Before the start of this lecture, you should be able to:

- Simplify integral expressions by Taylor expansion

- Compute the density of states of the free electron model

- Apply the concepts of group velocity and effective mass to solve problems

!!! summary "Learning goals"

After this lecture you will be able to:

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@@ -257,4 +266,4 @@ Suppose we have a 1D semiconductor with a conduction band described by $$E_{cb}

2. Why is it acceptable? Write down an approximate expression of these bands.

3. Write down an expression for the density of states _per unit length_ for both bands using the approximated expressions. Compare with the actual density of states per unit length.

4. Calculate the electron density in the conduction band and the hole density in the valence band.

5. What would the chemical potential $\mu$ be in case of an intrinsic semiconductor?

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5. What would the chemical potential $\mu$ be in case of an intrinsic semiconductor?