Question 5.7: For heterojunctions in the GaAs–AlGaAs system, the direct (Г...
For heterojunctions in the GaAs–AlGaAs system, the direct (Г) band gap difference \Delta E^{\Gamma }_{g} is accommodated approximately \frac{2}{3} in the conduction band and \frac{1}{3} in the valence band. For an Al composition of 0.3, the AlGaAs is direct (see Fig. 3–6) with \Delta E^{\Gamma }_{g}= 1.85 eV. Sketch the band diagrams for two heterojunction cases: N^{+ }-Al_{0.3} Ga_{0.7} As on n-type GaAs, and N^{+ }-Al_{0.3} Ga_{0.7} As on p^{+ }- GaAs^{18}
^{18}In discussing heterojunctions, it is common to use a capital N or P to designate the wide band gap material
Taking ΔE_{g} = 1.85 – 1.43 = 0.42 eV, the band offsets are ΔE_{c} = Solution
0.28 eV and ΔE_{v} = 0 .14 eV. In each case we draw the equilibrium Fermi level, add the appropriate bands far from the junction, add the band offsets while estimating the relative amounts of band bending and position of x = 0 for the particular doping on the two sides, and finally sketch the band edges so that E_{g} is maintained in each separate semiconductor right up to the heterojunction at x = 0.
