Diffusion of Au and Cu in a Temperature Gradient

Abstract

Measurements have been made of relative marker movements in Au and Cu in the presence of temperature gradients of the order of 1200°K/cm. These experiments yielded results which indicate that a net vacancy current is established in these metals under appropriate experimental conditions. The magnitude and direction of the observed effects are consistent with kinetic theory predictions in conjunction with previously determined vacancy energies. A three-dimensional extension of existing kinetic theory is developed and important factors which do not appear in one-dimensional treatments are discussed. Porosity development in Cu was found under certain conditions and this may be a visual demonstration of the existence of a thermal diffusion effect in Cu.

Molecular-dynamics calculation of the vacancy heat of transport

“…Finally, we comment on the negative value of Q Ã v reported in experiment for Cu. 18,21 We note that the measured value of Q Ã v À h f v is negative, but of the same general magnitude as those predicted using simulation here and in Refs. 8 and 9.…”

“…8 and 9 agree qualitatively with experiment for Au. [21][22][23] In particular, for the case of Au, the value of Q Ã v À h f v is found to be negative in both experiment and simulation. However, the magnitude of the values predicted by simulation is significantly different from what is found in experiment.…”

“…8 and 9, we use the computed value for h fv at T ¼ 0 using the Cherns potential. 12 For the experimental results, we use the reported values for [21][22][23] and h fv . 17,18 We find that for the case of Au at T $ 1100 K, the results in Table V all predict a positive value for Q Ã v , and hence experiment and simulation are at least in qualitative agreement.…”

Thermomigration of Cu–Sn and Ni–Sn intermetallic compounds during electromigration in Pb-free SnAg solder joints

“…In the present study, the Cu atoms diffuse to the cold end in solder joints, which is inconsistent with the results for thermomigration on pure Cu. 25 The results in Bumps 1 and 4 indicate that the voids appear in the chip side, which is the hot end. This finding implies that the thermomigration flux for Cu overwhelms that of Sn.…”

Diffusion under temperature gradient: A phase-field model study

“…Examples of the thermomigration effect can be found in literature published over the past 5 decades. [2][3][4][5][6][7][8][9][10][11][12][13][14] There are two important parameters in the thermomigra-tion study: the mobility or diffusivity of atoms present, and their heat of transport ͑Q i ‫ء‬ ͒ that is related to the amount of heat carried per atom of species i. 3 In general, the value of Q i ‫ء‬ is the contribution of the flux of species i to the flux of heat, and determines the affinity of a species toward the cold or hot end.…”