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

• B
• Robotduck
In summary: However, if one is interested in potential energy, the ##E-\vec k## relationship can be represented in terms of the electron energy (PE). In other words, the wave vector change associated with a transition from one energy state to another is what determines the difference between the two energies, which we call the kinetic energy and the potential energy. "In summary, the concept of K.E. and P.E. in a semiconductor is explained. The difference between the higher energy state and Ec is Kinetic energy.
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.

"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 = (kx ,ky ,kz ). 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

bhobba
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.

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

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. ?

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.

Last edited:
Robotduck

## 1. What is an energy band diagram?

An energy band diagram is a graph that shows the energy levels of electrons in a material, typically a semiconductor. It illustrates the relationship between the kinetic energy (K.E.) and potential energy (P.E.) of electrons within the material.

## 2. How is the K.E. and P.E. of an electron represented in an energy band diagram?

The K.E. of an electron is represented by its position on the y-axis, with higher energy levels located higher on the graph. The P.E. of an electron is represented by the slope of the energy bands, with steeper slopes indicating a larger energy gap between bands.

## 3. What is the significance of the energy band diagram in semiconductors?

The energy band diagram is important for understanding the behavior of electrons in semiconductors. It helps to explain how electrons move and interact with each other in the material, and how this affects the electrical properties of the semiconductor.

## 4. How does the energy band diagram change with temperature?

As temperature increases, the energy bands in a semiconductor become wider and more closely spaced. This is because higher temperatures cause more electrons to have enough energy to jump to higher energy levels, resulting in a larger range of possible energy levels.

## 5. What factors can affect the K.E. and P.E. of electrons in a semiconductor?

The K.E. and P.E. of electrons in a semiconductor can be influenced by external factors such as temperature, electric fields, and impurities in the material. Additionally, the composition and structure of the semiconductor itself can also impact the energy levels of electrons.

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