Why Are Effective Mass and Bands Simplified in Semiconductor Analysis?

[Enialis]

Effective mass and bands in semiconductors

In the study of the basic semiconductor physics devices we usually draw flat bands without taking into account the spatial dependence of them. Now why is it correct? I suppose that the "real band diagram" informations are included into the effective mass term but usually we find on experimental tables only few values. Can someone explain me this?

 

[sokrates]

You have confused a couple of things here.

The spatial band diagrams you see ( they are flat - if there's no electrostatic drop within the device) are in the position space.

They give information about the electrostatics of the device, such as, the depletion region drops, charge neutral parts, the source barrier etc...

It is in REAL space.

The E-k diagrams, on the other hand, which are used for extracting effective masses, are in MOMENTUM space. They are functions of different momenta and subbands.

So you can visualize it this way: At every point of the spatial band diagram, you can put a parabolic E-k diagram and look into what's happening in the E-k diagram.

This is typically done in the analysis of ballistic devices, where the population of negative and positive (momentum) states are nicely decoupled into two sets in real space, coming from two different contacts.

Anyway, so there are TWO types of band diagrams frequently mentioned in the literature, E-k is NOT the flat diagrams you see.