[SOLVED] EEE225 Semiconductors for Electronics and Devices Problem Sheet 2 Web

EEE225 Semiconductors for Electronics and Devices

Problem Sheet 2

1.    Germanium has a band gap of 0.7eV and, for pure material, the Fermi level lies near the middle of the gap. What is the probability that a state in the upper band is occupied at 0K, 300K, and 500K? Explain the physical significance of these results. What other property of the band structure, other than the probability of occupancy of states, influences the electrical properties of the material?

2.   Athermistor made from intrinsic silicon is to be used to control the current surge in a projector when it is switched on. The thermistor has a resistance of 100Ω at room temperature (17°C). When it is connected in series with the projector lamp, at what temperature will its resistance fall to 1.0Ω? Assume that the energy gap for silicon is 1.08eV and that the carrier mobilities do not vary appreciably over the operating range of temperatures. Comment on the result.

3.   Intrinsic germanium has a gap energy of 0.72eV and its conductivity is 2.13 S m-1  at 300K. What is its conductivity at 400K? Comment on the result. Would the conductivities at each of these temperatures be changed if the semiconductor received radiation of wavelength (a) 1μm and (b) 2μm?

4.   A particular semiconductor, which is initially intrinsic with an energy gap, Eg, of 1.1eV, is doped very slightly n-type, in such a manner that the Fermi level is displaced by 10% of the gap energy from its intrinsic position. Compare the conductivities at 20°C  before and after doping, assuming carrier mobilities of μh  = 0.05m2 V-1s-1  and μe  = 0.13 m2 V-1s-1, commenting on the result.

6    In a certain semiconductor the ratio of electron mobility, μe, to hole mobility, μh, is equal to 10, the number density of free holes isp = 1020m-3, and the number density of free electrons is n = 1019 m-3. The measured conductivity is 0.455 S m-1. Calculate the mobilities.

7    A sample of germanium doped with 1020 donor atoms per cubic meter and 7 ×  1019  acceptor atoms per cubic metre. At the same temperature as the sample, the resistivity of intrinsic germanium is 0.6Ω m. Find the total current density when an electric field of 200V m-1  is applied. The electron and hole mobilities in germanium may be assumed to be 0.38 m2 V-1s-1 and 0.18 m2 V-1s-1 respectively.

9    A 10mm ×10mm × 10mm cube of silicon at room temperature has 1019m-3  of gallium (p-type) impurities and  1.5  ×  1019m-3   of arsenic  (n-type)  impurities  in the material. Determine the resistance of the cube between any two faces, assuming: ni  = 1.5 × 1016  m-3; μe  = 0.12 m2 V-1s- 1; and μh = 0.05 m2 V-1s-1