How to understand that drifted-diffusion equation in semi-conductors is semi-classical?

Question

I am studying the mathematical models in drifted-diffusion equations and find that drift-diffusion equation belongs to semi-classical models. However, it seems that compared to the Boltzmann equations, all terms in drifted-diffusion equations seem to be "classical". Thus why do we classify it in the category of semi-classical models?

The following is the drifted -diffusion equation:

My understanding is that, drifted-diffusion comes from Boltzmann equations and when we need to solve it, boundary conditions, parameter modeling(e.g., R) is semi-classical. Is this understanding correct?

Answer 1

Those equations are classical, but what about the inputs to those equations? How do you calculate the carrier concentrations? The mobilities?

Semi-classical means you build classical equations on top of a quantum foundation. If you just look at the top of the structure, you'll sometimes only see the classical part. In that case, you need to go another level down to see the quantum part.