A COMPARISON OF SOME EFFICIENCY FACTORS IN PHOTOVOLTAICS

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. We here discuss this efficiency factor for a general density of states g(x), where x = h(nu)/kT(p) and T(p) is the pump temperature. Its maximum with respect to variations of the bandgap E(g) occurs at a certain value of E(g), say E(g)0, yielding eta-ult(x(g)0), where x(g)0 = E(g)0/kT(p). The efficiency-eta of a simple solar cell in the presence of surroundings at temperature T(s) is proportional to eta-(T(p), T(s)) = intergral-infinity/x(g){[1/exp(x)-1)]-[1/(exp(((x-nu)/T(s))T(p))-1)]}g(x)dx. Its maximum with respect to x(g) and upsilon is eta-max (T(p), T(s)). We show here that the Shockley-Queisser efficiency is the same as eta-max, provided the ambient is set at absolute zero of temperature: eta-ult(x(g)0) = eta-max (T(p),0). Comments are also made on: (i) the possibility of several maxima of eta-ult(x(g)0) 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.