Schematic model configuration (not to scale) for (a) columnar GBs and (b) horizontal GBs. The axis and axis are defined to be parallel and perpendicular to the plane of the junction, as indicated.
Band structure parallel to the main junction at . All cases are for columnar GBs at zero external bias under one-sun illumination. (a) Neutral GB, (b) small , (c) large , and (d) large .
Carrier densities and recombination rate parallel to the main junction for band diagrams shown in Fig. 2 (note the expanded horizontal scale). The sheet density of recombination is found by multiplying by the GB width . Corresponding integrated current losses shown in parentheses.
Neutral GB recombination at horizontal grain boundaries located a distance from the CdS∕CIGS interface. All parameters are normalized to the performance of the GB-free model. .
Neutral GB recombination on columnar grain boundaries. The grain size (distance between two GBs) is . All parameters are normalized to the performance of the GB-free model.
Neutral GB recombination, . Relative carrier concentration, , in the 2D model (left) and , , and recombination along the GB at (right) under one-sun illumination at (a) and (b) (slightly below ). The axis describes the distance from the CdS∕CIGS interface and the lateral position. corresponds to the location of the columnar GB.
parameters , , FF, and for (electron repulsion), (weak hole repulsion), and (strong hole repulsion). All band bendings are defined under one-sun illumination at zero bias and at a distance from the junction. The dashed lines represent results for neutral GBs with varying and are only shown for reference.
Small hole-repulsive band bending, . Relative carrier concentration, , in the 2D model (left) and , , and recombination at the GB (right) under one-sun illumination at (a) and (b) (slightly below ).
Large hole-repulsive band bending, . Relative carrier concentration in the 2D model (left) and , , and recombination R at the GB (right) under one-sun illumination at (a) and (b) (slightly below ).
Effect of charge-induced band bending on current. (a) Short-circuit current density (normalized to the GB-free case) at zero bias. For large positive band bending the collection is very good and approaches the absorption limit. (b) Effective GB recombination velocity . For , the recombination is limited by the suppressed hole concentration.
parameters , , FF, and for and . Larger values give identical results to .
Large valence-band offset , . Relative carrier concentration in the 2D model (left) and , , and recombination at the GB (right) under one-sun illumination at (a) and (b) (slightly below ).
Valence-band offset and band bending . .
Typical current-voltage curves for (a) neutral GB recombination, (b) small hole-repelling band bending, (c) large hole-repelling band bending, and (d) large valence-band offsets. . All cases assume columnar GBs with grain size of .
Simulation input parameters. Barrier heights and ; surface recombination velocity ; layer width ; dielectric constant ; mobility ; shallow dopant density and ; band-gap energy ; effective density of states and ; conduction-band offset between two adjacent layers ; acceptor or donor defect density and ; defect peak energy and ; defect distribution width ; capture cross section ; and grain-boundary states (sheet density) . The subscript refers to electron∕hole properties.
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