Finger Resistance

To provide higher conductivity the top of a cell has a series of regularly spaced finger. While tapered fingers theoretically provide lower losses technology limitations mean that fingers are usually uniform in width. The resistive loss in a finger is calculated as below. At the end of this page there is a graph showing how the parameters affect power loss in the cell.

Calculation of Power Loss in the Fingers

Calculation of the power loss in a single finger. The width is assumed constant and it is assumed that the current is uniformly generated and that it flows perpendicularly into the finger, i.e., no current flow directly into the busbar.

Consider an element dx at a distance x from the end of the finger.

The current through the element dx is: \(x J_{MP} S_{f}\),

where Jmp is the current at maximum power point and Sf is the finger spacing.

The resistance of the element dx is: \(\frac{d x \rho_{f}}{w_{f} d_{f}}\),

where wf is the finger width, df is the finger depth (or height) and ρf is the effective resistivity of the metal.

The power loss in the element dx is: \(I^{2} R=\frac{d x \rho_{f}}{w_{f} d_{f}}\left(x J_{MP} S_{f}\right)^{2}\)

Integrating x from 0 to L gives the power loss in the finger:

$$\int_{0}^{L} \frac{\left(x J_{M P} S_{f}\right)^{2} \rho_{f}}{w_{f} d_{f}} d x=\frac{1}{3} L^{3} J_{M P}^{2} S_{f}^{2} \frac{\rho_{f}}{w_{f} d_{f}}$$