# Conduction Energy Band for Intrinsic Silicon

1. Oct 20, 2005

### Corneo

I am trying to find a way to calculate the Ec for intrinsic silicon at room temperature. I can't seem to find anything in my textbook for that. I have searched on line and the closest thing I can find is

$$E_c = E_g + \frac {\hbar^2 k^2}{2m_e}$$

I know what Eg = 1.12 eV for intrinsic silicon at room temp. However is there another way? Possibly a table or CRC?

2. Oct 20, 2005

### ZapperZ

Staff Emeritus
Er... I don't quite understand what exactly it is what you want to do. Do you want to find the band width of the conduction band up to the vacuum level? Or do you want to "calculate" the band structure of silicon in particular? The latter isn't trivial, and will require something such as a linear combination of atomic orbital (lcao) technique.

Zz.

3. Oct 20, 2005

### Corneo

Sorry if I wasn't clear. Perhaps I should stake it like so.
I wish to calculate the electron density in the conduction band for intrinsic silicon at T = 300K.
The formula I found is
$$n = N_c exp\left [ -\frac {E_c - Ef}{kT}\right] \text { with } N_c = 2 \left( \frac {2 \pi m_e kT}{h^2}\right)^{3/2}$$

But I don't know what Ec nor Ef is. How can I find out?

4. Oct 20, 2005

### ZapperZ

Staff Emeritus
In an intrinsic semiconductor, Ef is the fermi energy and sits right in the middle of the band gap. Ec and Ev are the energy of the bottom of the conduction band and the energy of the top of the valence band, respectively.

This means that Ec - Ev = Egap. It also means that since Ef is right in the middle of the gap, Ec - Ef = Egap/2

[sorry, too lazy to do LaTex]

Zz.