The morphological stability in supercritical fluid chemical deposition of films near the critical point

ELSEVIER Journal of Crystal Growth 155 (1995) 276-285

The morphological stability in supercritical fluid chemical deposition of films near the critical point

Oleg A. Louchev *yl, Vladimir K. Popov, Evguenii N. Antonov Research Center for Technological Lasers of the Russian Academy of Sciences, Troitsk, Moscow District 142092, Russian Federation

Received 2.5 February 1995; manuscript received in final form 21 April 1995

Abstract

In this paper, the results of experimental and theoretical studies of the chemical deposition of copper films from metalorganic compounds dissolved in supercritical C,F, are reported. The optimal conditions for the growth of highly adherent Cu films with good surface morphology have been determined. A theoretical analysis of the kinetics, the stability of the growth interface together with the transport phenomena inside the supercritical cell shows that the morphological stability is determined by the interplay of three factors. These are the bulk diffusion near the interface, the thermally activated kinetics, and the heat transfer across the depoiited layer. It is shown that the morphological stability of the grown film is ensured by an enhanced turbulent convection occurring if the operation pressure and temperature are close enough to the critical point.

1. Introduction

Supercritical fluid chemical deposition (SFCD) is a novel technique for the production of thin films [1,2]. In this process, a supercritical fluid (SF) is considered as a highly compressed gas whose temperature and pressure are above their critical values. SFs demonstrate a unique combi- nation of both gas-and liquid-like properties. Like liquids, they can dissolve solid compounds, but like gases they have low viscosities and high diffu- sivities. Due to their high compressibility, their

* Corresponding author. Fax: +81 298 52 7449; E-mail:

[email protected].

’ Present address: NIRIM, Namiki I-1, Tsukuba, lbaraki

305, Japan.

solvent power may be easily tuned by altering the pressure and, therefore, the density of the SF. In the SFCD technique the precursor species can be dissolved in a high pressure cell prior to the deposition of a film on the substrate, carried out by means of resistive or laser heating [2].

The SFCD technique has a few important ad- vantages over the conventional CVD since the feasibility of the particular CVD technique may be restricted by various limitations, such as low equilibrium pressure of available precursors, their high toxicity, low deposition rates, etc. SF media allow one to use non-volatile precursors. This extends the range of possible precursors and their combination for the growth of metal, semicon- ductor and dielectric films. Moreover, this pro- vides an opportunity to use less toxic and more inexpensive compounds. The precursor mixture

0022.0248/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved

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O.A. Louchev et al./Journal of Clystal Growth 155 (1995) 276-285 277

can be prepared by simple weighing of the neces- sary species, followed by dissolution in SF carrier. In addition, SFCD techniques allow one to use thermally instable precursors due to the low criti- cal temperatures of the SF solvents (for Xe and CO 2 Tcr = 16.6°C and 31.1°C, respectively).

In film deposition techniques, one often faces [4-7] the problem of morphological instability of the deposition interface. This instability is an intr insic growth p h e n o m e n o n dr iven by diffusion-like mechanisms at the deposition inter- face, and leads to the waviness of the interface. This in turn leads to the appearance of micron and submicron solid structures, which alter the transport, optical and mechanical properties of the grown films. The inhibition of the morpholog- ical instability presents an important task of fun- damental interest for the production of different films. In the present communication, we focus on the process of the chemical deposition of copper films from a metalorganic precursor dissolved in SF -C2F 6. We show both experimentally and the- oretically that this technique ensures the morpho- logical stability of the growth interface if the operational pressure and temperature are held close enough to the critical point of the solvent medium. This stabilization is associated with the turbulent natural convective heat and mass trans- fer inside the cell, which are considerably en- hanced near the critical point.

