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Condensed matter-integral over density of states

  1. Mar 24, 2008 #1
    condensed matter--integral over density of states

    1. The problem statement, all variables and given/known data
    http://online.physics.uiuc.edu/courses/phys460/fall06/handouts/460-lect12.pdf

    Could someone explain to me why the first equation on slide 22 is true?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 24, 2008 #2

    malawi_glenn

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    you mean:

    Quantitative evaluation?
     
  4. Mar 24, 2008 #3
    What? I mean I don't understand why it is true. It is also on page 142 of Kittel.
     
  5. Mar 24, 2008 #4

    malawi_glenn

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    Oki I just mean the eq under that headline.

    any way here it goes:

    take eq 24 on p 142. and read the 3lines above it.

    What is the fermi dirac distribution at T = 0K? well f (T goes to 0) = 1.. (see eq 5 p.136 and take limit t goes to 0).

    and you only have to integrate up to the fermi energy at 0K due to the density of state function. see fig 5 p.140.
     
  6. Mar 24, 2008 #5
    f (T goes to 0) = 1 only if mu > epsilon
     
  7. Mar 24, 2008 #6

    malawi_glenn

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    Oh yes, it meant when kT << E_f

    :)
     
  8. Mar 24, 2008 #7
    Why does that imply that mu is greater than epsilon?
     
  9. Mar 24, 2008 #8
    Oh--yes it is the equation under that headline--sorry.
     
  10. Mar 24, 2008 #9
    I see,the area of region 1 must be the same as the area of region 2.
     
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