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Numerical modeling of a dielectric modulated surrounding-triple-gate germanium-source MOSFET (DM-STGGS-MOSFET)-based biosensor

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Abstract

This paper presents for the first time an analytical model of a dielectric modulated surrounding-triple-gate MOSFET with a germanium source-based biosensor, which shows excellent improvement in sensitivity when compared to a silicon source. The mathematical analysis is based on the center-channel potential which is obtained by solving Poisson's equation in the cylindrical coordinate system using a parabolic approximation. The channel potential profile, threshold voltage, drain current, and subthreshold swing are obtained mathematically. Biosensing performance is investigated for different charged and neutral biomolecules by varying different device metrics including cavity thickness, channel thickness, cavity length, channel do**, and drain voltage. The analytical results are validated and verified with numerical simulations conducted with the ATLAS TCAD simulator and show outstanding agreement with the simulated results.

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Acknowledgements

The authors are grateful to the Director, Maharaja Agrasen Institute of Technology, Delhi, for providing the facilities to carry out this research work. One of the authors (Amit Das) would like to thank UGC, Government of India, for financial assistance to carry out this research work.

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Authors and Affiliations

  1. School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, 110067, India

    Amit Das & Binod Kumar Kanaujia

  2. Department of Electronics and Communication Engineering, Delhi Technological University, New Delhi, 110042, India

    Sonam Rewari

  3. Department of Electrical and Electronics Engineering, Maharaja Agrasen Institute of Technology, New Delhi, 110086, India

    S. S. Deswal

  4. Department of Electronics and Communication Engineering, Maharaja Agrasen Institute of Technology, New Delhi, 110086, India

    R. S. Gupta

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  1. Amit Das
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Appendices

Appendix A

$$e_{1} = 2\left[ {\frac{\alpha }{{\mu_{1} }}\cosh \left( {\frac{{z_{1} - z_{2} }}{{\mu_{1} }}} \right) + \frac{\beta }{{\mu_{2} }}\cosh \left( {\frac{{z_{2} - z_{3} }}{{\mu_{2} }}} \right)} \right],e_{2} = 2\frac{\beta }{{\mu_{2} }},e_{3} = 2\left[ {\frac{\beta }{{\mu_{2} }}\cosh \left( {\frac{{z_{2} - z_{3} }}{{\mu_{2} }}} \right) + \frac{\gamma }{{\mu_{3} }}\cosh \left( {\frac{{z_{3} - z_{4} }}{{\mu_{3} }}} \right)} \right],e_{4} = \left( {e_{1} e_{3} - e_{{_{2} }}^{2} } \right)^{ - 1}$$
$$s = \frac{\alpha }{{\mu_{1} }}s_{1} - \frac{\beta }{{\mu_{2} }}s_{2} ,t = \frac{\gamma }{{\mu_{3} }}t_{1} - \frac{\beta }{{\mu_{2} }}t_{2}$$
$$s_{1} = s_{1a} - s_{1b} ,s_{2} = s_{2a} - s_{2b} \quad s_{1a} = \theta_{1} e^{{\frac{{z_{2} }}{{\mu_{1} }}}} \left( {e^{{\frac{{ - z_{1} }}{{\mu_{1} }}}} - e^{{\frac{{ - z_{2} }}{{\mu_{1} }}}} } \right)\quad s_{1b} = \theta_{1} e^{{\frac{{ - z_{2} }}{{\mu_{1} }}}} \left( {e^{{\frac{{z_{2} }}{{\mu_{1} }}}} - e^{{\frac{{z_{1} }}{{\mu_{1} }}}} } \right) - 2V_{bi,1}$$
$$s_{2a} = \theta_{2} e^{{\frac{{z_{2} }}{{\mu_{2} }}}} \left( {e^{{\frac{{ - z_{2} }}{{\mu_{2} }}}} - e^{{\frac{{ - z_{3} }}{{\mu_{2} }}}} } \right),s_{2b} = \theta_{2} e^{{\frac{{ - z_{2} }}{{\mu_{2} }}}} \left( {e^{{\frac{{z_{3} }}{{\mu_{2} }}}} - e^{{\frac{{z_{2} }}{{\mu_{2} }}}} } \right)$$
$$t_{1} = t_{1a} - t_{1b} ,t_{2} = t_{2a} - t_{2b} ,t_{1a} = \theta_{3} e^{{\frac{{z_{3} }}{{\mu_{3} }}}} \left( {e^{{\frac{{ - z_{3} }}{{\mu_{3} }}}} - e^{{\frac{{ - z_{4} }}{{\mu_{3} }}}} } \right) - 2V_{bi,2}$$
$$t_{1b} = \theta_{3} e^{{\frac{{ - z_{3} }}{{\mu_{3} }}}} \left( {e^{{\frac{{z_{4} }}{{\mu_{3} }}}} - e^{{\frac{{z_{3} }}{{\mu_{3} }}}} } \right) + 2V_{DS} ,\quad t_{2a} = \theta_{2} e^{{\frac{{z_{3} }}{{\mu_{2} }}}} \left( {e^{{\frac{{ - z_{2} }}{{\mu_{2} }}}} - e^{{\frac{{ - z_{3} }}{{\mu_{2} }}}} } \right)$$
$$t_{2b} = \theta_{2} e^{{\frac{{ - z_{3} }}{{\mu_{2} }}}} \left( {e^{{\frac{{z_{3} }}{{\mu_{2} }}}} - e^{{\frac{{z_{2} }}{{\mu_{2} }}}} } \right)$$

