Question 9.1: Assuming representative values of Z* = -10, Q* = 10 kJ/mol, ...
Assuming representative values of Z^* = -10, Q^* = 10 kJ/mol, j_e = 1 × 10^{10} A/m^2 , ρ= 1 × 10^{-7} Ω-m, T = 1000 K, and \ dT/dx = 10^7 K/m , does electromigration or thermomigration dominate?
Substituting in Eqn (9.8) we have:
\frac {J_{e}}{J_{th}}=\frac{Z^*q \rho j_{e}}{-(Q^{*}/T)dT/dx} 9.8
\frac{J_{e}}{J_{th}}=\frac{-10 \times 1.6 \times 10^{-19} \times 1 \times 10^{-7}\times 1 \times 10^{10}\times 6.02\times 10^{23}}{-(10,000/1000)\times10^7}=9.6(Note that to make units match, Avogadro’s number must be included in the numerator.) This calculation suggests that electromigration dominates thermotransport. Without knowing the temperature distributions and material constants in a contact it is sometimes easier to make measurements. This was done by Runde et al. [5], who deposited minute quantities of radioactive zinc on one of two aluminum contact electrodes. A buildup of Zn observed on the counter electrode, consistent with the current polarity, demonstrated that electromigration had occurred. The transfer of metal at contacts changes the alloy composition and generally raises R_{c}