Abstract
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The exponent <formula formulatype="inline"><tex>$(\lambda)$</tex></formula> of the modified Airy function solution of the quantized energy levels in the MOS potential well, which is used in the physically based quantum-mechanical compact gate <formula formulatype="inline"><tex>$C$</tex></formula>– <formula formulatype="inline"><tex>$V$</tex></formula> model of Li <etal/>, has been found to be dependent on the barrier height at the Si–dielectric interface and the substrate doping density. The physical origins of this dependence are discussed. An empirical equation that considers these effects is proposed for <formula formulatype="inline"><tex>$\lambda$</tex></formula>. Comparison with the experimental <formula formulatype="inline"><tex>$C$</tex></formula>–<formula formulatype="inline"><tex>$V$</tex></formula> data of MOS devices with high-<formula formulatype="inline"><tex>$k$</tex></formula> gate dielectrics shows that inclusion of these effects in the compact <formula formulatype="inline"><tex>$C$</tex></formula>– <formula formulatype="inline"><tex>$V$</tex></formula> model of Li <etal/> is necessary for the accurate simulation of MOS field-effect transistors with high-<formula formulatype="inline"><tex>$k$</tex></formula> gate dielectrics. </para>
Published Version
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