Appendix B

$$n_{11} = 4d_{11} - 1,n_{12} = 4d_{22} + 2\xi_{1} + 4\phi_{f} ,n_{13} = 4d_{3} - 4\phi_{f}^{2} - \xi_{1}^{2} - 4\phi_{f} \xi_{1} ,d_{11} = d_{33} = d_{1} d_{3} ,d_{22} = d_{1} + d_{3}$$
$$d_{2} = \alpha n_{1} ,\quad d_{4} = \alpha n_{2} ,\quad \phi_{f} = V_{T} \ln \left( {\frac{{N_{Ch} }}{{n_{i(Si)} }}} \right)$$
$$d_{1} = \alpha \left[ {\left( {e^{{\frac{{ - z_{1} }}{{\mu_{1} }}}} - e^{{\frac{{ - z_{2} }}{{\mu_{1} }}}} } \right) - e^{{\frac{{ - z_{1} }}{{\mu_{1} }}}} e_{3} e_{4} \left( {m_{1} - m_{2} } \right) - e^{{\frac{{ - z_{1} }}{{\mu_{1} }}}} e_{2} e_{4} \left( {m_{4} - m_{5} } \right)} \right]$$

\(d_{3} = \alpha \left[ {\left( {e^{{\frac{{z_{2} }}{{\mu_{1} }}}} - e^{{\frac{{z_{1} }}{{\mu_{1} }}}} } \right) + e^{{\frac{{z_{1} }}{{\mu_{1} }}}} e_{3} e_{4} \left( {m_{1} - m_{2} } \right) - e^{{\frac{{z_{1} }}{{\mu_{1} }}}} e_{2} e_{4} \left( {m_{4} - m_{5} } \right)} \right],V_{T} = \frac{{k_{B} T}}{q}\) ,

