reflection topograph of the back surface, (12.5 x); and (f) (1120) rocking curve of the back surface.
H
______
(6d)
strained. The (1100) topograph of the striated crystal (fig. 4c) also shows that the crystal is highly strained, The Bragg reflecting center section contains stress lines, and the platelet was so warped that neither end was oriented for Bragg reflection. The fact the striated plate-
lets were more brittle than the thin, smooth platelets also indicates that the striated crystals contained more internal strain. The opposing surfaces of the striated platelet deviate more from parallelism than do the surfaces of the thin, smooth platelet. This is seen by comparing the Fizeau fringe pattern in fig. 2d with that in fig. 4d. It should be pointed out that the platelet in fig. 4a is one of the smoother striated platelets. Most of the striated platelets do not exhibit a fringe pattern because they are too rough.
40
KENNEIH
A. JONES
(7a)
(8a)
I
____
~‘-~r?-
~
1
(8b)
(7b)
(8c) Fig. 8. Micrographs of the different striation configurations. (a) Single striations terminating on the surface where a ridge terminates (100/); (b) an entire layer terminating on the platelet surface (18 ‘); (c) ridges extending out over the end of platelet (100 .).
(7c) Fig. 7. Micrographs of polished and etched cross sections contaming the c axis of: (a) a striated platelet (100’ ); (b) a striated platelet ~kith a thick layer on top of a thin layer (500 ); and (c) a smooth thin platelet (500 ~.
The back reflection topographs and rocking curves of the rough surface containing striations (fig. 6a) and the smoother Uig. 6d) surface ofa thick, striated platelet show that the two surfaces were structurally different. The (1230) topograph of the striated surface thg. ób) contains a number ofdark lines that correspond roughly to the ridges in fig. 6a. This shows that the ridges had . . . a different orientation than the rest of the platelet. That portions of the rough side of the platelet had different
GROWTH OF
CdS
orientations is seen in the (1120) rocking curve (fig. 6c) where the rocking curve has more than one Kct, and one Kct2 peaks. The (1230) topograph (fig. 6e) of the smooth surface is substantially different than the (l2~0)topograph (fig. 6b) in that it has a diffuse pattern characteristic of a highly strained crystal rather than the long narrow diffracting regions of the front side. The rocking curve for the smooth side (fig. 6f) also shows that this side of the crystal is highly strained as the rocking curve is broad. However, it indicates that this side of the crystal is single crystalline as there are only two peaks. The topographs of the thicker platelets revealed that some of them contained dislocations whereas no dislocations were observed in the thin, smooth platelets. The (1210) and (0002) transmission topographs of a (1010) platelet in figs. 9a and 9b show that there were a number of line defects lying in the basal plane. Because the defects had a much stronger contrast in the (1210) topograph it is likely that they were the 24). 30° +[12A 10] hypothesis dislocations thatobserved is consistent previously with by theMohling above ob servations is that striations are formed by the imperfect epitaxial growth of c oriented needles on the platelet surface. The striations are visible because the c needles have vicinal prismatic surfaces. Some of the layers and some of the striations terminate before they reach the end of the platelet because they do not have time to grow out to the end. The thickness of the striated platelets increases with time because new epitaxial layers have more time to nucleate and grow. The layered structure seen in the cross sections of the striated platelets indicates that the striations are formed by epitaxial growth on the platelet surface. This is particularly true of fig. 7b where there is a thick layer on a thin layer. Also, the striations often appear on only one face of the platelet because one face is more exposed to the gas flow, The X-ray topographs and rocking curves show that the striated platelets are imperfect and are highly strained. According to my hypothesis this is due to imperfect epitaxy of the c needles. The back reflection topograph of the striated face of a platelet (fig. 6b) supports this idea as some of the needles producing the striations have a slightly different orientation than the rest of the platelet, but each individual needle has the same orientation along its entire length. The internal stresses ob-
41
PLATELETS
~
_______________________________________________
(9a)
-_____________________________________________
Fig. 9. ~
(9b) Transmission X-ray topographs of a (1010) platelet con(a) (1210) topograph (100 x); (b) (0002)
served on both sides of the platelet, then, are due to the warping of the crystal that partially compensates for the lattice mismatch generated by the imperfect epitaxy. The dislocations observed in some of the platelets are also produced by the imperfect epitaxy.
