Phonon-limited Electron Mobility Research Articles

Semi-classical Monte Carlo study of the impact of tensile strain on the performance limits of monolayer MoS2 n-channel MOSFETs

The effects of tensile strain and contact transmissivity on the performance limits of monolayer molybdenum disulfide (MoS2) nanoscale n-channel MOSFETs are studied using a semi-classical Monte Carlo method. Density functional theory calculations were performed to parametrize the electronic band structure of MoS2 subject to tensile and shear strain. Tensile strain decreases the bandgap, increases the inter-valley band-edge energy separation between the light-mass K-valleys and heavier-mass Q-valleys, and decreases the K-valley effective mass in a way that depends on the direction and the amount of the applied strain. Biaxial tensile strain and uniaxial tensile strain along the x- or y-directions are found to have the largest effect. In bulk materials, low-field phonon-limited electron mobility is enhanced, peak and saturation drift velocities are increased, and high-field negative differential resistance becomes more pronounced. Both 200 and 15 nm gate length MoS2 MOSFETs with end-contacts with ideal (unity) and more realistic (significantly sub-unity) contact interface transmissivity were simulated. These MoS2 devices exhibited substantial sensitivity to strain with ideal contact transmissivity, and more so for the 15 nm quasi-ballistic device scale than 200 nm long-channel devices. However, the results showed much less strain sensitivity for devices with more realistic contact transmissivities, which may be good or bad depending on whether strain-insensitive or strain-sensitive performance is desired for a particular application and may be possible to modify with improved contact geometries.

(Invited) The Future of Nanoelectronics Devices from a Theoretical Point of View: The Search for New Channel Materials

Scaling electronic devices to the nanometer scale requires, among other constrains, a reduction of the thickness of the channel. This results in quantum confinement of the carriers which, in turn, causes an unavoidable degradation of the charge-transport properties. The advent of graphene seems to have opened a new avenue to circumvent the problem: The extremely high carrier mobility in such an atomically thin layer has caused an explosion of interest on other atomically-thin (“two-dimensional”, 2D) materials that, hopefully, may exhibit excellent transport-properties even when scaled to sub-nm thickness and replace Si in ULSI devices.Since many of the 2D materials that have been considered are poorly known (even their existence is often questionable), theoretical studies of their electronic and charge-transport properties have become necessary to select, among the huge number of possible candidate materials, those that may exhibit the desired properties.In this presentation, we will summarize theoretical work performed in our group regarding the search for these ‘new channel materials’.We will first discuss how the outstanding properties of graphene are hard to replicate, since they originate from its Dirac-like dispersion and, even in other non-σh-symmetric Dirac-like materials, such as silicene or germanene, the interaction of electrons with acoustic flexural vibrations (the so-called “ZA phonons) may destroy such outstanding properties1, as shown in Fig. 1 in the case of silicene.Next, taking phosphorene as an example, we will discuss how the ab initio methods (density functional theory, DFT) used to study these materials may provide a useful guideline but are still affected by severe uncertainties.2 In fact, theoretical predictions (namely, the carrier mobility) may depend strongly on different choices of pseudopotentials and exchange-correlation functionals employed when using DFT. This is an unfortunate situation dictated by the fact that transport calculations are sensitive to small changes of the band structures (of the order of the thermal energy, for example, when dealing with the energy of satellite valleys and intervalley scattering), a level of accuracy that remains beyond what DFT can offer. Table I shows the situation for transition metal dichalcogenides (TMD) monolayers.Next, considering now TMD monolayers, we will consider how their charge-transport properties are affected by the ‘dielectric environment’ (insulating substrate, gate insulator, metallic gates).3 Indeed, electronic transport in two-dimensional (2D) materials is often studied theoretically assuming free-standing (mono)layers. However, in practical applications the monolayers are supported by an insulator and, often, top-gated. In this case, insulators with a high dielectric constant (‘high-κ insulators’) screen the interaction between charge carriers and phonons, resulting in a higher carrier mobility. However, this beneficial effect is negated by the additional scattering with interface modes resulting from the coupling of the insulator optical phonons and the 2D electron gas of the monolayer (2D plasmons), the so-called ‘remote phonon scattering’ (Table II). We shall finally present results obtained from Monte Carlo simulations of field-effect transistors employing various transition metal dichalcogenides (TMDs) as channel materials and discuss the role played by dielectric screening and remote-phonon scattering for a variety of insulators and TMDs.A look at Table II shows that WeS2 appears is the most promising material, especially in complementary MOS applications. However, we should keep in mind that the phonon-limited electron mobility in Si slabs of a dielectric thickness comparable to TMD monolayers (approximately 1.2 nm) is about 500 cm2V−1s−1, being depressed by scattering with surface roughness. Thus, in a fair comparison among Si and many TMD monolayers, the advantage afforded by the latter 2D materials appears to be minimal. We shall conclude by discussing the possible broader cause of this conclusion4. Massimo V. Fischetti and William G. Vandenberghe, Phys. Rev. B 93, 155413 (2016).G. Gaddemane et al., Phys. Rev. B 98, 115416 (2018).S. Gopalan et al., Phys. Rev. Appl. 18, 054062 (2022).L. Cheng, C. Zhang, and Y. Liu, Phys. Rev. Lett. 125, 177701 (2020). Figure 1

