ELSEVIER
Thin Solid Films 312 ( I O O 8 ) 195-2(11
The reactant depletion effect on chemically vapor deposited SiC films with pressure and gas ambient Han-Su Kim, Doo-Jin Choi
*
lh'pttrllth'tll ~!/'('¢ratttic Engim'erin,k,. )'onxei Unicer,vitv, 134 Shinchon. Smh.,m.n-Ku, Scrml. Sotah Km'e. Received 24 March 1907: accepted 10 Sel'~lcrnlx.'r t997
Abstract Polycrystalline /3-silicon carbide (SIC) Iilms were chemically vapor-deposited onto graphite substrate using MTS(CH~SiCI~) as precursor and Ar or H, dilulion gas, at ternperatures ranging I'roni 1273 to 1573 K and total pressures from 1.3 to I0.0 kPa. We investigated the effect of reactant deplelion, which usually occurs in the horizontal hot wall reactor, on the characteristics of SiC films with Iotal pressure and gas amhienl. Cry~;alline phases and preferred orientations are determined by X-ray diffraction (XRD) and surface morphology is identified with scanning electron microscopy (SEM). The effect of reaclant depletion was correlated with the decrease or the deposition rate in a gas Ilow direclion, ils effect becomes larger with increasing, deposition tetnperalure and total pressure, but remarkably diminished when Ar was used as a dilution gas in place of H ,. With the increase ~ff reactant depletion, preferred orientation of SiC films changes li-om [220] to [i II] and surface nlorphologies of those al.,,o develop into the four-fold symmetry faceted structure in a gas llow directk,u. With the diminution of reactant depletion, SiC films have uniform preferred orientation of [111] and surl:ace rnorphok,gics at all deposition positions. ~ 1998 Elsevier Science S,A, Ke.vwords." Chemical v;.tr~or depo.~ilion: Silicon carbide; X-ray diffraction: Surface morphology
!. Introduction Silicon carbide (Si(7) has prominent properties such as excellent hardness and chemical resistance at high temperatures [ I - 3 ] . So its application primarily includes hightemperature structural materials [4,5]. Because of wide energy band gap, high electrical mobility, and thermal stability, it has been also used as a high-temperature semiconductor [6]. From the standpoint of reactor type, CVD (Chemical Vapor Deposition) reactors are classified us a hot and cold wall [7]. Especially in the case of hot wall type CVD reactors, the .serious problem is encountered, a reactant depletion effect lhat decreases the deposition rate downstream [8]. There:tfter several attempts have been made to diminish the reactant depletion effect, Eversteyn et al. [91 suggesled that prepared films, which use tilted suseeptor wilh adjusting gas flow velocity in comparison with nontilted one, have a tendency to grow uniformly at overall deposition positions. The literature by Desu and Katidindi [10] revealed that the films have uniform deposition rates along deposition positions by increasinu tile
"
('orresl)tmtling a u l i l o r ,
(M)Jlb(~O01)/98/$ f9.(X) ~'~ It)t)8 l!lscvicr St'i,,.'nce S,A, All iit]llts lu.~.el~u'd. Pll S01)4(1-61)911(97)00744- X
temperature in the gas flow direcliotl. However. upto dale. most o f researches on reactant depletion effect have been focused on the kinetic approach, not on actual change of films properties with deposition paramelers [I 1,12]. But, recently. Kim el al. [13] studied the effect of reactant depletion on the preferred orientation and microstructure of SiC films as a function of deposition temperature, It has not }'el been a report on the change of properties of sic I'ilms due lo reactant depletion effect as a function of lOUd . d . s ~?S, pressure and nature of dilution '2' in this study, we examine the effect of reaclanl depletion on the characteristics of SiC films with iolal pressure, Also we investigate tile effect of gas ambient on the oiminution of reactant depletion by partly introducing Ar in place of H_, as a dilution gas.
