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Impact of triple-material gate and highly doped source/drain extensions on sensitivity of DNA biosensors

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Abstract

Gate engineering and highly doped source/drain region have been investigated to design a new DNA sensor for use in biomedical applications based on a double gate (DG) dielectric modulated (DM) junctionless (JL) metal oxide semiconductor field effect transistor (MOSFET) with triple material (TM) gate. Based on the dielectric modulation effect, DNA molecules in the nanogap cavity change due to the charge density of biomolecules, producing a change in the threshold voltage of the device. Analytical and numerical analysis was carried out to reveal the impact of physical parameters on the sensitivity of the proposed biosensor. Various characteristics, such as the surface potential, threshold voltage, and drain current were also investigated. The effectiveness of the proposed TM-DG-DM-JL-MOSFET structure with highly doped source/drain extensions is confirmed by comparison of the results with those for a conventional single-materiel (SM) gate DM-JL-MOSFET, revealing a good improvement in sensitivity and making the proposed structure an attractive solution for use in DNA-based sensor applications.

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Authors and Affiliations

  1. Laboratory of Advanced Automatic and Analysis of Systems (LAAAS), Department of Electronics, University of Batna2, 05000, Batna, Algeria

    M. Ouarghi, Z. Dibi & N. Hedjazi

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  1. M. Ouarghi
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  2. Z. Dibi
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  3. N. Hedjazi
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Correspondence to M. Ouarghi.

Appendices

Appendix A

$$ \sigma_{i} = - \frac{{\beta_{i} }}{{\alpha_{i} }}, $$
$$ D_{1 } = \frac{{(V_{\text{bi}} - \sigma_{1} ) - \left( {V_{1} - \sigma_{1} } \right)\mathrm{e}^{{ - L_{1} \sqrt {\alpha_{1} } }} }}{{1 - \mathrm{e}^{{ - 2L_{1} \sqrt {\alpha_{1} } }} }} , $$
$$ E_{1 } = \frac{{\left( {V_{1} - \sigma_{1} } \right) - (V_{\text{bi}} - \sigma_{1} )\mathrm{e}^{{ - L_{1} \sqrt {\alpha_{1} } }} }}{{1 - \mathrm{e}^{{ - 2L_{1} \sqrt {\alpha_{1} } }} }}, $$
$$ D_{2} = \frac{{(V_{1} - \sigma_{2} ) - \left( {V_{2} - \sigma_{2} } \right)\mathrm{e}^{{ - L_{2} \sqrt {\alpha_{2} } }} }}{{1 - \mathrm{e}^{{ - 2L_{2} \sqrt {\alpha_{2} } }} }} , $$
$$ E_{2 } = \frac{{\left( {V_{2} - \sigma_{2} } \right) - (V_{1} - \sigma_{2} )\mathrm{e}^{{ - L_{2} \sqrt {\alpha_{2} } }} }}{{1 - \mathrm{e}^{{ - 2L_{2} \sqrt {\alpha_{2} } }} }}, $$
$$ D_{3} = \frac{{\left( {V_{2} - \sigma_{3} } \right) - (V_{\text{bi}} + V_{\text{ds}} - \sigma_{3} )\mathrm{e}^{{ - L_{3} \sqrt {\alpha_{3} } }} }}{{1 - \mathrm{e}^{{ - 2L_{3} \sqrt {\alpha_{3} } }} }}, $$

where Vbi is the built-in potential, V1 and V2 are intermediate potentials, obtained by maintaining the continuity of the potential at the interface between region I, II, and III. Thus, we obtain

$$ A_{1} V_{1} + B_{1} V_{2} = F_{1}, $$
$$ A_{2} V_{1} + B_{2} V_{2} = {\text{F}}_{2}, $$

