Ultra-Small, High-Frequency, and Substrate-Immune Microtube Inductors Transformed from 2D to 3D

Abstract

Monolithic on-chip inductors are key passive devices in radio frequency integrated circuits (RFICs). Currently, 70-80% of the on-wafer area of most RFIC chips is occupied by the sprawling planar spiral inductors, and its operation frequency is limited to a few GHz. With continuous scaling of the transistor technology, miniaturization and high frequency operation of inductors have become the bottleneck to meet future demands of wireless communication systems. Here we report on-chip self-rolled-up 3D microtube inductors with extremely small footprint, unprecedented high frequency performance and weak dependence on substrate conductivity. The serpentine metal strips are deposited on an oppositely strained silicon nitrides (SiNx) bilayer. After releasing from the sacrificial layer underneath, the metal/SiNx layer is scrolled into a 3D hollow tubular structure by the strain induced unidirectional self-rolled-up technology. Compared to the planar spiral inductors with similar inductances and quality (Q) factors, the footprint of tube inductors is reduced by as much as two orders of magnitude, and the frequency at peak Q factor improves more than 5 times on doped substrates. The self-rolled-up 3D nanotechnology platform employed here, that "processes in 2D but functions in 3D", is positioned to serve as a global solution for extreme RFIC miniaturization with improved performance.

Figure 1. Schematic illustration of the 3D tube inductor design and images of fabricated devices before and after rolled up.

(A) Schematic diagram of the 2D pattern of a tube inductor before rolled-up, with metal strips of width W_s and length L_s connected in series by connecting lines of width W_c and length L_c, and terminated with the feed-lines. The zoomed-in inset shows the cross-sectional structure and material stack. Note that current directions for all turns in the same strip are the same, leading to positive mutual inductance. For adjacent metal strips in the same or different planes, the current directions are opposite, however, the cancelling inductance is negligible when L_c is long enough. (B) The corresponding rolled-up tube inductor. Inset shows the cross-sectional view of the hollow tube where the wall consists of multi-turns of SiN_x bilayer and metal (Au/Ni) strips. (C) Optical image of the before-rolled-up 2D inductor pattern with 4 metal strips (W_s = 30 14μm and L_c = 20 μm) and RF ground pads and feed-lines. The dimension of the metal strip pattern is 200 μm (width) × 500 μm (length) as indicated. (D) SEM image of the 4 metal strips tube inductor with 15 coiled turns, after the metal strip is self-rolled-up along the direction indicated together with the strained SiN_x membrane by the unidirectional rolling technique. (E) Cross-sectional SEM image of the 3D tube inductor with 15 coiled turns. The inner diameter (ID) is 10 μm and the outer diameter (OD) is 15 μm. The scale bar represents 10 μm.

Figure 2. RF performance of tube inductors and their substrate immunity.

(A) Measured inductances (solid lines) and Q factors (symbol lines) versus operation frequency for a series of tube inductors with 6 metal strips, W_s = 30 μm, but different number (3, 9, and 15) of coiled turns on a ρ = 10 ~ 20 Ω·cm p-Si substrate. (B) Measured inductances (solid lines) and Q factors (symbol lines) versus operation frequency for a series of tube inductors with 15 coiled turns but different number of strips (2, 4, and 6). (C) Family of curves of inductance as a function of coiled turns for tube inductors with different number of strips (2, 4 and 6) with W_s = 20 μm. The open symbols are experimental data, and solid curves are modeled data. (D) Experimental Q_max and f_Qmax of tube inductors with various configurations on three different substrates, plotted versus the corresponding inductance values. The dashed lines represent the linear fit of each data set obtained from respective substrates.

Figure 3. Benchmark 3D plot.

Inductance, footprint, and Q_max of rolled-up 3D tube inductors (represented by red pillars) are plotted together with those for planar spiral inductors used in the 0.18 μm and 32 nm node CMOS technology. The marked frequencies correspond to f_Qmax of the inductors. The metal type and thickness for the tube inductor and the two generations of planar inductors are as indicated. The substrate resistivity is ρ = 1 ~ 5 Ω·cm p-type for the red and blue pillars and ρ = 10 Ω·cm p-type for the green pillars.