Relaxation time approximation

[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.

 

[charng]

The relaxation time approximation is a commonly used method in semiconductor physics to simplify the analysis of electronic behavior in semiconductors. It assumes that the electronic states in the material are in equilibrium and that the relaxation of the electrons to this equilibrium state is much faster than any changes in the external conditions. This allows for the use of simple equations to describe the electronic properties of the material.

One of the key parameters in the relaxation time approximation is the effective mass, which takes into account the spatial dependence of the bands in semiconductors. This effective mass is a simplification of the more complex band structure, but it still accurately describes the behavior of electrons in the material. The effective mass is also dependent on the material and can vary for different types of semiconductors.

In experimental tables, you may only find a few values for the effective mass because it is typically measured and reported for specific materials and conditions. However, it is important to note that the effective mass can change under different conditions, such as temperature or doping levels. Therefore, it is not a constant value but rather a parameter that can be adjusted to fit the specific conditions of the material being studied.

In conclusion, the relaxation time approximation and effective mass are useful tools in simplifying the analysis of semiconductor behavior. While they may not provide a complete picture of the band structure, they accurately describe the electronic properties of the material under certain conditions. It is important to consider the limitations and variations of these parameters when interpreting experimental data.