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A useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials. Instead of having discrete energies as in the case of free atoms, the available energy states form bands. Read on the link. You ask: My question is very simple. I just want to know that is conduction ...

8

Kittel (at least my 5th edition) goes through this derivation. Refer to the diagram below and remember that in semiconductor physics the chemical potential $\mu$ is also the Fermi level $E_F$ below. The derivation essentially involves calculating the concentration of electrons and holes at temperature T in the conduction and valence bands respectively, ...

5

As other have noted, it's discrete but with fine enough spacing to treat as continuous. However I disagree that quantum mechanics is the reason. You see the exact same thing in a classical 1-D chain of masses connected by springs. The allowed wave vectors $\vec{k}$ in the bands are reciprocal lattice vectors, and the number of reciprocal lattice vectors is ...

4

As this model is itself associated with quantum model, so it seems obvious that energy levels occur in steps or we can say that they are discrete but experimental analysis says that they are continuous and it's intuitive that they are too close that's why we call them a band i.e a band of too close energy levels.

2

For aan absorption process, the electron absorbed a photon of energy $E_\omega$ and transition to conduction band $E_c(k_c)$ from valance band $E_v(k_v)$. This process satisfies both energy and momentum conservation: energy conservation $$E_\omega = E_c - E_v,$$ and momentue conservation $$\hbar k_\omega = \hbar k_c - \hbar k_v.$$ The dispersion of a ...

1

You can have more bands than the size of the matrix. Think of Harper's equation: $$\psi_{n+1}+\psi_{n-1} + (\lambda \cos q n)\psi_n = E\psi_n$$ This is a nearest-neighbour hopping problem with an position dependent on-site potential. The unit cell is not one site, but instead depends on the periodicity determined by $q$. If you have to go $N$ sites to get ...

1

After I posted my original answer, I realized that there's a better explanation, and it explains the name "continuum model": (for simplicity, I'll omit sublattice degree of freedom) Suppose that the eigenstate is:  \widetilde{\psi}(k_0)= \begin{pmatrix} \widetilde{\Psi}_1(k_0)\\ \widetilde{\Psi}_2(k_0) \end{pmatrix} = \begin{pmatrix} \sum_{k_1} \...

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