| Topic: |
Science > Physics |
| User: |
"Gernot Pfanner" |
| Date: |
23 May 2005 08:12:02 AM |
| Object: |
Tight binding & density of states (DoS) |
Hi!
I have successfully calculated the band structure of Silicon by solving
the parametrized Hamiltonian matrix (tight binding approach) for various
values of k in the first Brillouin zone.
But how do I calculate the density of states?
I don't have a single clue, how to do that, so all your help
would be very appreciated.
In this spirit
With thanks in advance
Yours Gernot
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| User: "Old Man" |
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| Title: Re: Tight binding & density of states (DoS) |
23 May 2005 11:02:31 PM |
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"Gernot Pfanner" <pfannerg@stud.uni-graz.at> wrote in message
news:pan.2005.05.23.13.12.02.459987@stud.uni-graz.at...
Hi!
I have successfully calculated the band structure of Silicon by solving
the parametrized Hamiltonian matrix (tight binding approach) for various
values of k in the first Brillouin zone.
But how do I calculate the density of states?
I don't have a single clue, how to do that, so all your help
would be very appreciated.
In this spirit
With thanks in advance
Each state occupies a phase-space volume of hbar^3.
[Old Man]
Yours Gernot
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| User: "Zigoteau" |
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| Title: Re: Tight binding & density of states (DoS) |
23 May 2005 09:47:54 AM |
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Hi, Gernot,
I have successfully calculated the band structure of Silicon by
solving
the parametrized Hamiltonian matrix (tight binding approach) for
various
values of k in the first Brillouin zone.
But how do I calculate the density of states?
The density of states is normally given as a function of energy, and
it's states.m^-3.eV^-1 (or equivalent)
I don't have a single clue, how to do that, so all your help
would be very appreciated.
Your calculation gives you the energy E of a state with a given
wavevector k. What you need to do is to map out the region of
reciprocal space with energy less than or equal to E. This region will
have a volume, and since it's reciprocal space the dimensions of this
"volume" are m^-3.
If you have a sample of silicon with toroidal boundary conditions, then
the allowed states are distributed uniformly in wavevector space. Hence
the total number of states with energy less than E is proportional to
this reciprocal-space volume, give or take various factors of h, 2 and
pi, which I will leave you to work out. To get the density of states,
just differentiate.
Cheers,
Zigoteau.
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