A Methodology for Obtaining Diffusion Coefficients in a three-phase Ternary Couple : InAs/nickel

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1 Internatonal Journal of Engneerng & Technology IJET-IJENS Vol: 11 No: 05 8 A Methodology for Obtanng Dffuson Coeffcents n a three-phase Ternary Couple : InAs/nckel Sutopo Department of Metallurgy and Materal, Faculty of Engneerng, Unversty of Indonesa Kampus Baru UI Depok, 1644 E-mal: sutopo@metal.u.ac.d Abstract-- A methodology was presented for determnng the nterdffuson coeffcents of phases formed n a ternary dffuson couple usng the measured growth rates and the concentraton profles across the couple. Usng ths methodology the nterdffuson coeffcents of thet-n 3 InAs phase were obtaned from several INAs/nckel couples. Assumng the cross-ntrnsc dffuson coeffcents to be neglgble, relatonshps between ntrnsc dffuson coeffcents were derved and values were obtaned for the three ntrnsc dffuson coeffcents of the T- phase. The ntrnsc dffusvty for nckel was the largest and that for arsenc the smallest. These data ratonalzed n terms of the structure of the T-phase. Index Term-- Coeffcent nterdffuson; Dffuson couples; Intrnsc dffuson; N 3 InAs. 1. INTRODUCTION Two types of composte materals systems have emerged n recent years: layered materals for applcaton n the electroncs ndustry and hgh-temperature composte materals for applcatons prmarly n the aerospace ndustry. Both types of materals are mult-component systems and ther ultmate performance depends on the stabltes at the nterfaces of the layered structural and the structural compostes. In ths paper, we wll focus on nterdffusonal phenomena at the nterfaces, where Professor J. S. Krkaldy has made monumental contrbuton. Snce ntermedate phases often occur n bnary, ternary and hgh-order systems, a knowledge of the formaton and dssoluton of these phases durng the fabrcaton, subsequent annealng and eventual servce treatment of these compostes s essental. A soluton to the growth of a two-phase bnary system was frst proposed by Wagner as gven by Yost [1]. Ths soluton was then extended to three-phase bnary systems by Castleman [] and Kdson [3] Heckel and co-workers [4] and Metn, and Inal [5] among others have appled ths soluton to the growth of mult-phase bnary systems. A general soluton for the layer growth of the ternary system was provded by Krkaldy [6-8]. Ths soluton was appled by Krkaldy and Brown [9] to study the growth of several two-phase copper-znc-tn dffuson couples and recently used by Nesbt and Heckel [10] to study several twophase nckel-chromum-alumnum dffuson couples. It has not been appled to the growth of mult-phase ternary dffuson couples. It s worth notng that Rapp, Ezs and Yurek [11] dd calculate the knetcs of dsplacement reacton Fe + Cu O = Cu + FeO. For electronc materals consstng of metal/semconductor and composte materals consstng of metal/ceramc systems, the phases formed do not normally have large ranges of homogenety. Determnaton of the nterdffuson coeffcent va the Matano-Boltzmann analyss [1,13] s less feasble snce accurate compostonal varatons wthn the sngle-phase regons are ntrnscally dffcult to measure expermentally. A number of experment have been carred out to determne the dffuson coeffcents nvolved metal/semconductor reactons. Jan et. al. [14] has used a method to determne the dffuson coeffcent based on ternary dffuson theory. The methodology used to obtan dffuson coeffcents from nvolved an analyss of the layer growth knetcs and the concentraton gradents wthn the sngle phase regons, f measureable range of homogenety exsts for these phases. Ths method has been used to obtan satsfactory results from the N/GaAs dffuson couples to form N 3 InAs. The N/InAs dffuson couples were expected to behave as the N/GaAs dffuson couples dd. The phase that formed n a ternary dffuson couple are closely lnked to ts correspondng ternary phase dagram: the phase dagrams of the N-Ga-As system [15] and the N-In-As system are qute smlar. Ths would lead one to expect that the N/InAs dffuson couples form a reacton layer of a ternary phase. N 3 InAs just as N/GaAs dffuson couples form the ternary phase N 3 GaAs. Dffuson n N 3 GaAs s thought to occur by an ntersttal mechansme proposed by Hähnel et. al. [16] It s expected that at a gven temperature the growth rate of the N 3 InAs would be larger that of the N 3 GaAs. Because ndum atoms are larger than gallum atoms, the ntersttal space n a N3InAs phase would be larger than those n N 3 GaAs. These two phenomena, the formaton of a sngle N 3 InAs reacton layer and an ncreased growth rate, were observed n ths experment.

