9.5.2014

**Problem 1**

In a certain semiconductor, the valence band can be approximated by the function $E = E_0 - \alpha k^2$ and the conduction band can be described by the function $E = E_1 + \beta (\vec{k}-\vec{k}_0)^2$. Here $E$ is the electron energy, $k$ is the wavenumber, $\alpha > 0$ and $\beta > 0$.

(a) What is the band gap of this semiconductor?

(b) Is this a direct or indirect bandgap semiconductor?

(c) What is the effective mass of the electrons and holes?

Express your answers in terms of $E_0$, $E_1$, $k_0$, $\alpha$, and $\beta$.

Solution

**Problem 2**

(a) Draw a p-channel MESFET showing the source, drain, and gate. Why is there no body contact?

(b) Draw the band diagram (valence band, conduction band) perpendicular to the gate-semiconductor interface.

(c) Why is a MESFET a fast transistor? What can be done to increase the speed of a MESFET?

**Problem 3**

Draw the charge density $\rho$ and the electric field as a function of position along a line from the metal gate to the substrate for a MOS capacitor in inversion with a n-type substrate.

**Problem 4**

Describe how a semiconductor laser diode works. What determines the frequency that is emitted? Why is there a threshold current? How is it different from an ordinary light emitting diode?