A comparison of some efficiency factors in photovoltaics

Abstract

Shockley and Queisser, in their fundamental paper, defined an 'ultimate efficiency' eta ult, as the ratio of electrical output power (assuming the voltage factor and the fill factor to be unity) to the radiative input power (assuming maximum light concentration) in an ideal solar cell. The authors discuss this efficiency factor for a general density of states g(x), where x=hv/kTp and Tp is the pump temperature. Its maximum with respect to variations of the bandgap Eg occurs at a certain value of Eg, say Eg0, yielding eta ult (xg0), where xg0 identical to Eg0/kTp. The efficiency eta of a simple solar cell in the presence of surroundings at temperature Ts is proportional to eta (Tp,Ts) identical to integral x(g)infinity ((1/(exp(x)-1))-(1/(exp(((x-v)/Ts)Tp)-1)))g(x) dx. Its maximum with respect to xg and nu is eta max (Tp, Ts). They show that the Shockley-Queisser efficiency is the same as eta max, provided the ambient is set at absolute zero of temperature: eta ult (xg0)= eta max (Tp, 0). Comments are also made on: (i) the possibility of several maxima of eta ult(xg0) for certain appropriately chosen g(x); and (ii) its dependence on the number of dimensions n=1,2,3,4,., infinity : 29,39,44,48,., 100%, if g(x) is chosen as if due to an n-dimensional cube.