Closed-Form Model for High-k MOSFET Channel Parameters: Reflecting Non-Saturating Inversion Surface Potential, Gate Stack Traps, and Work Function Anomaly

Abstract

Closed-form, textbook-appropriate equations have been derived for the drain current ID, the channel conductance gD, and the trans-conductance gm of high-k MOSFETs, incorporating high-k gate stack charges Qdi,gsc, non-saturating inversion surface potential increase Δφs,inv, and work-function difference ϕMS. These ab initio relations, developed without imposing any assumptions, provide a clear view of the degrading effects of the high-k gate stack charges, the non-saturating inversion surface potential, and the semiconductor-metal work function difference on ID, gD, and gm. Rational estimates have been made of the latter which illustrate the relative weights of each of the three non-ideal factors in the degradation of the channel parameters of the high-k gate stack. The degradation appears to be most severe for the channel conductance, followed by the drain current, and then the trans-conductance. The work-function anomaly does not directly affect the trans-conductance for which the major degrading factor is the non-saturating surface potential. Even for moderate drain voltages, the numerical estimates reveal the drain current versus the drain voltage relation to become more non-linear in the case of the high-k gate stack. Comparison with the available experimental high-k gate stack data supports the import of these equations.