2. Experimental details The experiments were performed in a horizontal ho! wall reactor, which has double-tube strttctur¢, ¢olllposed of alumina and mullite tube l',~r outer and inner hide, I"~slX'clively. The depositiotl apparatus and tile letllrr~ratut~ pixy-
196
tt.-S, Kim. IL-.L Chni / lltin St,lid l'ilm.~ ~312 ~ i~,~),S'l It)5-2t11
file have been reported in a previous work [13]. Different from the previous work, three deposition posilions in a same batch, each separated by 3.54 cm. ~.ere chosen in] the ga~: flow direction, or denoted as S I, $2. $3. (Hereafter, we refer to each deposition position as S l, $2. $3 in this study.) $2 h~,s nmximum temperatt, re in the reactor, but the difference of temperature between S I and $2 or $2 and $3, was within 10 K for whole deposition temperatures, Isotropic graphite that has similar thermal expansion coefficient to that of SiC was used as a :;ubstrate in order to promote adhesion between deposit and substrate. The graphite susceptor was tilted at about 10° for the dimint,lion of reactant depletion. MTS (methyltrichlomsihme: CH~SiCI 3) was used as a source prect, rsor because its equivalent ralio of Si to C resulted in the easy deposition of stoichiometric fihns. Hydrogen was uscd as a carrier gas, which transfers source precursor through the bubbler to reactor. Hydrogen or Argon was used as a dilution gas, which regulates the concentration of the mixture involving MTS vapor and a carrier gas (H~). Thus. hydrogen was simultaneously used as a carrier gas and a dilution gas in this study. However. Argon was used only as a dilution gas. Dilution gas and carrier gas containing MTS vapor were mixed each other before introduction the reactor. The flow rate of MTS vapor was controlled by adjusting the bubbler presst, re and the flow rate of the carrier gas (H,). The tcmrerature of the bubbler containing liquid MTS was maintained at 273 K. The pressure in the reactor was monitored with a capacitance manometer and controlled with a throttle valve located between the reactor and the mechanical pump. The deposition conditions were as follows, Deposition temperature ranged from 1273 to 1573 K and total pressure from 1.3 to 10.0 kPa. The flow rate of MTS and carrier gas (H .,) were fixed at 100 seem. respectively. The flow rate of dilution gas (H., or At) changed from 0 to 900 seem. The crystalline phase and the preferred orientation were characterized by means of an X-ray diffractometer (XRD). In order to analyze the microstructure of as-deposited films. :vc u:,ed a sc:ummg electro.u microscopy (SEM). The deposition rates w~.re obtained from the weighl gain of as-deposited films dtvlded by substrate area and time. The possible errors for these acquired all data of the deposition rates were within approximately 3c~.
08 -e 1523 K - "--. 1473 ,- ¥ 1423 .~"
r~
O.. 1373
08
• .
.
.
.
.
.
+ -~1323
~ ~111
o
g ~ 04 '.,~
&"
- .............
"~"O-~
................. + ................ X ..........
'O
+ ......................... • X .......................
.IX
no $1
$2
$3
D e p o s i t i o n position
Fig. I Variation of dcpo.~ition n.h: with delm.,,ilion lcillpcralure a|ld dcposilion .~ilc ( l'u, , = 1.3 kPa, H ,:M']'S = 3:1 ).
deposition rate at each deposition position is shown it] Fig. 2, TIle extent of decrease of the deposition rate with increasing the total pressure ill the gas flow direction is not as large as that with deposition temperature, especially ranging from 4.0 to 0.7 kPa, However, if deposition rate of each deposition position [S I and $3] was examined with various pressures on the basis of 1.3 kPa, we could see the tendency that the gradient of deposition rate over deposition position between S I and $3 is sliglltly larger with increasing the total pressure. Therefore, it is considered thai the reactant depletion also tends to become larger with increasing total pressure, This tendency is consistent with other study [12]. The phenomenon that the curves were crossing was observed in Fig. 2. This result is considered as l'ollmvs. The incremm~ts of deposition rate at S I position with increasing the total pressure are lower than those 08
..- = -.10.0 kP3 I ~7
'~ , , \ "\-
i " " 6.7 k P , I & .... 4.0 kPa I Iv=1.3 kPa I
E O5
3. Results and discussion Fig. i shows the deper~dence of deposition rate on the temperature and position,~ in pure t-I 2 atmosphere. The result reveals that the reactant depletion, that is. the decrease of the deposition rate in the gas flow direction, hegins at 1373 K and b,~comes larger with increasing temperature. This result i,,; similar to the previously reported work [I,3]. At the deposition temperature of 1.573 K in pure H: atmosphere, the effect of total pressure on the
Q
03
$1
$2 Deposition position
$3
Fig, 2. I)epcndcnu¢ uf depusitilm rate on I1~lal I~re,~surc and delmxilion silo (711q. :: 1573 K. II ,:MTS 3:1).
