Diffusion in Copper and Copper Alloys. Part I. Volume and Surface Self-Diffusion in Copper
Cite as: Journal of Physical and Chemical Reference Data 2, 643 (1973); https://doi.org/10.1063/1.3253129 Published Online: 29 October 2009
Daniel B. Butrymowicz, John R. Manning, and Michael E. Read
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© 1973 The U. S. Secretary of Commerce on behalf of the United States. Diffusion in Copper and Copper Alloys
Part I. Volume and Surface Self-Diffusion in Copper
DanielB. Butrymowicz:, John R. Manning, and Michael E. Read
Institute for Materials Research, National Bureau of Standards, Washington, D. C. 20234
A survey, comparison, and critical analysis is presented of data compiled fr.om t~e sci~nt~c literature concerning copper self-di1fusion. Topics include volume diffusion, dislocat1o~ PI~ diffus~on, surface diffusion, sintering, electromigration, thermomigration, pressure effect on diffuSlO~, st~am~nhanced diffusion nuclear magnetic resonance measurements of solid state diffusion and diffUSion m molten copper. An extensive bibliography is presented along with ligures, tabular presentation of data, and discussion of results.
Key words: Copper; diffusion; electromigration; liquid copper diliusion; nuclear m~e~lC resoulW"". and diffusion; pressure effects on diffusion; self-diffusion; sintering; surface diffUSiOn; thermo migration.
Contents present purposes to review this subject in several pa~ts. Copper self-diffusion is treated in this first part. AttentIon Page is focused on copper diffusion itself, rather than on forma 1. Introduction______643 tion and annealing of crystal defects. Also, emphasis is on 2. CU"'-)CU (Volume Diffusion)______645 the direct experiwt;uLal n~:;ult:;, with diffusion theory heing 2.1. High Temperature Range______645 discussed only where it aids in selecting among conflicting 2.2. Low Temperature Range-Possible Cur- data or in predicting and interpreting experimental results. vature in log D vs T-l PIoL______647 The primary quantities of interest for diffusion are the 3. Dislocation Pipe Diffusion______648 diffusion coefficient, D, and the activation energy for 4. Surface Diffusion______649 diffusion, Q. The diffusion coefficient is defined hy the 5. Copper Sintering______650 equation 6. J£lectromigration______651 7. Thermomigration______652 J= -D«(Jc/iJx), (1) 8. Pressure Effects______652 where iJc/ iJx is the concentration gradient of the diffusing 9. Strain-Enhanced Diffusion ____ ------__ -.:. - 652 species along a direcLiull (:Ii) uf illten~5t and the diffusion 10. Nuclear Magnetic Resonance Measurements of flux, ], is the amount of diffusing species crossing unit area Diffusion_ ------__ - -_ 652 normal to the x-axis per unit time. D itself is a constant of n. Molten Copper______652 proportionality and usually is expressed in units of cm2js. 12. References ______- ______- ______653 Experimentally, D is usually found to depend exponentially on temperature according to an Arrhenius type equation, 1. Introduction D-Du exp ( Q/RT). (2) Copper and copper alloys are important commercial Thus, a straight line is usually obtained when log D is materials which often are used at temperatures where dif plotted as a function of T-l. Here T is the absolute tem fusion proce:SSe5 :strongly affect their properties. Signi£.c~nt perature, Do and Q are experimentally mea:;un::u cun::;Lants changes in mechanical and electrical properties can occur which can be determined from the intercept and the slope through surface alloying, compositional changes at inter of that line, and R is the universal gas constant (1.987 faces, and interface degradation resulting directly from cal K-I mol-l = 8.314 J. K-I·mol-l). diffusion. Many metallurgical processes such as creep, The quantity Q in eq (2) is usually found expressed in precipitation, ageing, and corrosion are diffusion-limited. the literature in units of kcal/mol, or in units of kcal Other important diffusion effects include homogenization alone (with the mole understood). Usually Q can be deter of alloys, electromigration effects on copper components mined to only two or three significant figures and has a in electrical circuits, diffusional breakdown of protective value between 10,000 and 100,000 cal/mol. Thus, when films, permeability of thin-walled tubing, and diffusion Q is expressed directly in terms of cal/mol, as is sometimes bonding. found in the literature, the las t few zeros before the decimal Because of the strong practical and scientific interest are not significant figures. A second type of unit for Qfre in diffusion involving copper and its alloys, references to quently found in the literature is the electron volt or elec this topic in the literature are very numerous. In view of tron volt per atom. When this unit is reported, it is under the large body of data to be reported, it is convenient for stood that R in eq (2) is replaced by Boltzmann's constant 23 5 Coprri!;ht © 1973 by the U.s. Secretary of Commerce OD behalf of the UDit~ States. '!?ia k (equal to 1.3806X10- J·K-l or 8.617X10- eV·K-I). copyright wiII be assigned to tho American Institute of Physico and the Ameneon Chemlcal 3oGl~lY. lQ ",,",buUl .u X"''iU~ll$ .~4\,"!i.uts ."'p.v-d.~~\.i.Qn o'b.-ould.1x> o..d.d..::OGQ.od.. One fundamental distinction which can be made between
643 J. Ph.ys. Chem. Ref. D
1 Numbers in brackets indicate the literature references. in eq (3) and (V)F is the atom drift velocity from driving
J. Phys. Chern. Ref. Data, Vol. 2, No.3, 1973 DIFFUSION IN COPPER AND COPPER ALLOYS 645
