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Crystallization of amorphous CoSi2 thin films I. kinetics of nucleation and growth
ELSEVIER
Materials
Chemistry
and Physics
38 (1994) 250-257
Crystallization of amorphous CoSi2 thin films I. kinetics of nucleation and growth J.M. Liang, L.J. Chen and I. Markov* Debarment
of ~uter~als
Science and Engkzeering, ~~ionn~ Tsing Haa Universes, Hsinchu (Taiwan, RUC)
G.U. Singco, L.T. Shi and C. Farrell IBM Research Division, 77.
Watson Research Center Yorktown Heights, NY 10598 (USA)
K.N. Tu Dep~rment
of Materials Science and Engineering,
University of California, Los Angeles CA 91x124 {USA)
(Received October $1993; accepted March 1,1994)
Abstract The kinetics of nucleation and growth of spherulites in amorphous CoSi2 thin films of 100 nm of thickness have been studied in situ by transmission electronmicroscopy. The tune dependence of the number of nucleishowed pronounced transient character. The growth rate was found to be constant upon isothermal annealing in the temperature range of 130 to 170 “C in a broad interval of time. The activation energy of incorporation of growth units into the crystal lattice was found to be 23.9 kcallmole. For the surface free energy between the crystallites and the amorphous phase the value 212 erg&m2 has been determined from the nucleation experiments. The nucleation was found to occur randomly in the bulk of the amorphous film with a constant rate during the transformation process as deduced from the average value n = 3.8 in the Avrami kinetic law for overall crystallization {=l-exp(-kt”).
1. Introduction Self aligned CoSiZ is emerging as a potential candidate for gate, interconnection and contact metallization in very large scale integrated circuits (VLSI) on Si. The formation of CoS& between the Si substrate and a Co thin film typically involves a high temperature annealing between 700 and 900 “C. The latter is undesirable in the processing of the microelectronic devices because of possible thermal damages such as redist~bution of dopant, phase transitions and generation of thermal stresses. Therefore, the formation of CoSi, at low temperatures is essential to the process. [l, 21 Upon codeposition of alloy films at room temperature, the as-deposited films are often amorphous and metastable with respect to the crystalline phase. The *Permanent
address: Institute of Physical Chemistry, Bulgarian Academy of
Sciences, 1040 Sofia, Bulgaria.
0254-0584/94/$07.00 0 1994 Ekevier SSDI 0254-0584~94~01376-R
Science
S.A. Ail rights
reserved
phase transformation from amorphous to a crystalline state thus appears as an important subject when we start from codeposited alloy thin films. The crystalline phase can in general have different composition from the amo~hous phase. In this case a long range diffusion is generally involved. In the simpler case of one and the same composition of the amorphous and the crystalline phase no long range diffusion is involved in the growth process and the latter is controlled by the incorporation of growth units into the crystal lattice. Then it is preferable to process the amorphous film by crystallization at much lower temperatures and shorter times to produce crystalline films with the same composition. A previous study showed that codeposited amorphous films of Co and Si with atomic ratio 1:2 crystallize at a temperature as low as 150 “C without a change of the
3.M. Liang et al. I Materials Chemistv
composition. [3] The nucleation and growth processes affect significantly the microstructure of the thin films, and in turn the extrinsic film properties. We report in this paper the results of an investigation of the kinetics of crystal nucleation in amorphous CoSi, thin films and growth of the crystallites by transmission electron microscopy. The paper is organized as follows. Tn section 2 we present the fundamental theoretical relationships of nucleation, growth and mass crystallization. In section 3 we describe the experimental procedure and in section 4 we present the experimental data and their theoretical interpretation. The results are summarized in section 5.
and Phydcs 38 (1994) 250-257
where As, is the entropy of melting. AT=T,,,-T is the undercooling and T, is the melting point. According to the classical theory of phase formation (for a review see ref. 6) the radius of the critical nucleus is given by the equation of Thomson - Gibbs
r* = 2 of2 AP
o,,,=oNAR2’
2. I Nuckation
is proportional
The amo~hous phase could be considered as a liquid with very high viscosity of the order of 1x10’” poise [4]. When heated above the temperature of vitrification the viscosity goes steeply down and the transport processes characteristic for the usual melts become possible. The heated amorphous phase (or melt} can then crystallize by processes of nucleation and growth. The steady state rate of formation of 3D nuclei in melts is given by [5]
o,,, = celh,
where J,, is a kinetic pre-exponent, AG* is the work for nucleus formation, and U is the activation energy for transfer of a growth unit (atom or a molecule) across the liquid-c~stal interface and its subsequent incorporation into the crystal lattice (kink sites). The Gibbs free energy for homogeneous formation of nuclei reads
where o is the surface free energy of the crystal-liquid interface, Sz is the volume of a molecule in the crystal phase and Ap is the supersaturation or the thermodynamic driving force of the nucleation process given by the difference of the chemical potentials of the infinitely large liquid and crystal phases. The latter is given by Ap = As, AT
(3)
(4)
Turnbull [S] correlated experimental results on nucleation in a series of molten metals (see also ref. 7) and found that the molar surface energy o, defined as
2. Theoretical
U+AG* J=J,exp(--TP)
251
(5) to the enthalpy of melting Ah, (6)
and the coefficient of proportionality ais near 0.5. Similar results were found for many other inorganic materials, including alkali halides [&lo].
