Two-Dimensional Electronics - Prospects and Challenges

During the past 10 years, two-dimensional materials have found incredible attention in the scientific community. The first two-dimensional material studied in detail was graphene, and many groups explored its potential for electronic applications. Meanwhile, researchers have extended their work to two-dimensional materials beyond graphene. At present, several hundred of these materials are known and part of them is considered to be useful for electronic applications. Rapid progress has been made in research concerning two-dimensional electronics, and a variety of transistors of different two-dimensional materials, including graphene, transition metal dichalcogenides, e.g., MoS2 and WS2, and phosphorene, have been reported. Other areas where two-dimensional materials are considered promising are sensors, transparent electrodes, or displays, to name just a few. This Special Issue of Electronics is devoted to all aspects of two-dimensional materials for electronic applications, including material preparation and analysis, device fabrication and characterization, device physics, modeling and simulation, and circuits. The devices of interest include, but are not limited to transistors (both field-effect transistors and alternative transistor concepts), sensors, optoelectronics devices, MEMS and NEMS, and displays

Carbon Based Nanoelectromechanical Resonators.

Owing to their light mass and high Young’s modulus, carbon nanotubes (CNTs) and graphene are promising candidates for nanoelectromechanical resonators capable of ultrasmall mass and force sensing. Unfortunately, the mass sensitivity of CNT resonators is impeded by the low quality factor (Q) caused by intrinsic losses. Therefore, one should minimize dissipations or seek an external way to enhance Q in order to overcome the fundamental limits. In this thesis, I first carried out a one-step direct transfer technique to fabricate pristine CNT nanoelectronic devices at ambient temperature. This process technique prevents unwanted contaminations, further reducing surface losses. Using this technique, CNT resonators was fabricated and a fully suspended CNT p-n diode with ideality factor equal to 1 was demonstrated as well. Subsequently, the frequency tuning mechanisms of CNT resonators were investigated in order to study their nonlinear dynamics. Downward frequency tuning caused by capacitive spring softening effect was demonstrated for the first time in CNT resonators adopting a dual-gate configuration. Leveraging the ability to modulate the spring constant, parametric amplification was demonstrated for Q enhancement in CNT resonators. Here, the simplest parametric amplification scheme was implemented by modulating the spring constant of CNTs at twice the resonance frequency through electrostatic gating. Consequently, at least 10 times Q enhancement was demonstrated and Q of 700 at room temperature was the highest record to date. Moreover, parametric amplification shows strong dependence on DC gate voltages, which is believed due to the difference of frequency tunability in different vibrational regimes. Graphene takes advantages over CNTs due to the availability of wafer-scale graphene films synthesized by chemical vapor deposition (CVD) method. Thus, I also examined graphene resonators fabricated from CVD graphene films. Ultra-high frequency (UHV) graphene resonators were demonstrated, and the Qs of graphene resonators are around 100. Future directions of graphene resonators include investigating the potential losses, exploring the origin of nonlinear damping, and demonstrating parametric amplification for Q enhancement.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91487/1/chungwu_1.pd