2. E x p e r i m e n t a l d e s i g n a n d resu l t s

To study the SFCD process of films under resistive heating, we used an experimental appa- ratus as shown in Fig. 1. The high pressure stain- less steel reaction cell has a substrate holder with a built-in resistive heater and thermocouples, pressure and temperature gauges, three BaF 2 windows, and inlet and outlet gas connections. This cell can operate under pressures up to 200 bar. The high pressure generator is a manually operated piston screw pump. The active volume capacity per stroke is 200 cm 3, and the maximum pressure generated is 500 bar. The gas handling system allows one to use three different gases (for example, Xe, CO 2 and C2F(,) or their mixture as

inlet D. l ~ outlct~ High Pressure Pump ~ ] . [ ~ . _ BaF2

| i " | -'" Window5 S } !

Subs t ra te~ . l~P~Uper¢ , i , i c . I F l o l d ' ~ . ~ with I M +

Precursor ~' H

I k L I I+I++++I'KI )"- .

Thermocouples i " " SFCO CPI}

Heater

Fig. l. Experimental cell for supercritical fluid chemical depo- sition.

supercritical fluids. BaF 2 windows allow one to use IR, visible and UV laser radiation to initiate reactions on a substrate surface, and to monitor the deposition process. Stainless steel foil (0.1 mm thickness) was used as an active element of the substrate heater. A Si wafer (300 /xm thick- ness) was mounted on this foil heater. The tem- perature was monitored by three thermocouples, two placed at the edges and one at the center, all on the opposite side of the heater from the substrate. Heating homogeneity was also con- trolled by an optical pyrometer. Substrate prepa- ration consisted of rinsing with spectroscopic grade acetone and ethanol, followed by an etch with 10% HF in distilled water. The sample was then placed onto the substrate holder inside the cell which was immediately sealed and purged a few times with a SF solvent (C2F6).

As a precursor for copper film deposition, Cu( I I )hexaf luoroace ty l -ace tona tehydra te (Al- drich) was used. This inexpensive metalorganic compound is easily soluble in SF [2], has low toxicity (because of the low vapor pressure at room temperature), and is stable in the atmo- sphere environment. It has been successfully used before in experiments on the laser induced CVD of copper films [3]. It was dissolved at various concentrations (from 10 - 4 to 2 × 10 -3 mol/1) in SF solvent directly inside the cell at a tempera- ture slightly above critical value. The temperature of the substrate was then altered in the range of 600-800°C. The typical duration of the SFCD exposure was 10 min. At the end of the process,

278 O.A. Louchev et aL /Journal o f Crystal Growth 155 (1995) 276-285

the SF mixture and cell wall temperature (moni- tored by a separate thermocouple) increased a few degrees centigrade due to the large thermal inertia of the massive walls of the SF cell.

A number of metallic films with a quite good surface morphology (analyzed by optical, scan- ning electron microscopy (SEM) and stylus pro- filometer measurements) and adhesive properties (tested by Scotch tape and scratch tests) has been grown with a thickness of 0.05-5/zm. The chemi- cal composition and stoichiometry of these films were analyzed by Auger electron spectroscopy. Typical Auger profiles of the surface layers and the internal domains of the copper film deposited on the Si substrate in SF-C2F 6 is shown in Fig. 2a. In these measurements the copper film was etched by Ar + beam (etching rate about 80 • ~ /min) from the surface to the Si substrate. The presence of oxygen in the film structure is clearly seen. This is mainly due to the water molecules in the precursor powder (we did not use any prelim- inary drying), which caused the partial oxidation of the film during deposition. The high concen-

1 0 0 -

9 0 -

B 0 -

7 0 -

6 0 -

. E , O - U ~ 4 0 -

2 t 0 -

2 O -

I 0 -

10

9

°

< 4

3

2

1

5 I 0 I 5 2 0 2 5 3 0 3 S 4 0

S P O T T E R T I H E . n i n -

_b

c , ,

,o'o ,o'o ~o'o , ' ° s~o ,go ,'~o B'00 B' . . . . . K I N E T I C E N E R G Y . ¢ V

Fig. 2. (a) Auger profile of copper film deposited at ~ , = 2 × 10 -4 m o l / l and T s = 700 K. (b) Auger spectrum of the internal domain of the copper film (after 10 min of etching by Ar + beam) deposited at ./Vii = 10 -3 mol / I and T s = 750 K.