$$n_{1} = \left[ { - \xi_{1} \left( {e^{{\frac{{ - z_{1} }}{{\mu_{1} }}}} - e^{{\frac{{ - z_{2} }}{{\mu_{1} }}}} } \right) + V_{bi,1} e^{{\frac{{ - z_{2} }}{{\mu_{1} }}}} - e^{{\frac{{ - z_{1} }}{{\mu_{1} }}}} e_{3} e_{4} \left( { - m_{1} \xi_{1} + m_{2} \xi_{2} - m_{3} } \right) + e^{{\frac{{ - z_{1} }}{{\mu_{1} }}}} e_{2} e_{4} \left( { - m_{4} \xi_{3} + m_{5} \xi_{2} - m_{6} } \right)} \right],n_{2} = \left[ { - \xi_{1} \left( {e^{{\frac{{z_{2} }}{{\mu_{1} }}}} - e^{{\frac{{z_{1} }}{{\mu_{1} }}}} } \right) - V_{bi,1} e^{{\frac{{z_{2} }}{{\mu_{1} }}}} + e^{{\frac{{z_{1} }}{{\mu_{1} }}}} e_{3} e_{4} \left( { - m_{1} \xi_{1} + m_{2} \xi_{2} - m_{3} } \right) - e^{{\frac{{z_{1} }}{{\mu_{1} }}}} e_{2} e_{4} \left( { - m_{4} \xi_{3} + m_{5} \xi_{2} - m_{6} } \right)} \right],\xi_{1} = \frac{{qN_{Ch} a}}{{2C_{{ox_{1} }} }} + \frac{{qN_{Ch} a^{2} }}{{4\varepsilon_{Ch} }} - V_{{FB_{1} }} ,\xi_{2} = \frac{{qN_{Ch} a}}{{2C_{{ox_{2} }} }} + \frac{{qN_{Ch} a^{2} }}{{4\varepsilon_{Ch} }} - V_{{FB_{2} }} ,\xi_{3} = \frac{{qN_{Ch} a}}{{2C_{{ox_{3} }} }} + \frac{{qN_{Ch} a^{2} }}{{4\varepsilon_{Ch} }} - V_{{FB_{3} }} ,m_{3} = \frac{ - 2\alpha }{{\mu_{1} }}V_{{bi_{1} }} ,m_{6} = \frac{2\gamma }{{\mu_{3} }}\left[ {V_{{bi_{2} }} + V_{DS} } \right]$$
$$m_{1} = \frac{\alpha }{{\mu_{1} }}\left[ {e^{{\frac{{z_{2} }}{{\mu_{1} }}}} \left( {e^{{\frac{{ - z_{1} }}{{\mu_{1} }}}} - e^{{\frac{{ - z_{2} }}{{\mu_{1} }}}} } \right) - e^{{\frac{{ - z_{2} }}{{\mu_{1} }}}} \left( {e^{{\frac{{z_{2} }}{{\mu_{1} }}}} - e^{{\frac{{z_{1} }}{{\mu_{1} }}}} } \right)} \right]$$
$$m_{2} = \frac{\beta }{{\mu_{2} }}\left[ {e^{{\frac{{z_{2} }}{{\mu_{2} }}}} \left( {e^{{\frac{{ - z_{2} }}{{\mu_{2} }}}} - e^{{\frac{{ - z_{3} }}{{\mu_{2} }}}} } \right) - e^{{\frac{{ - z_{2} }}{{\mu_{2} }}}} \left( {e^{{\frac{{z_{3} }}{{\mu_{2} }}}} - e^{{\frac{{z_{2} }}{{\mu_{2} }}}} } \right)} \right]$$
$$m_{4} = \frac{\gamma }{{\mu_{3} }}\left[ {e^{{\frac{{z_{3} }}{{\mu_{3} }}}} \left( {e^{{\frac{{ - z_{3} }}{{\mu_{3} }}}} - e^{{\frac{{ - z_{4} }}{{\mu_{3} }}}} } \right) - e^{{\frac{{ - z_{3} }}{{\mu_{3} }}}} \left( {e^{{\frac{{z_{4} }}{{\mu_{3} }}}} - e^{{\frac{{z_{3} }}{{\mu_{3} }}}} } \right)} \right]$$
$$m_{5} = \frac{\beta }{{\mu_{2} }}\left[ {e^{{\frac{{z_{3} }}{{\mu_{2} }}}} \left( {e^{{\frac{{ - z_{2} }}{{\mu_{2} }}}} - e^{{\frac{{ - z_{3} }}{{\mu_{2} }}}} } \right) - e^{{\frac{{ - z_{3} }}{{\mu_{2} }}}} \left( {e^{{\frac{{z_{3} }}{{\mu_{2} }}}} - e^{{\frac{{z_{2} }}{{\mu_{2} }}}} } \right)} \right]$$

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Das, A., Rewari, S., Kanaujia, B.K. et al. Numerical modeling of a dielectric modulated surrounding-triple-gate germanium-source MOSFET (DM-STGGS-MOSFET)-based biosensor. J Comput Electron 22, 742–759 (2023). https://doi.org/10.1007/s10825-023-02008-w

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