The liquid- crystal interface particularly in the case of inorganic materials is expected to be atomically rough and the crystallites to grow rounded 1111. That is why molecules from the liquid can be incorporated directly into kink sites on the crystal surface once they cross the interface. Assuming both phases have one and the same composition (long range diffusion is excluded) the rate of growth is given by [6, 121
v=hv( @p(-
AS, U k-~)expFkT)(
I-exp(-
A& kF-))
(7)
where d is the distance a molecule should cover in order to join the crystal lattice which is usually taken as one at.omic diameter, v is a vibrational frequency, A,&= As,(T,-T,) is the supersaturation at the crystal liquid interface with Ti being the temperature at the interface, and (a/6)? is the geometric probability a molecule from the liquid phase to find a kink site upon its arrival at the crystal surface, 6 being the average spacing between the kink sites. Assuming the heat of crystallization is not taken away from the advancing interface fast enough it will accumulate and the ambient phase around the growing crystalhtes will be heated. As a result the temperature Ti will approach the temperature of melting T,, [13]. The under-cooling at the growth front ATi = T,, - T, will be
252
3.M. Liang et al. I ~ate~uls
Cleats
and Physics 38 (1994) 250-257
small but non-zero and eq. (7) is simplified to v = flATi
(8)
where
(9) (cmisec K) is the so called kinetic coefficient of growth from the melt [12]. The growth of the spherulites will be determined by the temperature gradient and will be “diffusion controlled” as the equations governing the diffusion and the thermal conductivity are one and the same [14]. The temperature around the growing crystallites will vary from Ti <, T, at the interface to the temperature T in the bulk of the sample. Keeping in mind that the nucleation rate is practically equal to zero below a critical undercooling “nucleation exclusion zones” will form around the growing crystallites in which the nucleation is suppressed [15, 161. As a result new nuclei cannot be formed in the near vicinity of the growing crystallites. In the other extreme the heat of crystallization is taken away from the growth front fast enough and the temperature at the interface approaches the temperature of the sample, i.e. ‘I, -“T [13]. At temperatures near the temperature of vitrification the undercooling AT = T,-T will be large enough so that the growth rate becomes practically independent of the undercooling. The growth is controlled by the rate of inco~oration of growth units into kink sites, i.e. the crystallites grow in an interface reaction controlled or a kinetic regime [12]. As the temperature is everywhere constant nucleation exclusion zones do not form. 2.3 Mass Crystallization In the case of progressive nucleation with a constant rate J (cm-3 se&) and a constant growth rate v (cm se+) in a 3D system the fraction of crystallized volume reads [17-191
{=l-exp(-;Jv’t4)
(10)
In deriving eq. (10) it was assumed that nuclei were randomly formed in the bulk of the parent phase and the nucleation probability was one and the same at each point of the volume [6,12]. In the case of solidification of very thin platelets in which the process of growth is thought to be preferably two - dimensional
c=l-exp(-FJv2t3)
(11)
where the nucleation rate J is in units of cm-2 se@. In both cases given above it was assumed that the nucleation takes place until the complete solidification of the sample (progressive nucleation). However, this may not be the case. The nuclei can be formed in a short (compared with the time of complete solidification of the sample) period of time in the onset of crystallization (instantaneous nucleation). The fraction of crystallized volume at a time t then is
{=l-exp(-$Nv3t3)
(12)
where N (cm-“) is the density of nuclei formed in the beginning of the process. In all cases listed above the kinetic solidification curve t(t)=
1-exp( -kr”)
(13)
is S-shaped. The value of the time exponent n can be easily found upon linearization of the 4(t) curves in coordinated ln[-ln(l- t(t)] vs. In(t) [6, 121. A difficulty in interpretation of the results may arise in the case when nucleation exclusion zones with enhanced temperature or reduced undercooling are formed and grow around the growing nuclei. The nucleation rate will become equal to zero before the complete solidification of the melt when the nucleation exclusion zones overlap and fill in the volume of the sample (soft impingement) [6]. If this is not the case the kinetics of solidification will be determined by the growth of the crystallites themselves (hard impingement) [6]. However, in both cases eqs. (10) - (12) should be formally obeyed.
3. Experimental lOO-nm-thick amorphous films of CoSiZ were prepared by electron beam codeposition of Co and Si atoms in a vacuum of 1 x 10-7 Torr onto a Si wafer containing arrays of etched windows with 0.25 mm area each. The windows were then coated with a 20 nm thick film of S&N4 to facilitate the examination of the solidification with transmission electron microscopy (TEM). Direct observations of the crystallization were carried out in situ in a JEOL 2000FX TEM with a heating stage. The annealing temperature was varied from 130
to 170 “C with 10 “C interval for various periods of time. The composition of the amorphous films was measured by Rutherford backscattering spectrometry. The crystallized phase was determined by electron diffraction to be CoS& with cubic CaF2 crystal structure. High resolution TEM (~RTEM) was carried out in a JEOL 4OOOEX with a point-to-point resolution of 0.18 nm to determine the atomic arrangements before and after the crystallization from the amorphous phase. The nucleation rate was determined by counting the number, N, of crystallites visible under the microscope and taking the slope of the resulting N(t) curves at constant temperature. Double pulse technique, 120,211 in which the nuclei formed at a given temperature are visualized by developing them at another temperature at which the nucleation is negligible, was not possible in our case because of the very high melting point, 1326 “C, of CoSi,. The rates of growth of the crystallites was determined from measurements of the sizeof selected particles with time. The ramping times to reach the growth temperature were typically 2-3 min. The fraction of the crystallized volume was determined either by image analysis of area1 fractions of highlighted particles or by stereology which measures the area1 fraction by measurements of the average intercept length per unit linear probe on TEM micrographs.
