厚度(层间耦合)对二维材料散射时间和输运的影响

2D elemental layered crystals, such as graphene and black phosphorus (B‐P), have received tremendous attentions due to their rich physical and chemical properties. In the applications of nanoelectronic devices, graphene shows super high electronic mobility, but it lacks bandgap which impedes development in logical devices. As an alternative, B‐P shows high mobility of up to about 1000 cm2 V−1 s−1. However, B‐P is very unstable and degrades rapidly in ambient conditions. Orthorhombic arsenic (black arsenic; b‐As) is the “cousin” of B‐P; theoretical prediction shows that b‐As also has excellent physical and chemical properties, but there is almost no experimental report on b‐As. Herein, it is reported on the unique transport characteristics and stability of monolayer and few‐layer b‐As crystals which are exfoliated from the natural mineral. The properties of field‐effect transistors (FETs) strongly depend on the thickness of crystals. In the monolayer limit, the performance shows relatively high carrier mobilities and large on/off ratios. Moreover, the b‐As crystals exhibit a relatively good ambient stability. The few‐layer arsenic based FET still function after exposure to air for about one month. Therefore, b‐As is expected to be a promising 2D material candidate in nanoelectronic devices.

… Due to their atomic thickness, 2D materials allow superior electrostatic control and as such, 2D … in its electronic properties, the dependence of the charge carrier mobility in MoS 2 on the …

We investigated the dependence of electron mobility on the thickness of MoS2 nanosheets by fabricating bottom-gate single and few-layer MoS2 thin-film transistors with SiO2 gate dielectrics and Au electrodes. All the fabricated MoS2 transistors showed on/off-current ratio of ∼107 and saturated output characteristics without high-k capping layers. As the MoS2 thickness increased from 1 to 6 layers, the field-effect mobility of the fabricated MoS2 transistors increased from ∼10 to ∼18 cm2V−1s−1. The increased subthreshold swing of the fabricated transistors with MoS2 thickness suggests that the increase of MoS2 mobility with thickness may be related to the dependence of the contact resistance and the dielectric constant of MoS2 layer on its thickness.

The correlation between the channel thickness and the carrier mobility is investigated by conducting static and low frequency (LF) noise characterization for ambipolar carriers in multilayer MoTe2 transistors. For channel thicknesses in the range of 5–15 nm, both the low-field carrier mobility and the Coulomb-scattering-limited carrier mobility (μC) are maximal at a thickness of ∼10 nm. For LF noise, the interplay of interface trap density (NST), which was minimal at ∼10 nm, and the interfacial Coulomb scattering parameter (αSC), which decreased up to 10 nm and saturated above 10 nm, explained the mobility (μC) peaked near 10 nm by the carrier fluctuation and charge distribution.

Thickness-dependent bandgap and carrier mobility of two-dimensional (2D) van der Waals (vdW) layered materials make them a promising material as a phototransistor that detects light signals and converts them to electrical signals. Thus far, to achieve a high photoresponsivity of 2D materials, enormous efforts have been made via material and dielectric engineering, as well as modifying device structure. Nevertheless, understanding the effect of interplay between the thickness and the carrier mobility to photoresponsivity is little known. Here, we demonstrate the tunable photoresponsivity (R) of 2D multilayer rhenium disulfide (ReS2), which is an attractive candidate for photodetection among 2D vdW materials owing to its layer-independent direct bandgap and decoupled vdW interaction. The gate bias (VG)-dependent photocurrent generation mechanism and R are presented for the channel thickness range of 1.7–27.5 nm. The high similarity between VG-dependent photocurrent and transconductance features in the ReS2 phototransistors clearly implies the importance of the channel thickness and the operating VG bias condition. Finally, the maximum R was found to be 4.1 × 105 A/W at 14.3 nm with the highest carrier mobility of ∼15.7 cm2⋅V−1⋅s−1 among the fabricated devices after excluding the contact resistance effect. This work sheds light on the strategy of how to obtain the highest R in 2D vdW-based phototransistors.

… of carrier density and carrier mobility, the gating effect should be discussed within the context of gate dependent density and mobility of the two carriers… -reproduced thickness dependent …

… , therefore enhancing carrier mobility of electrical transport. The ultrathin thickness and … the operation speed by the enhancement of carrier mobility. A number of studies have been …

… can reduce electron–phonon scattering in 2D materials and … We identify two regimes in the gate-dependent electrical … f-MoS 2 devices of different thicknesses are measured in this work. …

Two-dimensional (2D) metal dichalcogenides (MX2) are the most common type of 2D semiconductors and have shown great potential for a wide range of chemical and physical applications. However, they are limited by a low electron/hole mobility, which has been recognized as one of the major challenges impeding their further developments, and urges efforts to understand the mobility-limiting factors and discovery of higher-mobility alternatives. Here using density functional perturbation theory and Wannier interpolation of the electron-phonon matrix to study a wide range of MX2, we find that the intrinsic carrier mobility, in contrast to common belief, neither correlates with the effective mass nor can be assessed by the widely used deformation potential theory; instead it is limited by the longitudinal optical (LO) phonon scattering for most MX2, while for MoS2 and WS2, the mobility is limited by the longitudinal acoustic (LA) phonon scattering. Furthermore, we find that the LO scattering strength is strongly correlated with the magnitude of the Born effective charge, suggesting that the carrier transport is greatly affected by the electric polarization change induced by the atomic vibration. This finding enables us to use the Born effective charge to rapidly screen the 2D MX2 database for high-mobility semiconductor candidates. Our work reveals the underlying factors governing the intrinsic carrier mobility of 2D MX2, offers a practical descriptor for discovering high-mobility candidates, and serves as a paradigm to accurately assess the carrier mobility in 2D semiconductors, thereby paving critical steps toward the development of 2D materials.