where

$$ A_{1} = \frac{{\mathrm{e}^{{2L_{1} \sqrt {\alpha_{1} } }} + 1}}{{\mathrm{e}^{{2L_{1} \sqrt {\alpha_{1} } }} - 1}} + \frac{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} + 1}}{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} - 1}}, $$
$$ B_{1} = \frac{ - 2}{{\mathrm{e}^{{L_{2} \sqrt {\alpha_{2} } }} - \mathrm{e}^{{ - L_{2} \sqrt {\alpha_{2} } }} }}, $$
$$\begin{aligned} F_{1} &= V_{\rm bi} \left( {\frac{2}{{\mathrm{e}^{{L_{1} \sqrt {\alpha_{1} } }} - \mathrm{e}^{{ - L_{1} \sqrt {\alpha_{1} } }} }}} \right)\\ & \quad + \delta_{1} \left( {\frac{2}{{\mathrm{e}^{{L_{1} \sqrt {\alpha_{1} } }} - \mathrm{e}^{{ - L_{1} \sqrt {\alpha_{1} } }} }} - \frac{{\mathrm{e}^{{2L_{1} \sqrt {\alpha_{1} } }} + 1}}{{\mathrm{e}^{{2L_{1} \sqrt {\alpha_{1} } }} - 1}}} \right)\\ & \quad + \delta_{2} \left( {\frac{2}{{\mathrm{e}^{{L_{2} \sqrt {\alpha_{2} } }} - \mathrm{e}^{{ - L_{2} \sqrt {\alpha_{2} } }} }} - \frac{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} + 1}}{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} - 1}}} \right),\end{aligned} $$
$$ A_{2} = \frac{ - 2}{{\mathrm{e}^{{L_{2} \sqrt {\alpha_{2} } }} - \mathrm{e}^{{ - L_{2} \sqrt {\alpha_{2} } }} }}, $$
$$ B_{2} = \frac{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} + 1}}{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} - 1}} + \frac{{\mathrm{e}^{{2L_{3} \sqrt {\alpha_{3} } }} + 1}}{{\mathrm{e}^{{2L_{3} \sqrt {\alpha_{3} } }} - 1}}, $$
$$\begin{aligned} F_{2} &= (V_{\rm bi} + V_{\rm ds} )\left( {\frac{2}{{\mathrm{e}^{{L_{3} \sqrt {\alpha_{3} } }} - \mathrm{e}^{{ - L_{3} \sqrt {\alpha_{3} } }} }}} \right)\\&\quad + \delta_{2} \left( {\frac{2}{{\mathrm{e}^{{L_{2} \sqrt {\alpha_{2} } }} - \mathrm{e}^{{ - L_{2} \sqrt {\alpha_{2} } }} }} - \frac{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} + 1}}{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} - 1}}} \right)\\&\quad + \delta_{3} \left( {\frac{2}{{\mathrm{e}^{{L_{3} \sqrt {\alpha_{3} } }} - \mathrm{e}^{{ - L_{3} \sqrt {\alpha_{3} } }} }} - \frac{{\mathrm{e}^{{2L_{3} \sqrt {\alpha_{3} } }} + 1}}{{\mathrm{e}^{{2L_{3} \sqrt {\alpha_{3} } }} - 1}}} \right).\end{aligned} $$

Using Crammer’s rule, it is possible to obtain the values of the intermediate potential V1 and V2 at the interfaces of regions I, II, and III as follows:

$$ V_{1} = \frac{{\left| {\begin{array}{*{20}c} {{{F}}_{1} } & {{{B}}_{1} } \\ {{{F}}_{2} } & {{{B}}_{2} } \\ \end{array} } \right|}}{{\left| {\begin{array}{*{20}c} {A_{1} } & {{{B}}_{1} } \\ {A_{2} } & {{{B}}_{2} } \\ \end{array} } \right|}} = \frac{{{{F}}_{1} {{B}}_{2} - F_{2} {{B}}_{1} }}{{A_{1} {{B}}_{2} - A_{2} {{B}}_{1} }} , $$
$$ V_{2} = \frac{{\left| {\begin{array}{*{20}c} {A_{1} } & {{{F}}_{1} } \\ {A_{2} } & {{{F}}_{2} } \\ \end{array} } \right|}}{{\left| {\begin{array}{*{20}c} {A_{1} } & {{{B}}_{1} } \\ {A_{2} } & {{{B}}_{2} } \\ \end{array} } \right|}} = \frac{{A_{1} {{F}}_{2} - F_{1} {{A}}_{2} }}{{A_{1} {{B}}_{2} - A_{2} {{B}}_{1} }}. $$

