- #1

su3liminal1

- 1

- 0

- Homework Statement
- Find the percentage of these states that have electrons in them, assuming the number of electrons above Ec+2kT is negligible.

- Relevant Equations
- -

I just want to clear some confusion I am having with the Fermi-Dirac distribution & density of states (DOS) of a semiconductor, which are given by

Say we have a piece of Silicon in equilibrium and its Fermi level lies 0.25 eV below the conduction band edge, i.e. E

For

At room temperature and using an effective mass of silicon is, say, m

For

Say we have a piece of Silicon in equilibrium and its Fermi level lies 0.25 eV below the conduction band edge, i.e. E

_{c}- E_{F}= 0.25 eV. Let us say we want to compute two things:**(1)**Total number of states in the range E_{c}≤ E ≤ E+ 2k_{B}T.**(2)**The percentage of these states that have electrons in them, assuming the number of electrons above E_{c}+2k_{B}T is negligible.For

**(1)**, it is straight forward: we just integrate the density of states function in the conduction band, g_{c}(E) over the indicated range:At room temperature and using an effective mass of silicon is, say, m

_{n}^{*}=1.09m_{0}. This yieldsFor

**(2)**, I know that the Fermi-Dirac distribution in this context represents the the probability of an electron occupying a state at energy E, which can also be interpreted as the ratio of filled state to total states at the energy. But I am really not sure what do here. Do I compute the difference of Fermi-Dirac distributions in that range, or do I integrate, or both are wrong?