Two-dimensional (2D) van der Waals semiconductors represent the thinnest, air stable semiconducting materials known. Their unique optical, electronic and mechanical properties hold great potential for harnessing them as key components in novel applications for electronics and optoelectronics. However, the charge transport behavior in 2D semiconductors is more susceptible to external surroundings (e.g. gaseous adsorbates from air and trapped charges in substrates) and their electronic performance is generally lower than corresponding bulk materials due to the fact that the surface and bulk coincide. In this article, we review recent progress on the charge transport properties and carrier mobility engineering of 2D transition metal chalcogenides, with a particular focus on the markedly high dependence of carrier mobility on thickness. We unveil the origin of this unique thickness dependence and elaborate the devised strategies to master it for carrier mobility optimization. Specifically, physical and chemical methods towards the optimization of the major factors influencing the extrinsic transport such as electrode/semiconductor contacts, interfacial Coulomb impurities and atomic defects are discussed. In particular, the use of ad hoc molecules makes it possible to engineer the interface with the dielectric and heal the vacancies in such materials. By casting fresh light on the theoretical and experimental studies, we provide a guide for improving the electronic performance of 2D semiconductors, with the ultimate goal of achieving technologically viable atomically thin (opto)electronics.

There has been emerging research of novel two-dimensional (2D) layered materials recently, due to their striking geometric, electronic and thermoelectric properties caused by the quantum confinement effect. However, the current reported thermoelectric performance of thin films is usually size-sensitive and hence may not be superior to that of their bulk counterparts. It is thus important to determine the size effect for low-dimensional thermoelectric materials, based on the theoretical tools of quantum mechanics. To achieve this goal, we studied 2D SnTe single crystals with a varied layer thickness as the characteristic length of materials, to eliminate the other coupled effects of interface engineering or universal defects in polycrystalline thin films. In this work, we demonstrate that the strategy of the quantum confinement effect is highly sensitive to the layer thickness of 2D SnTe materials, and a critical size of 3 layers exists, above which an abrupt degradation of the mobility and thermoelectric parameters occurs. The thermoelectric performance is optimal in monolayer SnTe and then gradually decays, until 6 layers, which gets close to the bulk feature. Correspondingly, the power factor (PF) and the ZT values exhibit evident layer-tunability as a combined effect of layer-dependent relaxation time, effective mass, electrical conductivity and Seebeck coefficient. Our study provides a profound physical understanding of the low-dimensionality strategy for high-performance thermoelectric materials. The intrinsic thermoelectric properties of ultra-thin 2D materials can be favourable as compared to those of the bulk single crystals.

Down‐scaling of transistor size in the lateral dimensions must be accompanied by a corresponding reduction in the channel thickness to ensure sufficient gate control to turn off the transistor. However, the carrier mobility of 3D bulk semiconductors degrades rapidly as the body thickness thins down due to more pronounced surface scattering. Two‐dimensional‐layered materials with perfect surface structures present a unique opportunity as they naturally have atomically thin and smooth layers while maintaining high carrier mobility. To benefit from continuous scaling, the performance of the scaled 2D transistors needs to outperform Si technology nowadays. There are already quite a few reviews discussing on the material property of potential 2D materials. It is believed that rigorous analysis based on industrial perspectives is needed. Herein, an analysis on channel material selection is presented and arguments on the four selected 2D semiconductors are provided, which can possibly meet the needs of future transistors, including WS2, SnSe, PtSe2, and InSe. The challenges and recent related research progresses for each material are also discussed.

… of the width, therefore, represents a perturbation which gives rise to a friction of the carrier. … fact which is reQected in a strong dependence of the carrier mobility on temperature. From (24…

2D semiconductors offer a promising pathway to replace silicon in next-generation electronics. Among their many advantages, 2D materials possess atomically-sharp surfaces and enable scaling the channel thickness down to the monolayer limit. However, these materials exhibit comparatively lower charge carrier mobility and higher contact resistance than 3D semiconductors, making it challenging to realize high-performance devices at scale. In this work, we search for high-mobility 2D materials by combining a high-throughput screening strategy with state-of-the-art calculations based on the ab initio Boltzmann transport equation. Our analysis singles out a known transition metal dichalcogenide, monolayer WS2, as the most promising 2D semiconductor, with the potential to reach ultra-high room-temperature hole mobilities in excess of 1300 cm2/Vs should Ohmic contacts and low defect densities be achieved. Our work also highlights the importance of performing full-blown ab initio transport calculations to achieve predictive accuracy, including spin–orbital couplings, quasiparticle corrections, dipole and quadrupole long-range electron–phonon interactions, as well as scattering by point defects and extended defects.