2 Internatonal Journal of Engneerng & Technology IJET-IJENS Vol: 11 No: TERNARY DIFFUSION THEORY Fgure 1 shows the concentraton profles for the growth of a β-phase from a ternary α/γ dffuson couple and the correspondng ternary sothermal secton at constant pressure. The wdth of the β-phase layer as a functon of tme s [4-9] w (1), - t - t w.,, Where w β s Thckness of a β-phase growng from a α/γ couple, ξ α,β, s poston of the α/β nterface z s A parameter relatng ξ α,β and t, t s tme, Z β,α s parameter relatng ξ β,γ and t, and W β s a parameter t. The above results can easly be adapted to the growth of an η-phase ternary system [4-9]. It s evdent from Eq. (1) that the growth of a phase β n a sem-nfnte ternary dffuson couple depends on the nterdffuson coeffcents of β and those of α and γ as well as the concentratons at the two nterfaces and the range of homogenety for these phases. It has often been found emprcally that the growth of a phase from a dffuson couple s parabolc wth tme and that the temperature dependence of the parabolc rate constant follows relatng w β,, and z - z Arrhenus behavor. However, there s no clear physcal nterpretaton for the parabolc rate constants and actvaton energes obtaned snce they depend on the propertes not only of the phase nvolved but also those of ts neghborng phases. Havng the value of Ď 1 s and Ď s for all the pertnent phases wth = 1,, the composton at the varous nterface and the ranges of homogenety from accurate phase dagram data, Eq. (1) allow us to calculate the growth of phases n a sem-nfnte ternary dffuson couple. However, as has been mentoned, for many systems of current technologcal nterest such Indum-Metal-Arsenc for electronc materals or for mult-component structural materals, values of Ď 1 s and Ď s are not known. As stated n the ntroducton, we wsh to obtan the nterdffuson coeffcents usng Eq. (1), the growth rates of ntermedate phases and the concentraton profle obtaned expermentally from sem-nfnte ternary InAs/Nckel dffuson couples. t Fg. 1. The relatonshp between the dffuson zone nterface concentratons for a three-phase Ternary dffuson couple at constant temperature snd pressure and the sothermal phase Dagram for ths ternary system 3. EXPERIMENTAL PROCEDURE Semconductor grade, (100)-orented n-type InAs wafers of 400 to 100 μm thckness and 99,99 % purty nckel rod 6 mm n dameter were used for dffuson couples. Wafer was cut nto 4.5 x 4.5 mm peces and the rod was cut out nto.5 mm thck dsks. The contact surface of N, frst ground wth slcon carbde papers # 30, 400, 600, 1000, then polshed wth alumna 1μm, 0.3 μm and 0.05 μm. N and InAs peces were rnsed twce n acetone, cleaned ultrasoncally n hot trchloroethylene for 10 mnutes, rnsed agan n acetone and then cleaned ultrasoncally n de-onzed water for 5 mnutes. The cleaned peces were etched n HCl : H O (1:1) soluton, N peces for 1 mnute and InAs peces for 4 mnutes. Immedately after etchng, N and InAs peces were pressed together wth two 6 mm n dameter quartz rods and sealed n 7 mm nsde dameter quartz tubng under pressure of 10-3 torr. The samples were annealed at temperatures rangng from 450 o C to 600 o C, for dfferent lengths of tme. After annealed, the dffuson couples were removed from the furnace, quenched n ce water. Frst cut was made approxmately 1 cm from both sdes of reacted metal and semconductor and the samples were mounted n epoxy mold wth the cross-secton facng down.. Fnally, as soon as ths epoxy cured, the mddle sectons of the dffuson couples were cut (those whch contaned the N/InAs secton). The standard metallographc grndng and polshng procedures were employed usng slcon carbde grndng papers from # 30 to # 1500 and alumna slurres from 1 μm to 0.05 μm, then metallographcally cross-secton for analyss. Samples were coated wth graphte and examned wth an Appled Research Laboratores SEMQ electron mcroprobe (EPMA), usng wavelength-dspersve spectroscopy (WDS) and employed elemental nckel and commercally produced InAs wafer as standards. 