Fig. 3. SEM photo of the grown copper film.

tration of carbon on the film surface (compared to the bulk) is a result of the precipitation of metalorganic molecules after the reduction of the pressure at the end of process. No post-deposi- tion cleaning of the surfaces was undertaken to remove such material. Some atmospheric oxida- tion of the surface could also have taken place. Nevertheless, this film has quite a low resistivity (about 10 /zl~/cm) and a very smooth, dense surface without any observable microstructure (see Fig. 3). All of these results are experimental evidence of a stable morphology of the growth interface of the film.

The experiments have been carried out under a cell pressure of 35 bar (PeR = 30.4 bar). The temperature of the substrate was T s = 700 K, the temperature of SF-C2F 6 was T O = 300 K (TcR = 293 K). The bulk concentration of the precursor was .dP0 = 2 × 10 - 4 mol/1. The thickness of the deposited layer ~ = 0.3 /zm. The corresponding deposition time was t D --~ 10 min. Thus, the depo- sition rate was V= 0.5 nm/s. It is important to note that an increase in the precursor concentra- tion and /or substrate temperature leads to an increase in the contamination of the growing film, mainly by carbon and oxygen. A typical Auger spectrum of the film deposited under the opera- tional parameters X 0 = 2 × 10 -3 mol/1, T s = 750 K and a pressure of C2F 6= 35 bar is shown in Fig. 2b. The carbon and oxygen in the film arises from the decomposition of the discarded iigand trapped in the film during the growth process.

0.4. Louchev et al. /Journal of Crystal Growth 155 (1995) 276-285 279

These residues arise from a much higher deposi- tion rate (V--- 10 nm/s compared with the experi- ment described above) and a relatively high den- sity of the SF/metalorganic mixture. This inhibits the diffusion of the ligand from the surface after the thermal decomposition of the precursor.

3. Theory

3.1. Growth kinetics

We assume that the thermal decomposition of the precursor is of the first-order Arrhenius-type reaction occurring on the heated interface, and not in the fluid bulk. Let us consider a layer of precursor molecules adsorbed on the growth in- terface. Assuming that the surface density of the precursor molecules is uniform and neglecting the surface diffusion, the local balance is deter- mined by three components. First, the flux of molecules incoming on the interface from the bulk is given as,

1 ( kaT s ]1/2 q a = z ~ m ] exp(-EA/kBTs)"4"s' (1)

where .4r s is the bulk density of precursor molecules at the growth interface, E A is the acti- vation energy of the physical adsorption, T s is the temperature of the interface, m is the molecular mass of precursor and Z is the compressibility factor depending on the SF pressure and temper- ature.

Second, the outgoing flux of molecules desorb- ing from the growth interface back into the fluid is given as,

q2=nuexp[--(EA + AEA)/kBTA], (2)

where n is the surface density of adsorbed molecules, A E n is the adsorption energy and u---1012-1013 Hz is the frequency of thermal vibration of adsorbed molecules.

Third, the outgoing flux of the precursor re- sulting from the thermal decomposition on the growth interface is given as,

q3 =/'/t. ' exp( - Ea/k BTs), (3)

where E R is the activation energy of the thermal decomposition. The balance of these three fluxes gives the following relationship between the bulk density of precursor in front of the growth inter- face, X s, and the corresponding surface density of the precursor, ns,

J s ( kBTs ),/2 ns -- ~-~ ~2-~m exp(--EA/kBTs)

x {exp[- (E A + AEA)/kBTA]

+ exp( --ER/kBT A)} - 1 (4)

The flux of Cu at the interface is given by the rate of thermal decomposition of adsorbed pre- cursor molecules q = nsv exp(-ER/knTs). The atoms appearing at the interface diffuse to atomic kinks, where they attach. Assuming that they do not evaporate from the interface under the pro- cess temperature (the diffusion length is larger than the mean distance between the kinks) the deposition rate is given as,

