<p>Reducing support, i.e., anchor, energy dissipation is a desired target in designing a microelectromechanical systems (MEMS) resonator with high quality factor (<i>Q</i>). This paper proposes two support tether structures, namely TYPE_A and TYPE_B, based on the acoustic wavelength (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="542_2025_5894_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>) to improve the <i>Q</i> of the length extensional mode MEMS resonator in terms of anchor quality factor (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="542_2025_5894_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(Q_{ANC}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>Q</mi> <mrow> <mi mathvariant="italic">ANC</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>) enhancement. These support tethers consist of five <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="542_2025_5894_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation> based-rectangular-shaped bars which are arranged continuously. The resonator operates at the resonant frequency of 70.1 MHz. The numerical simulation results with the built-in finite element method (FEM) in COMSOL show that the optimized <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="542_2025_5894_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(Q_{ANC}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>Q</mi> <mrow> <mi mathvariant="italic">ANC</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> values of the resonator for both TYPE_A and TYPE_B achieve 73320.67, and 89893.84, respectively. These two proposed tether structures are also compared to the conventional <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="542_2025_5894_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda /4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo stretchy="false">/</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation> one in enhancing the <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="542_2025_5894_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(Q_{ANC}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>Q</mi> <mrow> <mi mathvariant="italic">ANC</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> of the resonator, which show an increase of the <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="542_2025_5894_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(Q_{ANC}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>Q</mi> <mrow> <mi mathvariant="italic">ANC</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> about 105.95 and 129.9 times, respectively. Besides, they are also compared to the counterpart TWHL and respectively show outperformed <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="542_2025_5894_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(Q_{ANC}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>Q</mi> <mrow> <mi mathvariant="italic">ANC</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> values of 2.57 and 3.15 times. In addition, several un-optimized values of the <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="542_2025_5894_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(Q_{ANC}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>Q</mi> <mrow> <mi mathvariant="italic">ANC</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> for the both proposed configurations are also higher than that for the counterparts. Moreover, with an extension simulation of the resonator for five different resonant frequencies, both structures TYPE_A and TYPE_B also demonstrate their superior <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="542_2025_5894_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(Q_{ANC}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>Q</mi> <mrow> <mi mathvariant="italic">ANC</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> improvement over the two counterparts.</p>

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Anchor loss reduction in TPoS MEMS resonator using acoustic wavelength-based support tether configurations

  • Thi Dep Ha

摘要

Reducing support, i.e., anchor, energy dissipation is a desired target in designing a microelectromechanical systems (MEMS) resonator with high quality factor (Q). This paper proposes two support tether structures, namely TYPE_A and TYPE_B, based on the acoustic wavelength ( \(\lambda \) λ ) to improve the Q of the length extensional mode MEMS resonator in terms of anchor quality factor ( \(Q_{ANC}\) Q ANC ) enhancement. These support tethers consist of five \(\lambda \) λ based-rectangular-shaped bars which are arranged continuously. The resonator operates at the resonant frequency of 70.1 MHz. The numerical simulation results with the built-in finite element method (FEM) in COMSOL show that the optimized \(Q_{ANC}\) Q ANC values of the resonator for both TYPE_A and TYPE_B achieve 73320.67, and 89893.84, respectively. These two proposed tether structures are also compared to the conventional \(\lambda /4\) λ / 4 one in enhancing the \(Q_{ANC}\) Q ANC of the resonator, which show an increase of the \(Q_{ANC}\) Q ANC about 105.95 and 129.9 times, respectively. Besides, they are also compared to the counterpart TWHL and respectively show outperformed \(Q_{ANC}\) Q ANC values of 2.57 and 3.15 times. In addition, several un-optimized values of the \(Q_{ANC}\) Q ANC for the both proposed configurations are also higher than that for the counterparts. Moreover, with an extension simulation of the resonator for five different resonant frequencies, both structures TYPE_A and TYPE_B also demonstrate their superior \(Q_{ANC}\) Q ANC improvement over the two counterparts.