4. Further discussion 4.1. THIN, SMOOTH PLATELETS There is much evidence in the literature that supports the observation that platelets grow out laterally from a c needle. Ibuki2 5) observed that CdS platelets grow laterally out from a c needle while Dev8) made a similar observation for zinc sulfide. Also all those who have
42
KENNETH
studied CdS platelets have found that at least some of them have a (1120) orientation, most investigators have detected a (1010) orientation, whereas only one other group of investigators has found platelets which had neither a (1170) nor a (1010) orientation26). However, all of the orientations observed by them contained the c axis, It has been suggested that two dimensional nucleation does occur on the prismatic planes of some needles at a critical supersaturation when they grow into a region of higher supersaturation. Devries and Sears2 7) have attributed the fattening and subsequent decrease of the growth rate in the direction of the needle axis of A1 2O3 needles to the onset of two dimensional 28) nucleation on the prismatic faces. Dittmar and Kohler observed the same growth behavior in sodium needles and they, too, attributed it to two dimensional flucleation. Observations made by Hildisch29) can be interpreted to mean that smooth, thin platelets nucleate and grow at a critical supersaturation. He noted that all of the smooth, thin platelets taken from the same section of the growth zone contained the same amount of excess cadmium, but the amount ofexcess varied from section to section. According to my hypothesis the platelets from the same section contained the same amount of excess cadmium because they nucleated and grew at the same critical supersaturation. The amount ofexcess varied from section to section because the temperature and therefore the critical supersaturation varied, There is evidence in the literature that a large supersaturation promotes platelet growth. Ibuki25) and Sears30) observed that CdS needles grow at small supersaturations and that platelets appear when the supersaturation is increased. Park and Reynolds’2) noted that ZnO platelets were likely to grow at the cooler end of the growth tube, and Sears31) observed that the number of mercury platelets was increased three orders of magnitude when the supersaturation was doubled, There is also evidence in the literature that small amounts of impurities can impede or facilitate platelet growth. This can be interpreted to mean that the impurities affect the critical supersaturation. Chickawa and Nakayama’) observed that the growth forms of the CdS crystals were altered by intentionally introducing different impurities. Also, Park and Reynolds’2)
A. JONES
observed ZnO platelet growth when oxygen was reacted with ZnS, but no platelet growth occurred when oxygen was reacted with ZnSe. The studies on how the temperature gradient affects the growth form of CdS32) and ZnS9) crystals indicate that the free energy gradient is a critical parameter. In both studies it was found that steep gradients favor the growth of platelets whereas needles were formed when the gradients were smaller. Fochs32) observed that platelet growth was favored when the temperature difference between the evaporation and the growth zones was changed rapidly, and needle growth was favored when the temperature difference was changed slowly and uniformly. He also noted gas thatwas platelets were when more likely to form when a carrier used than growth took place in a closed tube. According to the hypothesis the surface energy of the close packed planes as well as the free energy gradient determine the platelet orientation. That the surface energy influences the orientation of CdS platelets has been suggested or implied by Caveny1 0) MohIing33), and Tang34). It was suggested that hexagonal wurtzite crystals grow in the form ofplatelets and cubic zincblende crystals do not because the cubic crystals have more than one crystallographically equivalent preferred growth direction. This also appears to be the case for metals as the metals that grow in the platelet form cadmium3 5) (hcp), zinc3 6) (hcp), and mercury3 1) (rhombohedral) do not have a cubic crystal structure. As mentioned in the introduction some of the theories of platelet growth involve a dislocation mechanism. The primary reason that this mechanism has been rejected is that I and many others”33’3739) have not observed any dislocations in the smooth, thin CdS platelets. Dislocation free cadmium3640), zinc36) and mercury31) platelets have also been grown. It has been suggested that the dislocations responsible for platelet growth slip out of the crystal’), but this possibility has been mathematically justified only for a single dislocation in a very thin needle2). Another objection to the dislocation mechanism is that it is difficult to envisage how it can explain the growth of (12~0)platelets. There is another objection to Chickawa and Nakayama’s’) growth mechanism. They claim that the original needle grows in the [1010] direction, but all of the other investigators believe that it grows in the [0001] —
—
GROWTH OF
CdS
direction. If it did grow in the [1010] direction it would be difficult to explain how the (1010) and the (12~0) platelets are formed and why all of the platelets that were examined contained the c axis, It has also been suggested that platelets are formed when a side whisker grows out from the primary needle forming a notch where the atoms preferentially precipitate4). The major objection to this growth mechanism is that I did not see any X-ray evidence of a side needle inside of a platelet. It was suggested that the side whisker was annealed out4), but this is difficult to accept as my annealing of some striated crystals did not noticeably reduce the imperfection or the internal strain of some striated platelets. If platelet growth were caused by the growth of a side whisker, it is more likely that the side whisker would remain and be visible as it is in the case of the ZnO fourling4’).