2 rr--m exp[ - (EA +ER)/kBTs]

× {exp[- (EA + AEA)/kBTs]

+ e x p ( - E R / k s r s ) }-', (5)

where O is the volume per one atom in solid. As usual, the adsorption/desorption process

occurs much faster than the thermal decomposi- tion due to the fact E R > E A + AEA, SO that e x p [ - ( E A + AEA)/kBT s] >> exp(-ER/kBT s) and we have,

V=/2/3 (Ts)./g s. (6)

Here,/3(T s) is the kinetic coefficient and is given by,

l ( k B T s ) '/2 /3(Ts) = Z ~, 2rrrn

xexp[ - ( e R - a e A ) / k . r s ] . (7)

This expression shows that the adsorption process effectively enhances the thermal decomposition of precursor on the interface by decreasing the energy barrier (ER-AEA). This feature allows us to neglect the bulk decomposition in comparison

280 0..4. Louchev et al./Journal of Clystal Growth 155 (1995) 276-285

with that on the surface in the cold-wall reactor technique.

Next, we present some estimations concerning the deposition experiment performed with Je" 0 = 2 × 10 -4 mol/1 and the corresponding deposition rate V= 0.5 nm/s (described in Section 2). As- suming that the deposition rate was not con- trolled by the diffusion, i.e..,V s = Jg'0, we obtain the value of the corresponding kinetic coefficient /3(T s) = V / ~ X s -~ 90 tzm/s (O = 4.66 × 10 -29 m3). The evaluation of the effective diffusion coefficient shows that the ratio of the diffusion resistance to the kinetic resistance [3L/Def e << 1, (for Deft, see Section 3.3). Therefore, the bulk diffusion resistance may be neglected for this experiment. The value of /3 together with the compressibility factor Z = 1 (at the substrate) corresponding to the operational pressure and substrate temperature (~ 700 K) allows us to obtain via Eq. (7) the following estimation of the effective activation energy, E R - A E A = 0.81 eV.

3.2. Stability criterion

The deposition rate is determined by the inter- play of chemical kinetics, heat and mass transfer. Let us now consider the perturbation of the flat interface in the form of a protuberance (see Fig. 4). Such protuberances may appear due to the thermal or molecular density fluctuations at the

o ~ x I

Interface

Fig. 4. Scheme for the analysis of the growth interface pertur- bation under the combined action of the concentration and the temperature gradients.

growth interface resulting, for instance, from the turbulent transport regimes in the supercritical cell. The deposition rate on the tip of this protu- berance will differ from that on the non-per- turbed plane due to (i) the change of the molecu- lar density in front of the tip .,4~ s and (ii) the change of the surface temperature at the tip T s. Let us consider the variation of the deposition rate 6 V corresponding to the variation of the growth interface 8,

6V= a [ [3( T s ) ~ s + Jrs6[3 ] . (8)

The corresponding variation of the molecular density, &/ r s= GNS, is associated with the molecular density gradient in front of the deposi- tion interface GN. The corresponding variation of the kinetic coefficient, 6[33 = (3[3/OT)GT~ is asso- ciated with the average gradient of the tempera- ture across the deposited layer G T = (ksGTs + kGGTG) / (k s + k G) = 2GTs.

