Test # 2 (Thursday, 21 April) Problem # 1 Admixing Al to Ag creates an Ag1-xAlx alloy (in which Al atoms substitute for Ag atoms) and leads to an increase of the Fermi energy. Using a free electron model and assuming that Al is trivalent while Ag is monovalent calculate the relative concentration, x, of Al atoms which is required to increase the Fermi energy by 1eV. Take into account that the Ag crystal has electron concentration n = 5.85⋅1022cm-3. Problem # 2 Suppose that the electronic structure of a solid that represents a two-dimensional square lattice of divalent atoms can be described using a nearly free electron model with a weak crystal potential such that 222Umaπ⎛⎞⎜⎟⎝⎠G=±, where ais the lattice parameter. Is this solid a metal, an insulator or a semiconductor? Explain why. Problem # 3 Both free electrons and phonons can be treated in terms of a gas of non-interacting particles. Why, then, the electron heat capacity at low temperatures is proportional to T, whereas
This is the end of the preview.
access the rest of the document.