Fermi Energy in Intrinsic Si, Ge, and GaAs

[NanoChrisK]

Homework Statement

Using the values of the density of states effective masses m_e* and m_h* in table 5.1, find the position of the Fermi energy in intrinsic Si, Ge, and GaAs with respect to the middle of the bandgap (E_g/2).

Table 5.1 shows the following density of states effective masses m_e*/m_e and m_h*/m_e:

m_e*/m_e:
Si: 1.08
Ge: 0.56
GaAs: 0.67

m_h*/m_e:
Si: 0.60
Ge: 0.40
GaAs: 0.50

Homework Equations

Fermi energy for an intrinsic semiconductor:

E_Fi = E_v + (1/2)E_g - (3/4)kT⋅ln(m_e*/m_h*)

The Attempt at a Solution

I believe understand the equation perfectly. The Fermi energy will be about half way between the edges of the valence and conduction bands, and will vary slightly with temperature depending on the - (3/4)kT⋅ln(m_e*/m_h*) term. The problem I am having is determining the values for E_v to use in the equation. I can only think of three possible solutions:

- I am expected to give the answer in the form of "the Fermi energy for intrinsic Si is X above the valence band (or X below the conduction band)"

- I really am expected to look up the values for E_v in a table somewhere.

- I'm supposed to calculate E_v somehow with a different equation (which I am unfamiliar with).

Can someone please point me in the right direction?

 

[NanoChrisK]

Looking at the question more closely, I noticed it asks for the Fermi energy "with respect to the middle of the bandgap (Eg/2)." Does this mean that I can just ignore the Ev + (1/2)Eg - (3/4)kT part of the equation? I think this is the solution.