A GaAs quantum well at low temperature has only its lowest subband occupied

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Semiconductor physics and devices · Semiconductor physics and devices

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

Problem

A GaAs quantum well at low temperature has only its lowest subband occupied, with the Fermi energy measured from that subband edge EF−E1=5.0 meVE_F-E_1=5.0\,\mathrm{meV}. Using the two-dimensional density of states for GaAs, D2D=m∗/πℏ2=2.8×1010 cm−2 meV−1D_{2D}=m^*/\pi\hbar^2=2.8\times10^{10}\,\mathrm{cm^{-2}\,meV^{-1}} (both spin states counted), find the sheet carrier density nsn_s.

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