forces. In general, mainly with purified copper-67 tracer (62.2 hour half-life) and with the diffusion temperatures measured to ± 1°C. (5) In view of the cal-dul sedal secLiuning amI counting techniques used; these results are probably very accurate. where F is the physical driving force exerted on individual The scatter in these data yields a very small statistical un diffusing atoms and 1/1 is a. numerical factor dependent on certainty in the activation energy, Q= SO.S±0.2 kcal 1 lattice geometry and the atom jump frequency ratios. For mol- =2.19±0.0l eV. self-diffusion, 1/1 equals the correlation factor, f, for self The other data shown in figure 1 agree very well with diffusion. For volume diffusion by a vacancy mechanism that of Rothman and Peterson in the high temperature in a face-centered cubic crystal, as found for copper, the range (870 to 1060 °C). Below 870°C a small discrepancy correlation factor equals 0.781S. For volume self-diffusion begins to appear which grows to more than 20 percent via divacancies, f equals 0.458. below 750 °C. The results of Kuper, Letaw, Slifkin, Sonder, Equation (S) is frequently used in determinations of and Tomizuka [12] are in very good agreement with those surface diffusion coefficients. When this is done, the of Beyeler and Adda [13, 14], but atthe lower temperatures surface forces, F, customarily are evaluated independently both of these results show D values which are appreciably and the correlation factor, f, is assumed equal to unity. larger than those of Rothman and Peterson. The measure Since it is believed that surface diffusion occurs mainly by ments by Kuper et al. and by Beyeler and Adda were done motion of adatoms across the surface, this value of f for on single crystals by serial-sectioning, radioactive-tracer surface diffusion appears reasonable. methods similar to those of Rothman and Peterson the When the force in eq (5) arises from an electric field E, ~nly indicated difference being that the tracer copp~r-64 as in electromigration, (12.8 hour half-life) was used. Since the difference in isotope used should not greatly affect the results, the dis F=q*E, (6) crepancyat temperatures below 7S0 °C still is not explained. where q* is called the effective charge of the diffusing Rothman and Peterson [11, IS] diffused copper-64 and entity. When the force arises from a temperature gradient copper-67 simultaneously into the same specimen in order aTI ax, as in thermomigration, one can define . to obtain isotope effect measurements. Measurements were made at five different temperatures in the range 894 to -Q**1/I aT F=-- (7) 1061 °C. They found less than a 2 percent difference in Tax' diffusion coefficient, (D64 -D67 )ID64 =0.OlSS±0.0007 with no systematic dependence on temperature. In separate where Q** is the meas)1red heat of transport. Writing eq diffusion experiments using copper-64 at 702 and 786°C, (7) in this form with 1/1 included in the expression for F where effects from diffusion along short-circuiting fa~t !H·.tnally provides a simplification in reporting experimental diffusion path:;; or fww Lhe :;hUI-L half-life of Lhe copl'er-G4 results, since then 1/1 does not enter into the determination tracer might be especially important, their· results from of Q** from measurements of (V)F' However, the basic copper-64 were S or 10 percent larger than their copper-67 atomic heat of transport, Q*, equal to the ratio of the heat results, which were determined from longer-duration flux to the atom flux, does not equal Q** but instead diffusion runs. This difference is larger than the It percent equals Q**1/I. effect obtained in the conventional isotope effect experi. In determining (V)F and hence F, investigators may ments reported above but still does not equal the dis mea:mre; a pwfile di:;placemcnt dill;!"ctly 01, EO!- se1f·Jilfusion, crepancy between the Rothman-Peterson diffusion coeffi may determine the velocity of a marker on a specimen cient values and those measured by other investigators at surface. The latter approach assumes that the marker these temperatures. velocity results from volume diffusion of atoms across the It way be noteu thaL Lhe activatiun euelgy and pl-e marker plane, with the apparent marker motion being in a exponential factor for the Arrhenius equation that fit the direction opposite to the atom flux. data of Kuper et aI. (Q=47.I2±0.33 kcal/mol, Do=0.20± 0.03 l'.m2/p', T=68!l-106~ or.) aerM Tflmarhhly wflllwith 2. CU*-tCu (Volume Diffusion) those values that fit the data of Beyeler and Adda (Q = 46.9 2.1. High Temperature Range kcal/mol, Do=O.lS cm'l./s, T=650--990 °C). Nevertheless, errors which affect diffusion measurements more frequently Self-diffusion in copper bas been measured by many result in measured D values that are too high rather than different investigators. A selection from the more recent too low, especially at lower temperatures. Thus, when two and apparently most reliable data is presented in figure 1. sets of data appear equally self-consistent, those reporting In thie figure, tho solid lino represents tho equa.tion, lhtl !Swalle!: uilIul:!ioIl ljutl!Itdeuts art; wure frequently D=0.78 exp (-SO.5 kcal mol-l/RT) cm2/s, correct. In the present case, the Arrhenius equation given by Rothman and Peterson probably is the best choice to whil'lh iF, 1J1loted by Rothman lInd PeteTF,On [11] as pro deF,l'.Tihe volnmp. rliffuF,ion in thfl range 700 to 1060 °C. viding the best least squares fit to their data, measured in As part of a broad investigation of diffusion in copper the temperature range 700 to 1060 °C. The experiments of nickel-zinc alloys, Anusavice and DeHoff (161 measured Rothman and Peterson were done on copper single crystals diffusion of copper-67 tracer in pure polycrystalline copper
J. Phys. Chern. Ref. Data, Vol. 2, No.3, 1973 646 BUTRYMOWICZ, MANNING, AND READ
TEMPERATURE (Oe) 1000 950 900 850 800 750 700 650
o Rothman and Peterson • Monma et al o Beyeler and Addo • Kuper et 01 ...... ell ...... X Anusavice and DeHoff (\J E 10-9 ~ I- Z LLJ (3 u.. u.. w a (,) z 10-10 a (fl ::::> u.. u.. Ci I I..L. ...I W (fl
a::: 10-11 w «(.) a::: I- • o 10-12 .....--'---_-'- ___--'" ____ '-- ___-'- ___-'- ___--'- __--' 7.5 8.0 8.5 9.0 9.5 10.0 10.5
FIGURE 1. Copper self diffusion in solid copper above 650°C.
