Growth stability in high temperature vapour growth

,. . . . . . . .

CIRYSTAL G R O W T H

ELSEVIER

Journal of Crystal Growth 162 (1996) 173-177

Growth stability in high temperature vapour growth Krzysztof Grasza *, Andrzej J~drzejczak Institute of Physics, Polish Academy of Sciences, Al. Ix~lnik6w32/46, PL 02-668 Warsaw, Poland

Received 15 May 1995; accepted 26 October 1995

Abstract

Growth stability is studied in a system for high temperature vapour growth of PbSnTe. The transition from unstable to stable growth conditions is observed. The observation compared with theoretical analysis of the concentration and temperature field in the crystal and vapour at the growth interface confirms the recently published theory of Louchev [1] [J. Crystal Growth 140 (1994) 219] concerning diffusion, heat transfer, equilibrium molecular density and kinetics mechanism of morphological instability in physical vapour deposition and our conception of constitutional supersaturation criterion [2] [Grasza, in: Mass and Heat Transfer, Elementary Crystal Growth]. It is shown, that, additionally to the dependence of the morphological stability on the kinetic coefficient, the relation of the temperature gradient across the depositing layer to the gradient of concentration of the deposited substance in front of the growth interface, and the dependence of equilibrium molecular density (pressure) of the depositing substance on temperature, are the most important factors influencing the stability of the solid-vapour interface.

1. Introduction Vapour growth is known to be a technique for growth of crystals of the best quality. Its limited application is associated not only with low rates but also with a slow progress in understanding of the physical phenomena involved in vapour growth. Originally, in the case of crystal growth from the vapour, a simplified form of a stability criterion was deduced from that given for the planar solid-liquid interface [3-6]. However, usually only the temperature gradient of the fluid phase was considered [3,4,7]. The growth kinetics anisotropy and this simplification, justified for most of the liquid-solid interfaces, can lead to huge errors in estimation of the critical growth conditions of the solid-vapour interface, as

* Corresponding author.

shown by Rosenberger et al. [7]. A m o d e m attempt to the problem of morphological stability of not faceted solid-vapour interfaces was presented by Grasza [2] and in form extended by the term including the kinetic coefficient by Louchev [1]. It is argued, that the simplified stability criterion for physical vapour deposition should neglect the influence of gas phase thermal conductance on the perturbation, due to much higher thermal conductivity of the solid than the vapour phase. In the case of diffusive mass transfer with fast surface incorporation processes the practical formula for stable growth takes the form [2] dT~

dT~

- - > - -

dz

dz

1 dc adz

,

(1)

where d T s / d z is the temperature gradient in the crystal close to the interface and d T v / d z is the

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174

K. Grasza, A. Jqdrzejczak / Journal of Crystal Growth 162 (1996) 173-177

equilibrium temperature gradient in the vapour phase in front of the interface, d c / d z is the vapour concentration gradient in front of the interface. The coefficient o~= d c o / d T is obtained from ClausiusClapeyron's formula with the saturation concentration c o of the vapour at the interface [1]. The aim of this work is to show experimental results which confirm the presented stability criterion and prove that the limitations on crystal growth velocity for stable vapour growth may be gradually attenuated. Above all, as shown experimentally by Wiedemeier and Wu [8,9], choosing the proper furnace temperature profile permits radical increase of the crystal growth rate still preserving the stable growth conditions.

interface temperature exceeds 795°C (details of the complementary experiments permitting temperature measurement are described in a previous paper [10]). These growth conditions may be realized by the location of the hotter end of the graphite core in a position where furnace temperature equals 825°C (Fig. 1). If at the source temperature 860°C the crystal temperature is lower than 795°C, polycrystalline columnar growth proceeds. Growth at the interface temperature lower than 780°C results in the appearance of fiat faces on each of the crystallities. At the moment, when the growing interface reaches the temperature 795°C, the solid-vapour interface becomes smooth and grain selection proceeds (Fig. 2).

