Semiconductors - Flat band Diagram vs Equilibrium Diagram

In summary, the flatband diagram is a diagram that is drawn when the energy band diagram of the semiconductor is flat, while the equilibrium diagram is a diagram that is drawn when the electrochemical potential (Fermi energy) of the mobile charge carriers is constant throughout the device.
  • #1
Marcin H
306
6

Homework Statement


Screen Shot 2018-04-19 at 2.59.44 PM.png


Homework Equations


Energy band diagram equations.

The Attempt at a Solution


This is more of a conceptual question, but this is the problem I am working on for reference. What is the difference between a flat band diagram and an equilibrium diagram? I know what they will look like by doing some googling, but I don't understand the difference between the two and what one tells us over the other. What are all the differences between them? Is the flatband diagram the diagram as soon as we bring our metal and semiconductor material together. Is that a snapshot of the moment they touch? And is the equilibrium band diagram after diffusion occurs? I am confused by the two in general and don't know what they tell us.

Here is what they will look like from googling:

Screen Shot 2018-04-19 at 3.02.52 PM.png

Screen Shot 2018-04-19 at 3.02.40 PM.png


I also, know how to find ФF, but that doesn't really help much with understanding these diagrams...

Edit* Also, how can we tell what regime the diagram will be in from the given information? How do we tell if it's depletion or accumulation or inversion?
 

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  • #2
The flatband case prevails when the energy band diagram of the semiconductor is flat, which implies that no space charge regions exist in the semiconductor device. The equilibrium case prevails when the electrochemical potential (Fermi energy) of the mobile charge carriers is constant throughout the device.

See, for example, chapter 3 and 6 in: https://ecee.colorado.edu/~bart/book/book/contents.htm
 
  • #3
Lord Jestocost said:
The flatband case prevails when the energy band diagram of the semiconductor is flat, which implies that no space charge regions exist in the semiconductor device. The equilibrium case prevails when the electrochemical potential (Fermi energy) of the mobile charge carriers is constant throughout the device.

See, for example, chapter 3 and 6 in: https://ecee.colorado.edu/~bart/book/book/contents.htm

Thank you for the response. I still don't understand how accumulation, depletion, and inversion work. How can we tell if a device is in one of those regions? In the problem we are not given a gate voltage, which is how I thought we find out which region the device is in. How do we find the region without the applied voltage?

It kind of makes sense when an applied voltage is there, but I am still a bit fuzzy on that. [Here is what the book has](https://imgur.com/a/TT2ORAQ)
 

1. What is a flat band diagram?

A flat band diagram is a graphical representation of the energy levels of electrons in a semiconductor material. It shows the energy levels of the conduction band and valence band as well as the Fermi level, which is the energy level at which there is an equal number of electrons and holes in the material. In a flat band diagram, the energy levels are constant throughout the material.

2. What is an equilibrium diagram?

An equilibrium diagram is a graphical representation of the energy levels of electrons in a semiconductor material at thermal equilibrium. It takes into account the effects of temperature and impurities on the energy levels of the material. In an equilibrium diagram, the energy levels are not constant but vary with temperature and impurity concentration.

3. How are flat band diagrams and equilibrium diagrams different?

The main difference between flat band diagrams and equilibrium diagrams is that flat band diagrams show the energy levels of a material without taking into account temperature and impurities, while equilibrium diagrams take these factors into consideration. In other words, flat band diagrams are a simplified version of equilibrium diagrams.

4. Why are flat band diagrams important in semiconductor research?

Flat band diagrams are important in semiconductor research because they provide a simplified understanding of the energy levels of a material, which is crucial for understanding its electrical properties. They can also be used to predict the behavior of a material under certain conditions, such as in the presence of an electric field or under different temperatures.

5. How can flat band and equilibrium diagrams be used in device design?

Flat band and equilibrium diagrams can be used in device design to determine the optimal conditions for a semiconductor material to function efficiently. They can also help in the selection of suitable materials for specific device applications. Additionally, these diagrams can aid in the design of electronic devices, such as transistors and solar cells, by providing insights into the behavior of the material at different energy levels.

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