The solid libe;" tbat fitting the data of Rothman and PetersoD (Ill with Q =50.5 kcal/mol aDd D. =0.78 .",'/••
in the temperature range 740 to 1045 °C by serial-sectioning and always with copper-64 as the tracer. The D values from techniques. The measurements below 850 °C yielded these measurements often have differed by factors of two diffusion coefficients which were approximately midway or more from those shown in figure· 1. These results are between those measured by Kuper et al. and by Rothman not shown on figure 1 but instead are summarized below; and Peterson (see fig. I). Similarly, the activation energy The first copper tracer measurements were reported in quoted by the authors had an intermediate value (48.3 1939 by Rollin [18], who used serial sectioning to measure kcal/mol) compared to the above investigations. At the diffusion of a 0.1 mm thick surface layer made radioactivtl highest temperatures, the diffusion coefficients measured by deuteron bombardment of a cylindrical block of copper. by Anusavice and DeHoff were actually smaller than those Soon thereafter, measurements were also reported by of Rothmun und Peterson, hut the average agreement Steisman, Shockley, and Nix [19] and by Raynor, is good. Thomassen, and Rouse [20]. These investigators deter Tracer-sectioning measurements by Monma, Suto, and mined D values from the decrease of measured surface Oikawa [17] for copper-64 diffusing in polycrystalline activity resulting from diffusion of copper layers con· copper also agree rather well with the data described above, taining copper-64 which had been electroplated on the as shown in figure 1. Since these experiments were done at surface of a copper polycrystal. In all of these sets of data, . high temperatures (863 to 1057 0c) where volume diffusion D values at only three temperatures were measured so that occurs easily, it is reasonable that fast diffusion along the activation energies were not well established. TheD meas· grain boundaries would not appreciably affect the results. urements of Raynor, Thomassen, and Rouse were con A number of other tracer measurements of self-diffusion sistently a factor of 2 or 3 higher than those shown in ill cuppt:c allSu havt: bt:t:n ma.dt:, mUlStly UIl pulYljJ:YISLab figun: 1. Dy IjOntlast, those of Rollin were lower than those
J. Phys. Chem. Ref. Data, Vol. 2, No.3, 1973 DIFFUSION IN COPPER AND COPPER ALLOYS 647 in figure 1 by a factor of 2 except at the highest temperature. divacancies is 25 percent at 1060 °C and decreases to 6 The results of Steigman, Shockley, and Nix provided a percent at 700°C. These temperatures are at the two ends of range of possible values at each temperature of ±25 to the temperature range covered by Rothman and Peterson. 40 percent but did include the figure 1 values within this It may be noted that the activation energy Qm calculated range. Maier and Nelson [21] in 1942 carried out a more for monovacancies is almost 3 kcal/mol smaller than the thorough investigation using both polycrystal and single overall value Q=50.5 kcal/mol measured by Rothman and crystal copper specimens. The serial sectioning analysis Peterson. The majority of this difference results from technique was followed. The resulting D's in all cases were inclusion of the divacancy term in the above equation. larger than those shown in figure 1 usually by about 50 The temperature dependence from the P/2 factors, which percent. All this early work appears lacking in accuracy arise from assuming temperature dependent entropy terms, and self-consistency compared with the more recent work is equivalent to that from an increase in activation energy shown in figure 1 and should be considered as superseded. of about 1 kcal/mol when applied to the temperature range Recent work by Kucera and Million [22, 23] using copper of Rothman and Peterson's data. polycrystals (mean grain size 2.3 mm) and a residual If one extrapolates high temperature measurements of activity method of measurement also yielded D values diffusion coefficients to estimate diffusion coefficients at noticeably hisher than siven by the solid line in fiSUre 1, lower temperatures, the equation above which includes the difference being about 20 percent over their entire divacancy contributions will yield significantly higher D* range from 800 to 1040 °C. values than will the single Arrhenius equation given by Mercer and co-workers [24] reported a series of experi Rothman and Peterson. This occurs because the dominant ments in which a copper aHoy foil was sandwiched between term at lower temperatures, associated with monovacancy two bulk specimens of pure copper. The alloying con diffusion, is governed by the smaller activation energy, stituent (either zinc, silver, cadmium, or cobalt) and the Qm =47.7 kcal/mol. For extrapolation purposes, accurate copper in the foil, which both had been rendered radio calculations of divacancy contributions at high tempera active by a reactor-radiation prior to formation of the tures may be important. couple, diffused symmetrically into the two bulk copper Wynblatt [28] performed a divacancy analysis which specimens and diffusion coefficients were calculated from was similar to, but somewhat simpler than, that of Mehrer the resulting Gaussian penetration profiles. The alloying and Seeger, since he did not include a temperature de (less than 