An algebraic expression to count the number of chips on a wafer

Most chip-counting algorithms use the Pythagorean theorem; in effect, a grid of chips is superimposed over the wafer, and the radial distance from the center of the water to the outermost vertex of each potential chip site is computed. Only those chips are counted for which this radial distance is less than the effective radius of the wafer. To minimize edge-related chip loss, chip fabrication is usually restricted to the area of the wafer that lies within a containment circle of a radius 1-2 mm than the actual wafer radius. A simple and reasonably accurate algebraic expression is presented that explicitly relates the number of chips per wafer to the wafer diameter and to the geometric parameters that characterize the chip, i.e. the edge-length, the kerf plus pad cage dimension and the aspect ratio. The expression is applied to determining the size of chip for which the product of chips per wafer and circuits per chip is maximized for a given wafer diameter.<>