Section A
Q1.
(a) In a long semiconductor bar (EG = 2 \text eV), conduction band electrons come in from the left in the positive x-direction with a kinetic energy of 3 eV. They move from location A to B to C to D. Between A and B, the electric field is zero; between locations B and C, there is a linearly varying voltage increase of 4 V; between C and D, the field is again zero. Assuming no scattering, sketch a simplified band diagram describing the motions of these electrons. Assuming that these electrons can be described as plane waves, with a free-electron mass, write down the wave function of the electrons at location D. Leave your result in terms of an arbitrary normalization constant. Assume the mass of free electron to be 9.11 × 10-31 kg.
(b) Calculate the Fermi energy EFO at 0°K for copper and estimate the average speed of the conduction electrons in Cu. The density of Cu is 8.96 gm/cm3 and atomic weight is 63.5. Given Avogadro's number is 6 × 1023.
(c) In the common source amplifier shown, evaluate voltage gain Av given RD = 2.7 k\Omega, μ = 50 and rds = 25 k\Omega. Derive the expression used.
(d) Define lumen and candela. The wavelength of visible light ranges from violet at approximately 380 nm to red at 720 nm. Obtain the bandwidth available of visible light.
(e) Implement the following expression using NAND gates only : Y = (a + c) (\overlinea + b + c)