1% impurity) present in these experiments at pendence in the activation entropy or enthalpy. Wynblatt the original foil position and the resulting chemical con applied his equations not only to the experimental values centration gradient in this region would cause deviations of Rothman and Peterson but also to those of Kuper et al. from pure self-diffusion. Nevertheless, values of D*eu [121 and Beyeler and Adda [13]. He found that the results which agree well with those shown in figure 1 were obtained for comparative activation energies and Do values for by this approach, with Q=49.56±0.30 kcal/mol and Do= monovacancies and divacancies depended strongly on which 0.62±0.025 cm2/s being quoted by Mercer as summarizing set of experimental data was used, and he concluded that these results for the temperature range 854 to 1066 °C. these statistical analyses provided only an insensitive
means of determining Qd-:-Qm and Ddo/D mo• The presence 2.2. Low Temperature Range-Possible Curvature in of large uncertainties in the values of the divacancy param log D vs 1-1 Plot. eters as calculated by Mehrer and Seeger has also been emphasized by Burton and Froozan [29], who in addition Mehrer and Seeger [25-27] have analyzed the tempera propose a different type of statistical analysis. ture dependence of the copper tracer self-diffusion coeffi To check these theories, only limited experimental results cients measured by Rothman and Peterson [11]. They find are available. Recent preliminary tracer measurements by that there if! a f!light npwRril CllTvRtuTe in R plot of these Lam and Rothman [::SU] in the temperature range 340 to values on a log D versus T-l plot, and they interpret this 380°C indicate values similar to those predicted by Mehrer curvature as arising partly from divacancies becoming and Seeger (within ±40%). These experimental results more important at the higher temperatures and partly from are 2 to 1, tim.et; ltlrger than thoBe predicted from Btraight a temperature dependence in the enthalpy and entropy of line extrapolation of Rothman and Peterson's high tem activation. Thus, in the usual case where the divacancy perature results and at the lowest temperatures are a binding energy, &.B, is less than the energy of formation factor of 2 smaller than might have been predicted from of monovacancies, the ratio of divacancies to mono extrapolation of the high temperature results of Kuper vacancies Increases with temperature. Mehrer and Seeger's et al. or Beyeler and Adda. calculations yield for self-diffusion in copper MortIock [31] used a chemical micro-sectioning tech D*=D'11IoTl/2 exp (-QrrJkT)+DdOTl/2 exp (-Qd/kT), nique to remove very thin layers (averaging 400 A in thickness) after tracer self-diffusion in pure copper for 5 where subscript m refers to monovacancies and subscript d hours at 523 °C. When the fraction of radioactivity remain to divacancies with Q".=2.07 eV-17.7 koal mol-I, Dmo- ing in the specimen wrus plotted as a function of the cumula 5.77XIo-a cm2s-IK-l/2, Qd=2.58 eV =59.4 kcal mol-I, tive thickness of specimen removed, three distinct diffusion 2 1 Ddo =161.5XIO-3 cm s- K-l/2, and E2.B=0.12 eV. regions were found within 1 p,m of the free surface, with With this interpretation, the portion of D* arising from the apparent diffusion coefficient being larger for the
J. Phys. Chem. Ref. Data, Vol. 2, No.3, 1973 648 BUTRYMOWICZ, MANNING, AND READ regions farther into the specimen. No diffusion coefficients based on measurements of germanium diffusion in cop were quoted, however.2 per. He again suggests that copper is a slow-diffuser in Estimates of the low temperature volume self-diffusion dislocation pipes and estimates that AdDd~1O-16 coefficients in copper also have been obtained by Bowden exp (-1.53 eV /kT) cm4s-1 in the temperature range and Balluffi [32] from the rate. of shrinkage of voids T~210 to 350 DC, where Ad is the dislocation pipe area 2 measured by transmission electron microscopy in quenched (taken here to be 2.5XIQ--15 cm ) and Dd is the diffusion pure copper specimens. Their measurements were done in coefficient in this area. At these temperatures, expressed the temperature range 390 to 560°C, and in general agree in terms of T/Tm where Tm is the melting point of the with extrapolation of the high temperature tracer self metal under consideration, these estimated values of AdDd diffusion measurements in pure copper, but with large in copper are two or more orders of magnitude smaller possible errors. The results lie above the extrapolation of than comparable measured values for aluminum self an Arrhenius line based on Q=50.5 kcal mol-1 as measured diffusion. ' by Rothman and Peterson [11] but lie in the general range of extrapolation of lines based on either Q= 47 ±0.1 4. Surface Diffusion kcal mol-1 determined by Kuper et al. [12] and Beyeler and Adda [13] or Q=47.7 kcal mol-1 determined by Mehrer The diffusion coefficients and activation energies re and Seeger [25] for the monovacancy term in their re ported in the literature for copper surface self-diffusion analysis of Rothman and Peterson's data. often are in serious disagreement. Reported activation In summary, the low temperature measurements of energies differ by a factor of two or more, with the D values volume self-diffusion in copper all seem to lie appreciably themselves sometimes differing by two orders of magnitude. above extrapolations of the straight line shown on figure l. Two main factors seem to be the sources of this disagree As discussed earlier, this line is believed to represent the ment. (1) The measured surface diffusion values depend most reliable data for diffusion at high temperatures (above strongly on the atmosphere in which diffusion takes place. 