Analysis of internal quantum efficiency in double-graded bandgap solar cells including sub-bandgap absorption

State of the art ZnO/CdS/Cu(In,Ga)Se2 (CIGS) solar cells use bandgap grading, requiring special tools for the analysis of the experimentally obtained characteristic curves. We develop an analytical model for the photon flux and internal quantum efficiency in double-graded bandgap solar cells, considering the effects of sub-bandgap absorption and grading-dependent carrier collection properties. The short-circuit photocurrent density is calculated as a function of carrier diffusion length and front/back bandgaps, establishing optimum design criteria under solar operation. Even for a diffusion length of only 0.5 μm in a 3-μm-thick absorber, and no contribution from the CdS layer, an optimum back bandgap of 1.35 eV is found, yielding short-circuit current densities of 36.0 (33.5) mA cm−2 for a front bandgap of 1.05 (1.68) eV. Furthermore, simplifications to the model for specific energy ranges allow to extract the Urbach Energy EU and the minimum bandgap Eg,min in the grading profile from experimental IQE curves. Finally, our model fits IQE measurements of 18% efficient CIGS solar cells, yielding values of EU between 31 and 41 meV, minimum bandgaps Eg,min between 1.10 and 1.16 eV, and diffusion lengths close to 0.5 μm.