PLATELETS
43
observed that by increasing the cadmium pressure he increased the platelet thickness. This could be due to an increase in the rate of nucleation of new epitaxial layers because the sticking coefficient of sulfur is much larger in the presence of excess cadmium46). It is also known that reducing the amount of hydrogen present in the carrier gas reduces the number of striations. This could be due to the fact that the presence of hydrogen gas encourages growth in the c direction4 7), Some chemical analyses indicate that the striations are formed by epitaxial growth as it has been shown that the striated platelets contain more impurities48), and striated platelets taken from the same section of the growth zone contain varying amounts of excess cadmium2 9), According to my hypothesis this is due to the longer time over which epitaxial growth occurs so that growth takes place under varying growth conditions. Chickawa and Nakayama1) have suggested that the 4.2. STRIATED PLATELETS striations are produced by 4- [1010] partial dislocations. Optical studies by many investigators indicate that This does not appear to be the case because partial disthe striations are produced by the imperfect epitaxial locations have been observed only in doped plategrowth of c oriented needles. Fochs3 2) observed that lets49’5 0). It was thought that doping impurities had the platelets grown over a shorter period of time had to be present to pin the dislocation in the platelet and fewer striations. This can be interpreted to mean that not allow it to slip out’). However, it now appears that fewer striations were formed because there was less time the impurities created the partial dislocations rather for epitaxial growth to occur. Others noted that the than pinned them because studies of 4- [1120] dislocastriations often appear on only one side of the plate- tions in undoped CdS platelets showed that they do not let”37), and Caveny37) observed that the striated sur- break up into partial dislocations24’50). Their inability face was the surface that faced the gas flow. The simil- to break up into partial dislocations has been attributed arity in the morphology of wurtzite films and the to the high stacking fault energy of CdS50’5’). striated platelets also suggests that the striations are It has also been suggested that platelets grow by a due to the epitaxial growth of c needles. The optical filling in process between needles4). Using this mechamicrographs of (1120) ZnO42) and (1013) CdS43) hete- nism it would be difficult to explain why the platelet is roepitaxial films are similar to fig. 8a in that they show more misoriented on the more striated surface. If the needles terminating on the surface and pointing in the smooth surface were formed by growth over the needles c direction. it should not be more perfectly oriented than the side Another study showed that the striations do not containing the needles because the orientation of an penetrate through the entire crystal but are confined to epitaxial layer is not better than the orientation of the a layer. It was shown that many striations disappeared substrate. It also is more difficult to explain the obwhen one side of a striated CdS platelet was etched44). servations that smooth, thin platelets from the same The X-ray results of Caveny3 7) also confirm our ob- growth area have the same amount of excess cadmium servation that the striated platelets are usually imper- whereas the striated platelets do not, and that striated feet as he noted that the striated platelets contained platelets contain more chemical impurities. misorientations up to 1°. Some changes in the platelet structure brought about 5. Conclusions by changes in the growth chemistry can be interpreted It has been hypothesized that the growth of a thin, to show that epitaxial growth takes place. Woods4 5) smooth platelet occurs when a needle growing in the
44
KENNETH
c direction grows into a region where the supersaturation is greater than a critical amount. At this point two dimensional nucleation occurs on the close packed prismatic planes. A ledge formed by the nuclei then acts as a site for a new c needle, new two dimensional nuclei form on the new needle, etc. It can therefore be said that the platelet is made up of a parallel band of coherent c needles. It is further suggested that the platelet grows in only one of at least six crystallographically equivalent directions because free energy gradients are produced by the carrier gas flow patterns. The platelet will then grow out in a basal direction that is determined by a cornbination of the free energy gradient and the crystallographically possible growth directions. It is also shown that the striations frequently observed on the surface of a CdS platelet are due to the imperfect epitaxial growth of c oriented needles. It is shown that, in addition to producing a rough surface, the c needles can produce growth defects and internal strains when they are not coherent with the substrate and with each other. Acknowledgements It is a pleasure to thank 0. N. Salmon, G. H. Dierssen, T. Gabor, R. A. Hatch, W. H. Strehlow, and R. L. Weiher for their many stimulating comments. I would also like to thank G. H. Dierssen for supplying the platelets and am grateful for the technical assistance of A. L. Cowles, R. B. Yougquist, and J. M. Magnusson. References I) J. Chickawa and T. Nakayama, J. AppI. Phys. 35(1964)2493. 2) J. P. Hirth and F. C. Frank, Phil. Mag. 3(1958)1110. 3) G. W. Sears and R. V. Coleman, J. Chem. Phys. 25 (1956) 635. 4) G. H. Dierssen and T. Gabor, to be published. 5) M. Volmer and I. Estermann, Z. Physik 7 (1921) 13. 6) R. Frerichs, Phys. Rev. 72(1946) 594. 7) E. P. Warekois, M. C. Lavine, A. N. Mariano and H. C. Gatos, J. AppI. Phys. 33 (1962) 690. 8) I. Dcv, Brit. J. App). Phys. 17 (1966) 769. 9) H. Samelson, J. AppI. Phys. 32 (1961) 309. 10) R. J. Caveny, J. Phys. Chem. Solids 29 (1968) 851. 11) R. B. Sharma, Indian I. Pure AppI. Phys. 7(1969) 736.