4. Results and Discussion Fig. 1 shows typical micrographs of CoSiZ spherulites from which the number of nuclei vs. time and the particle size vs. time curves and the kinetic solidification curves are determined. Fig. 2 shows number of nuclei vs. time curves at four different temperatures. As seen they represents straight lines whose slopes give the steady state nucleation rates. Note the existence of induction periods which are typical for nucleation in condensed phases. [22] We will not consider in this paper the transient behavior of nucleation as the data are obtained without the use of a double pulse technique. Fig. 3 shows the time dependence of the particle size at five ~fferent temperatures. The slopes of the straight lines give the rates of growth of the spherulites shown in Fig. 1. The data about the rates of nucleation and growth are summarized in Table 1. Fig. 4 represents the Arrhenius plot of the rate of growth vs. the reciprocal temperature.The valueU = 23.9 kcallmole has been calculated from the slope of the straight line for the activation energy for transfer of a growth unit across the liquid _ crystal interface. This value is somewhat lower than the values typical for inorganic glassforming melts (Li,0.2SiOZ, SiOZ, GeO?,), which are usually of the order of 100 kcal/mole [22-241. This is due obviously to the fact that CoS& is not a
typical glassforming material. Besides, the straight line in Fig. 4 is an indication that AU / kT>b 1. With Ah,,, = 0.107 eV per atom as measured in the second part of this paper [25] we find As, = 19.37 J1mole.K and A&/ kT = 6.3 for the highest temperature involved, i.e. exp (-Api / kT )=I8 x 10-3<< 1. As discussed above if the melt around the growing crystallites is heated to much higher temperature than the one given in the experiment the kinetics of growth will become in fact controlled by long range diffusion as the conduction of heat in condensed phases is governed by the same equations as the diffusion [12,13]. The pre-exponent in eq. (7) kV( iI2 exn( - bs, 1 was found from the Arrhenius plot to be 7.75 x 16;4 cmlsec. Witha-4.22~10-~cm,v=3~10~3sec-~,a/lj= 1/2and h--a, the entropy of melting was estimated to be As, = 11.7 Jl mo1e.K. If the maximum surface roughness, a/6 = 1, is assumed [14], As, = 23.2 J1mole.K. Comparing these values with the value 19.37 Jlmo1e.K calculated from calorimetric data [25] allows us to conclude that the rate of growth does not depend practically on the undercooling although some negligible heating of the melt in the near vicinity of the crystals is not excluded. As seen from equations (l), (2) and (3) the nucleation rate includes in itself exponents of the barrier U for incorporation of growth units into kink sites which is temperature independent and the work for nucleus formation AC’ which is inversely proportional to the square of the undercooling AT = T, - T. In order to separate both exponents and find the work for nucleus formation from the experimental data we construct a plot of ln[J exp(U/kT)] vs. l/T(T, - T)z taking for U the value 23.9 kcal/mole obtained from the growth data. The same result is obtained if we plot ln(J/v) vs. l/T(T, - T)r. The only difference is that in the latter case the points are more scattered around the straight line. The plot of ln[J exp(U/kT)] vs. l/T(T,, - T)* is shown in fig. 5. A straight line with a slope - 1.73 x 1010 and intercept from the ordinate 82.6 result when we interpret the data in the logarithmic co-ordinates characteristic of the classical nucleation theory. From the slope of the straight line we calculated the value AG’ = 1.73 x lo-‘9 J for the work for nucleus formation at T = 150 “C, or AG*/kT = 30. For the surface free energy of the nucleus liquid boundary with fi = 23.71 cmYmole one obtains the reasonable value CT= 212 erg/cm*. For the number of molecules in the critical nucleus from eq. (3) one obtains n* = 471r*3/352= 9. In other words at the temperatures of the experiment the critical nucleus consists practically of two unit c&Is. On the other hand, this result invalidates the determination of the surface free energy. It has been shown, however, that the classical nucleation theory predicts reasonable values for the surface free energy even in cases of very small nuclei, when the parameters
254
J.M. Liang et al. / Materials Chemistry and Physics 38 (1994) 2SO-257
Fig. 1. Micrographs showing the formation and isotropic growth of CoSiz crystallites in samples annealed at 340°C for (a), (d) 60, (b), (e) 65 and (c), (f) 75 min, respectively.
255
J.M. Liang et al. I’ Materials Chemistry and Plzysics 38 (3994) 250-257
TABLE 1. Values of nucleation and growth rates for samples annealed at different temperatures.
TW)
J(cnr3 ruin-‘)
v(cm/min)
130 140 150 160 170
5.09 x 10” 1.26 x lOi 3.00 x 10’2 7.58 x 1012
5.43 x lo-’ 1.00 x 106 2.44 x 10-6 5.00 x 10” 6.95 x 10”
2.20
2.30
2.40
2.50
1OWkT
Fig. 4. Arrhenius plot of the rate of growth vs. reciprocal temperature.
54.0
0
10
20
30
40
50
!
---7
60
Time (mitt)
Fig. 2. Number of particles per cm3 vs. time curves at four different temperatures.
1.68
1.70
1.72
1.74
109/T(T,,,-T)’
T
Fig. 5. A plot of In[J exp(U/kT)] vs. l/T(T,-T)2.
u3
b 4
c
x
20
40
60
80
100
Time (mitt)
Fig. 3. Time dependence tures.
of particles size at five different tempera-
defined with the help of the phenomenological thermodynamics lose their physical meaning 1261. Finally, for J, one obtains 7.7 x 1O35cm-3 se@, or for the kinetic pre-exponent of the nucleation rate J, exp(-UlkT) one obtains the reasonable value 3.6 x 1023cm-3 se@. One additional check of the interpretation of the experimental data presented so far is to calculate the Tumbull’s parameter a= oNA au3 / Ah,,, (see equations (5) and (6)). With o= 212 erg cm-z, a= 3.94 x 1023cm3/ molecule and Ah, = 3.097x 1011erg mole-’ we find a= 0.48 in excellent agreement with data for many inorganic materials. Fig. 6 shows the time dependence of the crystallized
I.M. Liang et al. / Materials Chemistry and Physics 38 (1994) 25X-257
256
0
160
0
150
A
TABLE 2. Valuesof k = nJv313calculated from the kinetic SoIidification curves and from the direct measurements of J and v.
140°C
1.0
T(“C)
AvramP)
140 150 160
8.09 x 10-a 3.86 x 1O-6 8.16 x 10-5
J&G’)
Ratio
1.32 x lO& 4.59 x 10-s 9.92 x 10”’
163 12 12
0.8
0.6
a) From kinetic solidification curves b) From multiplication of directly measured J and v
0.4 0.2 0.0 0
20
40
60
80
100
120
Time (min) Fig. 6. The timedependence temperatures.