Optomechanical resonators based on low dimensional materials

Mechanical resonators based on low dimensional materials have attracted a lot of attention due to their remarkable properties. Their ultra-low mass and high Q factors make them exceptional sensors, offering new possibilities in the studies of the material strength and the thermodynamic properties of low dimensional materials. The goal of this thesis is to shed light on the thermal and elastic properties of low dimensional materials across a wide temperature range. The first part of the thesis is focused on the study of the temperature dependence of the stiffness of carbon nanotubes. By measuring the resonance frequency of singly clamped carbon nanotube resonators as a function of temperature, we can obtain information on the Young’s modulus of the measured carbon nanotubes. We observe a relative shift of the Young’s modulus over a large temperature range with a slope of -(173 +/- 65) ppm/K, consistent with two different theoretical models based on the thermal dynamics of the lattice. The results show the dependence of the fundamental mechanical mode on the phonons in carbon nanotubes via the Young’s modulus. The measured data also indicates the coupling between mechanical modes and the phonon thermal bath in nanotubes. The phonon thermal bath in our experiments likely operates in the Akhiezer limit. In the second part of the thesis, we present the temperature dependence of the thermal conductivity and the specific heat capacity in the MoSe2 monolayer in a larger temperature range. Both the thermal conductivity and the specific heat capacity measurements are consistent with predictions based on first-principles. The results show that the phonon transport in a MoSe2 monolayer can be both diffusive and ballistic, depending on the temperature of the monolayer. The method used in this measurement can be used to investigate the thermal properties of many two-dimensional materials. Furthermore, it opens the possibility to investigate interesting thermal transport regimes in two-dimensional materials like hydro-dynamic regime or anomalous heat conduction.Los resonadores mecánicos basados en materiales de baja dimensionalidad han llamado la atención de la comunidad científica debido a sus singulares propiedades. Su pequeña masa y sus altos factores de calidad (Q) los convierten en sensores excepcionales, ofreciendo un nuevo abanico de posibilidades en el estudio de las propiedades mecánicas y termodinamicas de los materiales de baja dimensionalidad. El objetivo de ésta tesis es el estudio de las propiedades térmicas y elásticas de los materiales de baja dimensionalidad en un amplio rango de temperaturas. La primera parte de la tesis se centra en la evolución de la rigidez de los nanotubo de carbono en función de la temperatura. La medida de la frecuencia de resonancia de un resonador basado en un nanotubos de carbono con un único punto de anclaje en función de la temperatura, ofrece información sobre el módulo de Young de dicho nanotubo. Observamos un cambio relativo del módulo de Young en un amplio rango de temperaturas con una pendiente de -(173 +/- 65) ppm/K, en acuerdo con dos modelos teóricos diferentes basados en la dinámica térmica de la red cristalina del material. Los resultados muestran la influencia de los fonones del nanotubo de carbono en el modo mecánico fundamental a través del módulo de Young. Los datos también indican el acoplamiento entre los modos mecánicos y el baño térmico de fonones en los nanotubos. Es probable que el baño térmico de fonones en nuestros experimentos opere en el límite de Akhiezer. En la segunda parte de la tesis, presentamos la evolución de la conductividad térmica y la capacidad calorífica específica de una monocapa MoSe2 en función de la temperatura para un rango más amplio. Tanto la conductividad térmica como las medidas de la capacidad calorífica específica concuerdan con las predicciones basadas en los primeros principios. Los resultados muestran que el transporte de fonones en la monocapa MoSe2 puede ser difusivo o balístico, dependiendo de la temperatura de dicha monocapa. El método utilizado en esta medida se puede utilizar para investigar las propiedades térmicas de muchos materiales bidimensionales. Asimismo, abre la posibilidad de investigar distintos regímenes de transporte térmico en materiales bidimensionales cómo el régimen hidrodinámico o la conducción de calor anómala.Postprint (published version

Carbon nanotube electromechanical systems: Non-linear dynamics and self-oscillation

This thesis is motivated by the many sensing applications of carbon nanotube (CNT) nano-electromechanical systems (NEMS), both previous state-of-the-art demonstrations and proposed new uses. This research is particularly focused on the long term goal of realizing the magnetic force sensing of molecular nanomagnets, proposed in reference [1]. The fabrication of micron long, small diameter, high quality suspended carbon nanotubes is a challenging task. Integrating ferromagnetic structures which are incompatible with the CNT growth procedures increases this challenge. In this thesis, devices suitable for magnetic force sensing experiments are realized by separating the chemical vapour deposition growth of CNTs from the device contacts and gates, while maintaining CNT quality. Using conventional readout techniques, the low-temperature measurement of the CNT NEMS mechanical state is usually limited by the CNT contact resistance and capacitance of the measurement cabling/circuit. I describe the use of a heterojunction bipolar transistor (HBT) amplifying circuit operating at cryogenic temperatures near the device to measure the mechanical amplitude at microsecond timescales. A Coulomb rectification scheme, in which the probe signal is at much lower frequency than the mechanical drive signal, allows investigation of the transient response with strongly non-linear driving. The transient dynamics in both the linear and non-linear regimes are measured and modeled by including Duffing and non-linear damping terms in a harmonic oscillator equation. The non-linear regime can result in faster sensing response times, on the order of 10 μs for the device and circuit presented. Self-driven oscillations in suspended carbon nanotubes can create apparent instabilities in the electrical conductance of the CNT. In literature, such instabilities have been observed in kondo regime or high bias transport. In this thesis, I observed self-driven oscillations which created significant conduction within the nominally Coulomb-blockaded low-bias transport. Using a master equation system model, these oscillations are shown to be the result of strongly energy dependent electron tunneling to the contacts of high quality CNT NEMS operated at sub-Kelvin temperatures. Finally, in a separate research project, I consider the noise characterization of spin qubits interacting with the environment. In particular, I address the problem of probing the spectral density S(ω) of semi-classical phase noise using a spin interacting with a continuous-wave (CW) resonant excitation field. Previous CW noise spectroscopy protocols have been based on the generalized Bloch equations (GBE) or the filter function formalism, and assumed weak coupling to a Markovian bath. However, those protocols can substantially underestimate S(ω) at low frequencies when the CW pulse amplitude becomes comparable to S(ω). I derive the coherence decay more generally by extending to higher orders in the noise strength and discarding the Markov approximation. Numerical simulations show that this provides a more accurate description of the spin dynamics compared to a simple exponential decay, especially on short timescales. Exploiting these results, a new protocol is developed that uses an experiment at a single CW pulse amplitude to extend the spectral range over which S(ω) can be reliably determined, down to ω=0

