Assuming representative values of Z* = -10, Q* = 10 kJ/mol, je = 1 X 10^10 A/m², ρ = 1 X 10^-7 Ω-m, T= l000 K and dT/dx = lO^7 K/m, does electromigration or thermomigration dominate?

Question

Assuming representative values of [latex]Z\ast =-10,Q∗=10 kJ/mol, j_{e}=1×10^{10} A/m^{2},\rho=1×10^{-7}\Omega-m,T=1000K[/latex] and [latex]dT/dx = 10^{7} K/m[/latex], does electromigration or thermomigration dominate?

Accepted Answer

Substituting in Eq. 9-6 we have

[latex]\frac{J_{e}}{J_{th}}=\frac{-10×1.6×10^{-19}×1×10^{-7}×1×10^{10}×6.62×10^{23}}{-\left( 10,000/100 \right)×10^{7}}=9.6[/latex].

[latex]\frac{J_{e}}{J_{th}}=\frac{Z\ast q\rho j_{e}}{-\left( Q\ast IT \right)dT/dx}[/latex] (9-6)

(Note that to make units match, Avogadro's number must be included in the numerator.) This calculation suggests that electromigration dominates thermo-transport.

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. Transfer of metal at contacts changes the alloy composition and generally raises [latex]R_c[/latex].

Question 9.1: Assuming representative values of Z* = -10, Q* = 10 kJ/mol, ...

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