Characterization and modeling of threshold voltage shift due to quantum mechanical effects in pMOSFET

Abstract The threshold voltage shift due to quantum mechanical effects (QMEs) has substantial influences on modern pMOSFET characteristics. Investigations of QMEs in a pMOSFET are classified into two approaches: full-band calculation and effective mass approximation. In this paper, formulation of carrier distribution in the pMOSFET inversion layer in the threshold region based on the effective mass approximation is presented, and a new method to calculate the threshold voltage shift due to QMEs is developed. The results with the effective mass approximation are compared with the full-band calculation and show satisfactory coincidence. Based on the present model, the subband structure of the hole inversion layer and the carrier distribution characteristics are investigated. The quantum mechanical and semi-classical two-dimensional density of states (2D DOS) are calculated and compared. The dependence of the threshold voltage shift due to QMEs on substrate doping concentration is then analyzed from the DOS point of view.