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

Closed-form, textbook-appropriate equations have been derived for the drain current I-D, the channel conductance gD, and the transconductance g(m) of high-k MOSFETs, incorporating high-k gate stack charges Q(di,gsc), non-saturating inversion surface potential increase Delta(phi s,inv), and work-function difference empty set(MS). 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 I-D, g(D), and g(m). 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. (C) 2012 The Electrochemical Society.