… of the interlayer van der Waals coupling in a number of 2D … the van der Waals coupled 2D materials for next-generation … therefore can be compensated by Umklapp scattering, that is, the …

Intercalation in few‐layer (2D) materials is a rapidly growing area of research to develop next‐generation energy‐storage and optoelectronic devices, including batteries, sensors, transistors, and electrically tunable displays. Identifying fundamental differences between intercalation in bulk and 2D materials will play a key role in developing functional devices. Herein, advances in few‐layer intercalation are addressed in the historical context of bulk intercalation. First, synthesis methods and structural properties are discussed, emphasizing electrochemical techniques, the mechanism of intercalation, and the formation of a solid‐electrolyte interphase. To address fundamental differences between bulk and 2D materials, scaling relationships describe how intercalation kinetics, structure, and electronic and optical properties depend on material thickness and lateral dimension. Here, diffusion rates, pseudocapacity, limits of staging, and electronic structure are compared for bulk and 2D materials. Next, the optoelectronic properties are summarized, focusing on charge transfer, conductivity, and electronic structure. For energy devices, opportunities also emerge to design van der Waals heterostructures with high capacities and excellent cycling performance. Initial studies of heterostructured electrodes are compared to state‐of‐the‐art battery materials. Finally, challenges and opportunities are presented for 2D materials in energy and optoelectronic applications, along with promising research directions in synthesis and characterization to engineer 2D materials for superior devices.

Layer-dependent electronic and optoelectronic properties in two-dimensional (2D) semiconductors provide a large degree of freedom to exploit high-performance devices for next-generation electronic and optoelctronics. However, there is still a lack...

… interlayer coupling in 2D materials can generate interlayer vibrational modes between adjacent layers, ie interlayer shear modes and interlayer … ], the relaxation time of interlayer carriers …

In van der Waals bonded or rotationally disordered multilayer stacks of two-dimensional (2D) materials, the electronic states remain tightly confined within individual 2D layers. As a result, electron–phonon interactions occur primarily within layers and interlayer electrical conductivities are low. In addition, strong covalent in-plane intralayer bonding combined with weak van der Waals interlayer bonding results in weak phonon-mediated thermal coupling between the layers. We demonstrate here, however, that Coulomb interactions between electrons in different layers of multilayer epitaxial graphene provide an important mechanism for interlayer thermal transport, even though all electronic states are strongly confined within individual 2D layers. This effect is manifested in the relaxation dynamics of hot carriers in ultrafast time-resolved terahertz spectroscopy. We develop a theory of interlayer Coulomb coupling containing no free parameters that accounts for the experimentally observed trends in hot-carrier dynamics as temperature and the number of layers is varied. The coupling between layers plays an important role in the properties of stacked two-dimensional materials. Here, the authors show that Coulomb interactions between electrons in different layers of graphene induce thermal transport even though all electronic states are confined to individual layers.

Interlayer electronic coupling or hybridization in two-dimensional (2D) van der Waals semiconductors has a nontrivial impact on layer-dependent properties. However, the underlying mechanisms governing interlayer coupling in 2D semiconductor systems remain poorly understood, hindering precise control of their layer-dependent properties for device applications. Herein, we present a comprehensive classification of interlayer electronic coupling and reveal how it impacts the layer-dependent electronic and optical properties across a series of 2D semiconductors based on density-functional theory (DFT) calculations. Our results indicate that the interlayer coupling strength of these 2D semiconductors is governed by the overlapping degree of out-of-plane orbitals, which is determined by the type and coupling distance of valence electronic states. The strongly coupling 2D semiconductors dominated by out-of-plane orbital interactions exhibit significant variation in bandgap and a notable shift in absorption peaks with the change of layer number. Conversely, the weakly coupling 2D semiconductors originate from in-plane orbital interactions or large coupling distance, making their bandgaps and optical absorption peaks insensitive to the change of layer number. This work sheds light on the interlayer electronic coupling mechanism in 2D semiconductors and suggests the possibility of modulating their electronic and optoelectronic properties for advanced device applications by utilizing the interlayer coupling effect.

2D van der Waals (vdW) heterostructures are receiving increasing research attention due to the theoretically amazing properties and unprecedented application potential. However, the as-synthesized heterostructures are generally underperforming due to the weak interlayer coupling, which inspires the researchers to find ways to modulate the interlayer coupling and properties, realizing the tailored performance for actual applications. There have been a lot of publications regarding the controllable regulation of the structures and properties of 2D vdW heterostructures in the past few years, while a review work summarizing the current advances is not yet available, though it is significant. This paper conducts a state-of-the-art review regarding the current research progress of performance modulation of vdW heterostructures by different techniques. First, the general synthesis methods of vdW heterostructures are summarized. Then, different performance modulation techniques, that is, mechanical-based, external fields-assisted, and particle beam irradiation-based methods, are discussed and compared in detail. Some of the newly proposed concepts are described. Thereafter, applications of vdW heterostructures with tailored properties are reviewed for the application prospects of the topic around this area. Moreover, the future research challenges and prospects are discussed, aiming at triggering more research interest and device applications around this topic.

… of the conductivity of multilayer graphene based on Boltzmann transport equation and 2D electron gas theory. Numerical simulations show that the conductivities of few-layer graphene …

… The electrical transport properties of magnetic … layers that changes from one layer to another, (2) the additional scattering resistivity due to the roughness of the interfaces between layers…

This paper records experiments and theoretical work concerned with the variation of conductivity with size in metals. Experimental results for the conductivity in thin wires of pure sodium of varying diameter in the absence of a magnetic field and also in the presence of longitudinal and transverse magnetic fields are given. Using the general statistical theory of metals the variation of resistance with size in the case of conductivity wires of square cross-section is calculated for comparison with the first set of experiments. A theoretical investigation follows of the alteration in conductivity produced in metallic films by the application of transverse magnetic fields, and this is compared with the corresponding experimental results obtained on the sodium cylinders.

