Shape Adjustment
Raw resistance values measured against the physical dimensions of a sample require a scalar adjustment to determine the true resistivity of a material. Calculating a geometric correction factor compensates for the concentration of current or stress near the edges of a part. This factor is essential when using a four point probe on thin films or small wafers where the boundary conditions are not infinite.
The calculation stops being accurate if the probe spacing is larger than the sample thickness.
Resistance Determination
Calculating this value involves applying a formula that accounts for the sample thickness and the distance between the electrodes. For a circular wafer, the factor depends on the ratio of the wafer diameter to the probe tip separation.
The Calculation
The adjustment is applied as a multiplier to the measured resistance to yield the sheet resistance in ohms per square. Theoretical derivations for these factors exist for most common shapes like rectangles and discs.
Application Influence
Improper selection of the factor leads to systematic errors in the characterization of semiconductor layers. Engineers use these values to ensure that the doping process remains within specification across the entire surface. Correct geometry adjustments allow for the comparison of data between different test stations.
