<p>Gate-induced drain leakage (GIDL) poses a critical challenge in scaled nanowire gate-all-around (GAA) metal–oxide–semiconductor field-effect transistor (MOSFETs), particularly when process-induced sidewall inclination (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11664_2025_12403_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation>) alters device electrostatics and exacerbates short-channel effects. Despite its significance, no analytical framework exists to model GIDL in trapezoidal GAA structures with non-vertical sidewalls. The model is derived from a quasi-three-dimensional (3D) scaling equation that incorporates an effective scaling length (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11664_2025_12403_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda _{\text {eff}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>λ</mi> <mtext>eff</mtext> </msub> </math></EquationSource> </InlineEquation>), which is expressed using the perimeter-weighted-sum and equivalent number of gates (ENG) technique. This model accounts for various device parameters including channel length (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11664_2025_12403_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_g\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>g</mi> </msub> </math></EquationSource> </InlineEquation>), top width (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11664_2025_12403_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="TEX">\(W_{\text {top}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>W</mi> <mtext>top</mtext> </msub> </math></EquationSource> </InlineEquation>), and channel height (<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11664_2025_12403_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_{\text {Fin}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mtext>Fin</mtext> </msub> </math></EquationSource> </InlineEquation>). The side-wall inclination angle (<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11664_2025_12403_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation>) is varied from <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11664_2025_12403_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="64" /> </InlineMediaObject> <EquationSource Format="TEX">\(0^\circ \text{ to } 25^\circ \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>0</mn> <mo>∘</mo> </msup> <mspace width="0.333333em" /> <mtext>to</mtext> <mspace width="0.333333em" /> <msup> <mn>25</mn> <mo>∘</mo> </msup> </mrow> </math></EquationSource> </InlineEquation> to study its impact on surface potential, electric field, and gate-induced leakage current (<InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11664_2025_12403_Article_IEq8.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\( I_{\text {GIDL}} \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>I</mi> <mtext>GIDL</mtext> </msub> </math></EquationSource> </InlineEquation>). The analytical predictions closely match both experimental and technology computer-aided design (TCAD) simulations, validating the modal accuracy. Results indicate that <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11664_2025_12403_Article_IEq9.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(I_{\text {GIDL}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>I</mi> <mtext>GIDL</mtext> </msub> </math></EquationSource> </InlineEquation> increases by approximately 1.4 to 2.44 times as <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11664_2025_12403_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> varies from <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11664_2025_12403_Article_IEq11.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(0^\circ \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>0</mn> <mo>∘</mo> </msup> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11664_2025_12403_Article_IEq12.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(25^\circ \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>25</mn> <mo>∘</mo> </msup> </math></EquationSource> </InlineEquation>. Moreover, sensitivity analysis highlights that <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11664_2025_12403_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="TEX">\(W_{\text {top}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>W</mi> <mtext>top</mtext> </msub> </math></EquationSource> </InlineEquation> exhibits the strongest influence on <InlineEquation ID="IEq14"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11664_2025_12403_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda _{\text {eff}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>λ</mi> <mtext>eff</mtext> </msub> </math></EquationSource> </InlineEquation> and hence on <InlineEquation ID="IEq15"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11664_2025_12403_Article_IEq9.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(I_{\text {GIDL}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>I</mi> <mtext>GIDL</mtext> </msub> </math></EquationSource> </InlineEquation>. These findings offer valuable insights for optimizing device performance by controlling sidewall geometries and structural parameters.</p>

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A Quasi-3D Model of Gate-Induced Drain Leakage Current of a Trapezoidal GAA MOSFET

  • Prity Sinha,
  • Ashraf Maniyar,
  • Pushp Raj,
  • Pramod Kumar Tiwari

摘要

Gate-induced drain leakage (GIDL) poses a critical challenge in scaled nanowire gate-all-around (GAA) metal–oxide–semiconductor field-effect transistor (MOSFETs), particularly when process-induced sidewall inclination ( \(\theta \) θ ) alters device electrostatics and exacerbates short-channel effects. Despite its significance, no analytical framework exists to model GIDL in trapezoidal GAA structures with non-vertical sidewalls. The model is derived from a quasi-three-dimensional (3D) scaling equation that incorporates an effective scaling length ( \(\lambda _{\text {eff}}\) λ eff ), which is expressed using the perimeter-weighted-sum and equivalent number of gates (ENG) technique. This model accounts for various device parameters including channel length ( \(L_g\) L g ), top width ( \(W_{\text {top}}\) W top ), and channel height ( \(H_{\text {Fin}}\) H Fin ). The side-wall inclination angle ( \(\theta \) θ ) is varied from \(0^\circ \text{ to } 25^\circ \) 0 to 25 to study its impact on surface potential, electric field, and gate-induced leakage current ( \( I_{\text {GIDL}} \) I GIDL ). The analytical predictions closely match both experimental and technology computer-aided design (TCAD) simulations, validating the modal accuracy. Results indicate that \(I_{\text {GIDL}}\) I GIDL increases by approximately 1.4 to 2.44 times as \(\theta \) θ varies from \(0^\circ \) 0 to \(25^\circ \) 25 . Moreover, sensitivity analysis highlights that \(W_{\text {top}}\) W top exhibits the strongest influence on \(\lambda _{\text {eff}}\) λ eff and hence on \(I_{\text {GIDL}}\) I GIDL . These findings offer valuable insights for optimizing device performance by controlling sidewall geometries and structural parameters.