I!.-S. Kim, D.-J. C l i o / / T h i n Solid ~.i/ms .¢12 f I*.~*)h'~ 1~)5 ~201
with increasing the deposition temperature. Also. the temperature of 1573 K where all the total pressure experiments were performed, was the largest effect of reactant depletion in out-experimental temperature range. With increasing total pressure, the lower increments of deposition rate could not compensate for the increasing effect of ,'eactant depletion. Thus, it may result in the lact that the curves were crossing. Silicon carbide fi!ms with MTS p,'ecursor m'e deposited through the following three steps [ I I, 12,14]. First, MTS precursor decomposes into St-containing species. C-containing species, and CI-conmining byproducts such as HCI. Second, several species of the above mentioned are 'adsorbed onto subs|rate. Third, adsorbed species react with each other, and then result in the formation of SiC. Accordingly, it is important to consider the amount ol" decomposition from MTS precursor and generation ol" HCI that decreases the deposition rate during overall reactions [i I, 15]. Also in the hot wall reactor MTS precursor may begin to decompose irate several species from the moment it passes thnmgh the inlet el" the re=~ctor before it reaches the maximunl temperature region, Thus, it is necessary to consider the residence time of gaseous species in the reactor, P~q~asouliotis mid Sotirchos [16] proposed that a longer n'sidcnce time of gaseous species le;.lds to the decrease of the deposition rate. As the temperature is raised, MTS precurst)r is activated to decompose into several species, resulting in the increase of concentratioqs of the species participating in reactions and byproducts like HCI :l:, well. Tsai et ai. [12] proposed that the larger reactant depletion with increasing total pressurc is attributed to the correlationship he|wee| concentnitions and the residence time of several species. Therefore tl~e signil'icm~t factors for determining reuctant depletion may he considered as the amount of decomposition from MTS precursor, HCI generation, and the residence time. In orde," to observe the variation of the reactant depletion with the gas ambient, we introduce Ar instead ol'H~ as a dilution gas. In the nlixed At' and H ~ zitmospherc, the effect of the temperature ~,n the deposition .'ate at each positil)i] i,~ ~htiwn in Fig. 3. The result shows thai reactant tlcplt, liiiil i~egill.,, at 1473 K. and b¢conles ntuch weaker ill colnp:.ii'ison wilh the i~ui't' 1-I> atnlosphere (Fi~,. 1)especially rallgin{2 fl't)lll 1373 to t523 K. Also above I473 K, the deposition nlic,~ of all tlel~OSition positions ~ll'C higher when Ar is used as the dilution ~as in Ci)lnparison with H ~. Sut~sCtluenlly for further study we intend It) ob.~ervc what kind of difference hclwecn the put¢ H: and the mixed Ar and H, ~lln~ospherc at'feels ihu reaclanl depletion hy varying the 17ow rale of o~ich dlhllion g~is. At deposition ieniperalul'c, of 142.t K, the el'fecis of the addition of each dilution gas (H, and Ar) on the doposiiilin rate ;.it each deposition position are shown in Figs. 4 and 5, respectively, There is ,lil ~cue,'al h?lld¢,lc)' Io I~c SOCll with respect to the addition for each diluiiol~ 7as. However. it should be noted thai reactant dcpletioil is still sccn in ihc pure H, alln~)sphcl'¢, but Oll iI~c t'otllrary, not niuch ollset'ved in the
197
"i-15r3K 1523 K || ....... 1473 K |
08
~v-.. 1423 K I ~ . - 1373KI , I .
.
.
.
.
.
.
.
.
.
.
+
............ ~ l , . , . . .
.1323K
I
•
--x-- 1273 K |
A
.c_ 0.6 E
I
04 I • ..................
&
V
V .......................
& 0 t"l
02
................
•+. .
.
.
.
.
.
.
.
.
.
.
.
X ................
•
+ . . . . . . . . . . . . . . . . . . . . .
+
X .......................
X
oo $1
$2 Depositon position
$3
[:i,.'~. 3. V;triation ~1 deposition ra,e with del~o.,,ilion tell|l~raltl~ and del}t~silitwi si,e ( I~,,, = 1.3 kP;L. Ar:H .:MTS = 2:1:1 ).
mixed Ar and H .. irrespective of the addition of dilution gas, That is. even though there is a variation of total flow rate with the addition of each dilution g.as. the kinds of dilution gas determine whether reactant depletion is present or not. These results may imply that the residence time, which is inversely proportional to the total flow rate, has little influ<'i, e ~,) the reactant depletion when different kinds of dilution gases are used. On the other hand, since Ar is intrinsically inactive with chemical species relati,,e to H~, the gaseous decomposition from MTS and HCI generation may be lower in Ar than in H,, Gaskel[ [17] reports that at 1000 K and 101.3 kPa. the density of Ar is higher
o 35
- • --
0 sccrn
......• .... 200 A ~ 400 ---~ .... 600 ,--i.-- 900
o 30 " ......
sccm sccm sccrn sccm
g :-:~,g 020
\ ~
~-~
°
....................
