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Electrostatic characterization and threshold voltage modeling of inversion type InGaAs gate-all-around MOSFET

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Abstract

This paper presents an analytical investigation of the electrostatic properties of a moderately doped symmetric gate-all-around nanowire MOSFET having InGaAs channel. The model is continuous from depletion to strong inversion regime that circumvents regional approach, thus smoothly capturing the transition of the charge profile in all regions of operation. The evolution of the model is facilitated by the solution of quasi 2-D Poisson equation with appropriate boundary conditions in a square gate-all-around geometry, incorporating fixed oxide charge and interface trap defects. The determination of mobile charge density leads to the capacitance-voltage (CV) characteristics as a function of gate bias. The CV profile is investigated subject to scaling of physical parameters and material properties. Further, a threshold voltage model is presented for a long channel gate-all-around device that utilizes the well-known double derivative method. This model accurately predicts the threshold voltage variation with fin width, oxide thickness and channel doping, highlighting room for further improvement in electrostatics by incorporating high-k dielectric. The excellent match between the model results and TCAD simulation reflects the validity of the proposed model.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This work has been carried out in the Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology (BUET). The authors gratefully acknowledge the support and facilities provided by BUET.

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  1. Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology, Dhaka, 1000, Bangladesh

    I. K. M. Reaz Rahman, Md. Irfan Khan & Quazi D. M. Khosru

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Appendix: Difference of surface-center potential in terms of Lambert function

Appendix: Difference of surface-center potential in terms of Lambert function

Generally the double derivative of potential can be written using coarse finite difference method [23] resulting into,

$$\begin{aligned} \frac{\mathrm{d}^2\phi }{\mathrm{d} x^2}\bigg |_{x=0}=\left( \frac{\phi (-\frac{W}{2})-\phi _0}{W/2}-\frac{\phi _0-\phi (\frac{W}{2})}{W/2}\right) \frac{1}{W/2} \end{aligned}$$
(A.1)

Under symmetric operation, \(E|_{x=0}=0\) and using simplifying assumptions leads to,

$$\begin{aligned} \phi (W/2)=\phi (-W/2) \end{aligned}$$
(A.2)

Substituting (2) into (A.1) we get,

$$\begin{aligned} \frac{8}{W^2}\left( \phi \left( \frac{W}{2}\right) -\phi _0\right)&=\frac{qN_\mathrm{A}}{2\epsilon _\mathrm{s}} \left( \frac{n_\mathrm{i}^2}{N_\mathrm{A}^2}\mathrm{e}^{\frac{\phi _0-V}{\phi _\mathrm{t}}}+1\right) \end{aligned}$$
(A.3)
$$\begin{aligned} \phi _\mathrm{s}-\phi _0&=\frac{qN_\mathrm{A}W^2}{16\epsilon _\mathrm{s}}\left( \frac{n_\mathrm{i}^2}{N_\mathrm{A}^2}\mathrm{e}^{\frac{\phi _0-V}{\phi _\mathrm{t}}}+1\right) \end{aligned}$$
(A.4)

After some mathematical manipulation, the normalized difference of potential can be expressed as,

$$\begin{aligned} \alpha =\alpha _\mathrm{st}+\mathrm{LW}\left( \frac{n_\mathrm{i}^2}{N_\mathrm{A}^2}\alpha _\mathrm{st}\mathrm{e}^{-\alpha _\mathrm{st}}\mathrm{e}^{\frac{\phi _\mathrm{s}-V}{\phi _\mathrm{t}}}\right) \end{aligned}$$
(A.5)

From (A.5) the following relation also holds,

$$\begin{aligned} \frac{n_\mathrm{i}^2}{N_\mathrm{A}^2}\mathrm{e}^{\frac{\phi _0-V}{\phi _\mathrm{t}}}-\alpha =-1-\alpha \left( 1-\frac{1}{\alpha _\mathrm{st}}\right) \end{aligned}$$
(A.6)

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Rahman, I.K.M.R., Khan, M.I. & Khosru, Q.D.M. Electrostatic characterization and threshold voltage modeling of inversion type InGaAs gate-all-around MOSFET. J Comput Electron 20, 1504–1512 (2021). https://doi.org/10.1007/s10825-021-01716-5

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