Using the above expressions we find,

6 V / ~ = a/3(Ts)(G N +.4"sKGT), (9)

where K =/3 -1 OB/OT. If 8 V / 8 > 0, the protuberance will grow faster

than the nonperturbed plane thereby disturbing the stability of the interface. If 8 V / 8 < 0, the protuberance will grow slower than the nonper- turbed plane and will disappear with time. Hence, the criterion of the morphological stability of the growth interface will be,

G = G N -I-./g'sKGT < 0. (10)

Substituting into this expression the molecular density gradient, G N =./Vsf l (Ts) /D , where D is the diffusion coefficient, we find,

G/A/" s = [3 (Ts ) /D + KG T < 0. (11)

The growth interface is stable if G < 0. If G > 0, the growth interface is unstable and the film growth proceeds with surface undulations. These lead, in turn, to multigrain and dendritic structures. Let us elucidate the physical meaning of the obtained criterion considering a perturbed interface. The first term of Gr~, the molecular density gradient, contributes to the enhancement of the perturbation, since it increases the molecu- lar density on the protuberance tip in comparison

O.A. Louchev et aL /Journal of Clystal Growth 155 (1995) 276-285 281

with the nonperturbed plane. The second term, X s K G T , corresponds to the perturbation of the kinetic coefficient under the action of the tem- perature gradient across the deposited layer. The value

1 O/3 K = ~ 0-T = 1 /2Ts + (ER - A E A ) / k B T Z (12)

is positive (the increase of the temperature en- hances the Arrhenius-type kinetics). Hence, when G T > 0, this term enhances the perturbation, but when G T < 0, this term leads to the inhibition of the perturbation. Therefore, when G T > 0, the kinetics, being thermally activated, enhances the instability associated with the molecular density gradient. On the other hand, when GT < 0 the kinetics inhibit the action of the diffusion driven instability of the interface, and thereby stabilize it.

The above simplified analysis does not take into account some important features of the pro- tuberance formation associated with the surface tension and the surface diffusion of the precur- sor, which are both important for the critical wavelength of the stable perturbations [7]. How- ever, in this paper, we have focused on the stabil- ity criterion and have not considered the surface structures appearing under "unstable" conditions where these effects become important.

3.3. Heat and mass transfer

Let us consider the heat and mass transfer phenomena occurring in the SF cell. The visual observations show that the deposition in the cell proceeds under intensive natural convective mix- ing. The corresponding Rayleigh number estima- tion gives,

f l T g A T L 3 Ra T = = 1011-1012, (13)

where v is the kinematic viscosity, a = k G / p c is the thermal diffusivity, g is the gravitational con- stant, AT = T s - T o is the temperature difference between the substrate and SF media, L is the characterist ic size of the cell and f i t = - p - l a p / c g T is the coefficient of thermal expan- sion.

The above range of the Rayleigh number cor- responds to developed turbulent convection. To estimate the value of the temperature gradient across the deposited layer, G T, we use an empiri- cal correlation for the natural convection heat transfer inside enclosures [8],

kef t = k GA Ra~r, (14)

where kaf is the effective heat conductance of the fluid inside the enclosure, k G is the molecu- lar heat conductance of the fluid, and A and n are parameters depending on the value of Ra T . For Ra T < 103, A = 1 and n = 0. For 103 < Ra T < 106, A = 0.105 and n = 0.33. For 106 < Ra T < 101°, A = 0.4 and n = 0.2. This dependence is shown to give a very good agreement of the experimental data for different types of the en- closures geometries [8].

This dependence allows us to estimate the heat transfer from the substrate through the SF medium to the cell wall and, thereby, the temper- ature gradient across the deposited layer as,

G T = 2ks l [k~ f f (Ts - T o ) / L + s c r ( T ~ - T,4],

(xs)

where k s is the film heat conductance, e is the emissivity and or is the Stefan constant. The second term in the above expression takes into account the radiative component of the heat transfer. This term may give a considerable con- tribution, especially under low pressures. We keep this term to give a comparative analysis of SFCD with CVD techniques. The molecular diffusion coefficient is given by [9,10],

D = D o ( T / T s T ) '~ exp( - S / T ) PsT/P, (16)

where D o is the diffusion coefficient at standard conditions (TsT, Psx), a and S are the empirical constants.

