Problem 1
Silicon is doped $n$-type at 2 ×10¹⁷ cm^-3 and $p$-type at 3 ×10¹⁶ cm^-3. Assuming that all of the dopants are ionized, what is the density of electrons in the conduction band and the density of holes in the valence band at 300 K?

For silicon, $n_i = $ 1.5 ×10¹⁰ cm^-3 at 300 K.

Problem 2

(a) Draw a $p$-channel MESFET indicating where the depletion layer would be at zero bias. Draw Ohmic contacts at the source and drain.

(b) For normal operation, should V_GS be positive or negative? Why?

(c) What is pinch-off?

(d) What is the primary mechanism that causes the current flow from gate to source? Drift, diffusion, thermionic emission, or tunneling?

(e) What is the primary mechanism that causes the current flow from source to drain? Drift, diffusion, thermionic emission, or tunneling?

(f) Draw the I_D vs. V_DS for various values of the gate voltage.

Problem 3

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

(b) How should this MOSFET be biased so that it is in the saturation regime?

(c) How does the drain current depend on the gate voltage in the saturation regime?

(d) How do you calculate the maximum frequency at which a MOSFET operates? About what frequency is this?

Problem 4
Draw the minority carrier concentration in a pnpn thyristor in forward bias.