Calorimetric Study of the Energetics and Kinetics of Interdiffusion in Cu/Cu 6 Thin Film Diffusion Couples K. F. Dreyer, W. K. Niels, R. R. Chromik, D. Grosman, and E. J. Cotts Department of Physics Binghamton University - State University of New York Binghamton, NY 13902-6016 Abstract - Differential scanning calorimetry was used to characterize the energetics and kinetics of interdiffusion in solder/metal diffusion couples. The heat of formation of Cu 3 from Cu 6 and Cu thin films was found to be H r = 4.3±0.3 kj/mole, similar to the results of previous measurements on bulk samples. We have seen that the nucleation of Cu 3 begins at temperatures near 360 K, but that the nucleation and initial growth of Cu 3 is not a well defined Arrhenius process in these diffusion couples. Later portions of our differential scanning calorimetry scans were identified with diffusion limited growth of Cu 3. From these calorimetry data we have estimated the averaged interdiffusion coefficient, D (cm2 /s) = D o exp(-e/k b T), where k b is Boltzmann s constant and D o = 3.2 x 10-2 cm 2 /s and E = 0.87 ev/atom. BODY As dimensions in electronic packages decrease, the importance of characterizing interdiffusion in solder/metal couples on a submicron length scale increases. 1-12 A number of studies have been performed on interdiffusion in Cu/ and Cu/Pb composites, generally in bulk diffusion couples. 1-4,6 In the present work we investigate the formation of Cu 3 in Cu/Cu 6 thin film multilayers 5 using differential scanning calorimetry. 8-11 The heat of formation of Cu 3, and an estimate of the effective interdiffusion coefficient in Cu 3, are found. In addition, the nucleation of the Cu 3 intermetallic layer is examined. Cu/ multilayer thin film samples were prepared by thermal evaporation in an evacuated chamber with a base pressure of 2 x 10-7 torr prior to evaporation. Alternating layers of Cu and were deposited on a glass slide located approximately 20 cm above the molten evaporants. The glass slide was located on a water, or liquid nitrogen, cooled substrate holder. Deposition rates (approximately 0.8 nm/s) were monitored using a quartz crystal rate monitor. The thin film composites were fabricated with an average stoichiometry of Cu 3, and a Cu/ bilayer thickness of either 29, 42 or 92 nm. (Subsequent references to the bilayer thickness of a composite refer to the Cu/ bilayer thicknesses, even after transformation to a Cu/Cu 6 couple). After deposition, the composites were held at room temperature for at least 24 h to allow the formation of Cu 6. 5 X-ray diffraction analysis, using Cu-Kα radiation in a standard θ-2θ geometry, was performed to ensure that all the layers had been consumed in the formation of Cu 6. The samples were then hermetically sealed in Al pans in a He atmosphere at a pressure of 10 Pa. Each Cu/Cu 6 composite sample was heated in a differential scanning calorimeter (a Perkin-Elmer DSC-2 interfaced to a microcomputer). The samples were heated at a constant rate of 20 K/min from a temperature of 290K to the desired isotherm temperature. For a full heat, the sample was heated at a constant rate to a temperature between 550 and 600 K. All anneals were repeated three times and the data of the third anneal was subtracted from the data of the first for data analysis. The reacted Cu/ composites were characterized by x-ray diffraction analysis.