The molecular diffusion transport under the given operational conditions is greatly enhanced by the turbulent convection. To take into account this effect we use an analogy between heat and mass transfer, and estimate an effective diffusion coefficient as,

D e f f = DA Ra'~, (17)

282 O.A. Loucheu et al. /Journal of Crystal Growth 155 (1995) 276-285

where Ra, = Ra,a/D is the mass transfer Rayleigh number.

The physical meaning of the effective heat and mass transfer parameters may be elucidated by the concept of a boundary layer. The intensive convective stirring leads to the uniformity of both the temperature and the concentration inside the SF bulk, so that their gradients are only localized in front of the growth interface. This occurs within the temperature and concentration boundary lay- ers, respectively. These boundary layers present the resistance to the heat and mass fluxes. Their thicknesses may be evaluated as 6, = L&/k,,) and 6, = LCD/D,,), respectively, for tempera- ture and diffusion boundary layers (L is the char- acteristic size of the cell). For our experiment, 6 T=& = 300 pm (a/D = 0.9).

In Figs. 5-8 we present a set of graphs describ- ing the dependences of stability criterion G/.Ns. Also displayed are different heat and mass trans- fer parameters versus the value of the operational pressure. In the calculations we used the follow- ing data: CL = 13 X 10T6 Pa. s, k, = 0.01 W/m K, c = 480 J/kg K, k, = 370 W/m K (copper at T, = 700 K) [9,10]. The parameters for the diffu- sion coefficient were taken as: D, - 1.3 X 10m5 m’/s, (Y = 1.6 and S = 140 K [lo]. The molecular diffusion coefficient in the stability criterion rele- vant to the substrate temperature T, = 700 K has the value of D = 4 X 10m5 m*/K. However, the

20

Fig. 5. The dependence of G/MS versus the operational pressure in the SFCD cell.

lg P, Pa

201,,,,,,,,,,,,,,,,,,,,~,,,~,,,,’,,,,,,,,,,1 5.0 5.5 6.0 6.5 7.0

lg P, PO 4.0 .I I

,q 3.0 E

: 0 1.0 x

0.0 ?,,,,.,,,,,,.,,,,,,.,,,,.,.,.,~,,,,,,,,,I 5.0 5.5 6.0 6.5 7.0

lg P, Pa

Fig. 6. The dependencies of the heat and mass transfer parameters in the SFCD cell versus the operational pressure: (a) the thermal Rayleigh number Ra,, (b) the temperature gradient across the growth interface G, and (c) the effective diffusion coefficient Den.

molecular diffusion coefficient taken for the esti- mation of the mass transfer Rayleigh number Ra, = Ra,a/D corresponds to the mean bulk temperature of SF medium. Because the temper- ature decrease near the growth interface is lim- ited by the temperature boundary layer, S, = 300 pm (much smaller than L = 20 mm), the diffu- sion coefficient as well as other constants such as

0..4. Louchev et al. / Journal of Crystal Growth 155 (1995) 276-285 283

/~, ks, and /3 T are taken at the SF temperature, T o . The dependence of p on P, T o and the compressibility factor Z is given by,

M P

p = Z ( P ' T ° ) R T ° , (18)

where M = 1.379 X 10-~ kg /mol is the molar mass of C2F 6. The coefficient of the thermal expansion, fiT, is expressed from Eq. (18) as,

1 0 p 1 1 0 Z

[~T = P aT ° To + Z OT o " (19)

The first term of this expression corresponds to the thermal expansion of an ideal gas while the second term takes into account a dependence of the compressibility factor on T o . As will be shown below this term plays a crucial role in transport phenomena in SF and, therefore, in the criterion of the morphological stability. The values of Z and OZ/OT are taken from Ref. [9].

In Fig. 5 we present by solid curve the depen- dence of G/./F" s on P starting from 103 Pa (rele- vant to CVD operation) to 107 Pa (relevant to SFCD) for To/TcR = 1.05. The broken line shows the dependence of G/. /K s calculated in the

"T

I -

0.11

0.10

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.00

To/TcR = 1 . 0 0 To/TcR = 1 . 0 5

. . . . To/TcR = 1 . 1 0

t l l l l ' l l l l l J l l l l l l l l l l l l q l l , l l l l l

5.0 5.5 6.0 6.5 7.0 Ig P, Po

Fig. 7. The dependence of the coefficient of the thermal expansion /3 T versus the operation pressure P for the differ- ent operation temperature T o of SF-C2F 6.