0
of the crystallized volume c(t) at different
The S-shape is clearly demonstrated.
160
0
150
A
140°C
2 1 0 -1 -2 -3 -4 -5 1
2
3
4
5
In 0) Fig. 7. Interpretation
of solidification curves shown in Fig. 6 in co-
ordinates In{-ln[l - t(t)]] vs. In(t).
volume t(t) at different temperatures. The S-shape is clearly demonstrated. In fig. 7 the curves are presented in co-ordinates In{-ln[l- t(t)]) vs. In(t). [6] The average value of the slopes is 3.8. The result is an indication that the nucleation process takes place randomly in the bulk of the amorphous film with a constant rate during the transformation process (progressive nucleation).
Instantaneous nucleation in the beginning of the solidification does not take place and the process of nucleation is three-dimensional irrespective of the small thickness of the samples. This conclusion is supported in addition from the values of o and a which have been obtained under the assumption of homogeneous nucleation. From the intercepts ofthe straight lines with the ordinate in Fig. 7 we calculate the coefficients k = nJv313 (see eq. (10)) and compare them with the values obtained from the directly measured rates of nucleation and growth. The data are compared in Table 2. As seen the Avrami coefficients are always smaller by one to two orders of magnitude than the ones calculated from directly measured values of J and v. This means that either the actual nucleation rate or the growth rate or both during the transformation are smaller than the directly measured ones. Eq. (10) has been derived assuming steady state nucleation rate. In fact we have a transient nucleation as seen in Fig. 2. Obviously the most influenced by the transient effects will be the lowest temperature case. The kinetic transformation curve is then shifted to longer times by the induction period. Correction of the Avrami curve obtained at 140 “C with the induction period from the N(t) curve shown in Fig. 2 leads to a value of k = xJv313 = 5~10~ seed, i.e. two orders of magnitude greater than the one listedin Table 2 in better agreement with the value 1.32 x 10-e seP. The effect of the time lags on the curves obtained at higher temperatures will be smaller. Thus if we attribute the above discrepancy to the transient behavior of the nucleation it follows that the transformation of the amorphous phase to a crystalline one takes place by ‘hard impingement” of the spherulites. In other words, nucleation exclusion zones do not exist and the approximation A&>> kT is justified. Note that if soft impingement occurred during solidification the values of k = ?rJv3/3 as calculated from the kinetic Avrami curves should be greater than the ones calculated from the values of J and v as the rate of growth of the nucleation exclusion zones is greater than that of the crystallites themselves. We will restrain ourselves from more detailed analysis of the influence of the transient effects of nucleation on the kinetics of transformation because of the inaccu-
J.M. Liang et ai. / Materials Chem&y
racy with which the induction
periods are measured.
and Physics 38 (1994) 2X7-257
2.57
of China National Science Council through Grant No. NSC83-0416EOO7-008 and IBM Research Division.
5. Conclusions References We have measured the rates of nucleationandgrowth and the time dependence of the crystallized fraction during the c~st~li~ation of thin films of ~o~hous CoS&. The nucleation rate is time dependent as is often the case of nucleation in condensed phases. The process of nucleation takes place randomly and homogeneously in the bulk of the film. The value of 212 erg/cm* has been determined for the surface free energy of the crystal nucleus - amorphous phase boundary. The critical nuclei consist of two unit cells. The ratio of the molar surface energy and the enthalpy of fusion was found to be 0.48 in agreement with data in other inorganic materials. The growth of the particles is controlled by the interfaci~ reaction of inco~oration of growth units into kink sites of the crystal lattice. In other words, the particles grow in a kinetic regime. No heating of the amorphous phase in the near vicinity of growing particles and the formation of nucleation exclusion zones have been detected. The entropy of melting as calculated from the particles growth rates is in agreement with the calculated from c~o~metric The average Avrami exponent is measurements. equal to 3.8 which appears as an additional indication of random progressive 3D nucleation. The product k = rc JvV3 as measured from the kinetic transformation curves is always smaller than the one calculated with the help of the directly measured rates of nucleation and growth which is an additional indication of hard impingement of the spherulites during the solidification. The latter discrepancy is explained with the transient character of the nucleation rate.