700°C). Analysis of the possible curvature which should, Diffusion occurs much more readily in an oxygen atmos appear in this line leads one to expect D* values at lower phere or in vacuum than in a hydrogen atmosphere. This temperatures (around 400°C) which are higher by approxi effect probably arises from the influence that S1Irface im mately a factor of two than the straight line extrapolation.3 purities can have on the diffusion process. Oxygen may remove the inhibiting effect of impurities or possibly may form complexes which actively aid diffusion. (2) At high 3. Dislocation Pipe Diffusion temperatures (above say 970 DC), an additional diffusion mechanism with higher activation energy appears to con Bowden and Balluffi [32] compared the shrinkage rate of tribute significantly to. surface diffusion. Measurements voids in pure copper which were connected to a free surface which Include higher temperature points tend to report by a dislocation to the shrinkage rate of voids which were higher activation energies. not so connected. Even at their lowest annealing tempera Most surface diffusion measurements have been made ture of 390°C, they found no effect from the dislocation. by ob::!erving the change::! that ::!urfnee diffusion cnUOCG in They concluded that the dislocation pipe diffusion coeffi surface topography. Here the tendency to minimize surface cient at 390 DC must be less than 4X 10-13 cm2/s, assuming energy provides the driving force for diffusion, as in grain a pipe radius of five ato~ic distances. From comparison boundary grooving experiments or in the topographically with similar measurements on aluminum crystals, Bowden opposite phenomenon of thermal smoothing of surface and Balluffi concluded that dislocation pipe diffusion features, such as scratches introduced on the surfaces. is slower relative to bulk· diffusion in copper than in Gjostein [34] and Bonzel and Gjostein [35:"'37] made a aluminum. . number of measurements of thermal smoothing of surface As part of a general review of fast diffusion down disloca scratches on copper using laser diffraction and inter tions in fcc metals, Balluffi [33] estimated values of self ferometric techniques. They conclude that the measure ili1fUSiOll ill the fast difful:iioll regiolls (the "dislocatioll ments most characteristic of true sqrface diffusiuu are pipes") near dislocations in pure copper. His estimate was those for a near vacuum with a slight oxygen atmosphere, assuming that the oxygen acts to remove impurities which
Z In a more recent publication [Mortlock, A. 1., and Price, D. M., uMeasurement of inhibit diffusion. In the temperatur'e range 500--960 DC, Lattice Diffusion in Copper at Relatively Low Temperatures," Metall. Trans. 4, 363-364 their data, which were obtained from measurements on (1973)], Mortlock and Price report similar measurements on a number of specimens in the temperature range 400 to 526 °e. Mortlock and Price calculate volume diffusion (nO) surfaces, can be represented by [9, 10] coefficients from the middle region and obtain results somewhat higher than extrapolations of the high temperature results. Diffusion coefficient values for Region~ I and III also D8~0.26 exp (-20.7 kcal mol-1/RT) cm2/s. were estimated. 3 Additional tracer-sectioning measurements of copper self-diffusion at low tempera From 1000 DC to the melting point (1083 0C), a much tures (301 to 632 °C) have recently been reported by Maier, Bassani, and Schiile. [Maier, K.~ uSelf-Diffusion in Copper between 630 and 300 oC," Thesis, University of Stuttgart, larger activation energy (approximately 63 kcal/mol) was (1973); Maier, K., Bassani, C., and SchUle, W., uSelf~Dif£usjon in Copper between 359 found, with D. at the melting point extrapolated to be and 632°C," Phys. Lett. (in press)]. Very thin sections were obtained by sputtering 4 2 techniques. Diffusion coefficients measured at' twelve different temperatures between about 5XlO- cm /s. (See figure 2.) 392 and 632 ·C agreed witbin :1:10 percent witb tbe equation of Mebrer and Seeger. Six In their hydrogen atmosphere measurements, Bonzel other meaSurements at lower temperatures showed higher D* values than those predicted 4 by Mehrer and Seeger. and Gjostein found lower D. values, ranging from 10-
J. Phys. Chem. Ref. Data, Vol. 2, No.3, 1973 DIFFUSION IN COPPER AND COPPER ALLOYS 649
TEMPERATURE (OC) 1000 900 800 700 600 500 lo-3~-+----~----~---r--~----T-~-----'----~---r------~--~ S 6 Oxygen Atmosphere (P~ = 5 x 10-5 Torr) J 4 --+--Brodshow et 01 E o Vacuum (P < 10-6 Torr) - 2 --0-- Bonzel and Gjostein Ih o • Bradshaw et 01 Hydrogen Atmosphere (PH = 760 Torr) 2 o Gjostein • Bradshaw et al Collins and SheY/mon ~ 4 I W o o 2 z o (i) 10-5 ~ 8 olL 6 I 4 lL ..J W CJ) 2 w «o u. 10-6 ~ General range of ~ 8 CJ) 6 Ds measurements in Hz atmosphere ffi 4 a.. a.. o o z
loqL------~------~------~~------~ ______~ ______~ __ ~ 7 6 II 12 13
