The parameter set for the diffusion of oxygen in silicon contains the pair of points (ln(D), 1/T) with values (-28.42, 6.0 × 10^-4) and (-34.54, 8.0 × 10^-4). What is the activation energy in eV?

Question

Quizplus · Accepted Answer

The activation energy (Ea) can be calculated using the Arrhenius equation in the form of ln(D) = ln(D0) - Ea/(kT), where D is the diffusion coefficient, D0 is a pre-exponential factor, Ea is the activation energy, k is the Boltzmann constant (8.617 x 10^-5 eV/K), and T is the temperature in Kelvin. Given two points (ln(D1), 1/T1) and (ln(D2), 1/T2), the slope of the line connecting them in a ln(D) vs. 1/T plot is -Ea/k. Thus, Ea = -slope * k.Calculating the slope: slope = (ln(D2) - ln(D1)) / (1/T2 - 1/T1) = (-34.54 + 28.42) / (8.0 x 10^-4 - 6.0 x 10^-4) = -6.12 / 2.0 x 10^-4 = -30600.Therefore, Ea = -(-30600) * 8.617 x 10^-5 eV/K = 2.64 eV.

The Parameter Set for the Diffusion of Oxygen in Silicon