4. For a semiconductora. What is the probability of finding an electron at Fermilevel?b. What is the density of states in the energy band gap?c. If two electrons have the same principal, angular, magneticand spin quantum number – can they reside in the same state, why orwhy not?d. Sketch the density of states, probability of occupancy andexplain how they change with temperature for bulk (3D) material foran p-type material e. Sketch the density of state for 3D (bulk),2D, 1D and 0D systems.
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SOLVED:In an intrinsic semiconductor, the band gap is so small that the Fermi-Dirac distribution results in some electrons populating the conduction band. It follows from the exponential form of the Fermi-Dirac distribution that the conductance G, the inverse of the resistance (with units of siemens, .1 S=1 Ω^-1), of an intrinsic semiconductor should have an Arrhenius-like temperature dependence, shown in practice to have the form G=G0 e^-E8 / 2 k T where Es is the band gap. The conductance of a
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