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2D Electronic Circuits for Sensing Applications

Diogo Baptista1,2,3, Ivo Colmiais1,2,3, Vitor Silva1,2,3, Pedro Alpuim1,4, and Paulo M. Mendes2,3

1INL - International Iberian Nanotechnology Laboratory, Av. Mestre José Veiga, 4715-330, Braga, Portugal

2CMEMS - Center for Microelectromechanical Systems, University of Minho, Campus de Azurém, 4800-058, Guimarães, Portugal

3LABBELS - Associate Laboratory, University of Minho, Campus de Gualtar, 4710-057, Braga, Portugal

4Center of Physics, University of Minho, Campus de Gualtar, 4710-057, Braga, Portugal

1.1 Introduction

Technology has always been around, be it the most straightforward wooden wheel or a more complex system like a modern car. Technology's and science's evolution pave the way for society's evolution. One of the most relevant breakthroughs in the past years was the transistor's discovery in 1947. This discovery allowed for replacing the vacuum tube, also known as the valve, with a device with a smaller footprint and higher efficiency. This discovery led to a massive bump in industrial society's evolution. Technology fully integrates people's lives, either directly in the devices they use (e.g. smartphones) or indirectly through those who provide them with a service (e.g. mobile operators' signal coverage).

This revolution was possible due to the miniaturization of the electronic components that integrate transistors while maintaining or improving their performance. According to Moore's Law, the number of transistors in the same chip area doubles every two years. This law has been confirmed for over 50?years, but it is getting to a point where reducing component size is reaching its physical limitations due to short-channel effects and interconnect's heating [1, 2]. Further research on new materials is required to replace silicon before a new paradigm in nanoelectronics - more than Moore - can be reached.

In recent years, two-dimensional (2D) materials have become the focus of many investigations to replace silicon to continue downscaling electronic devices [3-6]. Many of these materials show excellent electronic, photoelectronic, and mechanical properties. Therefore, investigating the implementation of a technology based on such materials is increasingly important as the Internet of Things (IoTs) becomes more prevalent and requires a massive number of devices with a small footprint to be integrated without much notice. Although these are promising materials, their integration with standard manufacturing processes and replicability outside of the laboratory is yet to be achieved [7]. Many other problems associated with interfacing 2D and other materials continue to be challenging since these interfaces usually degrade their electronic properties, especially the carrier mobility, reducing their overall performance [8, 9].

The first 2D material discovered was graphene by Andre Geim and Konstantin Novoselov in 2004, which led them to win the Nobel Prize in Physics in 2010 [10]. The graphene was obtained using tape to exfoliate graphite until it reached a single atomic layer. The discovery of graphene launched curiosity and investigations toward graphene and other 2D materials. These days, the investigation of 2D materials has progressed immensely, to the point where we can already separate 2D materials into families according to their elements' chemical composition, unit cell, electronic, optical, or structural properties [11]. The most known families are X-enes and transition-metal dichalcogenides (TMDs). X-enes group single element materials with atoms organized in a hexagonal lattice, which is the case of graphene, silicene, germanene, and others. TMDs group 2D materials of the form MX2, where M is a transition metal from the 4th, 5th or 6th group, and X is a chalcogen from group 16th. The most known TMDs are molybdenum disulfide, tungsten disulfide, and molybdenum diselenide. Since some 2D materials were discovered recently, their science and technology are not sufficiently mature to place them as candidates for next-generation electronic materials. Therefore, limit our discussion to graphene and MoS2 since, as of today, they are by far the most studied materials.

Graphene consists of a single graphite layer of carbon atoms arranged in a hexagonal lattice. Graphene can be grown at a large scale by chemical vapor deposition (CVD) [12, 13] or liquid-phase exfoliation (LPE). One of the problems with graphene fabrication is that it cannot be grown directly on most substrates. It is usually deposited on a transition metal catalyst foil - often copper or nickel - and then transferred using a wet or dry transfer process to the desired substrate [14]. Because of the need to transfer to the final substrate, graphene's performance is affected by the degradation of its carrier mobility during this transfer process [15]. Graphene has remarkable properties, such as extremely high carrier mobility (2000?cm2 V-1 s-1 for any mechanically transferred graphene [16] and 200?000?cm2 V-1 s-1 for suspended graphene [17]) when compared to silicon (1400?cm2 V-1 s-1 for electrons and 450?cm2 V-1 s-1 for holes), good electrical conductivity (~104 O-1 cm-1 [17]), high thermal conductivity (5300?Wm-1 K-1 [18]), and high Young's modulus (0.5-1.0?TPa [16]). This material is a gapless semiconductor, meaning it has a 0?eV energy gap. Because of this intrinsic property, this material cannot be used in devices where the off state is needed since the material always conducts electricity by holes or electrons. These properties make graphene a possible solution to overcome silicon limitations in certain applications and can be implemented in devices with a broad range of uses, from high-speed electronics to sensing applications.

MoS2 belongs to the TMDs family and consists of a molybdenum layer sandwiched between two sulfur layers. This material appears in nature as molybdenite, and, like graphene, can be fabricated using CVD or exfoliation techniques. Unlike graphene, MoS2 properties are not all well-defined, but its carrier mobility has been shown to have values up to 200?cm2 V-1 s-1 at room temperature and Young's modulus of 0.33?TPa [19]. Different from graphene, MoS2 has a direct bandgap of 1.8?eV [20], which means it can be used in devices that need to have an off state.

Due to the remarkable properties of these materials, their implementation on capacitors, inductors, and field-effect transistors (FETs) has already been reported in numerous papers. In Sections 1.2, 1.3, and 1.4, the literature on these components will be explored, regarding their physical implementation and the models that try to predict these components' behavior.

1.2 Graphene Inductors

On-chip inductors revolutionized RF electronics in the 1990s, but not everything is excellent. These inductors are planar and must have a large area, as dictated by electromagnetic laws, which means they cannot be downsized alongside standard transistors while maintaining high inductance density. In some cases, it is reported that planar inductors occupy up to 50% of an integrated circuit area. Thus, they hinder further miniaturization and integration. Finding new approaches to making these devices is imperative.

It is well known that the inductance is shape- and size-dependent, but in graphene a third factor can be explored, known as kinetic inductance. This material property arises from the inertia of charge carriers moving in alternating electric fields. Like all mass particles, charge carriers preserve their momentum, so when in an alternating electric field, it takes a finite time to change their momentum according to the field, which manifests as kinetic inductance. It is not very important in conventional metals because their conductance is associated with higher carrier concentration and macroscopic thickness. The kinetic inductance manifests as an equivalent series inductance, adding to the geometric inductance associated with the shape/size. Therefore, materials with high kinetic inductance must be used to reduce inductor size while maintaining high inductance density. Graphene is being exploited as a possible solution to the inductance component miniaturization issue due to its atomic thickness and relatively high conductivity, based on high carrier mobility and low carrier concentration. Consequently, graphene has high kinetic inductance and a small footprint.

A multilayer graphene (MLG) inductor is proposed in [21], shown in Figure 1.1. The authors' choice of using MLG is to ensure a lower quantum contact resistance (resistance associated with the interface between graphene and metal contact). This approach raises two problems: when compared with metals, graphene has a much lower conductivity; compared to SLG, the MLG exhibits reduced charge carrier inertia due to...