Quadratic coupling between a classical nanomechanical oscillator and a single spin

Though the motions of macroscopic objects must ultimately be governed by quantum mechanics, the distinctive features of quantum mechanics can be hidden or washed out by thermal excitations and coupling to the environment. For the work of this thesis, we tried to develop a hybrid system consisting a classical and a quantum component, which can be used to probe the quantum nature of both these components. This hybrid system quadratically coupled a nanomechanical oscillator (NMO) with a single spin in presence of a uniform external magnetic field. The NMO was fabricated out of single-layer graphene, grown using Chemical Vapor Deposition (CVD) and patterned using various lithography and etching techniques. The NMO was driven electrically and detected optically. The NMO's resonant frequencies, and their stabilities were studied. The spin originated from a nitrogen vacancy (NV) center in a diamond nanocrystal which is positioned on the NMO. In presence of an external magnetic field, we show that the NV centers are excellent $\theta^{2}$ sensors. Their sensitivity is shown to increase much faster than linearly with the external magnetic field and diverges as the external field approaches an internally-defined limit. Both these components of the hybrid system get coupled by physical placement of NV-containing diamond nanocrystals on top of NMO undergoing torsional mode of oscillation, in presence of an external magnetic field. The capability of the NV centers to detect the quadratic behavior of the oscillation angle of the NMO with excellent sensitivity, ensures quantum non-demolition (QND) measurement of both components of the hybrid system. This enables a bridge between the quantum and classical worlds for a simple readout of the NV center spin and observation of the discrete states of the NMO. This system could become the building block for a wide range of quantum nanomechanical devices

Anomalous Random Telegraphy Signal in Suspended Graphene with Oxygen Adsorption

Graphene is a promising material for sensing applications because of its large specific surface area and low noise. In many applications, graphene will inevitably be in contact with oxygen since it is the second most abundant gas in the atmosphere. Therefore, it is of interest to understand how this gas affects the sensor properties. In this work, the effect of oxygen on the low-frequency noise of suspended graphene is demonstrated. Devices with suspended graphene nanoribbons with a width (W) and length (L) of 200 nm were fabricated. The resistance as a function of time was measured in a vacuum and pure oxygen atmosphere through an ac lock-in method. After signal processing with wavelet denoising and analysis, it is demonstrated that oxygen causes random telegraphy signal (RTS) in the millisecond scale, with an average dwell time of 2.9 milliseconds in the high-resistance state, and 2 milliseconds in the low-resistance state. It is also shown that this RTS occurs only at some periods, which indicates that, upon adsorption, the molecules take some time until they find the most energetically favorable adsorption state. Also, a slow-down in the RTS time constants is observed, which infers that less active sites are available as time goes on because of oxygen adsorption. Therefore, it is very important to consider these effects to guarantee high sensitivity and high durability for graphene-based sensors that will be exposed to oxygen during their lifetime

Mechanical Properties of Low Dimensional Materials

Recent advances in low dimensional materials (LDMs) have paved the way for unprecedented technological advancements. The drive to reduce the dimensions of electronics has compelled researchers to devise newer techniques to not only synthesize novel materials, but also tailor their properties. Although micro and nanomaterials have shown phenomenal electronic properties, their mechanical robustness and a thorough understanding of their structure-property relationship are critical for their use in practical applications. However, the challenges in probing these mechanical properties dramatically increase as their dimensions shrink, rendering the commonly used techniques inadequate. This Dissertation focuses on developing techniques for accurate determination of elastic modulus of LDMs and their mechanical responses under tensile and shear stresses. Fibers with micron-sized diameters continuously undergo tensile and shear deformations through many phases of their processing and applications. Significant attention has been given to their tensile response and their structure-tensile properties relations are well understood, but the same cannot be said about their shear responses or the structure-shear properties. This is partly due to the lack of appropriate instruments that are capable of performing direct shear measurements. In an attempt to fill this void, this Dissertation describes the design of an inexpensive tabletop instrument, referred to as the twister, which can measure the shear modulus (G) and other longitudinal shear properties of micron-sized individual fibers. An automated system applies a pre-determined twist to the fiber sample and measures the resulting torque using a sensitive optical detector. The accuracy of the instrument was verified by measuring G for high purity copper and tungsten fibers. Two industrially important fibers, IM7 carbon fiber and Kevlar® 119, were found to have G = 17 and 2.4 GPa, respectively. In addition to measuring the shear properties directly on a single strand of fiber, the technique was automated to allow hysteresis, creep and fatigue studies. Zinc oxide (ZnO) semiconducting nanostructures are well known for their piezoelectric properties and are being integrated into several nanoelectro-mechanical (NEMS) devices. In spite of numerous studies on the mechanical response of ZnO nanostructures, there is not a consensus in its measured bending modulus (E). In this Dissertation, by employing an all-electrical Harmonic Detection of Resonance (HDR) technique on ZnO nanowhisker (NW) resonators, the underlying origin for electrically-induced mechanical oscillations in a ZnO NW was elucidated. Based on visual detection and electrical measurement of mechanical resonances under a scanning electron microscope (SEM), it was shown that the use of an electron beam as a resonance detection tool alters the intrinsic electrical character of the ZnO NW, and makes it difficult to identify the source of the charge necessary for the electrostatic actuation. A systematic study of the amplitude of electrically actuated as-grown and gold-coated ZnO NWs in the presence (absence) of an electron beam using an SEM (dark-field optical microscope) suggests that the oscillations seen in our ZnO NWs are due to intrinsic static charges. In experiments involving mechanical resonances of micro and nanostructured resonators, HDR is a tool for detecting transverse resonances and E of the cantilever material. To add to this HDR capability, a novel method of measuring the G using HDR is presented. We used a helically coiled carbon nanowire (HCNW) in singly-clamped cantilever configuration, and analyzed the complex (transverse and longitudinal) resonance behavior of the nonlinear geometry. Accordingly, a synergistic protocol was developed which (i) integrated analytical, numerical (i.e., finite element using COMSOL ®) and experimental (HDR) methods to obtain an empirically validated closed form expression for the G and resonance frequency of a singly-clamped HCNW, and (ii) provided an alternative for solving 12th order differential equations. A visual detection of resonances (using in situ SEM) combined with HDR revealed intriguing non-planar resonance modes at much lower driving forces relative to those needed for linear carbon nanotube cantilevers. Interestingly, despite the presence of mechanical and geometrical nonlinearities in the HCNW resonance behavior, the ratio of the first two transverse modes f2/f1 was found to be similar to the ratio predicted by the Euler-Bernoulli theorem for linear cantilevers

