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A Complete Analytical RF Model for Nanoscale Semiconductor-On-Insulator MOSFET

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Abstract

Properly validated theoretical models are needed to understand the device and circuit level performance of MOSFET at high frequency. Analytical as well as compact models have special significance due to its SPICE simulator compatibility. Perhaps, most of the RF modelling approaches requires experimental Y, Z or S parameters to start with, which limits their acceptability in SPICE simulators. Considering this, under an innovative approach, starting from basic device physics, a complete generalized analytical RF model is developed for Semiconductor-On-Insulator MOSFET. Mathematical expressions for important MOSFET parameters valid at RF range are developed. Numbers of unique and justified mathematical formulations are adopted throughout the analysis to keep the parameter expressions simple but accurate. Parameters expressions are used to simulate and plot Y parameters with different structural and operational variables. These results are compared with reference results to check for validity. RF performance of current and upcoming Semiconductor-On-Insulator MOSFET structures are simulated and compared for better device selectivity.

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Authors and Affiliations

  1. Department of ECE, Kings Engineering College, Chennai, Tamil Nadu, India

    C. Rajarajachozhan

  2. Department of EECE, GST, GITAM Deemed to Be University, Bengaluru Campus, Karnataka, India

    S. Karthick

  3. Department of ECE, Bannari Amman Institute of Technology, Sathyamangalam, Tamil Nadu, India

    Sanjoy Deb

  4. Department of ECE, Manipur Institute of Technology, Takyelpat, Imphal, Manipur, India

    N. Basanta Singh

Authors
  1. C. Rajarajachozhan
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  2. S. Karthick
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  3. Sanjoy Deb
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  4. N. Basanta Singh
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Contributions

1st author – C Rajarajachozhan: Analytical modeling and simulation work, Original draft preparation, Final draft validation

2nd author – S Karthick: Study conception and design, checked the results and validation, Literature review.

3rd author – Sanjoy Deb: Supervision, Formal analysis and investigation.

4th author – N Basanta Singh: Final Draft Preparation.

Corresponding author

Correspondence to C. Rajarajachozhan.

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We declare that the manuscript entitled “A Complete Analytical RF Model for Nanoscale Semiconductor-On-Insulator MOSFET” is original, has not been full or partly published before, and is not currently being considered for publication elsewhere.

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Appendix

Appendix

Equations number mentioned as Refer in manuscript are accounted below:

$$\mathrm i.\;\mathrm A=\frac{{\mathrm V}_{\mathrm{bi}}\left(1-\mathrm e^{\sqrt{{\mathrm P}_2}\mathrm L}\right)+2{\mathrm V}_{\mathrm{bi}}\sinh(\sqrt{{\mathrm P}_2}\mathrm L)-{\mathrm V}_1\left(\mathrm e^{\sqrt{{\mathrm P}_2}\mathrm L}-1\right)+2{\mathrm V}_1\sinh(\sqrt{{\mathrm P}_2}\mathrm L)+{\mathrm V}_{\mathrm{ds}}}{2\sinh\sqrt{{\mathrm P}_2}\mathrm L}$$

The entire numerator terms are considered to be for simplification. So expression A can be written as