FIGURE 2. Surface diffusion of copper on copper. Because of the scatter of the data, only a general range is indicated for surface diffusion in a hydrogen atmosphere and only selectrA example< of hydrogen-atmosphere data (which indicates typical trenda over appreciable temperature ranges) are shown. The data of CoUins snd Shewmon are indicated ItS covering a range of values at each temperature since these results showed a sigw ni6cant dependence on crystallographic surface orientation. In the ranges displayed here~ both the largest and smallest '\1alucs measured by Co-Uins and SheWJllOD at each temperature have been omitted. Since "a Do value of 0.15 cm'/s provides better agreement with the oxygen l:lUllu~phclt; .J cm2/s at 1030 °C to 10-7 cm2/s at 660°C. By contrast, surface profiles. An apparent decrease in DB by a factor of their oxygen atmosphere value of D. at uuO °C hi 5XIO-ll two was Msociated with the onset of fal'.p.ting. cm2/s. Below 660°C, surface diffusion in a hydrogen Bradshaw, Brandon, and Wheeler [38] relying mainly atmosphere decreased drastically so that it could no longer on grain boundary grooving experiments also studied the he measured. The lower temperature me:3Rl1rp.mp.ntfl (hp.low effect of various atmospheres on copper surface self SOO DC) showed a strong dependence on the duration of diffusion. The measured diffusion coefficients agree only the diffusion anneal. Bonzel and Gjostein suggest that an roughly with those of Bonzel and Gjostein but do show a accumulation of impurities may be decreasing the measured regular decrease as oxygen was removed and then hydrogen Da at the longer diffusion times and note that an extra added in the atmosphere. Their Q value!; Wt;lC all in the polation to zero diffusion time yields more consistent range from 17 to 22 kcal/mol. Their D. values at 660°C results. This correction also yields D. values which lie are listed in table 1. Although their hydrogen atmosphere within the hatched region in figure 2 rather Lhau value:; Q values arc slightly larger than their oxygen atmosphere an order of magnitude smaller. At temperatures below and vacuum-pressure values, all are noticeably less than 910 DC, faceting was observed on the supposedly sinusoidal the 40 or 50 kcal/mol which other investigators have J. Phys. Chem. Ref. Data, Vol. 2, No.3, 1973 650 BUTRYMOWICZ, MANNING, AND READ TABLE 1. Surface self-diffusion parameters on copper (after smoothing of chemically etched periodic profiles on copper Bradshaw et al.) surfaces at 890 to 1015 °C in hydrogen atmospheres. They Pressure D.(at 660 "C) report that their results were probably appreciably affected Atmosphere (torr) (cm2/s) by volume diffusion but for surface diffusion find an activa tion energy of 27 kcal/mol, about half that for volume ... B .;J , 760 1X10- diffusion. Bonzel and Gjostein [50] noted that a driving ,...,5 X 10-6 3XlO:-B force which was too large by exactly a factor of two was v~~.... ~ ",1 X10-7 6 3 X 10- introduced into the results reported in reference (481. O";'unpn 5X10-6 8 X 10-6 '0 As a result, the diffusion coefficients quoted in that refer ence should be multiplied by a factor of two. found for copper surface diffusion in a hydrogen Other less-extensive measurements of copper surface atmosphere. self· diffusion. by means of grain boundary grooving tech r.ollim Hn£l Shewmon [~q] found that in a hydrogen niques have been reported by Mullins and Shewmon [51], atmosphere introduction of H2S would increase D. for Gjostein and Rhines [52], and Hough [53] and by means copper by a factor of 2 to 4. Their measurements, done by of healing of surface defects by Geguzin and Ovcharenko grain boundary grooving in the temperature range 830 to [54] and Menzel [55]. These results are generally within 1030 °C, included results for eight different crystallographic the experimental error of results reported above. surface orientations. They found that changing the surface Rhead and coworkers [56-58] during surface diffusion orientation typically could cause a factor of 2 difference in introduced (as a vapor) small amounts of impurities, such the measured D s values. This orientation dependence is as lead, which can form copper alloys or compounds having similar to that found earlier by Choi and Shewmon [40-42]. lower melting points than pure copper. This appreciably In the range 850--1060 °C, Choi and Shewmon measured increased the measured D. for copper, especially at tem D. values for (lll) surfaces which were a factor of 1.5 to 3 peratures above 900°C. Values of D. as high as 10-1 cm2/s larger than those measured for (100) surfaces, with (llO) have been measured in such, cases. These high values measurements having an intermediate value. These meas perhaps result from formation of a quasi-two-dimensional urements showed temperature dependences which would liquid at the surface or perhaps from other cooperative correspond to activation energies of around 40 to 50 phenomena. (For discussions, see references 59-61.) A kcal/mol, nearly the same as for self-diffusion. Such values thorough review of this topic and of other possible impurity are common for Ds measured ina hydrogen atmosphere. effects, which can either decrease or increase D., has been Perraillon, Torrens, and Levy [43J in copper-64 tracer given by Bonzel [10]. measurements of surface diffusion on copper between Melmed et al. (621 employed field electron emission 520 to 600°C found that diffusion