On-chip intercalated-graphene inductors for next-generation radio frequency electronics

Abstract

. This will require a tremendous number of miniaturized wireless connections that are driven by radio frequency (RF) integrated circuits (RF-ICs) that demand scalability, flexibility, high performance and ease of integration. Moreover, the market value of radio frequency identification (RF-ID), which employs electromagnetic fields to automatically identify and track tags attached to objects, is expected to rise to US$18.68 billion by 2026 4 . Planar on-chip metal inductors (Fig. 1a) are essential passive devices in RF-ICs and can occupy up to 50% of the chip area. They also contribute a major part of the form factor of RF-IDs (see Supplementary Section 1). However, unlike the continuous scaling of transistors and interconnects in IC technology, which was achieved with an increase in performance, progress toward miniaturization of on-chip inductors has remained elusive, mainly due to the fact that large inductor areas, dictated by fundamental electromagnetics, are required to deliver desirable inductance values and performance targets ( Fig. 1b; see also Supplementary Section 2).To achieve continuous size scaling while fulfilling the inductance and performance requirements, improvement in the inductance density is essential, which is defined by inductance per unit area = total inductance (L total ) / inductor area, where L total is the sum of the magnetic inductance (L M ) and the kinetic inductance (L K ) (Fig. 1a). Magnetic inductance is the property of an electrical conductor by which a change in current through it, causing a change in the magnetic flux, induces an electromotive force in both the conductor itself (self-inductance) and in any nearby conductors (mutual inductance) that opposes the change. Kinetic inductance is the manifestation of the inertial mass of mobile charge carriers in alternating electric fields as an equivalent series inductance. L K arises naturally as the inductive impedance per unit length of the conductor in the Drude model for a.c. electrical conductivity. Hence, the magnetic inductance is determined by the geometrical/ structural design of the inductor, while kinetic inductance is purely a material property (see Supplementary Section 3 for more details). Therefore, structural design and materials innovation, that determine L M and L K , respectively, are two simultaneous ways to improve the inductance density. As shown in the example in Fig. 1b, a comparable L K (if it exists) with respect to L M can significantly improve both the inductance and the quality factor (Q-factor, or Q, the ratio of the inductive reactance to the resistance of an inductor at a given frequency, which is a measure of its efficiency). However, because in conventional metals L K is negligibly small (because of relatively weak carrier inertia) compared to L M , almost all studies in the past few decades have been focused on structural improvements to make full use of the magnetic field, such as layout optimization 5 , micro-electromechanical-system fabrication 6,7 , three-dimensional self-rolled-up 8 and ve...

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