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University of Pennsylvania ESE 521 The Physics of Solid State Energy Devices Due: April 10, 2013 Prof. C. R. Kagan Homework #5 1. An ideal metal-semiconductor contact is made of a metal that has ΦM=4.75 eV, and a semiconductor that has χ=4.00 eV with ni=1010/cm3, ND=1016/cm3, and EG=1.00 eV; kT=0.026 eV. (a) Calculate the barrier for electrons in the metal. (b) Calculate Vbi, the barrier for electrons in the semiconductor. (c) Calculate the value of the depletion region width at thermal equilibrium. (d) Calculate the maximum electric field. (e) Sketch the energy band diagram in thermal equilibrium. 2. The ideal M-S contact has a semiconductor with χ=4 eV, ni=1010/cm3, ND=1016/cm3EG=1.2 eV, and kT=0.026 eV. Various metals are applied to the semiconductor with ΦM=4, 4.25, 4.5, 4.75, and 5 eV. (a) Calculate and sketch ΦBvs Φ(b) Calculate and sketch qVbivs Φ(c) If εS=12 obtain an equation, with numerical coefficients, for the depletion region width vs. ΦMif VA=0 (d) What is the probability that an electron will have an energy equal to ΦBif ΦM=4.75 eV? 3. For the ideal barrier in silicon, let N, M M