Discussion Forum

Recently I've been working Comsol's semiconductor module, trying to model the drift-diffusion equations with an external electric field term. There's no way to add an external electric field node to the semi node, but on looking around further in the documentation I noticed a promising expression under

Semiconductor Module > Introduction > The Semiconductor Module Physics Interface Guide

where an image shows an added term in the electric potential expression, due to a band gap narrowing effect. By default the expression reads (for electrons)

E_c = - ( V + \chi_0),

Where E_c corresponds to the potential function for the electric field in the drift diffusion equations. But with bandgap narrowing the expression becomes

E_c = - ( V + \chi_0) - \alpha * \delta E_g

where \alpha and \delta E_g can be user defined. This is ostensibly quite similar to adding an external electric field term, albeit via a scalar potential.

Now the question is, need the user definition for the term \alpha * \delta E_g be a constant? Most any physical situation requires the electric potential to vary in space, and it's not apparent to me that the band gap narrowing functionality can handle this (unfortunately, I don't know as much semiconductor physics/Comsol as I'd like to). Further, this approach seems like a hack of Comsol's semiconductor module, i.e., an unintended use of of it's functionality, and may not be workable or advisable for good results.

I am curious to know if anyone can weigh in on this approach, or even the problem in general. Anyone else tried solving the semiconductor drift diffusion equations with an external electric field?