Heat Flow (W/mol) 10 0-10 -20-30 -40-50 -60 350 400 450 500 550 Temperature (K) Figure 1: The heat-flow as a function of temperature for a constant scan rate of 20 K/min, measured by means of differential scanning calorimetry. The sample was a multilayered, Cu/Cu 6 composite with a 92 nm bilayer thickness and an average stoichiometry of Cu 3 produced by evaporation of the two metals and room temperature annealing. The heat flow versus temperature for a Cu/Cu 6 multilayered composite of 92 nm bilayer thickness is shown in Fig. 1. A significant heat flow signal is first observed at a temperature of approxi mately 360 K. Between temperatures of approximately 380 and 420 K the heat flow signal remains almost constant. The large peak in the heat flow data at a temperature near 440 K corresponds to previous reports of temperatures where Cu 3 was observed by different means to begin to grow in Cu/ diffusion couples. 1-6 X-ray diffraction analysis indicated that the DSC signals observed in Figs. 1-3 correspond to the growth of Cu 3. After these anneals, all peaks observed in x- ray diffraction scans were indexed to the equilibrium Cu 3 phase. In an effort to determine whether the low temperature shoulder on the observed peaks in DSC traces (cf. Figs. 1 and 2) was also associated with the growth of Cu 3, different composites were heated once to a temperature of 425 K and cooled to room temperature. X-ray diffraction analysis of these samples revealed Bragg peaks corresponding to Cu or to Cu 6, with new Bragg peaks indexed to the Cu 3 phase. It was concluded that the heat flow data of Fig. 1, as well as those of numerous other calorimetry scans of Cu/Cu 6 composites over this temperature range, correspond to the growth of Cu 3. We consider the reaction forming Cu 3 from Cu and Cu 6 : 1 20 (Cu + 9Cu) = 1 6 5 4 (Cu ), H 3 r, (1) where H r is the enthalpy per mole of atoms for the reaction. Integration between temperatures of 360 K and 600 K of the observed heat flow signals during full heats resulted in an average value for H r = 4.3 +/-0.3 kj/mol. Using previous observations 13 of the heats of formation from Cu and of bulk Cu 3 and Cu 6, an estimated value, H r,est, can be calculated. These heats of formation were H f (Cu 3 ) = 7.7±0.5 kj/mol and H f (Cu 6 ) = 5.8±0.6 kj/mol, respectively. 13 The estimate yields: H r,est = H f (Cu 3 ) - 0.55 H f (Cu 6 ) = 4.5±0.8 kj/mol, in good agreement with our measured value. An observed variation with heating rate of the heat flow curves indicates that the growth of the Cu 3 phase in these samples is not dictated by simple one dimensional, diffusion limited growth kinetics 6-8,12 until later times in the reactions. In Fig. 2 the heat flow as a function of temperature is displayed for 42 nm bilayer, Cu/Cu 6 composites, each heated at a different rate. For one dimensional growth in a planar geometry the heat flow, dh/dt is directly proportional to the rate of growth, dx/dt, of the Cu 3 layer thickness: dh/dt = A ρ H r /M dx/dt, (2)
where A is the interfacial area in the Cu/Cu 6 composite, and ρ and M are, respectively, the density and molar mass of the growing phase. 9 For diffusion limited growth: dx dt = k2 2x, (3) where x is the thickness of the growing layer, and k 2 is a reaction constant. At a given temperature, k 2 can be related to the averaged interdiffusion coefficient, D : k 2 = 2G β C D, (4) where C is the concentration difference across the growing intermetallic layer, and G β is related to the concentration change across the interfaces. 6-10 Previous simulations, 12 and experimental results, 8-10 of full heat DSC data for diffusion limited growth in planar layers have shown (cf. Eq. 4) that at a given temperature, dh/dt is greater for samples heated at greater rates. For diffusion limited growth (Eq. 4) these DSC traces should never cross each other, in contrast to the data of Fig. 2. This is illustrated for diffusion limited growth in the inset to Fig.2, where DSC traces are simulated for the samples and heating rates of Fig. 2 using a previously determined form for the reaction constant. 2 Figure 2: The heat-flow as a function of temperature for different scan rates, measured by means of differential scanning calorimetry. The samples were 42 nm bilayers prepared similarly to those of Fig. 1. Four different scans are presented, corresponding to heating rates of 10, 20, 40, and 80 K/min. The maximum signal amplitude occurred at higher temperatures for higher scan rates. The results of a simulation of such DSC data are provided for similar samples and heating rates in the inset figure. The simulations assume diffusion limited growth and use the reaction constant of Ref. 2. If nucleation of the Cu 3 phase, and its lateral growth, has not resulted in an essentially planar layer of Cu 3 across the entire Cu/Cu 6 interface, deviations from the one dimensional, diffusion limited growth kinetics of Eq. 3 would be expected. 7-12 In Fig. 3 the heat flow for an isotherm at 430 K is displayed. A vertical line has been added to the plot to indicate the begin ning of the isotherm. The magnitude of the heat flow continued to increase for a significant length of time during the isotherm for this sample, and numerous other samples, in contrast to diffusion limited, or interface controlled, growth kinetics. 7 These observations are con sistent with a continuing formation of the Cu 3 phase along the Cu/Cu 6 interface. At long times during isothermal anneals the heat flow is observed to decrease with time, consis tent with diffusion limited growth kinetics. 7-12 Integration of Eq. 4 with respect to time indi cates that x 2 k 2 = t. Using Eq. 3, we determine values of x 2 from our measurement of the square of the integrated heat flow, H 2. Plots of H 2 as a function of time reveal straight line regions corresponding to the portion of the DSC curves where the magnitude of the heat flow signal is decreasing ( e.g. Fig. 3). From linear fits to these regions we determine values of k 2. In Fig. 4 we plot the logarithm of values of k 2 as a function of inverse temperature. Over the temperature range of our data we observe a linear variation of the logarithm of k 2 with inverse temperature, consistent with thermally activated (Arrhenius) interdiffusion.
