1. Extend the theory of Section 9.1 to include the difference in dielectric constant between GaAs and AlGaAs, by matching Dz at the heterojunctions rather than Ez. Is the difference likely to be significant in practice?
2. The composition of the structure used in Figure 9.1 was given in Section 9.1. Estimate analytically its threshold voltage and, using equation (9.14), the density of electrons at equilibrium and with VG= +0.2 V, which can be compared with 3.0 x 1015m-2 from the numerical simulation. What fraction of the electrons from the donors goes to the 2DEG, and what density of surface states is needed to keep the Fermi level pinned? What would happen if the doping were in error by ±20%? (This is only too common!)