4. RESULTS AND DISCUSSION When InAs and nckel are brought nto contact, a ternary phase wth the nomnal composton N 3 InAs, desgned as T, s formed. N 3 InAs s not a true ternary phase, but a part

3 Internatonal Journal of Engneerng & Technology IJET-IJENS Vol: 11 No: of N sold soluton whch extends to N 3 In. Bulk N/InAs dffuson couples experments were carred out at 450 o C, 500 o C, 550 o C and 600 o C for dfferent perods of tme. The results obtaned at 450 o C, 500 o C, 550 o C and 600 o C are presented n Fg.. In all of these dffuson couples, only the- T-phase formed between the end phase, InAs and nckel. Fg. 3a shows a typcal mcrograph and Fg. 3b EPMA composton profle, whch was taken from N/InAs dffuson couple annealed at 600 o C for 9 hours. Longer annealed tme may cause dsappearance of the N 3 InAs phase. The growth of T n terms of ts thckness, x, as a functon of t s gven n Fg.. Wthn the scatter of the data, x vares lnearly wth t 1/ for all four temperatures, ndcatng dffuson-controlled knetcs. The parabolc growth constants obtaned from Fg are shown n Fg. 4, whch reflects the lnear log(growth constant) versus 1000/T relatonshp. To obtan the dffuson coeffcents of N 3 InAs from ts growth rate and concentraton profles across the dffuson couples we must have the approprate dffuson equatons. In a three phase ternary dffuson couple system made up of component A, B, and C, a typcal concentraton profle mght look lke n Fg. 1. The growth of a three-phase ternary dffuson couple nvolves two nterfaces. At each of these nterface, there are two ndependent mass balance, equatons as gven by equaton () and (3), was a total of four ndependent equatons. Fg. 3a. Photomcrograph backscatterng electron mage. b. EPMA compostonal profle of N/InAs dffuson couple annealed at 600 o C for 9 hours showng the formaton N 3InAs phase. Fg.. The growth rates of T-N3InAs from N/InAs as a functon annealng temperture and tme. Fg. 4. The growth rates of T-N3InAs from N/InAs bulk dffuson couples annealed at 450 o C, 500 o C, 550 o C and 600 o C. For the α/β nterface:

4 Internatonal Journal of Engneerng & Technology IJET-IJENS Vol: 11 No: 05 31,,,, C - C J - J t For the β/γ nterface :,,,,, C - C J - J t () (3) Thus, the equaton at each nterface can be ntegrated wth respect to tme, assumng constant. Ď s to yeld four equatons, two at the α/β boundary 1,, 1,, C - C, 1 K1, -D K -D K D D (4) And two at the β/γ boundary, K, t ntrnsc dffuson coeffcent and nterdffuson coeffcents developed by Darken [17] and alternatve method proposed by Dayananda et. al. [18, 19] and Garmella et. al. {0]. Assumng the cross-term of the dffuson coeffcents to be neglgble, the thee ntrnsc dffuson coeffcents,.e. D 1, D,D 3, are suffcent to descrbe the behavor of a ternary phase. Darken s relatonshp becomes : Ď 11 = D 1 + C 1 (D 3 D 1 ) (7) Ď 1 = C 1 (D 3 - D ) (8) Ď 1 = C ( D 3 - D 1 ) (9) Ď = D + C ( D 3 - D ) (10) Where C 1 and C are concentraton of components 1 and. In ths experment, C 1 and C are assumed to be average concentraton of components 1 and n the N 3 InAs reacton layer. 