Effects of asymmetric MgZnO barriers on polar optical phonon-limited electron mobility in wurtzite ZnO thin films

MgZnO barriers are commonly applied to passivate wurtzite ZnO films to enhance electron mobility, while the Mg mole fraction x is usually controlled below 0.4 to avoid phase separation. Few theoretical analyses have focused on electron mobility at large x since the phase separation leads to a complex scattering mechanism. This work investigates the effects of asymmetric MgZnO barriers on electron mobility, which is one source of complexity. Four asymmetric quantum wells simultaneously contribute to the electron mobility in proportions when the wurtzite and rock salt coexist in the mixed-phase MgZnO barriers with large Mg mole fractions. Besides, built-in electric fields also contribute to the asymmetry by tilting the bands. The polar optical phonon-limited electron mobility in asymmetric MgxZn1−xO/ZnO/Mg0.45Zn0.55O quantum wells is simulated between 176 and 333 cm2/V s as x ranges from 0.1 to 1. Our calculations show that confined optical phonons play a leading role in the quantum well with wurtzite barriers. Interface optical phonons are primary in the wells with rock salt barriers since most electrons are pushed close to the interface by the strong built-in electric field. The results indicate that wurtzite barriers are more favorable to achieving stable high mobility above 238 cm2/V s as the Mg mole fraction ranges from 0.14 to 0.33, which is commonly applied in practice.

Electron and Hole Mobility of SnO2 from Full-Band Electron–Phonon and Ionized Impurity Scattering Computations

Mobility is a key parameter for SnO2, which is extensively studied as a practical transparent oxide n-type semiconductor. In experiments, the mobility of electrons in bulk SnO2 single crystals varies from 70 to 260 cm2V−1s−1 at room temperature. Here, we calculate the mobility as limited by electron–phonon and ionized impurity scattering by coupling the Boltzmann transport equation with density functional theory electronic structures. The linearized Boltzmann transport equation is solved numerically beyond the commonly employed constant relaxation-time approximation by taking into account all energy and momentum dependencies of the scattering rates. Acoustic deformation potential and polar optical phonons are considered for electron–phonon scattering, where polar optical phonon scattering is found to be the main factor which determines the mobility of both electrons and holes at room temperature. The calculated phonon-limited electron mobility is found to be 265 cm2V−1s−1, whereas that of holes is found to be 7.6 cm2V−1s−1. We present the mobility as a function of the carrier concentration, which shows the upper mobility limit. The large difference between the mobilities of n-type and p-type SnO2 is a result of the different effective masses between electrons and holes.

Increasing the mobility and power-electronics figure of merit of AlGaN with atomically thin AlN/GaN digital-alloy superlattices

Alloy scattering in random AlGaN alloys drastically reduces the electron mobility and, therefore, the power-electronics figure of merit. As a result, Al compositions greater than 75% are required to obtain even a twofold increase in the Baliga figure of merit compared to GaN. However, beyond approximately 80% Al composition, donors in AlGaN undergo the DX transition, which makes impurity doping increasingly more difficult. Moreover, the contact resistance increases exponentially with the increase in Al content, and integration with dielectrics becomes difficult due to the upward shift of the conduction band. Atomically thin superlattices of AlN and GaN, also known as digital alloys, are known to grow experimentally under appropriate growth conditions. These chemically ordered nanostructures could offer significantly enhanced figure of merit compared to their random alloy counterparts due to the absence of alloy scattering, as well as better integration with contact metals and dielectrics. In this work, we investigate the electronic structure and phonon-limited electron mobility of atomically thin AlN/GaN digital-alloy superlattices using first-principles calculations based on density-functional and many-body perturbation theory. The bandgap of the atomically thin superlattices reaches 4.8 eV, and the in-plane (out-of-plane) mobility is 369 (452) cm2 V−1 s−1. Using the modified Baliga figure of merit that accounts for the dopant ionization energy, we demonstrate that atomically thin AlN/GaN superlattices with a monolayer sublattice periodicity have the highest modified Baliga figure of merit among several technologically relevant ultra-wide bandgap materials, including random AlGaN, β-Ga2O3, cBN, and diamond.

