$3.($a$)$ Draw band offsets $($conduction and valence$)$ that reflect type$-$I and type$-$II systems and describe with an example a bulk analogy that reflects these band structures used in solar cells $(5$pts$)$

$($b$)$ Illustrate$/$sketch the band offsets of a typical heterostructure solar cell. Label the emitter and base and the doping of the respective regions. Name a material system in which such a device is currently implemented commercially $(5$pts$)$

$($c$)$ Describe the practical reasons such a heterostructure is used and discuss both positive AND negatives aspects of these systems in the practical materials currently implemented. $(5$pts$)$

$($d$)$ Quantum Well devices have been suggested as a potential system for photovoltaics. Describe where and why such devices might enable better solar cell performance and potential issues with such systems $(5$pts$)$

$4.$ Considering the Figure below, suggest a triple junction system that might operate in excess of current state$-$of$-$the$-$art multijunction solar cells. Explain your choices in terms the properties of the materials chosen, your reason for picking the systems you have decided upon, and why both intrinsically and extrinsically the system you have proposed has not, or might not have, been implemented. $(10$pts$)$