Hello,
I wanted to know if this way to calculate the DOS for the Free-electron model and nearly-free electron model is correct:
The energy for the free electron model can be expressed as:
E→k=ℏ2||→k||22m
And for the nearly-free electron model, we express:
E→k=Δ+ℏ22meff||→k||2
So, if we want to have the number of quantum states below a given energy Ek:
Φ(Ek)×(2πL)D=2×VD
where D is the dimension, and VD is the distance in 1D (VD=k), the area of a circle in 2D (VD=πk2) and the volume of a sphere in 3D (VD=43πk3).
From here, we express Φ(Ek) in function of the energy, and we make the derivation to obtain the DOS.
Thank you in advance for your answer