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Published in:
2010 | OriginalPaper | Chapter
3. Graphical Interpretation of the Charge Sheet Model
Author : Prof. Paul G. A. Jespers
Published in: The g m /I D Methodology, A Sizing Tool for Low-voltage Analog CMOS Circuits
Publisher: Springer US
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Abstract
An interesting representation of the drain current can be obtained when the expression below is used for the drain current (Tsividis 1999): The equation is derived from, the proportionality of the minority carrier density to the exponential function acknowledged by Boltzmann statistics:
$${I}_{D} = \mu {C}_{ox}^{{\prime}}\frac{W} {L} \cdot {\int \nolimits }_{{V }_{S}}^{{V }_{D} }\left (- \frac{{Q}_{i}^{{\prime}}} {{C}_{ox}^{{\prime}}}\right )\,\mathit{dV }\,$$
(3.1)
$${Q}_{i}^{{\prime}}\propto \exp \left (\frac{{\psi }_{S} - 2{\phi }_{B} - V } {{U}_{T}} \right )$$
(3.2)