The layer exchange technique enables high-quality multilayer graphene (MLG) on arbitrary substrates, which is a key to combining advanced electronic devices with carbon materials. We synthesize uniform MLG layers of various thicknesses, t, ranging from 5 nm to 200 nm using Ni-induced layer exchange at 800 °C. Raman and transmission electron microscopy studies show the crystal quality of MLG is relatively low for t ≤ 20 nm and dramatically improves for t ≥ 50 nm when we prepare a diffusion controlling Al2O3 interlayer between the C and Ni layers. Hall effect measurements reveal the carrier mobility for t = 50 nm is 550 cm2/Vs, which is the highest Hall mobility in MLG directly formed on an insulator. The electrical conductivity (2700 S/cm) also exceeds a highly oriented pyrolytic graphite synthesized at 3000 °C or higher. Synthesis technology of MLG with a wide range of thicknesses will enable exploration of extensive device applications of carbon materials.

… voltages, we measure the layer number dependence of the effective barrier… electrical properties from simultaneously recorded local I–V data. In addition, we investigate the layer number …

Group III layered monochalcogenide gallium sulfide, GaS, is one of the latest additions to the two-dimensional (2D) materials family, and of particular interest for visible-UV optoelectronic applications due to its wide bandgap energy in the range 2.35–3.05 eV going from bulk to monolayer. Interestingly, when going to the few-layer regime, changes in the electronic structure occur, resulting in a change in the properties of the material. Therefore, a systematic study on the thickness dependence of the different properties of GaS is needed. Here, we analyze mechanically exfoliated GaS layers transferred to glass substrates. Specifically, we report the dependence of the Raman spectra, photoluminescence, optical transmittance, resistivity, and work function on the thickness of GaS. Those findings can be used as guidance in designing devices based on GaS.

We report a systematic investigation of the temperature dependence of electrical resistance behaviours in tri- and four-layer graphene interconnects. Nonlinear current–voltage characteristics were observed at different temperatures, which are attributed to the heating effect. With the resistance curve derivative analysis method, our experimental results suggest that Coulomb interactions play an essential role in our devices. The room temperature measurements further indicate that the graphene layers exhibit the characteristics of semiconductors mainly due to the Coulomb scattering effects. By combining the Coulomb and short-range scattering theory, we derive an analytical model to explain the temperature dependence of the resistance, which agrees well with the experimental results.

… Anisotropic effects related to the excitons in 2D materials are … charge carrier scattering and electronic transport. We first provide the basic semiclassical theory of anisotropic transport (…

Low-symmetry layered materials such as black phosphorus (BP) have been revived recently due to their high intrinsic mobility and in-plane anisotropic properties, which can be used in anisotropic electronic and optoelectronic devices. Since the anisotropic properties have a close relationship with their anisotropic structural characters, especially for materials with low-symmetry, exploring new low-symmetry layered materials and investigating their anisotropic properties have inspired numerous research efforts. In this paper, we review the recent experimental progresses on low-symmetry layered materials and their corresponding anisotropic electrical transport, magneto-transport, optoelectronic, thermoelectric, ferroelectric, and piezoelectric properties. The boom of new low-symmetry layered materials with high anisotropy could open up considerable possibilities for next-generation anisotropic multifunctional electronic devices.

Layered van der Waals (vdW) semiconductors have emerged as preferred materials for building next-generation electronic devices, such as diodes and field-effect transistors (FETs), because of their capability of providing high mobility at the nanometer-scale thickness, as well as their flexibility and pristine interfaces. However, the inherent “vdW gaps” in these materials lead to much larger cross-plane resistivity, with respect to in-plane resistivity, thereby forming intriguing transport anisotropy. In this article, using extensive numerical simulations, it is found that this anisotropy introduces anomalous current transport behavior in vdW-based electron devices in which the current conducts in both the in-plane and cross-plane directions, including stacked heterojunction diodes and thin-film transistors (TFTs). Our study reveals for the first time that transport anisotropy degrades the performance of these devices, especially when devices are scaled ( $ < 0.6~\mu \text{m}$ ) and/or relatively thicker materials (>4 nm) are used. Potential solutions to alleviate degradation are discussed as well.

… physics compared to isotropic 2D materials, thus providing a … anisotropy. This article reviews the recent advance in characterization and applications of in-plane anisotropic 2D materials…

… Anisotropic electronic transport is a possible route towards nanoscale circuitry design, particularly in two-dimensional materials. … spatial anisotropies in both charge and spin transport. …

After the breakthrough of the study on the two-dimensional (2D) layered phosphorus, group-V elemental ultrathin 2D layers have captured considerable attentions in recent years on account of their unique and promising electrical transport properties, including semiconductor features with direct and desirable energy band structures, outstanding carrier mobilities, controllable and tunable characteristics under applied strain, electric and magnetic fields, highly anisotropic phenomena along both in-plane and out-plane directions, topological transmission states, and negative Poisson’s ratio. Accordingly, a number of investigations on this family of 2D materials have been conducting rapidly, while initiating great potential and new opportunities on the nanoscale science and applications in optoelectronic, magneto-electronics, thermo-electronic, ferroelectric, topological spintronics, and so on. Herein, a specific review is provided with systematical summarizations and refinements on the recent advances of the electrical transport in group-V elemental ultrathin 2D layers from the blossoming field of research, while comprehensive discussion and some recommendations are put forward, with an expectation of broadening and deepening understanding of the family of 2D layers. Lastly, we provide critical motivation and challenge for future explorations in this promising territory.

