Evaluation of piezoresistive coefficient variation in silicon stress sensors using a four-point bending test fixture

The variation of the piezoresistive coefficients from several rosettes on the same die, the same wafer, and finally at different doping levels across a number of wafers was examined. A thorough error analysis of the method of applying a known uniaxial state of stress using a four-point bending (4PB) fixture was completed. A sensor error analysis demonstrated that it is very difficult to determine accurate values for the sum (π₁₁+π₁₂) using the common two-element rosette, particularly in p-type material. However, an empirical equation was found that provides an estimate for this coefficient. The second piezoresistive coefficient π₄₄ can be measured accurately. However, the results presented for π₄₄ differ from those of previous authors by some 33%. Thus, it appears necessary to measure this value for a given wafer lot