Quantum size aspects of the piezoresistive effect in ultra thin piezoresistors

Proximal probe sensors with an ability to detect extremely small forces (10(-15)-10(-18)N) play significant role in scanning probe microscopy applications. The detection of extremely low forces, require producing micromachined cantilevers with as small as possible spring constants, which is considered by the optimization of the sensor design. In the last year many papers describing the fabrication process of producing ultrathin cantilevers (below 100nm) with integrated piezoresistors for deflection read-out have been published. In the case of such cantilevers the required thickness of piezoresistors is in the range of 50nm. From a quantum mechanical point of view, an electrical carrier transport confinement in direction perpendicular to the cantilever surface can be expected and in this manner we have to consider the quantum size effect. The goal of the project described in this paper is to calculate and determine the piezoresistive coefficients in p type Si thin (under 50nm) piezoresistors taking into account the quantum size effect and to compare them with the corresponding coefficients for bulk material. The calculation of the band structure will use the mathematical apparatus of an exact analytical diagonalization six-band k.p model, modified with the envelope function approximation. The behaviour of the thin piezoresistors employed as integrated deflection read-out will be also discussed. Moreover, critical issues in the realization of piezoresistors formed by MOS transistor channel will be presented.