1 ξ β,γ =, 1,, C - C, 1 K1, -D K -D K D D (5) A ffth equaton s gven by K,,, w - W t (6) t Table I Intrnsk dffuson coeffcents, Ď N, Ď In and Ď As T (oc) Ď N (cm /sec) Ď In (cm /sec) Ď As (cm /sec) x x x x x x x x x x x x 10-9 Q (kj/mol) 117 ± 8 77 ± 8 47 ± Where ξ α,β and ξ β,γ are the nterface postons, Ď 1 s an nterdffuson coeffcent, C 1 s an nterface concentraton, t s annealng tme, w s the wdth of reacton layer, and W s the growth constant. K β,α s a functon of the nterdffuson coeffcents, the concentraton gradents, the concentraton at the surface. As dscussed n secton and presented n Fg. 1, the growth of a three-phase ternary dffuson couple nvolved two nterfaces. At each of these nterfaces, there are two ndependent mass balance equatons, yeldng a total of ndependent equatons. In addton, we have one more equaton,.e. Eq (1) for the growth of a partcular phase β. However, for such a system we have a total 1 nterdffuson coeffcent, Ď s (four Ď s for each of the three phases), and two nterface postons,.e. ξ InAs,T and ξ T,N. In order to solve ths problem, there s a need to reduce the total number of unknown parameters to be determned. In a N/InAs couple, phase A s nckel, phase B s the N3InAs reacted layer, and phase C s InAs. Due to the low solublty of N n InAs and the low solublty of In and As n nckel, dffuson n pure A and C may neglected. Ths reduces the number unknowns to sx: ξ α,β, ξ β,γ, Ď 11, Ď 1, Ď 1, Ď. The number of unknowns may be reduce to fve usng relatons between Fg. 5. Arrhenus plot of Ď N, Ď In and Ď As wth actvaton energes beng 117, 77 and 47 kj/mole respectvely. Although ths methodology can be used to obtaned numercal values for the nterdffusonal cross-terms, t should be noted that ths analyss was performed under the assumpton of neglgble cross-ntrnsc dffuson coeffcents, whch s reasonable for phases wth lmted ranges of homogenety. However, the phase T-N3InAs does possess

5 Internatonal Journal of Engneerng & Technology IJET-IJENS Vol: 11 No: 05 3 are apprecable for range of homogenety, and therefore ths assumpton may be somewhat smplstc. Furthermore, t should be remembered that n performng these calculatons, dffusve fluxes n the nckel and InAs phases were assumed to approach zero. The result values for ntrnsc dffuson coeffcents and nterdffuson coeffcents of T-N 3 InAs are gven n Table I and II and presented n Fg. 5 and 6, respectvely. The results show that nckel s the fastest dffusng speces, ndum the next fastest and arsenc s the slowest. Table II Interdffuson coeffcents,, Ď 11, Ď 1, Ď 1, Ď wth 1 beng N and As (Determne from ntrnsc dffuson coeffcents) T ( o C) Ď 11 Ď 1 Ď 1 Ď x x x x x x x x x x x x x x x x 10-9 Q(kJ/mol) 11 ± ± ± 9 90 ± 8 Fg. 6. Arrhenus plot of Ď 11, Ď 1, Ď 1, Ď wth 1 beng N and As (determned by usng ntrnsc dffusvtes), the actvaton energes are 11, 151, 149 and 90 kj/mol respectvely. 5. CONCLUSION It has been shown that the growth rates of ntermedate phases and expermentally determned concentraton profles across the phases may be used to determne ther nterdffuson coeffcents, whch may n turn be utlzed to calculate the growth of phases n ternary dffuson couple as functon of tme at a gven temperature. Furthermore, the analyss may be used to fnd ntrnsc dffuson coeffcents n each phase, whch may be helpful n developng atomc nterpretatons of dffuson n ths phases. The analyss outlned above was appled the growth of T-N 3 InAs n sem-nfnte, N/InAs dffuson couple to determne dffuson coeffcents. In