Fill Factor (FF) of a Cell
Fill factor is defined as the ratio of the maximum power output of a solar cell to the product of its open-circuit voltage and short-circuit current. The fill factor (FF) for a cell can be written as
where Imax is the maximum output current, m is a constant with typical value of unity, Kis the Boltzmann鈥檚 constant, Tis the temperature (K), q is the unit charge, Isc is the short-circuit current, Is is the saturation current, and Voc is the open-circuit voltage. The maximum current can be determined by the following equation:
Determining a precise value for the fill factor requires numerical solutions of the semiconductor carrier transport equations in conjunction with the Poisson equation. Two factors that affect the fill factor of a solar cell are the emitter efficiency degradation and the series resistance. At the maximum power point, the excess carrier concentration in the bulk region of the VGMJ cell is significantly reduced from its value under the open-circuit voltage condition. The fill factor is strictly dependent on the bulk carrier lifetimes and sunlight concentration factors ranging from 1 to 1000 suns. Typical values of FF with one-dimensional VGMJ cell of 0.8 or greater are possible from 1 to 1000 suns with bulk lifetimes of 50 psec or greater. With a bulk carrier lifetime of 50 psec the fill factor will be better than 0.8 at 300 suns.
Two components of the series resistance, namely, the internal resistance of the individual elements and the external series resistance due to cell metallization and the interconnect conductors, affect the open-circuit voltage. The ohmic power loss in the internal series resistance of the VGMJ cell is very low due to the small dimensions of its elements and the significant conductivity modulation of the bulk region in these elements, when the cell is operated under concentrated sunlight conditions ranging from 1 to 1000 suns. However, this loss at 10,000 suns is significant and can degrade the fill factor close to 0.74 for bulk lifetimes of 10 psec or longer. Note
it is extremely easy to keep the power loss in the external series resistance to below 1 percent even at sunlight concentration factor of 1000 suns. This would require an interconnect conductor cross-section of only about 0.02 mm2 per centimeter of the running length. Similarly, the metallization to connect the adjacent elements on the wafer can be accomplished with minimum resistance. Metal runs with 1 mm thickness would yield less than 0.1 percent series resistance power loss at 1000 suns.