Acknowledgments The researeh was supported partially by the Republic
1. K.N. Tit and J.W. Mayer, in J.M. Poate, K.N. Tu and J.W. Mayer (eds.).Thin Fitn7s ~nterdi~~~~o~ and Reactions, Academic. New York. 1978, p. 329. 2. M.A Nicolet and S.S. Lau, in N.G. Einspruch and G.R. Larrabee teds.), Materials and Process Charactetization, Academica. New York, 1983, p. 453. 3. K.N. Tu. D.A. Smith and B.Z. Weiss, Phys. Rev. f33h (1987) 8948. 4. D. Turnbull, Contemp. Phys., IO (1969) 473. 5. D. Turnbull, J. Appt. Phys., 21 (1950) 1022. 6. J.W. Christian, The Theory of Tr#zsformati~)~zin Metals Ed Alioys, Part I. ~quilibriltm and General Kinetic Theory, 2nd Edition. Pergamon Press, Oxford, 198 1. 7. J.H. Hollomon and D. Turnhull, in B. Chalmers (ed.), Progress in Metal Physics, vol. 4, Pergamon Press, London, 1953. p. 333. 8. E.R. Buckle and4.R. Ubbeiohde. Proc. Roy. Sot.. AZS9(1%0) 325. 9. K.A. Jackson. in DE. Gushee fed.), ~t~cleat~on~~e~u~e~u. American (‘hem. Sot., 1966, p. 35. 10. A.G Walton.in ACZettlemoyer (ed.),Nucleation,MarcelDekker, Inc.. New York. 1969, p. 225. 11. K.A. Jackson, Growth and Perfection of Crystals, John Wiley and Sons, Inc.. New York - London, 1958, p. 319. 12. A.A. Chemov, Modern Crystallography III, Springer Series in Solid State Science, vol. 36, Springer Verlag, Berlin, 1984. 13. F. Spaepen and D. Turnbu~l. in J.M. Poate and J.W. Mayer (eds.). Laser Annealing of Semiconductors, Academic Press, 1982, p.1.5. 14. D. Turnbull, Metall. Trans. B, 12 (1981) 217. 15. R.A Sigsbee and G.M. Pound, Adv. Cull. interface Sci., 2 (1967) 335. 16.1. Markov and D. Kashchiev, .I. Crystal Growth, 16 (1972) 170. 17. A.N. Kolmogorov. Comm. Acad. Set, USSR, (Phys.-Math. Series),
3 (1937) 355. 18. W.A. Johnson and R.F. Mehl, Trans. AIME, 135 (1939) 416. 19. M. Avrami.J. C/rem Phys., 7(1939) 1103~8(1940~212;9(1941) 177. 20, G. Tamman, I)er Glaszustand, L. Voss Verlag, Leipzig. 1933. 2 1.P.F. James, Phys. Chem. Glasses, I5 (1974) 9.5. 22. S. Toschev and I. Gutzow, Kristall und Technik, 7 (1972) 43. 23. J.D. Mackenzie. Modem Aspects of the ~jtre[}us State, Butterworths, London, 1960. p. 188. 24. N. Okui. J. Mater. Sci., 2.5 (1990) 1623. 25. K.N, Tu, unpublisled work. 26. A. Milchev and S. Stoyanov, J. Electroanal. Chem. 72 (1976) 33.
Materials
Chemistry
and Physics
38 (1994) 250-257
Crystallization of amorphous CoSi2 thin films I. kinetics of nucleation and growth J.M. Liang, L.J. Chen and I. Markov* Debarment
of ~uter~als
Science and Engkzeering, ~~ionn~ Tsing Haa Universes, Hsinchu (Taiwan, RUC)
G.U. Singco, L.T. Shi and C. Farrell IBM Research Division, 77.
Watson Research Center Yorktown Heights, NY 10598 (USA)
K.N. Tu Dep~rment
of Materials Science and Engineering,
University of California, Los Angeles CA 91x124 {USA)
(Received October $1993; accepted March 1,1994)
Abstract The kinetics of nucleation and growth of spherulites in amorphous CoSi2 thin films of 100 nm of thickness have been studied in situ by transmission electronmicroscopy. The tune dependence of the number of nucleishowed pronounced transient character. The growth rate was found to be constant upon isothermal annealing in the temperature range of 130 to 170 “C in a broad interval of time. The activation energy of incorporation of growth units into the crystal lattice was found to be 23.9 kcallmole. For the surface free energy between the crystallites and the amorphous phase the value 212 erg&m2 has been determined from the nucleation experiments. The nucleation was found to occur randomly in the bulk of the amorphous film with a constant rate during the transformation process as deduced from the average value n = 3.8 in the Avrami kinetic law for overall crystallization {=l-exp(-kt”).
1. Introduction Self aligned CoSiZ is emerging as a potential candidate for gate, interconnection and contact metallization in very large scale integrated circuits (VLSI) on Si. The formation of CoS& between the Si substrate and a Co thin film typically involves a high temperature annealing between 700 and 900 “C. The latter is undesirable in the processing of the microelectronic devices because of possible thermal damages such as redist~bution of dopant, phase transitions and generation of thermal stresses. Therefore, the formation of CoSi, at low temperatures is essential to the process. [l, 21 Upon codeposition of alloy films at room temperature, the as-deposited films are often amorphous and metastable with respect to the crystalline phase. The *Permanent
address: Institute of Physical Chemistry, Bulgarian Academy of
Sciences, 1040 Sofia, Bulgaria.
0254-0584/94/$07.00 0 1994 Ekevier SSDI 0254-0584~94~01376-R
Science
S.A. Ail rights
reserved
phase transformation from amorphous to a crystalline state thus appears as an important subject when we start from codeposited alloy thin films. The crystalline phase can in general have different composition from the amo~hous phase. In this case a long range diffusion is generally involved. In the simpler case of one and the same composition of the amorphous and the crystalline phase no long range diffusion is involved in the growth process and the latter is controlled by the incorporation of growth units into the crystal lattice. Then it is preferable to process the amorphous film by crystallization at much lower temperatures and shorter times to produce crystalline films with the same composition. A previous study showed that codeposited amorphous films of Co and Si with atomic ratio 1:2 crystallize at a temperature as low as 150 “C without a change of the
3.M. Liang et al. I Materials Chemistv
composition. [3] The nucleation and growth processes affect significantly the microstructure of the thin films, and in turn the extrinsic film properties. We report in this paper the results of an investigation of the kinetics of crystal nucleation in amorphous CoSi, thin films and growth of the crystallites by transmission electron microscopy. The paper is organized as follows. Tn section 2 we present the fundamental theoretical relationships of nucleation, growth and mass crystallization. In section 3 we describe the experimental procedure and in section 4 we present the experimental data and their theoretical interpretation. The results are summarized in section 5.
