Department of Electronic and Electrical Engineering
EEE225 Semiconductors for Electronics and Devices
Problem Sheet 1 (revision)
1. A bar of intrinsic germanium at 300 K has 2.5 x 1019 electrons per cubic metre in the conduction band. Find the net current density when an electric field of 500Vm-1 is applied to the bar. Assume μh = 0. 19m2 v −1s −1 and μe = 0.39m2 v−1s −1 .
2. The resistivity of intrinsic silicon at 27℃ is 3000Ω m. Assuming μe = 0. 17m2 v−1s −1 and μh = 0.035m2 v−1s −1 , calculate the intrinsic carrier density ni at this temperature.
3. A current density of 103 A m-2 flows through an n-type germanium crystal of resistivity 0.05Ω m. Calculate the time taken for electrons to travel 5 × 10-5 m, if the mobility is μe = 0.39m2 v−1s −1 .
4. Compare the drift velocity of an electron moving in a field of 10000V m-1 in pure germanium, with the final velocity of an electron that has moved through a distance l0mm in the same field in a vacuum. The free electron mass is 9.11 × 10-31kg, and the mobility μe = 0.39m2 v−1s −1 in germanium.
5. A rod of p-type germanium 6mm long, 1mm wide and 0.5mm thick has an electrical resistance of l20Ω . What is the impurity concentration? What proportion of the conductivity is due to electrons in the conduction band? (Take μh = 0. 19m2 v−1s −1 , μe = 0.39m2 v−1s −1 , and ni = 2.5 × 1019 m-3.)
6. Calculate the faction of electrons in the conduction band at room temperature for (a) pure Germanium (Eg = 0.72eV), (b) pure Silicon (Eg = 1.10eV) and (c) pure diamond (Eg = 5.6eV), and comment on the results.
7. Pure silicon has resistivity 2000Ω m at room temperature, and the density of conduction electrons is 1.4 × 1016m-3. Calculate the resistivities of two other, doped, samples containing acceptor concentrations of 1021m-3 and 1023m-3 respectively. Assume that the hole mobility remains the same as in pure silicon and that it is equal to 0.26 times the electron mobility.