Consider a 10 nm thick layer of semiconductor material, which is surrounded by impenetrable barriers. The semiconductor layer consists of (a) GaAs, (b) AIAS, (c) Al0.35Ga0.65As. And (d) Al0.65Ga0.35As. (1). Use the effective mass approximation to estimate the energy of the first subband minimum for electrons for each material. (2). Repeat this calculation to estimate the first heavy-hole subband minimum in each material. (3). Determine the energy difference between the lowest electron and hole states in each material. (4). Photoluminescence techniques can be used experimentally to measure the difference between electron and hole states in semiconductor systems. Assuming that the measurement system has a 1 meV sensitivity and the detectable minimum threshold energy is 1.44 eV. Estimate the maximum thickness semiconductor layer in which the lowest-energy subbands can be observed for each material. Band Structure of Semiconductor Alloys .. Table 4.6: Bandgaps for III-V alloys. Alloy Al, Ga As Al, In.As Ga, In.As Ga In,.,Sb Al, Ga. Sb AlIn Sb Eg. (ev) 1.42 +1.247 x 0.360+ 2.012x + 0.698.x 0.360+ 1.064 x 0.172 +0.139x+0.415x 0.726+ 1.129x+0.368x 0.172 + 1.621 x + 0.430x Table 4.7. Effective masses for the alloy Al Ga.As. Type of minimum T-point X-minima L-minima Heavy hole Light hole Effective mass, ma/mo 0.067 +0.083 x 0.32-0.06x 0.11 + 0.03 x 0.62 +0.14 x 0.087.0063 x