$$A=\frac{V_P}{2\,\sinh\,\sqrt{{\mathrm P}_2}\mathrm L}$$
(48)
$$\mathrm{ii}.\;\varphi_s\left(x\right)=\frac{V_P}{2\,\sinh\,\mathrm{ML}}exp\sqrt{\frac{P_2}{P_1}}x+\frac{{\mathrm V}_{\mathrm Q}}{2\,\sinh\,\mathrm{ML}}exp\left(-\sqrt{\frac{P_2}{P_1}}\right)x-\frac{P_3}{P_2}$$
(49)
$$\mathrm{iii}.\,{\mathrm{ E}}_{1}=\left\{\begin{array}{c}\frac{\mathrm{q}\left[1+\frac{2{C}_{c}{\mathrm{t}}_{\mathrm{b}}}{{\in }_{\mathrm{b}}}\right] {{\left({\mathrm{t}}_{\mathrm{c}}^{\mathrm{^{\prime}}}\right)}^{2}{\mathrm{n}}_{\mathrm{a}}}_{ }}{2{\in }_{\mathrm{Ch}}\left[{\upeta }_{2}\left(\frac{{\mathrm{C}}_{\mathrm{g}}{\mathrm{t}}_{\mathrm{b}}}{{\in }_{\mathrm{b}}}+\frac{{\mathrm{C}}_{\mathrm{g}}}{{C}_{c}}\right)+1+\left(\frac{{\mathrm{C}}_{\mathrm{g}}{\mathrm{t}}_{\mathrm{b}}}{{\in }_{\mathrm{b}}}+\frac{{\mathrm{C}}_{\mathrm{g}}}{{C}_{c}}\right)\right]}-\frac{{\mathrm{V}}_{\mathrm{Subf}}}{\left[{\upeta }_{2}\left(\frac{{\mathrm{C}}_{\mathrm{g}}{\mathrm{t}}_{\mathrm{b}}}{{\in }_{\mathrm{b}}}+\frac{{\mathrm{C}}_{\mathrm{g}}}{{C}_{c}}\right)+1+\left(\frac{{\mathrm{C}}_{\mathrm{g}}{\mathrm{t}}_{\mathrm{b}}}{{\in }_{\mathrm{b}}}+\frac{{\mathrm{C}}_{\mathrm{g}}}{{C}_{c}}\right)\right]}\\ +\frac{{\upeta }_{1}\left[\frac{{\mathrm{C}}_{\mathrm{g}}{\mathrm{t}}_{\mathrm{b}}}{{\in }_{\mathrm{b}}}+\frac{{\mathrm{C}}_{\mathrm{g}}}{{\mathrm{C}}_{\mathrm{c}}}\right]}{\left[{\upeta }_{2}\left(\frac{{\mathrm{C}}_{\mathrm{g}}{\mathrm{t}}_{\mathrm{b}}}{{\in }_{\mathrm{b}}}+\frac{{\mathrm{C}}_{\mathrm{g}}}{{C}_{c}}\right)+1+\left(\frac{{\mathrm{C}}_{\mathrm{g}}{\mathrm{t}}_{\mathrm{b}}}{{\in }_{\mathrm{b}}}+\frac{{\mathrm{C}}_{\mathrm{g}}}{{C}_{c}}\right)\right]}\end{array}\right\}- {\mathrm{V}}_{\mathrm{gs}}\left\{\frac{[\frac{{\mathrm{C}}_{\mathrm{g}}{\mathrm{t}}_{\mathrm{b}}}{{\in }_{\mathrm{b}}}+\frac{{\mathrm{C}}_{\mathrm{f}}}{{\mathrm{C}}_{\mathrm{c}}}]}{{\upeta }_{2}(\frac{{\mathrm{C}}_{\mathrm{g}}{\mathrm{t}}_{\mathrm{b}}}{{\in }_{\mathrm{b}}}+\frac{{\mathrm{C}}_{\mathrm{g}}}{{C}_{c}})+1+(\frac{{\mathrm{C}}_{\mathrm{g}}{\mathrm{t}}_{\mathrm{b}}}{{\in }_{\mathrm{b}}}+\frac{{\mathrm{C}}_{\mathrm{g}}}{{C}_{c}})}\right\}$$
(50)
