AFM cantilever with ultra-thin transistor-channel piezoresistor: quantum confinement

This paper presents a comparison between the piezoresistivity effects on bulk silicon and its modification in the 2D case of the induced channel in the metal oxide semiconductor field effect transistor (MOSFET). The Schrödinger equation used for the calculations in this paper is based on the 6×6 kp Hamiltonian, which includes the effect of spin orbit interactions, band mixing, and strain. The effect of confinement is treated from the Schrödinger equation, coupled with the Poisson equation. In such a way, the valence band structure for the p-induced channel in MOSFET is resolved from a numerical self-consistent solution of the Schrödinger–Poisson system of equations. The calculations are made to show what happens when a MOSFET-like piezoresistor is substituted for one of the ordinary resistors of a Wheatstone bridge.