Problem 1

A $p$+ well is doped into an $p$ substrate to create an ohmic contact. The interface between $p$ and $p$+ is at $x=0$. No bias voltage is applied.

(a) Draw the band diagram (conduction band, valence band, Fermi energy) around $x=0$.

(b) Draw the electric field and the charge density around $x=0$. Which way is the electric field pointing? Explain why the field points in this direction.

Problem 2

(a) Draw an $n$-channel MOSFET showing the source, drain, gate, and body contacts.

(b) Draw the band diagram in accumulation for this MOSFET (conduction band, valence band, Fermi energy), and the electric field as a function of position along a line from the gate through the oxide into the body.

(c) How are the source-body and drain-body pn-junctions biased (forward or reverse) when the transitor is in saturation?

Problem 3

(a) Draw an n-channel MESFET.

(b) Explain how a MESFET works.

(c) Describe the current mechanism when the gate diode is forward biased.

Problem 4

(a) Describe how a light emitting diode works.

(b) The depletion region of an LED has a certain thickness in the dark. What determines this thickness? What happens to the depletion width when the LED is turned on?

(c) What happens to the built-in voltage as the LED up?