Graphene resonators for mass sensing applications

PhD ThesisGraphene’s exceptional physical and mechanical properties make it an excellent nanomaterial for MEMS/NEMS devices with wide reaching applications. This thesis explores graphene as a nanomaterial, its use in mass sensing applications and the suitability of existing theoretical models to describe its behaviour as a rectangular resonator. Several local and nonlocal continuum models have been proposed in literature for the vibration analysis of graphene resonators. But with very little experimental data to validate these theoretical models, most of the solutions employed to solve these models compare their results with results from other theoretical models, leading to doubts about their validity and accuracy. In addition to providing a guide for determining the suitable theoretical model for different sized rectangular graphene resonators, this work establishes that a small-scale parameter 0 of any value between 0 and 2 needs to be incorporated in any local continuum modelled applied to micro-sized graphene sheets to avoid overestimation of the frequency of the sheets. A fabrication route for NEMS and MEMS devices with rectangular graphene resonators up to 32 by 7 is also developed with the provision for magnetomotive actuation via Lorentz force with possible capacitive readout capabilities. This is important as the use of graphene in MEMS/NEMS is being hurriedly transitioned from the Research space to the marketplace

Nanomechanical and nanoelectromechanical phenomena in 2D-atomic crystals:a scanning probe microscopy approach

In this thesis we probe the morphological, nanomechanical and nanoelectromechanical properties of 2D materials: graphene, MoS2 and h-BN. Throughout this study we extensively use scanning probe techniques of ultrasonic force microscopy (UFM), direct-contact electrostatic force microscopy (DC-EFM) and heterodyne force microscopy (HFM). With the use of these techniques we report the observation of the nanoscale Moir`e pattern when graphene is aligned on h-BN and we propose that the imaging with atomic force microscopy of such a sample is partly due to the variance in both sample adhesion and mechanical stiffness. In addition to this we probe the ability for UFM to detect the subsurface mechanical properties in 2D materials and confirm that the anisotropy present effectively enhances its ability to do so. We apply this knowledge of UFM and 2D materials to detect the decoupling of graphene, grown on 4H-SiC, from the substrate through the intercalation with hydrogen. In the final part of this thesis we discuss the electromechanical phenomena observable in 2D materials and related devices. Through the electrostatic actuation of graphene resonator type devices we are able to probe the electrostatic environment beneath the graphene layer, information that is unavailable to non-contact mode techniques. We then develop this method of DC-EFM to incorporate a sensitivity to the time-dependent properties by introducing the heterodyne mixing principle. This new technique developed, called electrostatic heterodyne force microscopy (E-HFM) is sensitive in the nano-second time domain whilst maintaining the nanoscale lateral and vertical resolution typical of an atomic force microscope. We propose that E-HFM will prove to be a valuable tool in characterising the behaviour of high-frequency small-scale nano electromechanical systems (NEMS) currently beyond the reach of conventional characterisation techniques. Finally we pave the way forward to future NEMS and demonstrate some of the steps taken towards progress in the field