The piezo-resistive effect in silicon for arbitrary crystal orientation

The piezo-resistive effect describes the change of resistance due to mechanical stress. Although known for a long time it is not so evident which wafer orientation and which layout minimizes resistance drifts due to stress changes. To this end, a general expression describing the piezo-resistance effect for arbitrary orientation in cubic crystal systems is deduced. Assuming the series connection of two nominally equal resistances with different directions of current flow, we discuss the influence of various components of the stress tensor on the total resistance. For the case of practical relevance with dominant in-plane normal and shear stresses, the two resistances should be oriented perpendicular to each other ("L-layout"). The highly anisotropic behavior is visualized for the first time by use of 3D plots. Practical conclusions are drawn how to minimize drift of electronic parameters caused by package related mechanical stress on integrated resistors and MOS transistors.