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Analytical model for the effects of the variation of ferrolectric material parameters on the minimum subthreshold swing in negative capacitance capacitor

Raheela Rasool, Najeeb-ud-Din and G. M. Rather

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 Corresponding author: Raheela Rasool, E-mail: raheela_03phd14@nitsri.net

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Abstract: In this paper, we analytically study the relationship between the coercive field, remnant polarization and the thickness of a ferroelectric material, required for the minimum subthreshold swing in a negative capacitance capacitor. The interdependence of the ferroelectric material properties shown in this study is defined by the capacitance matching conditions in the subthreshold region in an NC capacitor. In this paper, we propose an analytical model to find the optimal ferroelectric thickness and channel doping to achieve a minimum subthreshold swing, due to a particular ferroelectric material. Our results have been validated against the numerical and experimental results already available in the literature. Furthermore, we obtain the minimum possible subthreshold swing for different ferroelectric materials used in the gate stack of an NC-FET in the context of a manufacturable semiconductor technology. Our results are presented in the form of a table, which shows the calculated channel doping, ferroelectric thickness and minimum subthreshold for five different ferroelectric materials.

Key words: NC-capacitorferroelectricssubthreshold swingnegative capacitance



[1]
Salahuddin S, Datta S. Use of Negative capaciatnce to provide volatge amplification for low power nanoscale devices. Nano Lett, 2008, 8(2), 405 doi: 10.1021/nl071804g
[2]
Khan A I, Bhowmik D, Yu P, et al. Experimental evidenceof ferroelectric Negative capacitance in nanoscale heterostructures. Appl Phys Lette, 2011, 99(11), 113501 doi: 10.1063/1.3634072
[3]
Seabaugh A C, Zhang Q. Low-voltage tunnel transistors for beyond CMOS logic. Proc IEEE, 2010, 98(12), 2095 doi: 10.1109/JPROC.2010.2070470
[4]
Gopalakrishnan K, Woo R, Jungemann C, et al. Impact ionization MOS (I-MOS) -Part I: Device and circuit simulation. IEEE Trans Electron Devices, 2005, 52(1), 69 doi: 10.1109/TED.2004.841344
[5]
Devonshire A F. Theory of ferrolelctrics. Adv Phys, 1954, 3(10), 85 doi: 10.1080/00018735400101173
[6]
Rabe K M, Ahn C H, Triscone J M. Physics of ferroelectrics: a modern perspective. Berlin: Springer, 2007
[7]
Ginzburg V L. Phase transitions in ferroelctrics: some historical remarks. UFN, 2001, 171(10), 1091 doi: 10.3367/UFNr.0171.200110j.1091
[8]
Rusu A, Salvatore G A, Jimenez D, et al. Metal-ferroelectric-metal-oxide semiconductor field effect transistor with sub-60mV/decade subthreshold swing and voltage amplification. IEEE International Electron Devices Meeting, 2010, 6.3.1
[9]
Taur Y, Ning T. Fundamentals of Modern VLSI device. Cambridge: Cambridge University Press, 1998.
[10]
Rasool R, Rather G M, ud-Din N. Analytic model for the electrical properties of negative capacitance metal-ferroelectric-insulator-silicon (MFIS) capacitor. Integrated Ferroelectrics, 2017, 185, 93 doi: 10.1080/10584587.2017.1370345
[11]
Jain A, Alam M A. Prospects of hysterisis free abrupt switching (0 mV/decade) in Landau switches. IEEE Trans Electron Devices, 2013, 60(12), 4269 doi: 10.1109/TED.2013.2286997
[12]
Khan A I, Yeung C W, Hu C, et al. Ferroelectric negative capacitance MOSFET: Capacitance tuning & antiferroelectric operation. IEDM Tech Dig, 2011, 255
[13]
Seeger J I, Crary S B. Analysis and simulation of MOS capacitor feedback for stabilizing electrostatically actuated mechanical devices. Trans Built Environ, 1997, 31(13), 1
[14]
Krowne C W, kirchoefer S W, Chang W, et al. Examination of possibility of negative capaciatnce using ferroelectric materials in solid state electronic devices. Nanoletters, 2011, 11(3), 988 doi: 10.1021/nl1037215
[15]
Jain A, Alam M A. Stability constraints define the minimum subthreshold swing of a negative capacitance field-effect transistor. IEEE Trans Electron Devices, 2014, 61(7), 2235 doi: 10.1109/TED.2014.2316167
[16]
Jiménez D, Miranda E, Godoy A. Analytic model for the surface potential and drain current in negative capacitance field-effect transistors. IEEE Trans Electron Devices, 2010, 57(10), 2405 doi: 10.1109/TED.2010.2062188
[17]
Pierret R F. Semiconductor device fundamentals. Pearson, 1995
[18]
Dasgupta S, Rajashekhar A, Majumdar K, et al. Sub-KT/Q switching in strong inversion in PbZr0.52Ti0.4O3 gated negative capaciatnce FETs. IEEE J Explor Solid State Comput Devices Circuits, 2015, 1, 43 doi: 10.1109/JXCDC.2015.2448414
[19]
Lee H, Yoon Y, Shin C. Current voltage model for negative capacitance field effect transistors. IEEE Electron Device Lett, 2017, 38(5), 669 doi: 10.1109/LED.2017.2679102
[20]
Lin C I, Khan A I, Salahuddin S, et al. Effects of the variation of ferroelectric properties on negative capacitance FET characteristics. IEEE Trans Electron Devices, 2016, 63(5), 2197 doi: 10.1109/TED.2016.2514783
[21]
Cano A, Jimenez D. Multidomain ferroelectricity as a limiting factor for voltage amplification in ferroelectric field-effect transistors. Appl Phys Lett, 2010, 97(13), 133509 doi: 10.1063/1.3494533
[22]
Boscke T S, Muller J, Bruhaus D, et al. Ferroelectricity in hafnium oxide: CMOS compatible ferroelectric field effect transistors. IEE Electron Devices Meeting, 2011, 24
[23]
Li Y, Lian Y, K Yao K, et al. Evaluation and optimization of short channel ferroelectric MOSFET for low power circuit application with BSIM4 and Landau theory. Solid State Electron, 2015, 114, 17 doi: 10.1016/j.sse.2015.07.001
[24]
Saeidi A, Jazaeri F, Stolichnov I, et al. Double-gate negative-capaciatnce MOSFET with PZT gate stack on ultra thin body SOI: An experimentally caliberated simulation study of device performance. IEEE Trans Electron Devices, 2016, 63(12), 4678 doi: 10.1109/TED.2016.2616035
Fig. 1.  (a) Schematic of MFMIS based NC-FET. (b) Equivalent capacitance divider.