and Phydcs 38 (1994) 250-257
where As, is the entropy of melting. AT=T,,,-T is the undercooling and T, is the melting point. According to the classical theory of phase formation (for a review see ref. 6) the radius of the critical nucleus is given by the equation of Thomson - Gibbs
r* = 2 of2 AP
o,,,=oNAR2’
2. I Nuckation
is proportional
The amo~hous phase could be considered as a liquid with very high viscosity of the order of 1x10’” poise [4]. When heated above the temperature of vitrification the viscosity goes steeply down and the transport processes characteristic for the usual melts become possible. The heated amorphous phase (or melt} can then crystallize by processes of nucleation and growth. The steady state rate of formation of 3D nuclei in melts is given by [5]
o,,, = celh,
where J,, is a kinetic pre-exponent, AG* is the work for nucleus formation, and U is the activation energy for transfer of a growth unit (atom or a molecule) across the liquid-c~stal interface and its subsequent incorporation into the crystal lattice (kink sites). The Gibbs free energy for homogeneous formation of nuclei reads
where o is the surface free energy of the crystal-liquid interface, Sz is the volume of a molecule in the crystal phase and Ap is the supersaturation or the thermodynamic driving force of the nucleation process given by the difference of the chemical potentials of the infinitely large liquid and crystal phases. The latter is given by Ap = As, AT
(3)
(4)
Turnbull [S] correlated experimental results on nucleation in a series of molten metals (see also ref. 7) and found that the molar surface energy o, defined as
2. Theoretical
U+AG* J=J,exp(--TP)
251
(5) to the enthalpy of melting Ah, (6)
and the coefficient of proportionality ais near 0.5. Similar results were found for many other inorganic materials, including alkali halides [&lo].
The liquid- crystal interface particularly in the case of inorganic materials is expected to be atomically rough and the crystallites to grow rounded 1111. That is why molecules from the liquid can be incorporated directly into kink sites on the crystal surface once they cross the interface. Assuming both phases have one and the same composition (long range diffusion is excluded) the rate of growth is given by [6, 121
v=hv( @p(-
AS, U k-~)expFkT)(
I-exp(-
A& kF-))
(7)
where d is the distance a molecule should cover in order to join the crystal lattice which is usually taken as one at.omic diameter, v is a vibrational frequency, A,&= As,(T,-T,) is the supersaturation at the crystal liquid interface with Ti being the temperature at the interface, and (a/6)? is the geometric probability a molecule from the liquid phase to find a kink site upon its arrival at the crystal surface, 6 being the average spacing between the kink sites. Assuming the heat of crystallization is not taken away from the advancing interface fast enough it will accumulate and the ambient phase around the growing crystalhtes will be heated. As a result the temperature Ti will approach the temperature of melting T,, [13]. The under-cooling at the growth front ATi = T,, - T, will be
252
3.M. Liang et al. I ~ate~uls
Cleats
and Physics 38 (1994) 250-257
small but non-zero and eq. (7) is simplified to v = flATi
(8)
where
(9) (cmisec K) is the so called kinetic coefficient of growth from the melt [12]. The growth of the spherulites will be determined by the temperature gradient and will be “diffusion controlled” as the equations governing the diffusion and the thermal conductivity are one and the same [14]. The temperature around the growing crystallites will vary from Ti <, T, at the interface to the temperature T in the bulk of the sample. Keeping in mind that the nucleation rate is practically equal to zero below a critical undercooling “nucleation exclusion zones” will form around the growing crystallites in which the nucleation is suppressed [15, 161. As a result new nuclei cannot be formed in the near vicinity of the growing crystallites. In the other extreme the heat of crystallization is taken away from the growth front fast enough and the temperature at the interface approaches the temperature of the sample, i.e. ‘I, -“T [13]. At temperatures near the temperature of vitrification the undercooling AT = T,-T will be large enough so that the growth rate becomes practically independent of the undercooling. The growth is controlled by the rate of inco~oration of growth units into kink sites, i.e. the crystallites grow in an interface reaction controlled or a kinetic regime [12]. As the temperature is everywhere constant nucleation exclusion zones do not form. 2.3 Mass Crystallization In the case of progressive nucleation with a constant rate J (cm-3 se&) and a constant growth rate v (cm se+) in a 3D system the fraction of crystallized volume reads [17-191
{=l-exp(-;Jv’t4)
(10)
In deriving eq. (10) it was assumed that nuclei were randomly formed in the bulk of the parent phase and the nucleation probability was one and the same at each point of the volume [6,12]. In the case of solidification of very thin platelets in which the process of growth is thought to be preferably two - dimensional
c=l-exp(-FJv2t3)
(11)
where the nucleation rate J is in units of cm-2 se@. In both cases given above it was assumed that the nucleation takes place until the complete solidification of the sample (progressive nucleation). However, this may not be the case. The nuclei can be formed in a short (compared with the time of complete solidification of the sample) period of time in the onset of crystallization (instantaneous nucleation). The fraction of crystallized volume at a time t then is
{=l-exp(-$Nv3t3)
(12)
where N (cm-“) is the density of nuclei formed in the beginning of the process. In all cases listed above the kinetic solidification curve t(t)=
1-exp( -kr”)
(13)
is S-shaped. The value of the time exponent n can be easily found upon linearization of the 4(t) curves in coordinated ln[-ln(l- t(t)] vs. In(t) [6, 121. A difficulty in interpretation of the results may arise in the case when nucleation exclusion zones with enhanced temperature or reduced undercooling are formed and grow around the growing nuclei. The nucleation rate will become equal to zero before the complete solidification of the melt when the nucleation exclusion zones overlap and fill in the volume of the sample (soft impingement) [6]. If this is not the case the kinetics of solidification will be determined by the growth of the crystallites themselves (hard impingement) [6]. However, in both cases eqs. (10) - (12) should be formally obeyed.