2. Experimental setup

4. Theoretical analysis

The system used is shown in Fig. 1. The Pbj_xSnxTe crystals ( x = 0 . 2 - 0 . 3 1 ) grew without contact with the ampoule wall. The experimental details are described elsewhere [10]. An additional graphite crucible filled with Pb + Sn was located in the hotter (upper) end of the ampoule. The location of the source material is fixed. In this experimental system the crystal grows at a constant velocity of about 0.5 m m / h since the gradient of the PbTe and SnTe vapour concentration weakly depends on time. The PbTe and SnTe species diffuse through the Te 2 vapour originating from the PbSnTe source, which contains 2 mol% of excessive tellurium. No intentionally added inert gas is present in the ampoule. In the complementary experiment the Pt-PtRh thennocouple was located inside the graphite core and in the crystal [10], to measure the temperature in the vicinity of the growing interface and the temperature gradient along the crystal. The ampoule position in the furnace changed slightly in different experiments, which changes did not disturb growth velocity and concentration gradient above the growth interface.

The vapour phase growth in the Pbj_,SnxTe vertical growth system with low x and excess of tellurium is dominated by PbTe vapour diffusing through the excessive component. Relation of the SnTe partial pressure to the partial pressure of PbTe vapour determines the composition of the grown crystal [11]. The partial pressure of the saturated vapour found from Clausius-Clapeyron law at the temperature distribution shown in Fig. 3a is pre-

Pb+S'l rmphite

At the source temperature of 860°C growth with a smooth solid-vapour interface is possible only if the

furnace temperature profile

-IE:

._E I i " / / ~

source

0

10

g

~5 --EQ -o

3. Experimental results

-~

~

~

g rQp hit "e ~core

wasted ~ Pt~ .Sn Te

/~7"~the;mocouple

/ 0 6oo

86o temperofure

"

( °C )

Fig. 1. Experimental system for the Pbl_ ~SnxTe crystal growth from the vapour without contact between crystal and ampoule wall.

K. Grasza, A. Jgdrzejczak /Journal of Crystal Growth 162 (1996) 173-177

sented in Fig. 3b. The parabola-like temperature profile (Fig. 3a) gives the "S"-like profile (Fig. 3b) of the equilibrium vapour pressure. The factor A in the equation from Fig. 3 has a meaning of difference

175

in entropy between the gas and the solid phase (heat of phase transition), the factor B is a constant resulting from integration of the Clausius-Clapeyron equation. In Fig. 3, A and B are taken equal to 9.7

STRUCTURE CHANGE

ICM Fig. 2. Section of the Pb0.69Sn0.3~Te crystal grown first under unstable and then under stable growth conditions. The transition between these two growth regimes is clearly visible in the form of the abrupt grain selection 4 - 5 mm from the first crystallized part of the crystal.

K. Grasza, A. J£drzejczak /Journal of Crystal Growth 162 (1996) 173-177

176

and 11 000, respectively. These orders of magnitude are typical for many materials grown from the vapour if the temperature is in kelvins. Thus, at lower temperatures, the higher temperature gradient corresponds to a lower concentration gradient. At the middle-range 800 < 900°C, the concentration gradient is high. Assuming that the concentration gradient of the crystal forming components is constant along the diffusion zone (Fig. 1), what is justified for low (less than 1) Peclet number growth conditions [12], we can plot the real concentration profile along the ampoule (Fig. 4). The concentration gradient in the diffusion zone is weakly dependent on time, independently on the length of the crystal. However, the concentration gradient along the slit between the crystal and the ampoule wall increases during growth due to increasing temperature at the solid-vapour interface. In particular, in the vicinity of the solidvapour interface this gradient increases two times if the interface temperature increases from 800 to 830°C while the temperature gradient in the crystal is kept unchanged [13]. Thus, during the period of crystal

v0.pour

(a) Pc~

/

:i'

.

850

/

/

800

.: i

750

/ i / : ' /

} i

700

0

900

/,'

Tpressufe (rnm Hg,

650"

u

,':•pr•sure

ternper(lfure (*C }

crystal

5

source

113

distance ( crn I'

Fig. 4. Distribution of temperature along the lateral surface of the graphite core, growing crystal, source material and furnace wall in two stages of crystal growth; and distribution of the PbTe partial pressure along the ampoule for succeeding growth stages deduced from the formula l o g ( p ) = B - A / T (A=11316+214, B= 10.336___0.231, T in K, p in mmHg [13]).

800

E

700

2

~

6

8

10

12

lz, distance(cm)

3.'(b) 2 m

o

2

~.

