Analytical Modeling of Harmonic Distortions in GAA Junctionless FETs for Reliable Low-Power Applications

Abstract

The harmonic distortions (HDs) of a rectangular gate-all-around (GAA) junctionless (JL) field-effect transistor (FET) are analyzed using three-dimensional (3D) analytical modeling. The potential function [$\psi (x,y,z)$] of the device is derived based on the semianalytical dimension-based weighted-sum approximation approach. This method eliminates the complex mathematical computations of conventional 3D analysis and, at the same time, provides an alternate solution that yields good accuracy. The effect of flexible depletion lengths in the OFF-state is also taken into consideration, by solving biquadratic equations. The expression for the drain current is derived considering the above-mentioned potential function. Moreover, with this current expression, the harmonic distortions are evaluated and analyzed for reliable low-power applications. The proposed model is validated by comparing the analytical results with simulated data obtained from the 3D ATLAS device simulator. In addition, the output and harmonic characteristics of a cascode amplifier designed using GAA JL FETs are studied in detail.

Appendix

$$\begin{aligned} \begin{aligned}&\gamma _1=\sqrt{\frac{1+\frac{C_{\text {ox}}}{\epsilon _{\text {Si}}}{\widetilde{z}} - \frac{C_{\text {ox}}}{\epsilon _{\text {Si}}W} {\widetilde{z}}^{2}}{\frac{2C_{\text {ox}}}{\epsilon _{\text {Si}}W}}}, \ \ \gamma _2=\frac{C_{\text {ox}}\phi _{1}}{\epsilon _{\text {Si}}} \left( \frac{{\widetilde{z}}^2}{W} - {\widetilde{z}} \right) \\&P_6=-\gamma _2-\gamma ^{2}_{1} \left[ \frac{qN_{\rm d}}{\epsilon _{\text {Si}}} + \frac{2C_{\text {ox}}\phi _{1}}{\epsilon _{\text {Si}} W} \right] , \ \ \eta _1= \frac{t_{\text {Si}}}{W + t_{\text {Si}}} \\&\gamma _3=\sqrt{\frac{1+\frac{C_{\text {ox}}W}{4 \epsilon _{\text {Si}}}}{\frac{2C_{\text {ox}}}{\epsilon _{\text {Si}}W}}}, \ \gamma _4=\frac{-C_{\text {ox}}W\phi _{1}}{4 \epsilon _{\text {Si}}}, \ \eta _2 = \frac{W}{W + t_{\text {Si}}} \\&P_9=\gamma _4+\gamma ^{2}_{3} \left[ \frac{qN_{\rm d}}{\epsilon _{\text {Si}}} + \frac{2C_{\text {ox}}\phi _{1}}{\epsilon _{\text {Si}} W} \right] , \ \gamma _6 = \exp \left( -\frac{L}{\gamma ^{'}}\right) - \exp \left( \frac{L}{\gamma ^{'}}\right), \\&\gamma _7 = \exp \left( -\frac{L}{\gamma ^{'}}\right) + \exp \left( \frac{L}{\gamma ^{'}}\right) , \ \ \gamma _8 = -\frac{2 \gamma ^{'} \gamma _7}{\gamma _6}, \\&\gamma _9 = -\frac{4 \gamma ^{'}}{\gamma _6}, \ \ \gamma _{10} = \frac{2 \epsilon _{\text {Si}} \psi _{\text {bi}}}{q N_{\rm d}} - \frac{4 \epsilon _{\text {Si}} \eta ^{'} P^{'}}{q N_{\rm d}}, \\&\gamma _{11} = \frac{2 \epsilon _{\text {Si}} (\psi _{\text {bi}} + V_{\rm d})}{q N_{\rm d}} - \frac{4 \epsilon _{\text {Si}} \eta ^{'} P^{'}}{q N_{\rm d}}, \ \ \gamma _{12} = 2 \gamma _{8}, \\&\gamma _{13} = \gamma ^{2}_{8} - 2 \gamma _{10} -\gamma _{8} \gamma _{9}, \ \gamma _{14} = \gamma ^{3}_{9} - \gamma _{8} \gamma _{10} -\gamma ^{2}_{8} \gamma _{9}, \\&\gamma _{15} = \gamma ^{2}_{10} + \gamma _{8} \gamma _{9} \gamma _{10} - \gamma ^{2}_{9} \gamma _{11}, \ \ \gamma _{16} = \gamma ^{2}_{8} - 2 \gamma _{11} - \gamma _{8} \gamma _{9}, \\&\gamma _{17} = \gamma ^{3}_{9} - 2 \gamma _{8} \gamma _{11} - \gamma ^{2}_{8} \gamma _{9}, \ \ \gamma _{18} = \gamma ^{2}_{11} + \gamma _{8} \gamma _{9} \gamma _{11} - \gamma ^{2}_{9} \gamma _{10}. \end{aligned} \end{aligned}$$

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