Abstract

This paper answers the frequently asked question, ldquoHow accurate are the approximate long-wide-channel thick-base MOS transistor baseline models that have been used to develop the compact models for computer-aided circuit designs?rdquo Three commonly used surface-potential-based( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U<sub>s</sub> <sub>=</sub> <sub>qPsis</sub> <sub>/</sub> <sub>kT</sub> </i> ) approximations of the ionized impurity bulk charge are evaluated as follows: <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alpha</sub> (i) ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Us</i> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> ; (ii) ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Us </i> -1) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> ; (iii)[ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Us</i> -1 + exp(- <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U</sub> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <sub>s</sub> </i> )] <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> . The double-integral baseline model for comparison includes the self-consistent remote charge-neutrality boundary condition, minority carriers, and space-constant impurity-concentration and oxide thickness. Percentage deviations of the approximations from the baseline model are computed for the dc drain current. Approximation (i) show a significant deviation, which is ~ 16% at threshold voltage, diverging rapidly in the subthreshold range toward flatband. Approximations (ii) and (iii) show a few percent (1% to 2%) deviations in both inversion and subthreshold ranges but diverge widely below subthreshold and in accummulation. A new analytical model is tested and shows better than 10% accuracy below subthreshold and in accummulation.

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