Hole quantization effects and threshold voltage shift in pMOSFET-assessed by improved one-band effective mass approximation

Threshold voltage (V_T) shift due to quantum mechanical (QM) effects in pMOSFET is investigated based on a six-band effective mass approximation (EMA). Due to the valence band mixing, both subband energies and density of states (DOS) show remarkable difference from those derived from traditional one-band EMA using the bulk Si effective masses. In comparison with the experimental results, it is found that V _T Shift in pMOSFET is significantly overestimated by the traditional one-band EMA, however it corresponds with our six-band EMA calculation. Based on the numerical results of our six-band EMA, new effective masses are determined empirically and their electric field dependence is also evaluated. Using these new effective masses instead of the bulk effective masses, one-band EMA still display effectiveness in describing hole quantization and V_T Shift in an empirical manner. A set of constant energy quantization/DOS effective masses (0.29/1.14, 0.22/0.75, 0.24/0.66 m₀) for the first three subbands, neglecting their electric field dependence, is proposed for the modeling of QM effects in pMOSFET in this improved version of the one-band EMA formula. Computing time is minimized and results can be obtained with sufficient accuracy and correspond well with reported experimental data, thus the improved one-band EMA formula provide a firm ground in routine device simulation for deep submicron MOS devices