occurred 1.5 to 2 times microscopy to study the rate of change of topographic faster on (Ill) planes than on (100) planes and measured features on copper field emission tips. The measurements activation energies on these planes of Q11l =38.3 kcal/mol were in a much lower temperature range (50-171 0c) and Qloo=27.9 kcal/mol. A similar dependence of tracer than those reported above and yielded an activation energy activation energy and of D. on the crystallographic orien for surface diffusion of 13 kcal/mol in this range. Warner tation of the surface plane was also found by Borisov, Gal, [63] made somewhat similar field electron emission meas and Gruzin at higher temperatures, 850 to 975°C [44]. urements but on larger samples than Melmed et aI. and Hackerman and Simpson [45] used radioactive copper-64 in the temperature range 700--1000 °C. Glum [64] suggests tracer to study surface diffusion at 750°C on copper in a that the higher activation energies (25 to 50 kcal/mol) hydrogen atmosphere and found that the rate depended found by Warner can reasonably be attributed to impurity not only on the plane exposed but also on diffusion direc effects. Neumann and Hirschwald [65] emphasize that the tion. Their measured dependence on diffusion plane was diffusion mechanism and hence the measured Q. values almost the reverse of that found in other investigations should be expected to depend on the temperature range. reported above. Also, their 'measured diffusion anisotropy Bowden and Balluffi [32] measured the annealing of on (100) surface planes is surprising since, theoretically, voids which intersected a copper surface at temperatures diffusion on Hat (100) surface planes should be isotropic between 254 and 408°C. The results were in general because of the four-fold symmetry. Some lower temperature agreement with an extrapolation of high temperature results studies (450 and 600°C) by Brandon and Bradshaw [46] obtained by other investigators in hydrogen atmospheres. on the smoothing of steps which were evaporated onto Nichols [66] evaluated D. by studying the coalescence copper surfaces showed an appreciable change in apparent of two gas-filled bubbles in the interior of a copper specimen D. values as the steps moved from one grain to another. at 900 ac. His result of D.=1.4XI0-' cm2/s obtained by In discussing their similar tracer measurements, Choi and this method agrees well with measurements from grain Shewmon [421 suggested that vapor transport may have boundaTY grooving and scratch smoothing experiments. contributed greatly to Hackerman and Simpson's results. PUl:il:ilLltl dftlt:LI:i of VulUllll:: ,1UTul:iluu U11 lhtlllUul grooving 5. Copper Sinrering experiments have been discussed by McAllister and Cutler [47]. Sintering of copper particles or wires has been studied Sizmann and co-workers [48, 49] measured the thermal and discussed by a large number of investigators [67-84], J. Phys. Chem. Ref. Data, Vol. 2, No.3, 1973 DIFFUSION IN COPPER AND COPPER ALLOYS 651 z 0 en ::::> I.L. I.L. 10-11 0 , 8 U. ..J I.IJ 6 (J') 4 2. 800 °C 750 QC •0 700 °C 10-12. 0 2. 4 6 8 10 12 PRESSURE (Kbar) FIGURE 3. Dependence of copper volume diffusion in copper on temperature and hydrostatic pressure after Beyeler and Adda [l3, 141. usually being interpreted in terms of volume and surface self-diffusion. With the grain boundary width taken as diffusion processes. Accurate diffusion results are difficult 5XlO-s em, it was estimated that DQ~2 cm2/s. to obtain by this method. Kuczynski f671 reported separate surface diffusion results for temperatures 400, 500, and 6. Electromigration 600 °e as did Kaufman, Whalen, and Sefton [69] at 700 °e. These D. values in general were consistent with the hy Electromigration measurements in pure copper by drogen atmosphere results reported above. BeeH~ and Kharkov and Kuzmenko [85, 86], Sullivan [87], Adda Greenwood [70] from the sintering rate of pores located et al. [88] and Grimme [89] all show migration of copper on grain boundaries in copper containing 1 wt. percent ions toward the anode in the temperature range 800 to oxygen calculated an activation energy Q=32±3 kcal/mol 1030 ce. This corresponds to a negative effective charge in the temperature range 386 to 788 °e for the rate-con for the copper ions and indicates that the electron wind trolling process, assumed to be copper grain boundary momentum transfer to the ions is more important than the J. Phys. Chem. Ref. Data, Vol. 2, No.3, 1973 652 BUTRYMO~ICZ, MANNING, AND READ direct effect of the field on the ion cores. Previous measure value Do=O.lB cmz/s given here and used in figure 3 ments by Wever [90) and Grone [91] indicated a reversal differs slightly from the rounded off value of Do = 0.2 cm2/ s in marker direction measurement at temperatures above published by Beyeler [14]. The value of 0.18 cm2/s was 950 or 1000 °C, but it now appears that this reversal does selected as giving better agreement with the data. not really occur. Sullivan, from the relative motion of The above values were calculated from experiments on !;cratch~!; 011 copptlr win: :;p~cimelll;, fuuwl I:W dr~t.:Live :;jJJgI~ cry:;tals ufcupper. Similar measurememson poly charge q* of -5.5±1.5 Ie \, where e is the electronic crystalline copper [14, 99] at 900°C with pressures of charge. A similar result, -8±3 1e I, was measured o to 8 kbar gave essentially