High-${Q}$ Variable Pitch Spiral Inductors for Increased Inductance Density and Figure-of-Merit

Abstract

Layout-optimized inductors with gradually varying width and spaced (tapered) spirals are well known for their higher quality factor ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> ) characteristics. For the first time, the significance of tapered inductors in achieving higher inductance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${L}$ </tex-math></inline-formula> ) density is brought out in this article. Instead of having a constant spiral pitch (width + space), gradually reducing pitch with increased turns is shown to significantly benefit <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${L}$ </tex-math></inline-formula> density without compromising on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> . Following this approach, inductor figure-of-merit (FOM) is shown to increase with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${L}$ </tex-math></inline-formula> density using variable pitch spirals while it is reduced in other spiral configurations. It is also revealed that for fixed inner and outer diameters, significant FOM improvement can be achieved only through increased <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${L}$ </tex-math></inline-formula> density and not through higher <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> . Moreover, the proposed approach is shown to have improved inductor FOM across substrate resistivities and metal thickness values. Prototype-tapered inductors (shown in <xref ref-type="fig" rid="fig1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Fig. 1</xref> ) designed using the proposed approach are fabricated using 0.35- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> BiCMOS technology. Measurements (which are in good agreement with electromagnetic (EM) simulations) show higher <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${L}$ </tex-math></inline-formula> values of 6.6 nH with a high- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> of 23 usable at 3.8 GHz, thereby achieving a very high FOM of 4.3. <fig id="fig1" orientation="portrait" position="float" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><label>Fig. 1.</label><caption> Chip images of prototype variable width and constant spacing inductors. (a) D1. (b) D2. </caption> <graphic orientation="portrait" position="float" xlink:href="sunda1ab-2937671.eps"/> </fig>