Appendix B

$$ m_{1 } = 2 \times \mathrm{e}^{{ - {{L}}_{1} \sqrt {\alpha_{1} } }} \left( {\frac{{\left( {V_{\rm bi} + r_{{i}} } \right)\mathrm{e}^{{ - {{L}}_{1} \sqrt {\alpha_{1} } }} - \left( {V_{s1} + r_{{i}} } \right)}}{{1 - {\text{e}}^{{ - 2{{L}}_{1} \sqrt {\alpha_{1} } }} }}} \right), $$
$$ m_{2 } = 2 \times \frac{{\left( {V_{\rm bi} + r_{{i}} } \right) - \left( {V_{s1} + r_{{i}} } \right)\mathrm{e}^{{ - {{L}}_{1} \sqrt {\alpha_{1} } }} }}{{1 - {\text{e}}^{{ - 2{{L}}_{1} \sqrt {\alpha_{1} } }} }}, $$
$$ n_{1} = 2\times \mathrm{e}^{{ - {{L}}_{1} \sqrt {\alpha_{1} } }} \left( {\frac{{1 - V_{s2} - \mathrm{e}^{{ - {{L}}_{1} \sqrt {\alpha_{1} } }} }}{{1 - {\text{e}}^{{ - 2{{L}}_{1} \sqrt {\alpha_{1} } }} }}} \right), $$
$$ n_{2} = 2\times \frac{{\mathrm{e}^{{ - {{L}}_{1} \sqrt {\alpha_{1} } }} - V_{{s2\mathrm{e}^{{ - {{L}}_{1} \sqrt {\alpha_{1} } }} }} - 1}}{{1 - {\text{e}}^{{ - 2{{L}}_{1} \sqrt {\alpha_{1} } }} }}, $$
$$ V_{\rm s1} = \frac{{{{C}}_{11} {{B}}_{2} - C_{21} {{B}}_{1} }}{{A_{1} {{B}}_{2} - A_{2} {{B}}_{1} }}V_{s2} = \frac{{C_{12} B_{2} - C_{22} B_{1} }}{{A_{1} B_{2} - A_{2} B_{1} }}, $$
$$ p_{i} = \frac{{qN_{\rm f} }}{{C_{i} }} + V_{\mathrm{fbi}} + 2\left( {V_{t} ln\frac{{N_{\rm d} }}{n_{\rm i}}} \right), $$
$$\begin{aligned} C_{11} &= \left( {\frac{2}{{\mathrm{e}^{{L_{2} \sqrt {\alpha_{2} } }} - \mathrm{e}^{{ - L_{2} \sqrt {\alpha_{2} } }} }} - \frac{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} + 1}}{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} - 1}}} \right)r_{2}\\ &\quad + \left( {\frac{2}{{\mathrm{e}^{{L_{1} \sqrt {\alpha_{1} } }} - \mathrm{e}^{{ - L_{1} \sqrt {\alpha_{1} } }} }} - \frac{{\mathrm{e}^{{2L_{1} \sqrt {\alpha_{1} } }} + 1}}{{\mathrm{e}^{{2L_{1} \sqrt {\alpha_{1} } }} - 1}}} \right)r_{1}\\&\quad + V_{\rm bi} \left( {\frac{2}{{\mathrm{e}^{{L_{1} \sqrt {\alpha_{1} } }} - \mathrm{e}^{{ - L_{1} \sqrt {\alpha_{1} } }} }}} \right), \end{aligned} $$
$$ \begin{aligned} C_{21} &= \frac{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} + 1}}{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} - 1}} - \frac{2}{{\mathrm{e}^{{L_{2} \sqrt {\alpha_{2} } }} - \mathrm{e}^{{ - L_{2} \sqrt {\alpha_{2} } }} }} + \frac{{\mathrm{e}^{{2L_{1} \sqrt {\alpha_{1} } }} + 1}}{{\mathrm{e}^{{2L_{1} \sqrt {\alpha_{1} } }} - 1}}\\&\quad - \frac{2}{{\mathrm{e}^{{L_{1} \sqrt {\alpha_{1} } }} - \mathrm{e}^{{ - L_{1} \sqrt {\alpha_{1} } }} }},\end{aligned} $$
$$ \begin{aligned} C_{12} &= \left( {\frac{2}{{\mathrm{e}^{{L_{2} \sqrt {\alpha_{2} } }} - \mathrm{e}^{{ - L_{2} \sqrt {\alpha_{2} } }} }} - \frac{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} + 1}}{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} - 1}}} \right)r_{2}\\&\quad + \left( {\frac{2}{{\mathrm{e}^{{L_{3} \sqrt {\alpha_{3} } }} - \mathrm{e}^{{ - L_{3} \sqrt {\alpha_{3} } }} }} - \frac{{\mathrm{e}^{{2L_{3} \sqrt {\alpha_{3} } }} + 1}}{{\mathrm{e}^{{2L_{3} \sqrt {\alpha_{3} } }} - 1}}} \right)r_{3}\\&\quad + \left( {V_{\rm bi} + V_{\rm ds} } \right)\left( {\frac{2}{{\mathrm{e}^{{L_{3} \sqrt {\alpha_{3} } }} - \mathrm{e}^{{ - L_{3} \sqrt {\alpha_{3} } }} }}} \right),\end{aligned} $$
$$ \begin{aligned} C_{22} &= \frac{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} + 1}}{{\mathrm{e}^{{2L_{2} \sqrt {\alpha_{2} } }} - 1}} - \frac{2}{{\mathrm{e}^{{L_{2} \sqrt {\alpha_{2} } }} - \mathrm{e}^{{ - L_{2} \sqrt {\alpha_{2} } }} }} + \frac{{\mathrm{e}^{{2L_{3} \sqrt {\alpha_{3} } }} + 1}}{{\mathrm{e}^{{2L_{3} \sqrt {\alpha_{3} } }} - 1}}\\&\quad - \frac{2}{{\mathrm{e}^{{L_{3} \sqrt {\alpha_{3} } }} - \mathrm{e}^{{ - L_{3} \sqrt {\alpha_{3} } }} }}, \end{aligned} $$
$$ r_{i} = - \frac{{{{qN}}_{\text{d}} }}{{\varepsilon_{\text{Si}} }} + V_{\mathrm{fb}i} ,\quad i = 1,2,3. $$

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Ouarghi, M., Dibi, Z. & Hedjazi, N. Impact of triple-material gate and highly doped source/drain extensions on sensitivity of DNA biosensors. J Comput Electron 17, 1797–1806 (2018). https://doi.org/10.1007/s10825-018-1228-3

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