Linear response theory of the driving forces for electromigration

• Published in: Thin solid films Vol. 25; no. 1; pp. 25 - 35
• Main Authors: Kumar, P., Sorbello, R.S.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 1975
• ISSN: 0040-6090; 1879-2731
• DOI: 10.1016/0040-6090(75)90240-0

Using linear response theory, we have obtained a response function for the force exerted on an impurity in the presence of an electric field. The response function measures the total force including both the local screening of the applied field and the dynamic polarization due to the “electron wind” (the electron-drag effect). Because of low frequency divergences, the response function cannot be evaluated by perturbation theory. We propose a non-perturbative approximation scheme whereby the force response in each order of perturbation theory is taken to be proportional to the electronic current in the next lower order. The constant of proportionality is calculated to lowest order in the density or strength of the scatterers. The summation of these terms for the force response yields expressions for the electron-drag force which, in the appropriate models, agree with the formulas of Huntington, Fiks, Bosvieux and Friedel, and Sorbello. The advantage of the force response function is that it permits calculation for cases which appear difficult to treat with the earlier theories. As an illustration, we analyze the case of surface electromigration within the linear response model.