Another factor that should be properly considered during the Solar cell design process is the emitter resistance. Emitter sheet resistance significantly contributes to the distributed series resistance of the solar cell. The series resistance (Rs) has an impact on the fill factor (FF) and in turn has an effect on the short circuit current (Isc) and as a result the efficiency. As a result, it is important to understand the properties of the emitter in order to achieve exceptional ohmic contact.
Based on the resistivity of the sheet, the power loss based on the emitter resistance can be calculated as a function of the finger spacing in the top contact. Yet, the distance that current flows in the emitter is variable. Current can be collected from the base near the finger and thus has only a short distance to flow to the finger or, otherwise, if the current enters the emitter between the fingers, then the resistive path length seen by this carrier is equal to half the grid spacing.
Emitter resistance losses calculation
The incremental power loss in a section dy is:
dPloss = I2dR
while the differential resistance is:
dR= ( ρ/b) dy
ρ:sheet resistivity in Ω/sqrb: the distance along the fingery:distance between two grid fingers
The current depends as well on y, where I(y) is the lateral current flow, which equals zero at the midpoint between the grating lines and linearly increases to the maximum at the grating line, under uniform illumination. The formula for the current is:
J: the current density;b: the distance along the fingery: the distance between two grid fingers
The total power loss is then equals:
S is the spacing between grid lines.
At the point of maximum power, the generated power equals:
The fractional power loss is:
Thus, we can as a result calculate the minimum spacing for the top contact grid. As an example, for the common silicon solar cell where ρ= 40 Ω / sq, Jmp = 30 mA/cm2, Vmp = 450 mV, to obtain an emitter power loss which is less than 4%, the finger spacing should be kept at a distance equal to less than 4 mm.