Fermi Energy of an Ideal Two-Dimensional Electron Gas Consider a structure consisting of two GaAs quantum wells that have been grown far apart in AlxGa1-xAs with the same Al composition x (x - 0.3). In well A the GaAs thickness is L, while in well B, it is 2L. Now, approximate the conduction bands in wells A and B by ideal quantum wells between infinitely high potential barriers. Suppose that the quantum wells contain electrons and that both wells have the same Fermi energy, E_F = 3F_A 1 where E_A 1 is the lowest quantized energy level in well A. 

(a) How many sub bands in each well contain electrons at zero temperature?

(b) What is the two-dimensional charge density NA and NB in each well? Give the answer in terms of known physical quantities such as h and L.