Some notes on the growth kinetics and morphology of VLS silicon crystals grown with platinum and gold as liquid-forming agents

Journal of Crystal Growth 43(1978) 235 —244 © North-Holland Publishing Company

SOME NOTES ON THE GROWTH KINETICS AND MORPHOLOGY OF VLS SILICON CRYSTALS GROWN WITH PLATINUM AND GOLD AS LIQUID-FORMING AGENTS J. WEYHER Institute for Materials Science and Engineering, Technical University, Warsaw, Poland Received 21 July 1977

the sixties. The result was a series of publications, which were summed up by Wagner [3]. The principles of VLS mechanism were studied mainly on sili-

The effects is presented of the alloying parameters of the agent and the substrate material upon the morphologic perfection of the crystals grown by the VLS technique. With discontinuity of the crystalline structure of the substrate and the growing crystal, the surface tension of the liquid is of prime importance to the growth. Crystals of round cross-sections are then the result. With the appropriate preparation of the substrate, the effect of its crystallographic orientation already in the alloying stage becomes significant. A horizontal temperature gradient in the growth zone results in the replacement of VLS by (VLS)h growth which depends on the initial quantity of the liquid. On the basis of the above observations, a geometric criterion is presented of morphologically perfect growth of silicon by the VLS technique with gold or platinum as the liquid-forming agent at a temperature of 1000—1100°C. A specific aspect is shown of VLS growth — namely, a combination of the VLS and VS mechanisms. A study has been made of the cross-sections of VLS silicon crystals grown close to each other in pairs, which, as a result of the VS process, grew together, acquiring a morphology appropriate to the VLS process at a particular temperature. Dependence is shown graphically of the rate ofgrowth of 511icon crystals upon their diameter for d ~ 130 im, with the use of platinum as the alloying agent. It is further shown that, with the exception of small diameters at which Gibbs— Thomson effect occurs, in the case of diameters exceeding —~10~m, the VLS growth rate decreases with increasing crystal diameters. On the basis of observations of crystal morphology and crystal growth rate, the lowest permissible value of SiCl 4 concentration in the vapor phase is determined for silicon growth with Pt and Au as liquid-forming agents. The notion is introduced of concentration-unstable VLS growth, with the above phenomenon being graphically analyzed. From the considerations on VLS growth kinetics, and on the basis of the observations concerning crystal morphology, it follows that liquid-phase diffusion is the rate-determining step in VLS growth.

con crystals [1—16], but the information obtained from experiments with the growth of other elements or chemical compounds is equally valuable from the vantage point of the knowledge of VLS mechanism [8—12,15,1 7—191. Despite a considerable number of works published, some of the aspects of VLS growth have not yet been satisfactorily explained. Particularly controversial seems to be the concept of VLS growth-limiting factors, based on the investigations of whiskers with diameters not exceeding several micrometers [10,11, The present work discusses factors limiting VLS growth of silicon crystals with a diameter up to 130 jim. Considerations are based on previously published results [16] and on new experimental data VLS growth kinetics. Also presented are notes concerning the technological factors responsible for proper VLS growth, as well as recent observations regarding the morphology of silicon crystals grown with gold and platinum. concerning

2. Experimental VLS crystallization was effected by radio-frequency heating inside a horizontal reaction tube with a silicon-coated graphite susceptor. The hydrogen reduction of SiCl4 in an open system was employed, the hydrogen being purified in a palladium diffuser. Details concerning the geometry of the reaction zone were published in ref. [13]. Platinum and gold (i.e., the liquid-forming impurities) were prepared by slic-

1. Introduction The VLS crystal growth mechanism discovered by Ellis [1,2] was thoroughly investigated in

Wagner and

235

J. Wevhcr / Growth kinetics and ozorphologv of VLS silicon crystals

236

lug a wire of 50 jim diameter. The wire slices were then placed on conventionally cleaned and etched ~111 } single-crystal silicon wafers (Czochralskigrown. dislocation-free, p-type, approx. 20 ohm/cm).

