Describe how the electron energy-wavevector (E-k) dispersion of the free electron gas is affected by the introduction of

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Describe How The Electron Energy Wavevector E K Dispersion Of The Free Electron Gas Is Affected By The Introduction Of 1 (45.49 KiB) Viewed 16 times

Describe how the electron energy-wavevector (E-k) dispersion of the free electron gas is affected by the introduction of the crystal lattice potential, illustrating your answer with sketches of the E-k dispersion plots. How does this modified dispersion then allow for the prediction of insulating behaviour and of semiconducting behaviour? [4 10 The number of free carriers per unit volume, n(T), in a pure semiconductor is given by n(T) where is a constant, ky is the Boltzmann constant, and T is temperature. What is the meaning of the parameter AE in the above formula? Use the plot in Figure A10.1 to estimate the value of AE giving your answer in units of eV. [Note that the y-axis has a base-10 logarithmic scale.] I= ce la 1019 Fit line 1018 1017 n (cm3) 1016 1015 1014 1013 0.001 0.002 0.003 T-1(K-1) Fig A10.1 Semi-log plot of carrier density as a function of reciprocal temperature. Adapted from: Morin & Maita Phys. Rev. 96, 28 (1954).