Two estimates about the two-dimensional electron gas.

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Semiconductor physics and devices · Surfaces, nanostructures and mesoscopic systems

Solid State Physics, Ch Heterostructures, quantum wells and the two-dimensional electron gas

Problem

Two estimates about the two-dimensional electron gas. ((a)) A modulation-doped GaAs quantum well (thick undoped spacer, highly purified growth) has sheet density ns=3.0×1011 cm−2n_s = 3.0\times10^{11}\,\mathrm{cm^{-2}} and mobility μn=1.0×107 cm2 V−1s−1\mu_n = 1.0\times10^{7}\,\mathrm{cm^2\,V^{-1}s^{-1}} at 0.3 K0.3\,\mathrm{K}. Estimate the electron mean free path ℓ\ell. Bulk GaAs carrying the same volume density (imagine the sheet spread uniformly through a 25 nm25\,\mathrm{nm} layer) has an ionised-impurity-limited mobility of about 5.0×103 cm2 V−1s−15.0\times10^{3}\,\mathrm{cm^2\,V^{-1}s^{-1}} at low temperature. By what factor does removing the impurities from the channel raise the mobility? ((b)) A GaAs/AlAs superlattice with period d=12 nmd=12\,\mathrm{nm} and a sample of bulk aluminium (lattice constant a=0.405 nma=0.405\,\mathrm{nm}) are placed in the same electric field. Using TB=h/eFdT_B=h/eFd, estimate the factor by which the superlattice's Bloch-oscillation period is shorter than aluminium's.

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