3.0

E 0.0

Z

© - 1 . 0

_ _ Z o / - r o . : l . O O _ _ T o / T c R = I . 0 5 SFCD /

. . . . To/TcR= 1.10 "~. /, 20 ~ /I

lO ? . _ / / O>O _ ~ ' - - - 1 " 1 /

'XI

O<O \ , \ 1 I I ,4

5.0 5 .5 6.0 6 .5 7.0

Ig P, Pc

Fig. 8. The dependencies of G / J F s versus the operation pressure P for the different operation temperature T O of SF-C2F 6.

framework of the model neglecting the contribu- tion of the natural convection to the heat and mass transfer (i.e. kef f - k C and De, - D). The comparison of the both curves outlines the crucial role of the convective transport inside the cell in the stability under elevated pressures. The bro- ken curve becomes positive and increases sharply. This is due to the fact that the molecular conduc- tance k G does not change noticeably and the value of G T is constant while the diffusion term G N increases linearly along with the increase of P (since D a I / P ) .

The curve corresponding to the model with account of convective transport exhibits the influ- ence of natural convection. This influence, first, extends the stability area for CVD technique up to atmospheric pressures. This is due to the fact that the destabilizing diffusion term GN/ . /Y s = [3(Ts)/Det f increases as pO.4 and the stabilizing term KG T increases as pO.6 while P is lower than 105 Pa. However, when the pressure exceeds 105 Pa the destabilizing term GN/. /Fs increases as pO.6 while the stabilizing term KG T increases as pO.4. This leads to the instability of the growth interface under P = 5 bar.

However, the increase of P up to the critical value decreases the stability criterion so that near

284 O.A. Locrchev et 01. /Jottmnl of Ctys~ul Growth 155 (199.5) 276-285

the critical point we find a second area of stabil- ity. This area is due to the existence of the maxima of convective heat and mass transfer parameters near the critical point. In Fig. 6a, 6b and 6c, we present the dependences of (i) the thermal Rayleigh number Ra,, (ii) the tempera- ture gradient across the deposited layer G, and (iii> the effective diffusion coefficient D,tr. The maxima on these graphs are due to the behavior of the coefficient of the thermal expansion & near the critical point, shown in Fig. 7 for differ- ent values of the ratio To/T,,. Near the critical point, the value of & has the maximum. Namely, for To/T,, = 1.05 the value of & increases from

PT = 3.5 x 1O-3 K-i up to &. = 3.6 x lo--’ K-i, i.e. by an order of magnitude. This is due to the behavior of the compressibility factor 2 near the critical point providing a considerable rise of the second term of Eq. (191, Z-‘JZ/dT,,. This leads to a sharp increase of the Rayleigh number, Ra, (see Fig. 6a). The enhanced convective transport leads to an increase of (i) the temperature gradi- ent across the deposited layer G-r (see Fig. 6b) and (i) the effective diffusion coefficient Deft (see Fig. 6~). The interplay of these parameters leads to the stabilization of the growth interface near the critical point. However, further increase of P far from the critical point leads to the decrease of & since the compressibility factor Z tends to 1 and the value of dZ/8T, tends to zero. This leads to decrease of the relevant Rayleigh number Ra, and, therefore, of G, and D,,. This makes the stability criterion to increase and to become fi- nally positive leading to the morphological insta- bility.