Recently, monoclinic-phase GaTe has attracted much attention due to its potential applications in nanoelectronics. Despite the experimental research, theoretical studies on the thermal and transport properties, which are necessary to provide information for future applications, are still absent. We have systematically investigated the electronic, phonon and electron transporting, and thermoelectric properties of monolayer and bulk GaTe using first-principles calculations plus the Boltzmann transport equation. At the valence band maximum and conduction band minimum, the effective mass shows large anisotropy as the band dispersions are along different k-paths. The group velocity of acoustic modes also shows large anisotropy owing to the in-plane low-symmetry. Our calculations reveal that the in-plane thermal conductivities, κa and κb, take 3.5 and 8.9 W m-1 K-1, respectively, for the bulk at 300 K, compared to κa = 5.5 and κb = 10.4 W m-1 K-1 of the monolayer. Due to the van der Waals interactions between interlayers, the out-of-plane thermal conductivity is very small, κc = 1.8 W m-1 K-1. The difference between the in-plane thermal conductivities of the bulk and the monolayer can be attributed to the strengthened Umklapp scattering, which is caused by the stiffening of the lowest-frequency optical mode in the bulk. The hole mobilities of the bulk is found to be about 12-35 cm2 V-1 s-1 at 300 K, in good agreement with the experimental results. The monolayer is found to have smaller mobility but larger anisotropy than those of the bulk. Interestingly, the out-of-plane conductivity is anomalously larger than the in-plane one for the bulk, which is attributed to the orbital overlaps between the interlayer Te atoms. Moreover, n-type GaTe is found to have much larger mobility and anisotropy than the p-type one, which is useful for future applications. Compared with the case of monolayer GaTe, thermoelectric performance can be enhanced by one order of magnitude for the bulk GaTe by exploiting the out-of-plane thermal and electrical conductivities.

We demonstrate a first-principles method to study magnetotransport in materials by solving the Boltzmann transport equation (BTE) in the presence of an external magnetic field. Our approach employs ab initio electron-phonon interactions and takes spin-orbit coupling into account. We apply our method to various semiconductors (Si and GaAs) and two-dimensional (2D) materials (graphene) as representative case studies. The magnetoresistance, Hall mobility and Hall factor in Si and GaAs are in very good agreement with experiments. In graphene, our method predicts a large magnetoresistance, consistent with experiments. Analysis of the steady-state electron occupations in graphene shows the dominant role of optical phonon scattering and the breaking of the relaxation time approximation. Our work provides a detailed understanding of the microscopic mechanisms governing magnetotransport coefficients, establishing the BTE in a magnetic field as a broadly applicable first-principles tool to investigate transport in semiconductors and 2D materials.

We present density functional theory calculations of the phonon-limited mobility in $n$-type monolayer graphene, silicene, and ${\mathrm{MoS}}_{2}$. The material properties, including the electron-phonon interaction, are calculated from first principles. We provide a detailed description of the normalized full-band relaxation time approximation for the linearized Boltzmann transport equation (BTE) that includes inelastic scattering processes. The bulk electron-phonon coupling is evaluated by a supercell method. The method employed is fully numerical and does therefore not require a semianalytic treatment of part of the problem and, importantly, it keeps the anisotropy information stored in the coupling as well as the band structure. In addition, we perform calculations of the low-field mobility and its dependence on carrier density and temperature to obtain a better understanding of transport in graphene, silicene, and monolayer ${\mathrm{MoS}}_{2}$. Unlike graphene, the carriers in silicene show strong interaction with the out-of-plane modes. We find that graphene has more than an order of magnitude higher mobility compared to silicene in the limit where the silicene out-of-plane interaction is reduced to zero (by substrate interaction, clamping, or similar). If the out-of-plane interaction is not actively reduced, the mobility of silicene will essentially be zero. For ${\mathrm{MoS}}_{2}$, we obtain several orders of magnitude lower mobilities compared to graphene in agreement with other recent theoretical results. The simulations illustrate the predictive capabilities of the newly implemented BTE solver applied in simulation tools based on first-principles and localized basis sets.

The electronic transport behaviour of materials determines their suitability for technological applications. We develop a computationally efficient method for calculating carrier scattering rates of solid-state semiconductors and insulators from first principles inputs. The present method extends existing polar and non-polar electron-phonon coupling, ionized impurity, and piezoelectric scattering mechanisms formulated for isotropic band structures to support highly anisotropic materials. We test the formalism by calculating the electronic transport properties of 23 semiconductors, including the large 48 atom CH3NH3PbI3 hybrid perovskite, and comparing the results against experimental measurements and more detailed scattering simulations. The Spearman rank coefficient of mobility against experiment (rs = 0.93) improves significantly on results obtained using a constant relaxation time approximation (rs = 0.52). We find our approach offers similar accuracy to state-of-the art methods at approximately 1/500th the computational cost, thus enabling its use in high-throughput computational workflows for the accurate screening of carrier mobilities, lifetimes, and thermoelectric power. It is difficult to compute the transport properties of a broad array of complex materials both accurately and inexpensively. Here, the authors develop a computationally efficient method for calculating carrier scattering rates of semiconductors, with good accuracy but low cost.

… transport equations, we illustrate different scattering … how the first-principles methods allow one to investigate transport … into the electron and phonon transport. The current status of the …

… graphane, and MoS 2 (single-layer and bulk limits), for which … ) structure validation from the transport and optical properties … and ionized impurity scattering to a selection of 2D materials […

The intrinsic carrier transport dynamics in phosphorene is theoretically examined. Utilizing a density functional theory treatment, the low-field mobility and the saturation velocity are characterized for both electrons and holes in the monolayer and bilayer structures. The analysis clearly elucidates the crystal orientation dependence manifested through the anisotropic band structure and the carrier-phonon scattering rates. In the monolayer, the hole mobility in the armchair direction is estimated to be approximately five times larger than in the zigzag direction at room temperature (460 cm2/V s vs. 90 cm2/V s). The bilayer transport, on the other hand, exhibits a more modest anisotropy with substantially higher mobilities (1610 cm2/V s and 760 cm2/V s, respectively). The calculations on the conduction-band electrons indicate a comparable dependence while the characteristic values are generally smaller by about a factor of two. The variation in the saturation velocity is found to be less pronounced. With the anticipated superior performance and the diminished anisotropy, few-layer phosphorene offers a promising opportunity particularly in p-type applications.