$$\mathrm{iv}.{\mathrm V}_{\mathrm{th}}=\frac{2\mathrm{DE}\;\mathrm{Sin}\mathrm h^2\left(\mathrm{ML}\right)\pm\sqrt{\left\{2\mathrm{DE}\;\mathrm{Sin}\mathrm h^2(\mathrm{ML})\right\}^2+4\left\{\mathrm E^2\mathrm{Sinh}^2\left(\mathrm{ML}\right)\right\}\times\left\{{\mathrm V}_{\mathrm P}{\mathrm V}_{\mathrm Q}-\mathrm D^2\mathrm{Sinh}^2\left(\mathrm{ML}\right)-4\mathrm V_{\mathrm{bi}}^2\mathrm{Sin}\mathrm h^2(\mathrm{ML})\right\}}}{2\left\{\mathrm E^2\mathrm{Sinh}^2\left(\mathrm{ML}\right)\right\}}$$
(51)
$$\mathrm{v}.\, {I}_{ds,lin}={\mu }_{n}^{\prime}{C}_{f}\left(\frac{W}{L}\right){\{V}_{gs}{V}_{ds}-0.5{V}_{ds}^{2}-[\frac{\left({G}^{2}-G+2F{X}_{1}{X}_{2}-2F{N}_{2} -2F{N}_{1}\right){V}_{ds}}{2F}+\frac{0.5{V}_{ds}^{2}(2F{X}_{2}-2F{X}_{1})}{2F} ]\}$$
(52)
$$\mathrm{vi}. {g}_{d,Linear}={|{\mu }_{n}{C}_{OX}\left(\frac{W}{L}\right)\left[-{V}_{ds}+{V}_{gs}-\left\{\frac{{Z}_{1}}{2F}+\frac{{V}_{ds}}{2F}\left(2F{X}_{2}-2F{X}_{1}\right)\right\}\right]|}_{{V}_{gs=constant}}$$
(53)
$$\mathrm{vii}. {V}_{ds}^{sat}=\frac{\left(\frac{W}{L-\Delta L}\right)\left({\mu }_{n}^{\prime}{C}_{g}{V}_{gs}\right)-\left(\frac{W}{L-\Delta L}\right)\left({\mu }_{n}^{\prime}{C}_{g}\left(\frac{{G}^{2}-G+2F{X}_{1}{X}_{2}-2F{N}_{2}-2F{N}_{1} }{2F}\right)\right)}{\left(\frac{W}{L-\Delta L}\right)({\mu }_{n}^{\prime}{C}_{g}+\frac{{\mu }_{n}^{\prime}{C}_{g}\left(-2F{X}_{1}+2F{X}_{2}\right)}{2F})}$$
(54)
$$\mathrm{viii}.\, {Q}_{s}^{\prime}={J}_{1}+\frac{{J}_{1}\sqrt{{X}_{1}{X}_{2}{V}_{T}}}{\mathrm{sinh}\left(ML\right)}\left(1+\frac{\left({X}_{2}-{X}_{1}\right){V}_{ds}}{2{X}_{1}{X}_{2}}\right)-\frac{{J}_{1}{B}_{1}}{{P}_{2}{V}_{T}}[\frac{q{N}_{A}}{{\varepsilon }_{c}}-\frac{2{V}_{bs}}{{\left({t}_{c}^{\prime}\right)}^{2}\left[1+\frac{2{C}_{c}{t}_{b}}{{\varepsilon }_{b}}\right]}-\frac{2\left({V}_{gs}-{\eta }_{1}\right)[\frac{{\varepsilon }_{s}{t}_{b}}{{\varepsilon }_{b}}+\frac{{C}_{g}}{{C}_{c}}]}{{({t}_{c}^{\prime})}^{2}[1+\frac{2{C}_{c}{t}_{b}}{{\varepsilon }_{b}}]}]$$
(55)
$$\mathrm{ix}.\, {A}_{1}=\frac{\left({R}_{gs}S{C}_{gs}+1\right)[{R}_{ds}{R}_{m}+({R}_{ds}S{C}_{ds}+1)]}{{R}_{gs}S{C}_{gs}{SC}_{gd}\left[{R}_{ds}{R}_{m}+{R}_{ds}S{C}_{ds}+1\right]+S{C}_{gd}\left[{R}_{ds}{R}_{m}+{R}_{ds}S{C}_{ds}+1\right]+S{C}_{gs}\left[{R}_{ds}{R}_{m}+\left({R}_{ds}S{C}_{ds}+1\right)\right]+{R}_{ds}S{C}_{gs}S{C}_{gd}}$$