Fig. 2.  Voltage-charge plot for a ferroelectric material.

Fig. 3.  (a) Capacitance versus charge plots for MOS capacitor, ferroelectric capacitor and the total capacitance of MFMIS capacitor. (b) Voltage charge plot of the MFMIS capacitor.

Table 1.   Ferroelectric thickness (tFE) and minimum subthreshold swing (Smin) for different ferroelectric materials.

ParameterPZT[20]BaTiO3[15]SBT[15]HfSiO[22]P(VDF-TrFE)[23]
α (cm/F)–2.25 × 109–5 × 108–3.25 × 109–8.65 × 1010–1.8 × 1011
β (cm3/F/C2)1.3 × 10182.2 × 10189.37 × 10181.92 × 10205.8 × 1022
γ (cm5/F/C4)9.83 × 10257.5 × 1027000
NA (cm–3)2.3 × 10203.3 × 10207.5 × 10195.7 × 10194 × 1018
tox (nm)22222
tFE (nm)22.319.315.55.82.8
Smin (mV/dec)52.846.541.63127
DownLoad: CSV
[1]
Salahuddin S, Datta S. Use of Negative capaciatnce to provide volatge amplification for low power nanoscale devices. Nano Lett, 2008, 8(2), 405 doi: 10.1021/nl071804g
[2]
Khan A I, Bhowmik D, Yu P, et al. Experimental evidenceof ferroelectric Negative capacitance in nanoscale heterostructures. Appl Phys Lette, 2011, 99(11), 113501 doi: 10.1063/1.3634072
[3]
Seabaugh A C, Zhang Q. Low-voltage tunnel transistors for beyond CMOS logic. Proc IEEE, 2010, 98(12), 2095 doi: 10.1109/JPROC.2010.2070470
[4]
Gopalakrishnan K, Woo R, Jungemann C, et al. Impact ionization MOS (I-MOS) -Part I: Device and circuit simulation. IEEE Trans Electron Devices, 2005, 52(1), 69 doi: 10.1109/TED.2004.841344
[5]
Devonshire A F. Theory of ferrolelctrics. Adv Phys, 1954, 3(10), 85 doi: 10.1080/00018735400101173
[6]
Rabe K M, Ahn C H, Triscone J M. Physics of ferroelectrics: a modern perspective. Berlin: Springer, 2007
[7]
Ginzburg V L. Phase transitions in ferroelctrics: some historical remarks. UFN, 2001, 171(10), 1091 doi: 10.3367/UFNr.0171.200110j.1091
[8]
Rusu A, Salvatore G A, Jimenez D, et al. Metal-ferroelectric-metal-oxide semiconductor field effect transistor with sub-60mV/decade subthreshold swing and voltage amplification. IEEE International Electron Devices Meeting, 2010, 6.3.1
[9]
Taur Y, Ning T. Fundamentals of Modern VLSI device. Cambridge: Cambridge University Press, 1998.
[10]
Rasool R, Rather G M, ud-Din N. Analytic model for the electrical properties of negative capacitance metal-ferroelectric-insulator-silicon (MFIS) capacitor. Integrated Ferroelectrics, 2017, 185, 93 doi: 10.1080/10584587.2017.1370345
[11]
Jain A, Alam M A. Prospects of hysterisis free abrupt switching (0 mV/decade) in Landau switches. IEEE Trans Electron Devices, 2013, 60(12), 4269 doi: 10.1109/TED.2013.2286997
[12]
Khan A I, Yeung C W, Hu C, et al. Ferroelectric negative capacitance MOSFET: Capacitance tuning & antiferroelectric operation. IEDM Tech Dig, 2011, 255
[13]
Seeger J I, Crary S B. Analysis and simulation of MOS capacitor feedback for stabilizing electrostatically actuated mechanical devices. Trans Built Environ, 1997, 31(13), 1
[14]
Krowne C W, kirchoefer S W, Chang W, et al. Examination of possibility of negative capaciatnce using ferroelectric materials in solid state electronic devices. Nanoletters, 2011, 11(3), 988 doi: 10.1021/nl1037215
[15]
Jain A, Alam M A. Stability constraints define the minimum subthreshold swing of a negative capacitance field-effect transistor. IEEE Trans Electron Devices, 2014, 61(7), 2235 doi: 10.1109/TED.2014.2316167
[16]
Jiménez D, Miranda E, Godoy A. Analytic model for the surface potential and drain current in negative capacitance field-effect transistors. IEEE Trans Electron Devices, 2010, 57(10), 2405 doi: 10.1109/TED.2010.2062188
[17]