In bismuth quantum films, a fascinating interplay between (bulk) quantum well and interface (edge) states is observed in this comprehensive study of DC magnetoconductance and Hall resistivity as a function of film thickness. While for thin layers (up to 40 bilayers, BL) conductance is governed by the surface states, strong contributions of a quantum well state dominate above 70 BL. Quantum corrections in a magnetic field normal to the surface, however, are dominated by the interface states for all thicknesses investigated for reasons discussed in the paper.

The dependences of the electrical conductivity, the Hall coefficient, and the Seebeck coefficient on the layer thickness d (d = 18−600 nm) of p-type topological insulator Bi2Te3 thin films grown by thermal evaporation in vacuum on glass substrates were obtained at room temperature. In the thickness range of d = 18–100 nm, sustained oscillations with a substantial amplitude were revealed. The observed oscillations are well approximated by a harmonic function with a period Δd = (9.5 ± 0.5) nm. At d &amp;gt; 100 nm, the transport coefficients practically do not change as d is increased. The oscillations of the kinetic properties are attributed to the quantum size effects due to the hole confinement in the Bi2Te3 quantum wells. The results of the theoretical calculations of Δd within the framework of a model of an infinitely deep potential well are in good agreement with the experimental results. It is suggested that the substantial amplitude of the oscillations and their sustained character as a function of d are connected with the topologically protected gapless surface states of Bi2Te3 and are inherent to topological insulators.

The dependence of charge carrier mobility on semiconductor channel thickness in field‐effect transistors is a universal phenomenon that has been studied extensively for various families of materials. Surprisingly, analogous studies involving metal oxide semiconductors are relatively scarce. Here, spray‐deposited In2O3 layers are employed as the model semiconductor system to study the impact of layer thickness on quantum confinement and electron transport along the transistor channel. The results reveal an exponential increase of the in‐plane electron mobility (µe) with increasing In2O3 thickness up to ≈10 nm, beyond which it plateaus at a maximum value of ≈35 cm2 V−1 s−1. Optical spectroscopy measurements performed on In2O3 layers reveal the emergence of quantum confinement for thickness <10 nm, which coincides with the thickness that µe starts deteriorating. By combining two‐ and four‐probe field‐effect mobility measurements with high‐resolution atomic force microscopy, it is shown that the reduction in µe is attributed primarily to surface scattering. The study provides important guidelines for the design of next generation metal oxide thin‐film transistors.

We present the thickness dependence of magnetotransport study on the mechanically exfoliated topological superconductor candidate SnTaS2. As the thickness decreases, the superconducting transition temperature Tc is gradually suppressed and ultimately out of detection when the thickness is comparable to the superconducting coherence length. The enhanced disorder with the decrease in thickness is expected to play an important role on the suppressed Tc. Furthermore, the distinct weak antilocalization effect is observed in the SnTaS2 nanoflakes, and the temperature-dependent phase coherence length extracted from weak antilocalization agrees with strong electron–phonon scattering in the sample. Our results provide insight into the electronic properties in the low dimensional limit of topological superconductor candidate SnTaS2.

… a theory for transport in small systems underconditions in which quantum size effects are … the thickness dependence of the density, obtained from (2.is plotted and is found to show …

The recent observation of Weyl fermions in the itinerant 4d ferromagnetic perovskite SrRuO3 points to this material being a good platform for exploring novel physics related to a pair of Weyl nodes in epitaxial heterostructures. In this letter, we report the thickness-dependent magnetotransport properties of ultra-high-quality epitaxial SrRuO3 films grown under optimized conditions on SrTiO3 substrates. Signatures of Weyl fermion transport, i.e., unsaturated linear positive magnetoresistance accompanied by a quantum oscillation having a {\pi} Berry phase, were observed in films with thicknesses as small as 10 nm. Residual resistivity increased with decreasing film thickness, indicating disorder near the interface between SrRuO3 and the SrTiO3 substrate. Since this disorder affects the magnetic and electrical properties of the films, the Curie temperature decreases and the coercive field increases with decreasing thickness. Thickness-dependent magnetotransport measurements revealed that the threshold residual resistivity ratio (RRR) to observe Weyl fermion transport is 21. These results provide guidelines for realizing quantum transport of Weyl fermions in SrRuO3 near heterointerfaces.

… There is a marked difference in the temperature and thickness dependence in the two limiting cases discussed above. In the former case, when 3ep «Ii/riz, the resistivity ratio is …

With high quality topological insulator Bi(2)Se(3) thin films, we report thickness-independent transport properties over wide thickness ranges. Conductance remained nominally constant as the sample thickness changed from 256 to ∼8  QL (where QL refers to quintuple layer, 1  QL≈1  nm). Two surface channels of very different behaviors were identified. The sheet carrier density of one channel remained constant at ∼3.0×10(13)  cm(-2) down to 2 QL, while the other, which exhibited quantum oscillations, remained constant at ∼8×10(12)  cm(-2) only down to ∼8  QL. The weak antilocalization parameters also exhibited similar thickness independence. These two channels are most consistent with the topological surface states and the surface accumulation layers, respectively.