3. Experimental lOO-nm-thick amorphous films of CoSiZ were prepared by electron beam codeposition of Co and Si atoms in a vacuum of 1 x 10-7 Torr onto a Si wafer containing arrays of etched windows with 0.25 mm area each. The windows were then coated with a 20 nm thick film of S&N4 to facilitate the examination of the solidification with transmission electron microscopy (TEM). Direct observations of the crystallization were carried out in situ in a JEOL 2000FX TEM with a heating stage. The annealing temperature was varied from 130
to 170 “C with 10 “C interval for various periods of time. The composition of the amorphous films was measured by Rutherford backscattering spectrometry. The crystallized phase was determined by electron diffraction to be CoS& with cubic CaF2 crystal structure. High resolution TEM (~RTEM) was carried out in a JEOL 4OOOEX with a point-to-point resolution of 0.18 nm to determine the atomic arrangements before and after the crystallization from the amorphous phase. The nucleation rate was determined by counting the number, N, of crystallites visible under the microscope and taking the slope of the resulting N(t) curves at constant temperature. Double pulse technique, 120,211 in which the nuclei formed at a given temperature are visualized by developing them at another temperature at which the nucleation is negligible, was not possible in our case because of the very high melting point, 1326 “C, of CoSi,. The rates of growth of the crystallites was determined from measurements of the sizeof selected particles with time. The ramping times to reach the growth temperature were typically 2-3 min. The fraction of the crystallized volume was determined either by image analysis of area1 fractions of highlighted particles or by stereology which measures the area1 fraction by measurements of the average intercept length per unit linear probe on TEM micrographs.
4. Results and Discussion Fig. 1 shows typical micrographs of CoSiZ spherulites from which the number of nuclei vs. time and the particle size vs. time curves and the kinetic solidification curves are determined. Fig. 2 shows number of nuclei vs. time curves at four different temperatures. As seen they represents straight lines whose slopes give the steady state nucleation rates. Note the existence of induction periods which are typical for nucleation in condensed phases. [22] We will not consider in this paper the transient behavior of nucleation as the data are obtained without the use of a double pulse technique. Fig. 3 shows the time dependence of the particle size at five ~fferent temperatures. The slopes of the straight lines give the rates of growth of the spherulites shown in Fig. 1. The data about the rates of nucleation and growth are summarized in Table 1. Fig. 4 represents the Arrhenius plot of the rate of growth vs. the reciprocal temperature.The valueU = 23.9 kcallmole has been calculated from the slope of the straight line for the activation energy for transfer of a growth unit across the liquid _ crystal interface. This value is somewhat lower than the values typical for inorganic glassforming melts (Li,0.2SiOZ, SiOZ, GeO?,), which are usually of the order of 100 kcal/mole [22-241. This is due obviously to the fact that CoS& is not a
typical glassforming material. Besides, the straight line in Fig. 4 is an indication that AU / kT>b 1. With Ah,,, = 0.107 eV per atom as measured in the second part of this paper [25] we find As, = 19.37 J1mole.K and A&/ kT = 6.3 for the highest temperature involved, i.e. exp (-Api / kT )=I8 x 10-3<< 1. As discussed above if the melt around the growing crystallites is heated to much higher temperature than the one given in the experiment the kinetics of growth will become in fact controlled by long range diffusion as the conduction of heat in condensed phases is governed by the same equations as the diffusion [12,13]. The pre-exponent in eq. (7) kV( iI2 exn( - bs, 1 was found from the Arrhenius plot to be 7.75 x 16;4 cmlsec. Witha-4.22~10-~cm,v=3~10~3sec-~,a/lj= 1/2and h--a, the entropy of melting was estimated to be As, = 11.7 Jl mo1e.K. If the maximum surface roughness, a/6 = 1, is assumed [14], As, = 23.2 J1mole.K. Comparing these values with the value 19.37 Jlmo1e.K calculated from calorimetric data [25] allows us to conclude that the rate of growth does not depend practically on the undercooling although some negligible heating of the melt in the near vicinity of the crystals is not excluded. As seen from equations (l), (2) and (3) the nucleation rate includes in itself exponents of the barrier U for incorporation of growth units into kink sites which is temperature independent and the work for nucleus formation AC’ which is inversely proportional to the square of the undercooling AT = T, - T. In order to separate both exponents and find the work for nucleus formation from the experimental data we construct a plot of ln[J exp(U/kT)] vs. l/T(T, - T)z taking for U the value 23.9 kcal/mole obtained from the growth data. The same result is obtained if we plot ln(J/v) vs. l/T(T, - T)r. The only difference is that in the latter case the points are more scattered around the straight line. The plot of ln[J exp(U/kT)] vs. l/T(T,, - T)* is shown in fig. 5. A straight line with a slope - 1.73 x 1010 and intercept from the ordinate 82.6 result when we interpret the data in the logarithmic co-ordinates characteristic of the classical nucleation theory. From the slope of the straight line we calculated the value AG’ = 1.73 x lo-‘9 J for the work for nucleus formation at T = 150 “C, or AG*/kT = 30. For the surface free energy of the nucleus liquid boundary with fi = 23.71 cmYmole one obtains the reasonable value CT= 212 erg/cm*. For the number of molecules in the critical nucleus from eq. (3) one obtains n* = 471r*3/352= 9. In other words at the temperatures of the experiment the critical nucleus consists practically of two unit c&Is. On the other hand, this result invalidates the determination of the surface free energy. It has been shown, however, that the classical nucleation theory predicts reasonable values for the surface free energy even in cases of very small nuclei, when the parameters
254
J.M. Liang et al. / Materials Chemistry and Physics 38 (1994) 2SO-257
Fig. 1. Micrographs showing the formation and isotropic growth of CoSiz crystallites in samples annealed at 340°C for (a), (d) 60, (b), (e) 65 and (c), (f) 75 min, respectively.
255
J.M. Liang et al. I’ Materials Chemistry and Plzysics 38 (3994) 250-257
TABLE 1. Values of nucleation and growth rates for samples annealed at different temperatures.
TW)
J(cnr3 ruin-‘)
v(cm/min)
130 140 150 160 170
5.09 x 10” 1.26 x lOi 3.00 x 10’2 7.58 x 1012
5.43 x lo-’ 1.00 x 106 2.44 x 10-6 5.00 x 10” 6.95 x 10”
2.20
2.30
2.40
2.50
1OWkT
Fig. 4. Arrhenius plot of the rate of growth vs. reciprocal temperature.
54.0
0
10
20
30
40
50
!
---7
60
Time (mitt)
Fig. 2. Number of particles per cm3 vs. time curves at four different temperatures.