The process of growth took place at a temperature of 1000 and 1100°C,the S1CI4 to hydrogen mole ratio being 0.009 3/min. to 0.012. TheVLS totalgrowth, hydrogen rate After theflow samples was 800 cm by SEM, using the surface topography were examined technique. 3. Results and discussion

—

3.1. Effects of growth conditions on the morphology of Si VLS cn’stals

4

Proper VLS growth is determined by the state of the substrate surface, alloying time and temperature, temperature gradients in the growth zone, and by the supply rate of silicon atoms from the vapor phase.

LJ~fl

3. 1.1. Alloying time It was found that the time of alloying — i.e. the time of isothermal anealing at growth temperature

I ig. I. Pt—Si alloying region; alloying temperature 1050°C, lone 2 mm. Optical picture.

O,5mrri .~:•“ ~

-.

I

~1

‘l,~.,. ~ 1

(hI

I ig. 2. SiVLS grou lh with incomplete (a) or nonexistent (b) continuity of substrate and crystal structure. SEM, n

=

60°.

J. Weyher / Growth kinetics and morphology of VLS silicon crystals

prior to the introduction of SiC!4 into the reaction zone should, for gold and platinum, amount to 10—IS mm (the speed of heating up to 1000— 1100°C was approximately 50°C/mm; substrate etched in polishing mixture). Shortening of the alloying time does not permit the liquid to achieve the composition of equilibrium on liquidus CE [20]. The morphology of the liquid droplet is inappropriate, which leads to some disturbances in the morphology of SiVLS crystals. Fig. 1 shows, by way of example, the optical picture of the Pt-Si alloying region formed at a temperature of 1050°C after 2 mm obtained alloying. after The the morphology alloying region applicationofofthe appropriate alloying conditions is presented in fig. 9a. Prolongation of the alloying time over 15 mm is of no basic —

237

significance to the proper VLS growth, nor is it any way justified. 3. 1.2. State of substrate plate surface

Growth on a chemically purified substrate, but not etched in a polishing mixture, is characterized by disturbances in the alloying kinetics and morphology of crystals probably, as a result of the occurrence of a Si02 layer. Despite the application of alloying conditions appropriate to the growth temperature of 1050°C(r = 10 mm), 1VLS as a result ofwith incomplete cohercrystals the substrate, ence of the growing S crystal positioning is accidental, and nucleation and growth of “clumps” of Si~whiskers frequently occurs fig. 2. The cross-sections of such crystals are —

—

—

a

Fig. 3. Pt—Si alloying region; alloying temperature 1050°C:time 60 mm. (a). Microanalysis of part of thic region; (b) surface relief, (c) Pt distribution.

238

.1. Weeher

/ Growth

kinetics and inorpl,ohwe

t VLS silicon crystals

six-sided, i.e., appropriate to the temperature range employed [31. Prolongation of the alloying time prior to growth on a substrate thus prepared, may cause surface diffusion of platinum or “spreading” of the platinum—silicon alloy as a result of change in the component force of liquid surface tension YLS in contact with the Si0 2 layer. Fig. 3a shows the morphology of the Pt—Si alloying region formed at a temperature of 1050°C, r = 60 mm. and fIgs. 3b—c present results of a qualitative analysis performed by means of an X-ray microanalyser (on part of this alloying region). After such an alloying course, series of thin 5mVLSaleader crystal SiVLS whiskers grow around the -- fig. 4. With the use of gold, on the other hand, a total lack of diffusion has been observed between substrate and the alloying element. This leads to alloying of gold with the silicon supplied froni the vapor phase and to local growth of rod-like S1VLS crystals of random orientation fig. 2b. The morphology of such crystals is determined only by liquid surface tension, and not by the crystallographic orientation of the silicon substrate plate.

250 urn -

-

I t~. 5. S~hCOflryo~~ th h~(Vl.S)h and Vi S mccIuni~tns ith Pt—Si alloy, SF\l. =

3. 1.3. Temperature gradient Normal VLS growth requires a vertical positive temperature gradient. A horizontal gradient. on the other hand, results in the replacement of VLS by (VLS)h growth, i.e., in crystallization in the horizontal direction, with the participation of the liquid zone. (VLS)h growth depends on the initial quantity of the liquid — fig. 5. Since horis’ontal motion of liquid droplets has been observed only during the supply of silicon atoms front the vapor phase, the Tel m “(VLS)h growth” seems to be more rational than “TGZM” 1201.