6

8

10

12

lt, distance (cm]

Fig. 3. (a) Parabola-like temperature profile. (b) "S"-like shape of the partial pressure (concentration) of the crystal forming component deduced from the temperature profile from (a).

growth resulting in an increase of the temperature of the interface by about 30°C, the eventual self-decrement of the axial temperature gradient in the crystal at the solid-vapour interface lower than twofold results in decrement of the ratio of the concentration gradient in the diffusion zone to the concentration gradient in the slit near the solid-vapour interface. As we can see in Fig. 4, in our experiment we deal with the transition of this ratio of concentration gradients from a value exceeding 1 to lower than 1. The abrupt grain selection visible on the section of the crystal grown in this experiment (Fig, 2), which takes place at the same moment when the concentrational gradients are equal, makes possible the as-

K. Grasza, A. Jcdrzejczak /Journal of Crystal Growth 162 (1996) 173-177

sumption, that this is the critical condition for growth stability. The concentration and partial pressure of the crystal forming components in the slit between the crystal and the ampoule wall are related to the temperature of the crystal by temperature dependence of the saturated vapour pressure. Hence from this experiment we can draw the conclusion that it is the relation between the temperature gradient along the crystal and the concentration gradient between the crystal and the source that decides the growth stability. This conclusion confirms the stability criterion expressed in Eq. (1).

177

cooling formula, valid for growth from the liquid phase, was applied to growth from the vapour phase. In this " c l a s s i c " constitutional supercooling criterion the relation of concentration and temperature gradients in the liquid is considered. In the growth from the vapour phase, the low thermal conductivity of the vapour makes the term "temperature gradient at the interface" difficult to define. Much greater contribution to temperature field at the interface results from temperature gradient in the solid than in the fluid, and the term comprising thermal conductivity of the solid in Mullins-Sekerka criterion dominates.

5. Conclusion The observation of the transition from unstable to stable growth conditions compared with theoretical analysis of the concentration and temperature field in the crystal and vapour at the growth interface leads to the conclusion that the relation between the concentration gradient of the crystal forming component in the vapour at the growth interface, and the temperature along the growing crystal at the interface, decides on the constitutional supersaturation and growth stability [2]. This observation confirms the recently published theory of Louchev [1] conceming diffusion, heat transfer, equilibrium molecular density and kinetics mechanism of morphological instability in physical vapour deposition. In the present paper it was shown that additionally to the dependence of the morphological stability on the kinetic coefficient, the most important factors influencing stability of the solid-vapour interface are: (a) the relation of the temperature gradient across the deposited layer to the gradient of concentration of the deposited substance in front of the growth interface, and (b) the dependence of the equilibrium molecular density (pressure) of the depositing substance on temperature. The same conclusion may be drawn from the well-known constitutional supercooling criteflon of Mullins-Sekerka, derived for growth from melt systems [5]. Unfortunately, to our knowledge, up to now only the simplified constitutional super-

Acknowledgements The authors thank Professor A. Chemov for helpful comments and suggestions.

References [1] G.A. Louchev, J. Crystal Growth 140 (1994) 219. [2] K. Grasza, Mass and Heat Transfer, in: Elementary Crystal Growth, Ed. K. Sangwal (SAAN, Lublin, 1994). [3] T.B. Reed, W.J. LaFleur and A.J. Strauss, J. Crystal Growth 3/4 (1968) 115. [4] M.M. Faktor and I. Garret, Growth of Crystals from the Vapour (Chapmann and Hall, London, 1971). [5] W.W. Mullins and R.F. Sekerka, J. Appl. Phys. 35 (1964) 444. [6] R.F. Sekerka, J. Crystal Growth 3/4 (1968) I-6. [7] F. Rosenberger, M.C. DeLong, D.W. Greenwell, J.M. Olson and G.H. Westphal, J. Crystal Growth 29 (1975) 49. [8] H. Wiedemeier and G. Wu, J. Electron. Mater. 22 (1993) 1121. [9] H. Wiedemeier and G. Wu, J. Electron. Mater. 22 (1993) 1369. [10] K. Grasza, J. Crystal Growth 128 (1993) 609. [11] T.V. Saunina, D.B. Chesnokova and D.A. Jaskov, J. Crystal Growth 71 (1985) 75. [12] D.W. Greenwell, B.L. Markham and F. Rosenberger, J. Crystal Growth 51 (1981) 413. [13] V.V. Sokolov, A.A. Pazancev, A.S. Patinkan and A.V. Novoselova, Izv. Akad. Nauk SSSR, Neorg. Mater. 5 (1969) 275.