Question

4. (a) The energy states of Landau levels are given by where wc is the cyclotron frequency Using this and the 2D density of states given by where m is the carrier effective mass, deduce the degeneracy of a Landau Level Sketch these Landau levels on a graph of number n(E) verses energy (E), and indicate the position of the Fermi Energy for a filling factor of 8 4 (b) Sketch the band diagram for a heterojunction between p-type AlGaAs and n-type GaAs showing that this can trap a (two-dimensional) hole gas at the interface Why would carriers in such a two dimensional system have significantly higher mobility than bulk doped material? (c) Given that the density of states in one dimension is 2 12m where v is the carrier velocity, consider the current through a 1D conductor between two reservoirs of charge carriers. Demonstrate that conductance is quantised when the channel length (/) is much smaller than the ballistic length (A) 6 Calculate the quantum unit of resistance from the ground state of this expression (n 1) Note: Electron charge is 1.619x10-19 C, Planck's constant h-6.62x10-4 m2 kg/s,

Answer 1

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