015
O'EO
$1
$2
$3
Deposition position
Iqu, 4, I)cp~v, ili~m rate o! SK" 17hu~ ,~bt~iined at dil'i~'ren, ;iddi,i,~|~,, ¢~t t i , i|lld dcpo,,iiioit po~,iti~l)', (1:I,.i, ::: 1423 K. l~t,,~ = |.3 kl)~l).
H.-3'. Kim, D.-.I. Clmi / 71fin So/i,i /"i/ms 312 ( 19982 195-+201
198
0
-
F-
35
I 0 30 A ,r"
0 sccm
20(; sccm ....a..... 400 sccm __.._: _ 600 s c c m -- 900 sccm
]
£
.•
025
C~
g
g
020 "
o
....... ZL-J
of (220) phme is increased, but thai o f ( l I I) phme decreased with increasing total pressure. On the contrary, at 8;2 and S3 positions, the X-ray peak of (111) plane is rather increased with increasing total pressure. As-deposited SiC films have been able to grow into either t i l l ] or [220] preferred orientation with processing conditions [ 1,2,13,19]. Lee [2{)] proposes that for FCC crystals, lower concentration lending to lower deposition rate results in the development of the lowest surface energy, or{l I I} plane. In the same way, higher depo:;ition rate caused by higher concentraticm results in the development o1" higher surface energy, or { ! 10} phme. Above 6.7 kPa, it is considered that
015 41,.................... -~"'~'~,~
010
t)t
$1
$2
M1)
(t~)
10.0
kPa
$3
Deposition position
Fig. 5. l)cpt}sition rale of SiC" I'ihn~ ol',t;fined ;it different iIddilion~ uf Ar :.rod deposition positions (71k.i, = 1423 K. P.,, = 1.3 kl'a).
than that of H 2 by a factor of about 20, but the viscosity of Ar is lower than that ol' H, by a factor of about 2.6. In ,'el+erence to above result, our calculation indicates that bound:try layer thickness on the surface of substratc ++hen Ar flux is added, is rrll.lch lower than when t-I +, is added l+m• whole deposition conditions in this study, it ++ considered that the thinner ihe boundary layer thickness, the larger the transport ot" reactant species across the boundary layer, and then resulting in a diminution of reactant depletion. Also this thinner botmdary layer thickness affects the competitive deposition mechanism between surf'ace reaction and mass transport controlled region [18]. That is, the thinner boundary layer thickness is favorable for the SiC film deposition at higher temperatures where mass tnmsport is predominant. Thus. when two dilution gases (H_~ and Ar) are introduced above 1473 K. the higher deposition rate in the presence of Ar may be associated with the botmdary I~,yer thickness. Therefore, we reach the conclusion that the diminution of reactant depletion in the mixed Ar and H~ atrnosphere relative to the pure H_, may be due to the suppression o1' gaseous decomposition l'rom MTS and FICI generation ahmg with the reduction oi boundary layer thickness. At deposition tempentture of 1573 K, the rest, Its of X-ray diffraction analysis as a function of Iota[ pressure +lr+d deposition position are shown in Fig. 6a, b and c. Sh~ce all of existent X+ray peaks, i.e., those of (!11), (22(}), (31 I), (200), and (222) planes, are identical with SiC o1" FCC (face centered cubic) structure, we can aflirnl thtlt deposits prirnarily consist of polycrystalliP.e ~-SiC films. Below the total pressure or' 6.7 kPa. the I'ilms preferentially grow into ( I I I) phme. irrespective of deposition pusitions. However. above 6.7 kPa. it is interesting t h a t the preferred orientation becomes changed at each deposition position. That is. at S i position, the X-ray peak
t
6.7 kPa
li
1.3 kPa i.
I
,m |
•
m ......
i
i
Go -
i
?o ....
(b) [
Bo
i
10.0 kPa
~
i;,
. )
t-
!
.ed
~.~..
v
¢-
6.7 kPa
. . . . . . . . . . . . . . . . . .
,..............
1,3 kPa
+!
¢...
