# Fermi energy question help

## Homework Statement

Find the densities of states 0.08 eV above the conduction band edge and 0.08 eV below the valence band edge for germanium.

Find the volume density of states (i.e. number of states per unit volume) with energies between the conduction band edge and 0.4 eV above the conduction band edge for germanium.

## Homework Equations

8pisqrt2/h^3*m^(3/2)sqrt(E-Ec)
Using this example as a reference http://ecee.colorado.edu/~bart/book/book/chapter2/pdf/ex2_3.pdf

## The Attempt at a Solution

m=6*10^18, in the example they ignored the *10^-18 on their 1.08 value
(((8pisqrt2*(9.10*10^-31*6)^(3/2))/(6.626*10^-34)^3))sqrt(.08*1.6*10^-19)
=1.76*10^47 m^-3J^-1

Why should I times it by *10^-22, like in the example above? What is the purpose of that or is it an error?

In the example above I don't understand how they calculated that or reduced their value so low. I tried it with the same numbers they gave and it didn't work at all.

This value seems way too high. I need to convert it to eV.

Part 2)
Should I use .02 for this example, for my E-Ec value?

## Answers and Replies

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rude man
Homework Helper
Gold Member
This should be posted in the advanced physics forum.

gneill
Mentor
I'm no expert on this topic, but I note that 10^-22 is the volume of the sample they are using (100 x 100 x 10 nm3) in cubic meters. I note also that the units of their formula work out to J-1 m-3, so to yield a result in J-1 multiplying by a volume is called for.

I further note that their intermediate result: 1.51 x 1056 m-3 J-1 is suspect. Plugging in their values I get an order of magnitude of 1046 rather than 1056, however their final result looks fine.

Daz
Gold Member
Are you sure you posted all of the information given in the question? You need the effective mass of electrons and holes in germanium to work that out. (The values are very different to the values for silicon.)