-‘

3.

from the vapor

phase is practically controlled by the concentration of silicon tetrachioride in hydrogen (mR). It has been experimentally established that for each of the alloying elements used, there is a lowest critical concentration value (mRi) below which both the formation of a liquid droplet and proper VLS growth are retarded. At mR
.t

1~~iEO%’~th ~~ilh I,t. after alloying time ~t 61) ~ temperature of 10511C. SF~d,a = 45°.

Such growth has been termed concentration-unstable. A graphical qualitative analysis of the above phenom-

J. Weyher / Growth kinetics and morphology of VLS silicon crystals

239

~

VR, depends on the presence and “intensity” of the

Fig. 6. Concentration-unstable silicon growth with platinum. SEM = 45~

action of catalysts, which the alloying elements constitute, and (VR)pt >(VR)AU [2]. It is evident from fig. 6 and observations of other samples after VLS growth with platinum and gold that with mR (V1)AU. However, a qualitative analysis is rather difficult, since, in addition to the different catalytic effect of gold and platinum, there occurs a differentiation for the two employed alloying elements of the parameter FVL/FLS [16], which may also affect VLS growth kinetics. For mR > mRi, VLS growth occurs by what is termed continuous growth mechanism [4], and theoretically, with an

enon for Si growth with Pt and Au is shown in fig. 7, The idea of this diagram is based on the principles given for epitaxial growth of silicon in the work of Tung [21], modified by the characteristic features of VLS growth. The speed of reaction in vapor phase,

v VR

Vvis-pi

accommodation factor a VR

=

I, might be fulfilled the

Vv~s5,

relation VVLS VR, In practice, in the reaction zone geometry employed [13], VVLS< VR fig. 7. =

—

(Vdp (Vh,

-

3. 1.5. Morphologically perfect SiVLS growth at a temperature of 1000—1100°C In normal growth conditions, morphologically perfect VLS growth occurs. In the above conditions, four characteristic stages in SiVLS growth may be distinguished: (A) Alloying of substrate silicon with the alloying element with no silicon from gaseous phase; the

-

I

(rnRl)p

~.

Fig. 7. Dependence of reaction in vapor phase (VR) and of VLS growth rate (V) on SiC14 concentration in hydrogen for the alloying elements Au and ~

symmetry of the alloying region is determined by the crystallographic orientation of the substrate. (B) Growth of a truncated pyramid with a triangular base and {2 11 } side faces. .

.

240

J. Wevher / Growth kinetics and morphology of VLS silicon rry~rals

AA~T

Fig. 8. Diagram of silicon VLS growth stages at a temperature of 1000 and 1100°C.

(C) Formation of three ~11 l} and three {21 l} side faces as a result of the configuration of the surface tension forces, characteristic of the employed tern-

perature range, as well as of their absolute values [161. (D) Growth of crystal of six-sided cross-section and

~

~211}

~2l 1} side faces. Such cross-section is characteristic

of the employed temperature range [221. A diagram of the above growth stages is presented in fig. 8, and the successive growth stages of real crystals are shown in figs. 9 and 10. In fig. 10, in the

_______

-~

Ic. 9. ( ,rowth siage~ ii re-il cr slak. correspondins to the diarain in hg. 8. Si \I, a = it -

region defined as the regrowth zone [22J, two layers may be distinguished: Ri, a layer formed from the silicon supersaturating the alloy termination, and R2, a layer formed during cooling from the growth to the eutectic temperature. If the temperature drop takes place immediately after closure of SiC1 4 supply, the RI zone does not occur. I

The growth stages described above may be distinguished in the case of the use of both gold and platinum. Certain differences in morphology connected with the increased surface tension of the Pt—Si alloy coiiipared with the Au--Si alloy are discussed in ref.