Low-temperature magnetotransport studies are reported for (112)Cd3As2 films grown on (111)CdTe by molecular beam epitaxy as a function of the Cd3As2 film thickness. All films show Shubnikov-de Haas oscillations. An even-integer quantum Hall effect is observed for films thinner than 70 nm. For the thinnest films, the bulk is gapped and transport at low temperatures occurs only via the gapless, two-dimensional states. The lowest Landau level is reached at ∼10 T, and the longitudinal resistance nearly vanishes at the plateaus in the Hall resistance. The results are discussed in the context of the current theoretical understanding of topological surface states in three-dimensional Dirac semimetals.

… The transport properties are investigated as a function of the barrier thickness in the limit of … are proven to be stable with increasing barrier thickness. It is shown that at large barrier …

… To understand the temperature-dependent SdH oscillations for the different thickness thin films, we obtain the oscillation frequency F from Landau fan diagrams (figures 3(b), (f) and (j)), …

… -field and is instead determined by the thickness of the layer. Thus, the scattering models, especially the field and thickness dependence of surface scattering mechanisms, are expected …

Author(s): Galletti, Luca; Schumann, Timo; Kealhofer, David A; Goyal, Manik; Stemmer, Susanne

The conductivity of gas-free thin films of amorphous germanium was measured as a function of temperature and film thickness. Existing theories of hopping conduction have been …

Magnetic topological insulator MnBi2Te4 is an intrinsic van der Waals layer structure compound. The interplay between magnetism and topology makes MnBi2Te4 a good platform to investigate controllable topological phase transition and emerging physical states such as quantum anomalous Hall state and Weyl semimetal phase. Crystal characterization showed a rhombohedral unit cell composing of Te-Bi-Te-Mn-Te-Bi-Te septuple layer (SL) coupled antiferromagnetically. Systematically investigation of surface states with angle-resolved photoemission spectroscopy and of bulk states with transport measurement showed detailed electronic structure of MnBi2Te4 crystal. Rich topological phases were observed in MnBi2Te4. Temperature, doping and external magnetic field could affect the different topological phases and induce phase transitions in certain conditions. Quantum anomalous Hall effect (QAHE) was realized at as high as 6.5 K in 5-SLs MnBi2Te4 flake. Furthermore, the negative to positive magnetoresistance transition and the thickness dependent QAHE Chern number of MnBi2Te4 provide strong evidences for the Weyl semimetal states in this material. Based on experiments done from 2019 to 2022, our review should shed light on future research opportunities on MnBi2Te4 compound.

… of quantum size effects (QSEs) in a thin film or quantum well (QW), the condition λ F >d must be fulfilled, where d is the film thickness … Our theoretical calculation of the dependence of the …

Abstract The objects of the present study were thin n-Bi2Se3 films with thicknesses d = 10–100 nm, grown by thermal evaporation of n-Bi2Se3 crystals in vacuum onto heated glass substrates. The room temperature d-dependences of the Seebeck coefficient, the Hall coefficient, and the electrical conductivity of the films exhibited an oscillatory behavior, which we attribute to quantum size effects. Such interpretation of the results is supported by the fact that experimentally determined values of the oscillation period are in quite good agreement with the theoretically calculated ones. We suggest that the large amplitude and undamped character of the oscillations in the studied range of thicknesses are connected with the topologically protected gapless surface states of Bi2Se3. The observed oscillatory character of the d-dependences of the transport coefficients should be taken into account when 2D-structures are applied in nanothermoelectricity and other fields of nanoscience and nanotechnology.

In a thin Weyl semimetal, a thickness dependent Weyl-orbit quantum oscillation was proposed to exist, originating from a nonlocal cyclotron orbit via electron tunnelings between top and bottom Fermi-arc surface states. Here, magneto-transport measurements were carried out on untwinned Weyl metal SrRuO 3 thin films. In particular, quantum oscillations with a frequency F s1  ≈ 30 T were identified, corresponding to a small Fermi pocket with a light effective mass. Its oscillation amplitude appears to be at maximum for thicknesses in a range of 10 to 20 nm, and the phase of oscillation exhibits a systematic change with film thickness. The constructed Landau fan diagram shows an unusual concave downward curvature in the 1/ μ 0 H n - n curve, where n is the Landau level index. From thickness and field-orientation dependence, the F s1 oscillation is attributed to be of surface origin. Those findings can be understood within the framework of the Weyl-orbit quantum oscillation effect with non-adiabatic corrections.

… Figure 3 shows the ohmic mobility for phonon scattering, versus layer width a, at T = 150 K. The upper curve is the mobility given by (35) and (48); the lower curve includes a correction …