Pierret R F. Semiconductor device fundamentals. Pearson, 1995
[18]
Dasgupta S, Rajashekhar A, Majumdar K, et al. Sub-KT/Q switching in strong inversion in PbZr0.52Ti0.4O3 gated negative capaciatnce FETs. IEEE J Explor Solid State Comput Devices Circuits, 2015, 1, 43 doi: 10.1109/JXCDC.2015.2448414
[19]
Lee H, Yoon Y, Shin C. Current voltage model for negative capacitance field effect transistors. IEEE Electron Device Lett, 2017, 38(5), 669 doi: 10.1109/LED.2017.2679102
[20]
Lin C I, Khan A I, Salahuddin S, et al. Effects of the variation of ferroelectric properties on negative capacitance FET characteristics. IEEE Trans Electron Devices, 2016, 63(5), 2197 doi: 10.1109/TED.2016.2514783
[21]
Cano A, Jimenez D. Multidomain ferroelectricity as a limiting factor for voltage amplification in ferroelectric field-effect transistors. Appl Phys Lett, 2010, 97(13), 133509 doi: 10.1063/1.3494533
[22]
Boscke T S, Muller J, Bruhaus D, et al. Ferroelectricity in hafnium oxide: CMOS compatible ferroelectric field effect transistors. IEE Electron Devices Meeting, 2011, 24
[23]
Li Y, Lian Y, K Yao K, et al. Evaluation and optimization of short channel ferroelectric MOSFET for low power circuit application with BSIM4 and Landau theory. Solid State Electron, 2015, 114, 17 doi: 10.1016/j.sse.2015.07.001
[24]
Saeidi A, Jazaeri F, Stolichnov I, et al. Double-gate negative-capaciatnce MOSFET with PZT gate stack on ultra thin body SOI: An experimentally caliberated simulation study of device performance. IEEE Trans Electron Devices, 2016, 63(12), 4678 doi: 10.1109/TED.2016.2616035
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    Received: 13 February 2019 Revised: 14 June 2019 Online: Accepted Manuscript: 13 August 2019Uncorrected proof: 13 August 2019Published: 09 December 2019

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      Raheela Rasool, Najeeb-ud-Din, G. M. Rather. Analytical model for the effects of the variation of ferrolectric material parameters on the minimum subthreshold swing in negative capacitance capacitor[J]. Journal of Semiconductors, 2019, 40(12): 122401. doi: 10.1088/1674-4926/40/12/122401 R Rasool, Najeeb-ud-Din, G M Rather, Analytical model for the effects of the variation of ferrolectric material parameters on the minimum subthreshold swing in negative capacitance capacitor[J]. J. Semicond., 2019, 40(12): 122401. doi: 10.1088/1674-4926/40/12/122401.Export: BibTex EndNote
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      Raheela Rasool, Najeeb-ud-Din, G. M. Rather. Analytical model for the effects of the variation of ferrolectric material parameters on the minimum subthreshold swing in negative capacitance capacitor[J]. Journal of Semiconductors, 2019, 40(12): 122401. doi: 10.1088/1674-4926/40/12/122401

      R Rasool, Najeeb-ud-Din, G M Rather, Analytical model for the effects of the variation of ferrolectric material parameters on the minimum subthreshold swing in negative capacitance capacitor[J]. J. Semicond., 2019, 40(12): 122401. doi: 10.1088/1674-4926/40/12/122401.
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      Analytical model for the effects of the variation of ferrolectric material parameters on the minimum subthreshold swing in negative capacitance capacitor

      doi: 10.1088/1674-4926/40/12/122401
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      • Corresponding author: E-mail: raheela_03phd14@nitsri.net
      • Received Date: 2019-02-13
      • Revised Date: 2019-06-14
      • Published Date: 2019-12-01

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