J. Weyher / Growth kinetics and morphology of VLS silicon crystals

241

[16]. It has also been shown that the morphologic crystals does not eliminate the possibility of occurrence of structural defects such as dislocations or entrapments. perfection of

3. 2. Combined VLS— VS growth

_______

\ ~

--

eral

Wagner [22] has shown that structurally and morphologically perfect silicon crystals of macroscopic dimensions can be obtained by deposition of silicon from vapor phase on VLS-grown crystals. Another method of increasing the original diameter of SiVLS crystals consists in “growing together” of two or sevcrystals positioned parallel and close to each other due to the VS process. Owing to the proper distribution of the platinum on the substrate plate, the growth of many crystals thus grown together has been achieved fig. 11. When grown together, such crystals acquire the morphology of the crystals grown, at a given temper—

Fig. 10. Morphologically perfect SiVLS crystal. SEM, a

/

=

, $1

-

mm

Fig. 11.

5’vLs crystals grown with

Pt at ‘0R > “tRl• The arrow indicates VLS—VS growth.

242

J. Weyher / Growth kim tics and morphology of VLS silicon ri-sta/s

03 a hg. 2. Cross-sei lions (a. e) and a longitudinal section (b) of silicon crystals grown by both VLS (c) and VLS—VS (a, b) mechanisms. Section (b) was Sirtl-etched.

ature, by the VLS mechanism. Fig. 12 shows sections of a VLS—VS grown crystal, and, for comparison, a cross section of a VLS grown. The structure of the

range of diameters of silicon crystals grown with platmum is shown in fig. 13 and a topograph of the surface of one of the samples on which measurements

grown-together crystals in almost perfect. Selective

were performed is presented in fig. 14. A similar

etching does not reveal a boundary between SiVLS and Sivs; dislocation etch pits have however been observed, which may indicate a small misorientation of the crystals growing together fig. 12b. —

to this constitute crystals with d < 5 jim, in the case of which the Gibbs—Thomson effect occurs. The above range of diameters is described in detail in refs. [10,11,19]. The dependence V°°ftd)for a wide

600

~ ,.

40

60

80

100

120

-

Fig. 13. Dependence of the growth rate of S1VLS crystals on their diameter. Growth with Pt. Curve 1: mR = 0.009; curve mR = 0.0095. 2:

J. Weyher / Growth kinetics and morphology of VLS silicon crystals

243

Fig. 14. Silicon wafer surlace after VLS growth with Pt. Illustration of the dependence 1’ = f (d). SE’sl. a

character of this dependence has been observed for both platinum and gold. From the analysis of the diagram in fig. 13 and froni the observations made previously in refs. [13,16], the following suggestions follow concerning the rate-determining step of VLS growth: (I) Diffusion in the vapor phase. This stage may, for mR ~ mRi, i.e., for stable VLS growth, be excluded, since the character of the relation V = fl~d)does not change with increasing mR (cf. curves I and 2 in fIg. 13); at mR
=

90

-

atoms in the liquid droplet near the edges of the growing crystal compared with the center of the droplet [16]. The above phenomenon occurs mainly in large-diameter crystals. The experimental data given above confirii~also Wagner’s statement: “The isoconcentration lines in the liquid are not parallel to the interface because of the geometry of the system. Therefore, the driving force at the interface is nonuniform, being smallest at the center.” [221. At mR ~ mRi, for d> S pm, crystals of larger diameter grow slower than thinner crystals— figs. 13 and 14. It may therefore be assumed that the path of diffusion in liquid has a substantial effect on growth kinetics. At mR
urn

I

.

..

‘.

p

—-

--

. .

.

.

-

I 1g. 15. Silicon wafer surface after VLS growth with Pt at mR < mRi. SEM, a = 90°.

244

J We titer

/ Growth

kinetics and morphology of VLS silicon crystals

of the deficit of silicon atoms in the vapor phase, diffusion in the liquid is no longer a VLS growth-limiting factor, and the rate of growth of crystals of different diameter becomes accidental — fig. IS. Conclusions from the considerations carried out above, amounting to the statement that diffusion in the liquid phase is the VLS growth-limiting factor, are inconsistent with conclusions derived from the investigations of whiskers of diameter d < 5 pm [11,1 5]. It seems, however, that generalizations concerning the growth kinetics of VLS mechanism should be made on the basis of the results of investigations of crystals with a diameter of not less than 10 pm, in order to eliminate the accompanying Gibbs—Thomson effect, together with a considerable change in the ~vL/~LS parameter which occurs in the case of small diameters

[161. 4. Conclusions (I) Tile effect of growth conditions on the growth of SiVLS crystals has been determined. It has also been shown that niorphologically perfect VLS growth requires a rigorous check of the state of the substrate, alloying parameters, temperature and time, temperature gradients in the growth zone, and of the amount of silicon supplied from the vapor phase. (2) The concept of coticentration-unstable VLS growth has been introduced and appropriately

defined. (3) Four basic stages have been distinguished in the formation of SiVLS crystals, and a geometric model of the individual growth stages of morphologically perfect crystals has been presented. This model constitutes a geometric criterion for the assessment of the normality of the VLS process.

