An Extended Kolmogorov–Avrami–Ishibashi (EKAI) Model to Simulate Dynamic Characteristics of Polycrystalline-Ferroelectric-Gate Field-Effect Transistors
A physics-based model on polarization switching in ferroelectric polycrystalline films is proposed. The calculation results by the model agree well with experimental results regarding dynamic operations of ferroelectric-gate field-effect transistors (FeFETs). In the model, an angle <i>θ</i&...
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MDPI AG
2024-02-01
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| Online Access: | https://www.mdpi.com/1996-1944/17/5/1077 |
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| author | Shigeki Sakai Mitsue Takahashi |
| author_facet | Shigeki Sakai Mitsue Takahashi |
| author_sort | Shigeki Sakai |
| collection | DOAJ |
| description | A physics-based model on polarization switching in ferroelectric polycrystalline films is proposed. The calculation results by the model agree well with experimental results regarding dynamic operations of ferroelectric-gate field-effect transistors (FeFETs). In the model, an angle <i>θ</i> for each grain in the ferroelectric polycrystal is defined, where <i>θ</i> is the angle between the spontaneous polarization and the film normal direction. Under a constant electric field for a single-crystal film with <i>θ</i> = 0, phenomena regarding polarization domain nucleation and wall propagation are well described by the Kolmogorov–Avrami–Ishibashi theory. Since the electric fields are time-dependent in FeFET operations and the <i>θ</i> values are distributed in the polycrystalline film, the model in this paper forms an extended Kolmogorov–Avrami–Ishibashi (EKAI) model. Under a low electric field, the nucleation and domain propagation proceed according to thermally activated processes, meaning that switching the time scale of a grain with the angle <i>θ</i> is proportional to an exponential form as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mo>(</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">t</mi><mo>.</mo><mo>/</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>z</mi></mrow></msub><mi>c</mi><mi>o</mi><mi>s</mi><mi>θ</mi><mo>)</mo></mrow></semantics></math></inline-formula> [<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>z</mi></mrow></msub></mrow></semantics></math></inline-formula>: the film-normal electric field]. Wide <i>θ</i> distribution makes the time response quite broad even on the logarithmic scale, which relates well with the broad switching time experimentally shown by FeFETs. The EKAI model is physics based and need not assume non-physical distribution functions in it. |
| first_indexed | 2024-04-25T00:25:14Z |
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| spelling | doaj.art-3ae9cede14e84291aa71b6ce2b263bbf2024-03-12T16:49:11ZengMDPI AGMaterials1996-19442024-02-01175107710.3390/ma17051077An Extended Kolmogorov–Avrami–Ishibashi (EKAI) Model to Simulate Dynamic Characteristics of Polycrystalline-Ferroelectric-Gate Field-Effect TransistorsShigeki Sakai0Mitsue Takahashi1National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba 305-8568, Ibaraki, JapanNational Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba 305-8568, Ibaraki, JapanA physics-based model on polarization switching in ferroelectric polycrystalline films is proposed. The calculation results by the model agree well with experimental results regarding dynamic operations of ferroelectric-gate field-effect transistors (FeFETs). In the model, an angle <i>θ</i> for each grain in the ferroelectric polycrystal is defined, where <i>θ</i> is the angle between the spontaneous polarization and the film normal direction. Under a constant electric field for a single-crystal film with <i>θ</i> = 0, phenomena regarding polarization domain nucleation and wall propagation are well described by the Kolmogorov–Avrami–Ishibashi theory. Since the electric fields are time-dependent in FeFET operations and the <i>θ</i> values are distributed in the polycrystalline film, the model in this paper forms an extended Kolmogorov–Avrami–Ishibashi (EKAI) model. Under a low electric field, the nucleation and domain propagation proceed according to thermally activated processes, meaning that switching the time scale of a grain with the angle <i>θ</i> is proportional to an exponential form as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mo>(</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">t</mi><mo>.</mo><mo>/</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>z</mi></mrow></msub><mi>c</mi><mi>o</mi><mi>s</mi><mi>θ</mi><mo>)</mo></mrow></semantics></math></inline-formula> [<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>z</mi></mrow></msub></mrow></semantics></math></inline-formula>: the film-normal electric field]. Wide <i>θ</i> distribution makes the time response quite broad even on the logarithmic scale, which relates well with the broad switching time experimentally shown by FeFETs. The EKAI model is physics based and need not assume non-physical distribution functions in it.https://www.mdpi.com/1996-1944/17/5/1077ferroelectricdynamic modelpolarization switchingdomain wallferroelectric field-effect transistorpolycrystal |
| spellingShingle | Shigeki Sakai Mitsue Takahashi An Extended Kolmogorov–Avrami–Ishibashi (EKAI) Model to Simulate Dynamic Characteristics of Polycrystalline-Ferroelectric-Gate Field-Effect Transistors Materials ferroelectric dynamic model polarization switching domain wall ferroelectric field-effect transistor polycrystal |
| title | An Extended Kolmogorov–Avrami–Ishibashi (EKAI) Model to Simulate Dynamic Characteristics of Polycrystalline-Ferroelectric-Gate Field-Effect Transistors |
| title_full | An Extended Kolmogorov–Avrami–Ishibashi (EKAI) Model to Simulate Dynamic Characteristics of Polycrystalline-Ferroelectric-Gate Field-Effect Transistors |
| title_fullStr | An Extended Kolmogorov–Avrami–Ishibashi (EKAI) Model to Simulate Dynamic Characteristics of Polycrystalline-Ferroelectric-Gate Field-Effect Transistors |
| title_full_unstemmed | An Extended Kolmogorov–Avrami–Ishibashi (EKAI) Model to Simulate Dynamic Characteristics of Polycrystalline-Ferroelectric-Gate Field-Effect Transistors |
| title_short | An Extended Kolmogorov–Avrami–Ishibashi (EKAI) Model to Simulate Dynamic Characteristics of Polycrystalline-Ferroelectric-Gate Field-Effect Transistors |
| title_sort | extended kolmogorov avrami ishibashi ekai model to simulate dynamic characteristics of polycrystalline ferroelectric gate field effect transistors |
| topic | ferroelectric dynamic model polarization switching domain wall ferroelectric field-effect transistor polycrystal |
| url | https://www.mdpi.com/1996-1944/17/5/1077 |
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