30
40
SO
60
70
•
•
i
+
(c) 1 .... ~ ~.
~_.~. . . . . . . . .
++,0 k + . _ , ..................................
J
~ ......
~_
6.7 kPa :=
l
1.3 kPa I _+,..
++
...............................................................
,'0
+
+
,'0
00
20 I:itz. b, Varkttion oI' XRI) imtlcm>, ,fl ~i(' fihn', dcpo,,itcd at 15Z+ K ~t~ a [Uq,l..'lil~.ll td totul prc~,nttrc tmtl deponilhm l~onhiml ill ,'.MT,S = 3:1): (u)
t t . - X Kim. I)...I. ( ' h . i / 77+it~ ,~+llid I"ilm.~ .+ I 2 ~ IU'A'O 19.~ +2r;l i
t
(111)
o .graphtte substrale
(a) i
(220)
(311)(222)
of) ¢-. O3
r..
O
ao
I
I
t
I
40
+0
+0
70
.0
20 Fig. 7, X R I ) patterns of Sit' l'llmS depu.qtetf ttl 1423 K with p.'ls mnt+ient (l~,,t = 1.3 kPa, Ih~w rate of dilute gas = 200 su'~:lU, ilov,' rate of c.'uTier p;is = 1()0 scorn, l]ow rate of M I ' S = I(XI ,,,ccm, $2 i+osilit;rl): (+.t) !1 ,. (b) At',
the increase of deposition rate at S I position is favoral+~te for the development of {220} phme r,'llller than that of {111} plane. However, at $2 and $3 positions associated with reactant depletion, lower deposition rates in ¢ompm'i-
son with that of SI position result in the development of {I 1I} plane, Accordingly tl~e variation of preferred orientation at eauh deposition position ~,~,illl increasing lotal pressure may be caused by reactant depletion el'feel, or the difference of the deposition rate with deposition position, Also. these results that reactant depletion leads to the ctw,nge of the prefcn'ed orientation of SiC films, were ceml'irmed by previously reported study with tile vuriation of lemperature [13]. At tile deposition temperature of 1423 K and deposition position of $2, tile results of X-ray diffraction almlysis with each dilution gas ambient ix shown in Fig. 7a and h. [Even if X R D pauel'ns of films are only shown at deposition position of $2, those of I'ilms grown at other positions, or S I and $3. with each gas ambient are similm" to $2. "1his result indicates that both films, obtained at differem ,gas ambient, primarily consist of polycrystalline /J-SiC mid have similar XRD patterns. As a result, cl'utr~Lcteristics of films where tile efl'e,,.'l of reactant depletion is less or not. are composed o1 relatively homogeneous crystalline phases with deposition position and not ~reatly ¢lmnged by the difference of ~zas ambient. Consequently the larger reactant depiction car= lead tO the elmnge of prel+erred orientation of SiC t'ihus in the gas flow direction. t:i,g, g shows surlilce morphohmies+, tit" SiC films at different total pressures mid dei+osJtion positions, At the tolal pressure of !.3 kPa. surf;tee mtlrphohl,gies are tmi-
(a)
(b)
i/
190
:::...
Fig. 8. ('ompm'ison of surlaee morl~hology with total pressure ,rod ,k'D~,~ithmD~ilmi~ (1~1~p = 1573 K, I! ,,'MTS = 3:1 ): ~l,ll I..~ I. Pa, tb) i0,O kPa.
21}11
It.-S. Kim, D..J. Choi /Thin Snlid Films 312 (1998) 195-201
(a)
(b)
Fig. 9. Surface morphology of SiC tihns obtained .'tl 1423 K wilh gas ambient and deposition position ( l],,t = t,3 kPa, Ilow rate of dilute gas = 2(11)seem, t3ow rate of carrier gas = 100 seem. Iqow rate of MTS = I00 seem): (a) H ,. (b) At'.
formly maintained at whole deposition positions, and only the sizes of faceted crystallites become reduced i,1 a gas flow direction. However. at the total pressure of 10.O kPa, surface morphologies tire greatly changed with deposition position. That is, with approaching downstream, the tourfold symmetry filceted structure is rnore distinctively developed. This result is considereu as iollows. At S I purllion, the competition among adsorbed species may le~d to facet structure composed of fine crystallite. Otherwise, at $3 position where reactant concentration becomes lower in comparison with S I, the relatively reduced competition may results in the larger four-fold symmetry facet crystalline by TPRE (Twin phme reentrant edge) mechanism [19.21]. Subsequently, these morphological changes with deposition position may be due to reactant depletion that becomes larger with increasing total pressure. At deposition temperature or" 1423 K, the dependence ot" surface morphology on each gas atmosphere of the mixed Ar and H, and the pure H, is shown in Fig. 9. From the results, as we expect, the difference of surface morphology with deposition position is seen neither in Ar nor H,. Only in the pure H, atmosphere, grain size is slightly decreased in thc gas Ilow direction similar to Fig. 8a. However, there is little decrease of crystalline size in the mixed Ar and H, ! atmosphere because of relatively uni.'orm deposition rate.