(4) The possibility of obtaining morphologically and structurally perfect Si crystals by a combined VLS— VS mechanism is indicated. (5) The growth rate of Si crystals is dependent on their diameter. The dependence V = f(d) decreases with increasing d within a wide range of diameters. Only for d < 5 pm, the growth rate decreases as a

of the Gibbs—Thonison effect. (6) Observations of the morphology of the alloy terresult

minations of SIVLS crystals, as well as the results of growth kinetics investigations, permit it to be presumned that diffusion in tile liquid phase is the VLS growth rate-determining step for 1iIR ~ mpj.

Acknowledgements The author wishes to thank Dr. J. Kozubowski, and Professors S. Wojciechowski and B. Ciszewski for many helpful discussions. I-Ic is also grateful to Dr. Sokolowski for advice, to L Kaczyñski, M. Sc., for X-ray investigations, and to M. Pawtöwska, M. Sc., for kind assistance in SEM investigation.

References Ill R.S. Wagner and W.C. Ellis, Appl. Phys. Letters 4 (1964) 89.

12] R.S. Wagner and W.C. Ellis, Trans. Met. Soc. AIME 233 (1965) 1053. 131 R.S. Wagner in: Whisker Technology, Ed. A.P. Levitt (\Viley, New York, 1970) pp. 47—119. 141 B. Mutaftschiev, R. Kern and C. Georges, Phys. Letters 16 (1965) 32. 151 I).W.F. James and C. Lewis, Omit. J Appi. Phys. 16 (1965) 1089.

161 J.D. I ilby and S. Nielsen, Brit. J. Appi. Phys. 17 (1966) 81. 171 J.l. l:ilby, S. Nielsen, G.J. Rich, G.R. Booker and J.M. Larcher, Phil. Mag. 16 (1967) 141. 181 E.l. Givargizov and N.N. Sheftal, J. Crystal Growth 9 (1971) 326. 19] G.A. Bootsma and Il.J. Gassen, J. Crystal Growth 10 (1971) 223. 1101 E.l. Givargizov and Yu.G. Kostjuk. Rost Kristallov (Crystal Growth), Vol. 9 (Nauka, Moscow, 1972) p. 242. 1.1. Givargizov and A.A. Chernov, Kristallografiya 18 (1973) 147. [121 Givargizov, J. Crystal Growth 20 (1973) 217. [131E.I. J. Weyher, Doctor Thesis, Military Academy of Technology, Warsaw—Bemowo (1974).

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[14] L. Kaczyhski and J. Weyher, Paper presented at 7th Intern. Conf. on X-Ray Optics and Microanalysis, Moscow—Kiev, 1974.

[15] E.l. Givargizov, J. Crystal Growth 31 (1975) 20.1161 J. Weyher, Mater. Sci. Eng. 20 (1975) 171. [17] G.A. Bootsma, W.F. Knippenberg and G. Verspui, J.

Crystal Growth 11(1971) 297. [181 E.I. Givargizov and N.N. Sheftal, Kristall und Technik 7 (1972) 37. [191 E.I. Givargizov, Kristall und Technik 10 (1975) 473. [20] R.S. Wagner and C.J. Doherty, J. Electrochem. Soc. 113 (1966) 1300.

1211 S.K. Tung, J. Electrochem. Soc. 112 (1965) 436. [221 R.S. Wagner, J. Appl. Phys. 38 (1967) 1554. [23] J.P. l-lirth and G.M. Pound, J. Phys. Chem. 64 (1960) 619. [24] J.W. Calm, W.B. 1-lilhig and G.W. Sears, Acta Met. 12 (1964) 1421.