Piezoresistance in Quantized Conduction Bands in Silicon Inversion Layers

Piezoresistance measurements have been carried out on n-type inversion layers on (100), (110), and (111) silicon at room temperature as a function of the gate voltage (perpendicular electric field). It has been shown that the values of the piezoresistance coefficients depend not only on the surface orientation but also on the magnitude of the gate voltage. The strongest surface field influence was observed in the (100) plane whereas no gate voltage dependence could be detected on (111) surfaces. The data obtained have been interpreted in terms of the quantization of energy levels in inversion layers. This quantization causes generally an occupation anisotropy of the valleys mostly pronounced for an electric field in the [100] direction and disappearing for a [111] direction of the field. Theoretical expressions for the (100) piezoresistance coefficients π11 and π12 have been derived taking into account the field dependences of the population effect and of the intervally scattering contribution, both affected by the valley anisotropy. Experimental data have been fitted to the theory. From this fit numerical values of the occupation anisotropy of the valleys and of the anisotropy of the relaxation times relating to the intervalley scattering have been obtained.