performng the calculatons, determnaton of the Interdffuson coeffcents for nckel and InAs was neglected and the cross-term dffusvtes for T-N 3 InAs (Ď 1 and Ď 1 ) were assumed to be vanshng small. By assumng cross-ntrnsc dffusonal terms to be neglgble, relatonshp between nterdffuson coeffcents and ntrnsc coeffcents were derved and the ntrnsc dffusvtes of nckel, ndum and arsenc n T- N 3 InAs were determned. The ntrnsc coeffcents were then substtuted nto these relatonshps, yeldng values of nterdffuson coeffcents and cross-nterdffusonal terms. The ntrnsc dffusvty of arsenc was found to be two orders of magntude smaller than that of nckel at 600 o C. REFERENCES [1] W. Jost, Dffuson n Solds, Lquds and Gasses, nd Ed.,Academc Press, New York, (1960), pp [] L. S. Castleman, Layer growth durng nterdffuson n the alumnum uranum alloy system, J. Nucl. Mater., 3 (1) (1961) pp [3] G. V. Kdson, Some aspects of the growth of dffuson layers n bnary systems, J. Nucl. Mater., 3 (1) (1961), pp [4] A. J.. Hckl and R. W. Heckel, Knetcs of phase layer growth durng alumnde coatng of nckel, Metall. Trans., 6A ((3) (1975), pp [5] E. Metn and O. T Inal, Knetcs of layer growth and multphase dffuson n on- ntrded ttanum, Metall. Trans., 0A (9) (1989), pp [6] J. S. Krkaldy, Dffuson n multcomponent metallc systems. I. Phenomennologcal theory for substtutonal sold soluton alloys, Can. J. Phys., 36 (7) (1958), pp [7] J. S. Krkaldy, Dffuson n multcomponent metallc systems. II. Soluton for two-phase systems wth applcatons to transformaton n Steel, Can. J. Phys., 36 (7) (1958), pp [8] J. S. Krkaldy, Dffuson n multcomponent metallc systems. III. The moton of planar phase nterfaces, Can. J. Phys., 36 (3) (1958), pp [9] J. S. Krkaldy and L. C. Brown, Dffuson behavor n ternary multphase systems, Can. Met.Quaterly, (1) (1963), pp [10] J. A. Nesbtt and R. W. Heckel, Interdffuson n N-rch, N-Cr- Al alloy at 1100 and 100 o C Part. I.. Dffuson paths and mcrostructures, Metall. Trans. 18A (1) (1987), pp [11] R. A. Rapp, A. Ezs and J. Yurek, Dsplacement reacton n sold state, Metall. Trans. 4B (5) (1973), pp [1] C. Matano, X-ray studes on dffuson of metals n copper, Jpn. J. Phys., 9 () (1934), pp [13] L. Boltzmann, Zur Integraton der Dffusonsglechung be Varabeln Dffusons-coeffcenten,53 (1894), pp [14] C. H. Jan, D. Swenson, X. y. Zheng, J. C. Ln and Y. A. Chang, On the determnaton of dffuson coeffcent n mult-phase ternary couples. Acta Metallurga et Matera, 39 (3) (1991), pp [15] C. H. Jan, Interfacal Phenomena n the Contact Metallzaton of GaAs wth N- Based Intermetallc Alloys, Ph. D. Thess, Unversty of Wsconsn- Madson, Madson, WI. USA,(1991). [16] R. Hähnell, W. Mekeley and H. Wever, Dffuson studes on the B8 phase of the N/Sb system, Phys. Status Sold A, 97 (1) (1986), pp [17] L. S. Darken, Dffuson of carbon n austente wth a dscontnuty n composton, Trans. AIME, 180 (1949), pp

6 Internatonal Journal of Engneerng & Technology IJET-IJENS Vol: 11 No: [18] M. A. Dayananda and Y. H. Sohn, A new analyss for the determnaton of ternary nterdffuson coeffcents from a sngle dffuson couple, Metall. Trans., 30A (3) (1999), pp K.M. Day, C. R. Ram-Mohan and M. A. Dayananda, Determnaton and assessment of ternary nterdffuson coeffcents from ndvdual dffuson couples, Journal of Phase Equlbra and Dffuson, 6 (6) (005), pp [19] N. Garmella,, H. J. Cho, Y. H. Sohn, Determnaton of Average Ternary Inter- Dffuson Coeffcents Usng Moments of Interdffuson Flux and Concentraton Profles, Defect and Dffuson Forum, ( 010), pp