Fermi-Dirac Distribution Function

In summary, the first question asks for the number of quantum states with energies between 9.0eV and 9.1eV, given the density of electron energy states g(E) = A sqrt E. To solve this, one can simply calculate the area under the curve of g(E) within this energy range. For the second question, the concept of density of states is defined as the number of states per unit energy interval, and is used to describe the distribution of allowed translational energy states. Using Fermi-Dirac statistics, one can show that the Fermi energy level lies in the middle of the energy gap Eg in an intrinsic semiconductor, assuming all energy levels in the valence band have an energy of
  • #1
eftalia
10
0
Hey all, I have two questions.

1) The density of electron energy states is given by g(E) = A sqrt E.

Evaluate how many quantum states there are with energies between 9.0eV and 9.1eV. Ansewr in terms of the quantity A.

2) Consider an intrinisic semiconductor. Let Nv and Nc be the number of electrons in the valence band and conduction abnds respectively. Let N = Nv + Nc. since the widths of energy levels in an energy band are small compared to the energy gap Eg, it is reasonable to assume that all the levels in an energy band have the same energy. Take energies of all levels in the valence badn to be 0 and energies of all levels in the conduction band to be Eg. Using Fermi-Dirac statistics, show that the Fermi energy level lies midway in the middle of energy gap Eg.

Sorry I am clueless as to how to approach both questions.. hope to get some help as to how to start. Thank you!
 
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  • #2
If you can't answer the first question, then you apparently don't understand what "density of states" means. Look that up in your textbook!
 
  • #3
Well.. I don't really understand despite reading my notes and supplementary books from the library :(. Do I integrate g(E) with respect to E with limits 9.1e and 9.0e? But I can't get the answer..
 
  • #4
What I mean is: the meaning of g(E) should be given in words in your textbook. That definition gives you the answer. So you tell me, how is g(E) defined in general?
 
  • #5
It says.. the density of states function describes the number of states per unit energy interval, and thus describes the way in which the states of allowed translational energy are distributed.
 
  • #6
Then that should give you the answer to your first question: if I tell you the number of accidents per second, and I tell you that I'm interested in the number of accidents in a 5-seconds time interval, then you would know what to calculate, right? Mutatis mutandis.

One more hint: your energy interval is so small, you don't even have to integrate (although you could easily do that, too).
 
  • #7
OHH! Okay I see it now. Thank you :)

Does anyone have any advice for the second question?
 
  • #8
Hi,

Could i know the meaning of density of states.

What i understood from Milman and Halkias is that it is the number of states per electron volt per unit volume (in the conduction band).
But, the conduction band is made of closely spaced discrete energy levels, which means that the energy of one state differs from that of the other. Then how can multiple states have the same energy?

Kindly correct me if i have misunderstood

thanks,
sunny
 

What is the Fermi-Dirac Distribution Function?

The Fermi-Dirac Distribution Function is a mathematical formula used to describe the probability of a particle being in a particular energy state in a system at thermal equilibrium. It takes into account the quantum mechanical properties of particles, such as their spin and the Pauli exclusion principle.

What is the significance of the Fermi-Dirac Distribution Function?

The Fermi-Dirac Distribution Function is important in understanding the behavior of particles in a system at thermal equilibrium, such as in a solid or gas. It helps to explain phenomena such as electrical conductivity, heat capacity, and the behavior of electrons in metals.

How is the Fermi-Dirac Distribution Function derived?

The Fermi-Dirac Distribution Function is derived using statistical mechanics, specifically the principles of quantum statistics. It is a result of applying the Pauli exclusion principle to a system of indistinguishable particles at thermal equilibrium.

What is the difference between the Fermi-Dirac Distribution Function and the Maxwell-Boltzmann Distribution?

The Fermi-Dirac Distribution Function and the Maxwell-Boltzmann Distribution are both used to describe the behavior of particles in a system at thermal equilibrium, but they differ in their assumptions and applications. The Fermi-Dirac Distribution is used for particles with half-integer spin, such as electrons, while the Maxwell-Boltzmann Distribution is used for particles with integer spin, such as atoms. The Fermi-Dirac Distribution also takes into account the Pauli exclusion principle, while the Maxwell-Boltzmann Distribution does not.

What are some real-world applications of the Fermi-Dirac Distribution Function?

The Fermi-Dirac Distribution Function has many applications in physics and engineering, including the study of semiconductors, superconductors, and thermoelectric materials. It is also used in the design of electronic devices, such as transistors and integrated circuits. In astrophysics, it is used to describe the behavior of particles in dense stellar objects like white dwarfs and neutron stars.

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