the same activation volume by Grimme from the motion of surface microindentations as in single crystals. as did rneaf'\uremf>nt~ J:lt 4, khJ:lr and on tubelike copper samples in the temperature range be BOO °C. The only appa,rent difference was that the diffusion tween 800 and 1030 cC. Kharkov and Kuzmenko, like Sulli coefficients themselves were consistently 1 to 5 percent van, made repeated measurements near 1000 "'C but larger in the polycrystalline samples than in the single measured appreciably larger effective charges of 14 I e I crystal samples. to - 38 I e \. Their method involved weighing of specimen halves before and after diffusion. Adda et a1. at tempera 9. Strain-Enhanced Diffusion tut'es of 820 to 860°C measured movement of tungsten markers (foils and wires) and found effective charges of An effect from elastic strain at low temperatures was -15\elto -26\el. reported by Druyvesteyn and' Berghout [l00]. The elec Hummel and Breitling [92, 93] found electromigration trical resistivity of a copper wire which had been quenched of copper ions in thin films of pure copper to be directed from high temperature was measured as a function of time toward the cathode in contrast to the above bulk diffusion at -30 °e. Thc rate at which the excess resistivity (pre results. They attribute this cathode-directed migration as sumably arising from quenched-in vacancies) was found po::;::;ibly being due Lo grain bounuary uiJIu::;iull. to J:lnnNll out inc,reased when the wire was loaded to 17 2 kg/mm , The change in annealing rate would correspond 7. Thermomigration to a change of diffusion coefficient by a factor 1.7 if the annealing were due to diffusion of vacancies. Measurements by Meechan and Lehman [941 yielded values of Q** =4:±:3 kcal mol-1 for measured heats of 10. Nuclear Magnetic Resonance Measurements transport in pure copper, as determined from marker of Diffusion motions iJJ J:I tf>mperatllrf> gradient of the order of 1200° K/cm in the temperature range 900 to 1000 °C. By contrast, El-Hannay and Zamir [l01] from measurements of the Jaffe and Shewmon [95J found an opposite effect, with nuclear relaxation times TI and n in copper powder as a copper ions apparently moving from the cold to the hot function of temperature (600 to 1000 0c) deduced values end of their copper specimens in the range 750 to 1000 °C. of Q=1.97±0.04 eV and Do=0.1l±O.05 cm2/s for Their Q** value of -7 kcal mol-1 is somewhat doubtful copper-63 and Q=2.00±0.04 eV and. Do=0.lS±0.07 since they also found a large change in dimension of their cm2/s for copper-65. These activation energies and Do cooling block, which was at temperatures below 750°C. values are in reasonable agreement with tracer results Adda et a!. (SS] found no copper thermomigration effect reported by other investigators for volume diffusion. The in their experiments. JOlctlvation energy rec.ults also axe consistent with previous Mikhlin [96J investigated the migration of pores in a measurements by Flynn, Seymour, and OdIe (102, 103J. temperature gradient and interpreted the results as arising These values, especially the Do values, cannot be expected from atom diffusion along the surface of the pores. to be as accurate as the tracer-sectioning results shown in figure 1. Nevertheless, when direct tracer results are not 8. Pressure Effects available, indirect measurements of diffusion by NMR methods may yield useful results. Beyeler and Adda [13, 14J measured the effect of hydro static pressures up to 10 khar on self-diffusion of copper-64 11. Molten Copper tracer in pure copper. They found that the measured diffusion coefficients in their temperature range of 700 to Self-diffusion coefficients of copper in molten copper 900°C (see figure 3) could be represented hy have been measured by a capillary reservoir method in the temperature range 1140 to 1260 °C by Henderson and D=Do exp- (Qo+P ll.V)/RT], Yang [l04J. A capillary which initially was filled with with Do=O.lS cm2/s, Qo=46.9 kcal/mol and ll.V=6.25 non-radioactive molten copper was immersed in a bath cmo/mol, where T is given in kelvin. Here llV is the ex containing a uniform concentration of radioactive tracer perimentally measured activation volume. To obtain the copper-64 and after diffusion the radioactivity in the capil "true" activation volume, related to the Gibbs free energy, lary was analyzed. The results could be represented by a small correction must be made. Both activation volumes the equation in this case equal approximately 9/10 of an atomic volume. 3 Measurements by McArdle and Tomizuka [97, 98] also D= (1.46:±:0.01) X10- indicate that llV is less than one atomic volume. The exp [-(9710:±:710) cal mol-1/RT] cm2/s. J. Phys. Chern. Ref. Data, Yol. 2, No.3, 1973 DIFFUSION IN COPPER AND COPPER ALLOYS 653 12. References [21] Maier, M. S." and Nelson, H. R., "Self.Diffusion of Copper," Trans. Am. Inst. Min. Metall. Eng. 147, 39-47 (1942) (also [1] Tomizuka, C. T., "Diffusion," in Solid State Physics, edited published as Trans. AIMME Tech. Publ. No. 1419, (1942) by K. 'Lark.Horowitz and V. A. Johnson (AcademIC Press, 13 pp.). New York, 1959) 6, Part A, Chapter 4.5, pp. 364-373. [22] Kucera, J., and Million, B., "Self.Diffusion of Copper in [21 ' Tomizuka, C. T., "Some Experimental Aspects of Diffusion eu.Al Solid Solutions," Met. 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