So far, layered PdSe2 has attracted much attention due to its completely tunable band-gap with varying layer numbers, yet the thickness-dependent transporting properties have been rarely studied. We have systematically studied the electronic structures, phonon and charge transport properties, and thermoelectric properties of few-layered (from 1L to 4L) and bulk PdSe2 by first-principles calculations and Boltzmann transport theory. As the thickness increases, the energy levels of band edges relative to 4s of selenium move oppositely due to their different bonding states, leading to the power-law decrease of the band-gap. Meanwhile, the electron effective mass decreases rapidly while the hole effective mass increases significantly compared with those unperturbed. Calculations on elastic constants reveal that both bulk and few-layered PdSe2 are mechanically stable, and the bulk is ductile with a Poisson's ratio of 0.27. The shifts of Raman active modes with respect to the thickness as well as their Gruneisen parameters are analyzed and the underlying physics is discussed. At room temperature, the thermal conductivities of the bulk are 7.7, 10.1 and 0.9 W m-1 K-1 along the a, b and c axes, respectively. It is found that the low-frequency modes (<2.0 THz) contribute about 80% of in-plane thermal conductivities. Due to the enhanced contribution from the ZA mode, the thermal conductivity of few-layered PdSe2 is much larger than that of the bulk. The ZA mode is mainly scattered by itself and the Umklapp scattering dominates in the process as the thickness increases. Calculations on charge transport reveal that the electron mobility increases from 2.5-13.2 (1L) to 121.9-167.8 (4L) cm2 V-1 s-1 with the decreasing anisotropy μb/μa, while the hole mobility remains to be ∼20 cm2 V-1 s-1, which is in good agreement with the experimental results. Calculations on the thermoelectric properties reveal that the ZT value as well as the power factor increases largely as the thickness increases and it gets to be optimum for the triple layer. Interestingly, the transport of electrons and phonons is decoupled along the out-of-plane direction, which makes bulk PdSe2 exhibit good thermoelectric performance along the c axis.

The total scattering rate and the transition probability for electron-phonon interaction in 1-D and 2-D semiconductor materials are calculated in taking into account the finite dimensions of the structure. Although noticeable, size effects on the scattering rate are generally small, with more pronounced features for 1-D structures than for 2-D structures. For 2-D layers, our theory agrees with recent experimental results whereas it contradicts the previous theory predicting large size effects and mass-independent electron-phonon scattering rates. In 1-D structures singularities in the phonon emission rate appear as a natural consequence of the 1-D density of states. However, for high energy the 1-D emission rate is found smaller than the corresponding 3-D rate. An additional consequence of the confinement is the quenching of the phonon absorption rate.

Recently, palladium diselenide (PdSe2) has emerged as a promising material with potential applications in electronic and optoelectronic devices due to its intriguing electronic and optical properties. The performance of the device is strongly dependent on the charge-carrier dynamics and the related hot phonon behavior. Here, we investigate the photoexcited-carrier dynamics and coherent acoustic phonon (CAP) oscillations in mechanically exfoliated PdSe2 flakes with a thickness ranging from 10.6 nm to 54 nm using time-resolved non-degenerate pump-probe transient reflection (TR) spectroscopy. The results imply that the CAP frequency is thickness-dependent. Polarization-resolved transient reflection (PRTR) measurements reveal the isotropic charge-carrier relaxation dynamics and the CAP frequency in the 10.6 nm region. In addition, the deformation potential (DP) mechanism dominates the generation of the CAP. Moreover, a sound velocity of 6.78 × 103 m s-1 is extracted from the variation of the oscillation period with the flake thickness and the delay time of the acoustic echo. These results provide insight into the ultrafast optical coherent acoustic phonon and optoelectronic properties of PdSe2 and may open new possibilities for PdSe2 applications in THz-frequency mechanical resonators.

… -Lo phonon scattering rates in 2D QWs with independent ,electron and phonon confinement. … We designate L and d for the thicknesses of electron and phonon QWs respectively, and zo …

Electron–phonon scatterings in solid-state systems are pivotal processes in determining many key physical quantities such as charge carrier mobilities and thermal conductivities. Here, we report direct probing of phonon mode specific electron–phonon scatterings in layered semiconducting transition metal dichalcogenides WSe2, MoSe2, WS2, and MoS2 through inelastic electron tunneling spectroscopy measurements, quantum transport simulations, and density functional calculation. We experimentally and theoretically characterize momentum-conserving single- and two-phonon electron–phonon scatterings involving up to as many as eight individual phonon modes in mono- and bilayer films, among which transverse, longitudinal acoustic and optical, and flexural optical phonons play significant roles in quantum charge flows. Moreover, the layer-number sensitive higher-order inelastic electron–phonon scatterings, which are confirmed to be generic in all four semiconducting layers, can be attributed to differing electronic structures, symmetry, and quantum interference effects during the scattering processes in the ultrathin semiconducting films. Electron–phonon scattering events in solid-state systems determine key physical quantities. Here, the authors probe momentum-conserving single- and two-phonon electron–phonon scattering events involving up to as many as eight individual phonon modes in 2D semiconductors.

In amorphous oxide semiconductors, rough interfaces influence transport in two main ways: changing the trap distributions and interface roughness scattering. Interface roughness scattering is expected to become important in high-mobility semiconductors in which charge transport takes place through a combination of trapping and band transport. Interface roughness scattering is quantitatively analyzed for amorphous oxide thin-film transistors (TFTs) within the framework of the Boltzmann transport equation. It is shown to be the main mobility limiting mechanism at room temperature under the conditions when carrier concentration is high and the interface is rough. The use of the precise extent of wavefunction overlap with the interface is important and the use of a finite potential barrier height at the insulator–semiconductor interface leads to more accurate calculations. The specific semiconductors considered are zinc tin oxide and indium gallium zinc oxide. It is shown that the consideration of interface roughness scattering can become important in evaluating transport in high-mobility TFTs.

… Thus, it is fair to say that the transport in γ-CuI thin films still … on the transport properties of polycrystalline γ-CuI thin films … on the transport mechanisms of CuI thin films by studying over …

… layer deposition. A dielectric surface morphology dominated interface scattering carrier transport … the effect of the dielectric polarization and the interface states on the carrier mobility is …

… scattering at surfaces, interfaces, and grain boundaries is investigated using polycrystalline and single-crystal Cu thin films … In fact, recent electron transport results from our laboratory …