(56)
$$\mathrm{X}.\,{B}_{1}=\frac{{R}_{ds}S{C}_{gs}}{{R}_{gs}S{C}_{gs}S{C}_{gd}\left[{R}_{ds}{R}_{m}+{R}_{ds}S{C}_{ds}+1\right]+S{C}_{gd}\left[{R}_{ds}{R}_{m}+{R}_{ds}S{C}_{ds}+1\right]+S{C}_{gs}\left[{R}_{ds}{R}_{m}+\left({R}_{ds}S{C}_{ds}+1\right)\right]+{R}_{ds}S{C}_{gs}S{C}_{gd}}$$
(57)
$$\mathrm{xi}.\, {C}_{1}=\frac{({R}_{gs}S{C}_{gs}+1){R}_{ds}S{C}_{gd}}{{R}_{gs}S{C}_{gs}S{C}_{gd}\left[{R}_{ds}{R}_{m}+{R}_{ds}S{C}_{ds}+1\right]+S{C}_{gd}\left[{R}_{ds}{R}_{m}+{R}_{ds}S{C}_{ds}+1\right]+S{C}_{gs}\left[{R}_{ds}{R}_{m}+\left({R}_{ds}S{C}_{ds}+1\right)\right]+{R}_{ds}S{C}_{gs}S{C}_{gd}}$$
(58)
$$\mathrm{xii}.\, {Z}_{11}={R}_{g}+\frac{{A}_{1}{D}_{1}j\omega {C}_{db}+\left[\left({B}_{1}j\omega {C}_{db}+1\right)\left({A}_{1}+{D}_{1}\right)\right]}{{D}_{1}j\omega {C}_{db}+\left({B}_{1}j\omega {C}_{db}+1\right)+\left[{A}_{1}{D}_{1}j\omega {C}_{db}+\left({A}_{1}+{D}_{1}\right)\left({B}_{1}j\omega {C}_{db}+1\right)\right]j\omega {C}_{gb}}$$
(59)
$$\mathrm{xiii}.\, {Z}_{12}=\frac{\left({A}_{1}j\omega {C}_{gb}+1\right){D}_{1}}{\left({A}_{1}j\omega {C}_{gb}+1\right){D}_{1}j\omega {C}_{db}+{B}_{1}j\omega {C}_{db}\left[{A}_{1}j\omega {C}_{gb}+{D}_{1}j\omega {C}_{gb}+1\right]+{A}_{1}j\omega {C}_{gb}+1+{D}_{1 }j\omega {C}_{gb}}$$
(60)
$$\mathrm{xiv}.\, {Z}_{21}=\frac{\left({B}_{1}j\omega {C}_{db}+1\right){D}_{1}}{\left({B}_{1}j\omega {C}_{db}+1\right)+{D}_{1}j\omega {C}_{db}+{A}_{1}j\omega {C}_{gb}\left({B}_{1}j\omega {C}_{db}+{D}_{1}j\omega {C}_{db}+1\right)+({B}_{1}j\omega {C}_{db}+1){D}_{1}j\omega {C}_{gb}}$$
(61)
$$\mathrm{xv}.\,Z_{22}=R_d+\frac{B_1\left[A_1j\omega C_{gb}+1+D_1j\omega C_{gb}\right]+\left[A_1j\omega C_{gb}+1\right]D_1}{B_1\left[A_1j\omega C_{gb}+1+D_1j\omega C_{gb}\right]+\left(A_1j\omega C_{gb}+D_1\right)j\omega C_{db}+\lbrack A_1j\omega C_{gb}+1+D_1j\omega C_{gb}\rbrack}$$
(62)

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Rajarajachozhan, C., Karthick, S., Deb, S. et al. A Complete Analytical RF Model for Nanoscale Semiconductor-On-Insulator MOSFET. Silicon 15, 3049–3062 (2023). https://doi.org/10.1007/s12633-022-02215-3

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