Consider a conventional modulation doped AlGaAs/GaAs HEMT structure. Assuming the AlGaAs barrier is uniformly doped and fully depleted, expect that very thin undped AlGaAs spacer exists at AlGaAs GaAs interface. 1.draw a schematic energy band diagram, charge distribution, and electric field distribution for the structure. 2. Assuming only the first and second sub-band is dominant, derive an expression for the 2DEG concentration (ns) vs. the Fermi level in terms of the two-dimensional density of states.