Figure 3: The heat-flow as a function of temperature for a constant scan rate of 20 K/min to a temperature of 430 K, follow by an isothermal anneal, measured by means of differential scanning calorimetry. The sample was similar to that of Fig. 1. interdiffusion. From the slope determined from a linear fit to our data, the activation energy was found to be 0.87eV/atom. Also plotted in Fig. 4 are values of k 2 determined from previous, classical measurements 2 of interdiffusion in bulk Cu/Cu 6 diffusion couples at higher tempera tures. Good agreement is found between these two different measurements; the activation energy determined from Onishi s work 2 was 0.82 ev/atom. A linear fit to the combined data sets for the bulk Cu/Cu 6 diffusion couples and for our thin film Cu/Cu 6 diffusion couples is included in Fig. 4, which has a slope corresponding to an activation energy of 0.79 ev/atom. We can also compare these results to a previous measurement 5 of the activation energy of 0.99 ev/atom made by Rutherford Backscat tering on thin films. 5 We calculate values of D from our measured values of k 2 using the equi librium values 1 of C, and G β. We find from our DSC data D (cm2 /s) = D o exp(-e/k b T), where D o = 3.2 x 10-2 cm 2 /s, and E = 0.87 ev/ atom, consistent with previous results. 1-3 Conclusions Figure 4: A plot of the logarithm of the reaction parameter, k 2, versus the inverse temperature multiplied times one thousand. O - Values of k 2 were calculated from plots of the square of the integrated heat flow versus temperature, as outlined in the text. The heat flow was measured by differential scanning calorimetry for 92 nm bilayer composites similar to those of Fig. 1. The data of Fig. 3 was analyzed, as was that of similar samples annealed at lower temperatures. - Values of k 2 obtained from Ref. 2, a previous study of diffusion in bulk samples. Differential scanning calorimetry studies of interdiffusion in Cu/Cu 6 diffusion couples have shown that the driving force for interdiffu sion is similar for both thin film and bulk diffusion couples. We have seen that the nucle ation of Cu 3 begins at temperatures near 360 K, but that the nucleation and initial growth of Cu 3 is not a well defined Arrhenius process in these diffusion couples. At later times we observed diffusion limited growth of Cu 3 at rates consistent with those observed previously in classical diffusion experiments. Acknowledgements We gratefully acknowledge discussions with James Clum and the support of the National Science Foundation, DMR 9202595, and DUE-9452604.
References 1. Z. Mei, A. J. Sunwoo, and J. W. Morris, Metal. Trans. A 23, 857 (1992). 2. M. Onishi and H. Fujibuchi, Trans. JIM 16, 539 (1975). 3. P. T. Vianco, K. L. Erickson, and P. L. Hopkins, J. Elec. Mat. 23, 721 (1994). 4. A. K. Bandyopadhyay and S. K. Sen, J. Appl. Phys. 67, 3681 (1990). 5. K. N. Tu and R. D. Thompson, Acta Met. 30, 947 (1982). 6. The Mechanics of Solder Alloy Interconnects, edited by D. R. Frear, S. N. Burchett, H. S. Mor gan, and J. H. Lau (Van Nostrand Reinhold, New York, 1994). 7. U. Gˆsele and K. N. Tu, J. Appl. Phys. 53, 3252 (1982). 8. D. Grosman and E. J. Cotts, Phys. Rev. B 48, 5579 (1993) 9. E. J. Cotts, Thermal Analysis in Metallurgy, edited by R. D. Shull and A. Joshi (Minerals, Metals and Mining Society; Warrendale, PA; 1992) pp 299-328. 10. B. E. White, M. E. Patt, and E. J. Cotts, Phys. Rev. B 42, 11017 (1990). 11. E. Ma, L. A. Clevenger, and C. V. Thompson, J. Mater. Sci. 7, 1350 (1992). 12. R. J. Highmore, R. E. Somekh, J. E. Evetts, and A. L. Greer, J. Less-Common Met. 140, 353 (1988). 13. O. Kubaschewski and J. A. Catterall, Thermochemical Data of Alloys (Pergammon Press, New York, 1956).