We should draw attention to the fact that the second area of the morphological stability ap- pears only if the operational temperature in SF cell is close enough to the critical temperature T CR. This is due to the dependence of the com- pressibility factor 2 on To. The strongest depen- dence of Z on P, To corresponds to the critical temperature T,, = TCR. Therefore, the maximal values of the coefficient of thermal expansion PT corresponds to To/T,, = 1.0. This is shown in Fig. 7 where the dependence of Pr on P is given for different values of T,,/T,,. For TJT,, = 1.0 the value of & increases about by 30 times while

for T,,/T,, = 1.1 this value increases only by 3 times. The sharp intensification of the convective transport and the corresponding stabilization of the morphological stability of the growth inter- face takes place only if the operational parame- ters of SF medium are close enough to the criti- cal point. To outline this conclusion we show in Fig. 8 the dependences of the stability criterion G/MS on P for different values of To/T,,. The largest area of the morphological stability under supercritical pressures corresponds to the opera- tion performed under the critical temperature To/T,-, = 1.0. It is worth noting that the depen- dence G/MS for To/T,, = 1.1 has also the char- acteristic minimum in the supercritical area. However, this minimum is not deep enough and the stabilization of the growth interface does not take place.

We should point out that our analysis of the transport phenomena based on the above empiri- cal correlations of the convective heat and mass transfer inside enclosures does not take into ac- count possible increases of the constants such as k,, p and D near the critical point since we do not have the necessary data. As a matter of fact these effects may be quite considerable. For in- stance, for CO, the value of k, is known to increase by about seven times near the critical point [9]. Nevertheless, we anticipate that these effects only enhance the stability of the growth interface and extend the stability range in the supercritical area of parameters. The possible increase of D decreases the instability term while the possible increase of k, yields an increase of the stability term as kE*. The increase of p near the critical point should lead to the decrease of the Rayleigh numbers. However, this will not noticeably alter the value of the effective parame-

ters &fry D,, since they are proportional to p -“.2.

4. Conclusions

The process of the supercritical fluid chemical deposition of thin films in the cold-wall SF cell with resistive heating of the substrate has been studied both experimentally and theoretically. The optimal conditions of growth of highly adher- ent Cu films with a good surface morphology

O.A. Louchev et al. /Journal of Crystal Growth 155 (1995) 276-285 285

from the metalorganic precursor dissolved in SF- CzF 6 have been determined. A theoretical analy- sis of the kinetics and stability of the growth interface shows that the morphological stability is determined by the interplay of the bulk diffusion, the thermally activated kinetics and the heat transfer across the deposited layer. For the con- ventional resistive heating the morphological in- stability is driven by the gradient of the molecular density of the precursor in front of the growth interface, while the temperature gradient across the deposited layer inhibits the action of the diffusion.

Two ranges of operating parameters corre- sponding to the stability exist. The first range corresponds to low pressure CVD operating con- ditions where the stability is ensured by the high molecular diffusivity. The second range corre- sponds to the operational parameters near the critical point. In this range the stability is ensured by the developed turbulent convective transport inside the supercritical cell which provides a sharp enhancement of the heat and mass transfer due to the maximum of the coefficient of thermal expansion near the critical point. However, the stability takes place only if the operational tem- perature of the SF medium is close enough to that of the critical point. The possible anomalies of the thermophysical properties near the critical point such as the heat conductance and diffusion may considerably enhance the stability and, therefore, extend the range of operating condi- tions corresponding to the morphological stabil- ity. Thus, our experiment and theoretical analysis show that supercritical fluid chemical deposition may be successfully used for production of films providing the stability of the growth interface in addition to other advantages such as easy han- dling and high solubility of different precursors.

Acknowledgements

This work has been supported by Grant No. 94-03-08457 from The Russian Foundation for Fundamental Research and Grant No. 1010- CT93-0003 from INTAS. This work has been partly supported by the contract from AMP, Inc. (USA). We are very thankful to Professors V.N. Bagratashvily and V.Ya. Panchenko for their in- terest in this problem and stimulating discussions. We express our sincere gratitude to Mr. G.V. Mishakov for the technical assistance during the experiments. Special thanks are expressed to Dr. P. Dennig for reading the manuscript.

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