Consequently, since the larger reactant depletion affects the preferred orientation and surlkice morphology of films with deposition position, it is most desirable that reactant depletion should he minimized tbr uniform characteristics of films. 4. Conclusion The reactant depletion that is encountered in a horizontal hot-wall CVD reactor, has a large impact on deposition rate. preferred orientation, and surface morphology of deposited films. The effect of the reactant deplelion becomes larger with increasing dci~osilJon temperature and tottll pressure. However, its effect can be diminished by introducing Ar instead of H: as a dilulion gas. Important factors for determining reactant depletion, are thought to be the amount o1" decomposition. HC! generation, and the residence time along with boundary hlyer thickness. As the effect of reactant depletion becomes larger, preferred orientation of SiC films changes t'rom [220] to [111] and surthce morphologies of those also greatly convert in a gas tlow direction. On the contrary, with the diminution of reactant depletion, SiC I'ilms have uniform preferred orientation of t i l l ] and surf;ice morphologies at all derJosJtion positions.
H.-S. Kim, D.-.I. Choi /"l'hh~ Solid b'ih~s 312 ¢1998} 195-201
References [I] J, Schliehling, Powder Met. Int. 12 (1981)) 141. [2] J. Schlichting, Powder Mei. int. 12 (1080) 196. [3] S. Sfimiya, Y. hlomatlt, Silicon C~lrbide Ceramics-I Fundamentals alld Solid Reaction. Elsevier, Amsterdam, |091. [4] D.P. Stinton, T.M. Besmarm, R,A. lain'den, Ceram, Bull, 67 (1988) MO. [5] W.R. Haigis, M.A. Pickering, Mater, Design 14 (1093) 130. [6l J.R. O'cormor, J, Smihens, Silicon Carbi~e a High Temperature Serniconductor, Pergamon, 1960. [7] R.F. Bunshah. Handbook of Oeposilion Technologies for Films and Coatings, Noyes Pul~lic:ltions, 1994. [8] M. Ohring, The Materials Scien~;e of Thin Films. Academic Press, 1992. [9] F.C. Eversteyn, P.J.W. Severin, C.H.J.v.d. Brekel. H.L. Peek. J. Electrochem. Soc. t 17 (1970) 025. [10] S.B. Desu. S.R. Kalidindi. JplL J. Appl. Phys. 29 (1990) 13111.
201
[! I] T.M, Beslllal|ll. B.W, Sheldon, T,S. Moss Ill. M.D, Kaster, j. Am, Ceram, Soc, 75 (1992) 2899, [12] C.Y. Tsai, S.B, i)esu, C,C, Chiu, J. Muter, Res. t)(1994} I{M, [13] DJ. Kim, DJ, Choi, Y.W, Kim, Thin Solid Films 2(16 (19951 192, [14] C,C. Chiu, S,B. Desu, Z J, Chen, C,Y, Tsai, J. Mater. Res. t) (1994) [15] D. Lespiaux. F, I,~.lnghtis, R, Naslaill, S, Sehanlnl, J, Se~,'ely, J, Ear, Ceram. Sty. 15 (1995) 81, [16] G.D. Papasotdiolis, S.V, Sotirchos, J. Electrt~:hent. So¢. 14..2(10951 3834. [I 7] D.R. Gaskcl|, An Introduction to Transport Phenornena in Materials Engineering, Macmillan, London, 1992, [18] H.S. Kim, D.J, Choi. J. Ain. Ccraln. See., subnlJlled. [19] D.J. Cheng. W.J. Shyy. D.ii. Kuo, M.tl. Hen. J. Electroeheftt. Sty. 134 (1087) 3145. [20] D.N. Lee, J. Mater. Sci, 24 (1989} 4375. [21] D.R. Hamilton. R.G. Seidenslicker, J, Appl. Phys, 31 (ILJf0J I 1(~5,