A silicon cell of gap normally emits from its front face into the full external…
PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · Energy resources and conversion · Energy resources and conversion
Energy from Physics, Ch How efficient a solar cell can be: detailed balance, tandems and the field
Problem
A silicon cell of gap Eg=1.12eV normally emits from its front face into the full external hemisphere (half-angle 90∘, index n=1 outside). A photonic reflector is added that returns every photon trying to leave at more than 30∘ from the normal, so emission (and absorption of diffuse light, which is neglected here) is confined to a cone of half-angle 30∘; the direct photocurrent from sunlight is unchanged. The cell runs unconcentrated at cell temperature Tc=300K.
((a)) Using the etendue term of the open-circuit voltage deficit, with the angular etendue taken as proportional to sin2θ (the same convention that gives the concentration limit Cmax=n2/sin2θ⊙), predict the change in Voc produced by the angular restriction on its own, all other deficit terms held fixed.
((b)) Under the unconcentrated blackbody Sun, with independently wired junctions, the best single gap gives 30.5% (1.26eV), the best two-junction stack 42%, the best three-junction stack 48.5%, and indefinitely many junctions about 68%. Find the efficiency gained by adding the second junction and by adding the third, and the headroom left to all junctions after the third. State the physical reason each added junction gains less than the one before.