B Energy Band Diagram: K.E. & P.E. of Electron in Semiconductor

[Robotduck]

TL;DR Summary

Potential Energy (P.E.) and Kinetic Energy (K.E.) of an electron

Hi,

Can anyone explain the concept of K.E. and P.E. in a semiconductor?
Why Ec (lower level of Conduction Band) is considered as P.E. ? and why the Difference between the higher energy state and Ec is Kinetic energy ?
I understand it if I look at the Bohr model but I am not clear how to look at P.E. and K.E. in an Energy Band diagram.

Thank you.

 

[Lord Jestocost]

"The band structure of a material is (essentially), a description of the way the total energy of electronic states varies as a function of their quantum number. k = (k_x ,k_y ,k_z ). In other words, the band structure of a material is a statement of the total energy relationship E(k), which is in turn the sum of the kinetic and potential energy contributions."

From: Section W1.4.2 The total energy
[PDF]
The band theory of solids - Understanding the Properties of Matter

 

[Robotduck]

Thank you so much for sharing this document. But it is difficult to understand.
I thought that the electrons in the conduction band are free to move. Free electron energy is considered as Kinetic energy. Then How come the energy of an electron right at Ec is Potential Energy ? I really am having difficulty in understanding this concept.

 

[Lord Jestocost]

In the free electron approximation the potential energy contribution is assumed to be zero.

 

[Robotduck]

I am sorry but I still do not follow this. Please tell me if I am wrong:

" When an electron is excited from Valence band to conduction band, let's say in case of a silicon we provide just Eg to an electron to excite it to Ec. At this state , the energy of an electron is stored as PE. The energy that we provided to an electron so that it can move to Ec is Kinetic energy. Am I right ? and this is given as Ec-Ev ( Ev is the reference)?
Now let's say , the same electron at Ec gets more energy externally to get excited to a higher state E1. so now E1-Ec is the kinetic energy and the electron energy at E1 is the P.E. ?

 

[Lord Jestocost]

When an electron is excited from the valence band to the conduction band, its total energy is changed by $E_C(\vec k_C)-E_V(\vec k_V)$, where $\vec k_V$ and $\vec k_C$ are the wave vectors (crystal momenta) of the electron in its initial valence band state (just before the transition) and in its final conduction band state (just after the transition), respectively. The total energy $E(\vec k)$ is the sum of the kinetic and potential energy contributions.
If one is interested in kinetic energy, one has to represent the $E-\vec k$ relationship in terms of the physical electron momentum.