1.68
1.70
1.72
1.74
109/T(T,,,-T)’
T
Fig. 5. A plot of In[J exp(U/kT)] vs. l/T(T,-T)2.
u3
b 4
c
x
20
40
60
80
100
Time (mitt)
Fig. 3. Time dependence tures.
of particles size at five different tempera-
defined with the help of the phenomenological thermodynamics lose their physical meaning 1261. Finally, for J, one obtains 7.7 x 1O35cm-3 se@, or for the kinetic pre-exponent of the nucleation rate J, exp(-UlkT) one obtains the reasonable value 3.6 x 1023cm-3 se@. One additional check of the interpretation of the experimental data presented so far is to calculate the Tumbull’s parameter a= oNA au3 / Ah,,, (see equations (5) and (6)). With o= 212 erg cm-z, a= 3.94 x 1023cm3/ molecule and Ah, = 3.097x 1011erg mole-’ we find a= 0.48 in excellent agreement with data for many inorganic materials. Fig. 6 shows the time dependence of the crystallized
I.M. Liang et al. / Materials Chemistry and Physics 38 (1994) 25X-257
256
0
160
0
150
A
TABLE 2. Valuesof k = nJv313calculated from the kinetic SoIidification curves and from the direct measurements of J and v.
140°C
1.0
T(“C)
AvramP)
140 150 160
8.09 x 10-a 3.86 x 1O-6 8.16 x 10-5
J&G’)
Ratio
1.32 x lO& 4.59 x 10-s 9.92 x 10”’
163 12 12
0.8
0.6
a) From kinetic solidification curves b) From multiplication of directly measured J and v
0.4 0.2 0.0 0
20
40
60
80
100
120
Time (min) Fig. 6. The timedependence temperatures.
0
of the crystallized volume c(t) at different
The S-shape is clearly demonstrated.
160
0
150
A
140°C
2 1 0 -1 -2 -3 -4 -5 1
2
3
4
5
In 0) Fig. 7. Interpretation
of solidification curves shown in Fig. 6 in co-
ordinates In{-ln[l - t(t)]] vs. In(t).
volume t(t) at different temperatures. The S-shape is clearly demonstrated. In fig. 7 the curves are presented in co-ordinates In{-ln[l- t(t)]) vs. In(t). [6] The average value of the slopes is 3.8. The result is an indication that the nucleation process takes place randomly in the bulk of the amorphous film with a constant rate during the transformation process (progressive nucleation).
Instantaneous nucleation in the beginning of the solidification does not take place and the process of nucleation is three-dimensional irrespective of the small thickness of the samples. This conclusion is supported in addition from the values of o and a which have been obtained under the assumption of homogeneous nucleation. From the intercepts ofthe straight lines with the ordinate in Fig. 7 we calculate the coefficients k = nJv313 (see eq. (10)) and compare them with the values obtained from the directly measured rates of nucleation and growth. The data are compared in Table 2. As seen the Avrami coefficients are always smaller by one to two orders of magnitude than the ones calculated from directly measured values of J and v. This means that either the actual nucleation rate or the growth rate or both during the transformation are smaller than the directly measured ones. Eq. (10) has been derived assuming steady state nucleation rate. In fact we have a transient nucleation as seen in Fig. 2. Obviously the most influenced by the transient effects will be the lowest temperature case. The kinetic transformation curve is then shifted to longer times by the induction period. Correction of the Avrami curve obtained at 140 “C with the induction period from the N(t) curve shown in Fig. 2 leads to a value of k = xJv313 = 5~10~ seed, i.e. two orders of magnitude greater than the one listedin Table 2 in better agreement with the value 1.32 x 10-e seP. The effect of the time lags on the curves obtained at higher temperatures will be smaller. Thus if we attribute the above discrepancy to the transient behavior of the nucleation it follows that the transformation of the amorphous phase to a crystalline one takes place by ‘hard impingement” of the spherulites. In other words, nucleation exclusion zones do not exist and the approximation A&>> kT is justified. Note that if soft impingement occurred during solidification the values of k = ?rJv3/3 as calculated from the kinetic Avrami curves should be greater than the ones calculated from the values of J and v as the rate of growth of the nucleation exclusion zones is greater than that of the crystallites themselves. We will restrain ourselves from more detailed analysis of the influence of the transient effects of nucleation on the kinetics of transformation because of the inaccu-
J.M. Liang et ai. / Materials Chem&y
racy with which the induction
periods are measured.
and Physics 38 (1994) 2X7-257
2.57
of China National Science Council through Grant No. NSC83-0416EOO7-008 and IBM Research Division.
5. Conclusions References We have measured the rates of nucleationandgrowth and the time dependence of the crystallized fraction during the c~st~li~ation of thin films of ~o~hous CoS&. The nucleation rate is time dependent as is often the case of nucleation in condensed phases. The process of nucleation takes place randomly and homogeneously in the bulk of the film. The value of 212 erg/cm* has been determined for the surface free energy of the crystal nucleus - amorphous phase boundary. The critical nuclei consist of two unit cells. The ratio of the molar surface energy and the enthalpy of fusion was found to be 0.48 in agreement with data in other inorganic materials. The growth of the particles is controlled by the interfaci~ reaction of inco~oration of growth units into kink sites of the crystal lattice. In other words, the particles grow in a kinetic regime. No heating of the amorphous phase in the near vicinity of growing particles and the formation of nucleation exclusion zones have been detected. The entropy of melting as calculated from the particles growth rates is in agreement with the calculated from c~o~metric The average Avrami exponent is measurements. equal to 3.8 which appears as an additional indication of random progressive 3D nucleation. The product k = rc JvV3 as measured from the kinetic transformation curves is always smaller than the one calculated with the help of the directly measured rates of nucleation and growth which is an additional indication of hard impingement of the spherulites during the solidification. The latter discrepancy is explained with the transient character of the nucleation rate.
Acknowledgments The researeh was supported partially by the Republic
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