How to Evaluate Quantum States and Fermi Energy Levels?

[eftalia]

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!

 

[borgwal]

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!

 

[eftalia]

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..

 

[borgwal]

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?

 

[eftalia]

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.

 

[borgwal]

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).

 

[eftalia]

OHH! Okay I see it now. Thank you :)

Does anyone have any advice for the second question?

 

[Sunny Joel]

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