A. JONES
12) Y. S. Park and D. C. Reynolds, J. Appl. Phys. 38(1967) 756. 13) H. Iwanaga and N. Shibata, Japan. J. AppI. Phys. 11 (1972) 121. 14) C. Paorici, J. Mater. Sci. 5 (1970) 918. 15) 1. Teramoto, Phil. Mag. 8 (1963) 357. 16) J. Crystal GrowthCan. 9 (1971) 346.29 (1951) 382. 17) E. F. Schonherr, Weinberg and B. Chalmers, J. Phys. 18) J. P. Hirth and G. M. Pound, in: Progress in Materials Science, Vol. 11 (Pergamon) ch. D. 19) I. L. Gelles and W. P. Binnie, Mater. Sci. Eng. 5 (1970) 71. 20) E. H. Kennard, Kinetic Theory of Gases (McGraw-Hill, New York, 1938) ch. IV. 21) L. S. Darken and R. W. Gurry, Physical Chemistry of Metals (McGraw-Hill, New York, 1953) ch. 18. 22) G. A. Wolff and J. G. Gualtieri, J. Am. Mineralogist 47 (1962) 562. 23) W. H. Strehlow, J. AppI. Phys. 41 (1970) 1810. 24) W. Mohling, J. Crystal Growth 1 (1967) 115. 25) 5. Ibuki, J. Phys. Soc. Japan 14(1959)1181. 26) Zh. G. Pisarenko and M. K. Sheinkman, Soviet Phys.-Solid State 3 (1960) 1158. 27) R. C. Devries and G. W. Sears, J. Chem. Phys. 31 (1959) 1256. 28) 29) 30) 31)
W. Dittmar and A. Kohier, J. Crystal Growth 2 (1968) 271. L. Hildisch, J. Crystal Growth 3/4 (1968) 131. G. W. Sears, Acta Met. 3 (1955) 367. G. W. Sears, J. Chem. Phys. 25 (1956) 637.
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P. D. Fochs, J. AppI. Phys. 31 (1960) 1733. W. Mohling, J. Crystal Growth 1 (1967) 115. Tang Ting-Yuan, Acta Phys. Sinica 18 (1962) 207. P. B. Price, Phil. Mag. 5 (1960) 473. P. B. Price, Phil. Mag. 5 (1960) 417.
37) R. J. Caveny, Phil. Mag. 12 (1965) 423. 38) W. Mohling, H. Peipst and L. Hildisch, Phys. Status Solidi 5 (1964) 101. 39) W. Mohling and J. Heydenreich, Phys. Status Solidi 7 (1964) 155. 40) P. B. Price, J. Appi. Phys. 32 (1961) 1747. 41) J. M. Cowley, A. L. G. Rees and J. A. Spink, Proc. Phys. Soc. (London) B 64 (1951) 638. 42) G. Galli and J. E. Coker, Appl. Phys. Letters 16 (1970) 439. 43) B. J. Curtis and H. Brunner, J. Crystal Growth 6 (1970) 269. 44) M. Ya. Skorokhod and L. I. Datsenko, Soviet Phys.-Cryst. 11 (1966) 272. 45) J. Woods, Brit. J. Appl. Phys. 10(1959) 529. 46) M. H. Christmann, K. A. Jones and K. H. Olsen, to be published. 47) L. van den Berg, Gov. Res. Rpts., AD688903 (1969). 48) Zh. G. Pisarenko and M. K. Sheinkman, Soviet Phys.-Solid State 3 (1960) 1158. 49) J. Chikawa, Japan. J. App). Phys. 3 (1964) 229. 50) B. N. Das and M. Weinstein, in: Proc. Intern. Conf. Il—VI Semiconductor Compounds (Benjamin, New York, 1967) p. 147. 51) B. N. Das, M. Weinstein and A. A. Menna, Mater. Res. Bull. 5(1970) 751.