Optical phonon limited electron mobility in ZnO nanowires wrapped by MgZnO shells

MgxZn1−xO shells are commonly used as a passivation barrier for improving electron mobility in ZnO nanowires by preventing electrons from charged surfaces. However, a high Mg mole fraction x instead makes lower electron mobility, which is usually attributed to the appearance of mixed-phase MgxZn1−xO as x increases. This work aims to find the optimal x for optical phonon limited electron mobility by considering the phase transformation in the MgZnO shell from wurtzite to rock salt, leading to a mixed-phase range of x. Our calculations show that the electron mobility μT can be effectively enhanced by keeping x below 0.057 when confined (CO1) optical phonons are only permitted for small wave vectors, and there is no interface (IF) optical phonon. Once x gets over 0.057, the propagating optical phonons are transformed into IF ones while CO1 phonons become permitted for all wave vectors resulting in a largely strengthened scattering effect and thus a drastic drop in the total electron mobility μT from 1215 to 310 cm2/V s. From then, μT begins to fall slowly as x increases even when the rock salt component in the shell appears to take the place of the wurtzite part, while the scattering from CO1 optical phonons remains primary. Furthermore, the enlarging core radius can weaken the electron–CO1 phonon interaction to enhance mobility.

The carrier mobility and sizable bandgap influorinated armchair boron nitride nanoribbons

The electronic transport properties of two-dimensional materials are strongly influenced by the charge carrier mobility and the energy bandgap. Furthermore, the carrier-phonon interaction governs the electrical response of any electrical device at a specific temperature. In light of this, the electron mobility and energy bandgap of fluorine (F) doped armchair Boron Nitride nanoribbons (a-BNNRs) are computed theoretically and analysed further. The acoustical deformation potential (ADP) scattering mechanism is taken into account to determine the mobility of the system. The calculations are carried out in presence of an applied electric field as well as different doping concentrations across a specified temperature range (200–300 K). The computed value of electron mobility for F-BNNR is of the order 104 cm2 V−1 s−1. Such higher magnitude of electron mobility suggests the semiconducting nature of BNNRs. Moreover, the variation of electron mobility as a function of temperature and doping concentration demonstrates a significant reduction in the acoustical phonon-limited electron mobility of fluorine-doped boron nitride nanoribbons. To estimate the energy bandgap, a set of equations are determined from the Fermi velocity expression using the nearly free electron (NFE) model. The computed energy bandgap is found to diminish with the increasing size of the nanoribbon. This behaviour of F-doped a-BNNRs envisages its applications in Visible-IR optical sensors.

Impact of Band Structure on Phonon-Limited Electron Mobility Behavior of Germanium-on-Insulator Layer with (001) and (111) Surfaces

Impact of Band Structure on Phonon-Limited Electron Mobility Behavior of Germanium-on-Insulator Layer with (001) and (111) Surfaces

Phonon-limited electron mobility in Si, GaAs, and GaP with exact treatment of dynamical quadrupoles

We describe a new approach to compute the electron-phonon self-energy and carrier mobilities in semiconductors. Our implementation does not require a localized basis set to interpolate the electron-phonon matrix elements, with the advantage that computations can be easily automated. Scattering potentials are interpolated on dense $\mathbf{q}$ meshes using Fourier transforms and ab initio models to describe the long-range potentials generated by dipoles and quadrupoles. To reduce significantly the computational cost, we take advantage of crystal symmetries and employ the linear tetrahedron method and double-grid integration schemes, in conjunction with filtering techniques in the Brillouin zone. We report results for the electron mobility in Si, GaAs, and GaP obtained with this new methodology.

Electronic transport properties of hydrogenated and fluorinated graphene: a computational study

Hydrogenation and fluorination have been presented as two possible methods to open a bandgap in graphene, required for field-effect transistor applications. In this work, we present a detailed study of the phonon-limited mobility of electrons and holes in hydrogenated graphene (graphane) and fluorinated graphene (graphene fluoride). We pay special attention to the out-of-plane acoustic (ZA) phonons, responsible for the highest scattering rates in graphane and graphene fluoride. Considering the most adverse cut-off for long-wavelength ZA phonons, we have obtained electron (hole) mobilities of 28 (41) cm2 V−1 s−1 for graphane and 96 (30) cm2 V−1 s−1 for graphene fluoride. Nonetheless, for a more favorable cut-off wavelength of ∼2.6 nm, significantly higher electron (hole) mobilities of 233 (389) cm2 V−1 s−1 for graphane and 460 (105) cm2 V−1 s−1 for graphene fluoride are achieved. Moreover, while complete suppression of ZA phonons can increase the electron (hole) mobility in graphane up to 278 (391) cm2 V−1 s−1, it does not affect the carrier mobilities in graphene fluoride. Velocity–field characteristics reveal that the electron velocity in graphane saturates at an electric field of ∼4 × 105 V cm−1. Comparing the mobilities with other two-dimensional (2D) semiconductors, we find that hydrogenation and fluorination are two promising avenues to realize a 2D semiconductor while providing good carrier mobilities.

First-principles calculation of phonon-limited mobility in planar [formula omitted] graphene

We present the phonon-limited electron mobility in planar T graphene and find that the mobility ∝T−5.53 at low temperature T. With the increase of temperature, the power exponent 5.53 decreases towards 1. Excitingly, the room-temperature mobility of planar T graphene is 2.78×106 cm2/Vs which is about 20.59 times as large as that of n-type graphene at the same carrier density. Different from graphene with longitudinal acoustic phonon dominating the mobility, an in-plane optical phonon mode contributes the most to the mobility of planar T graphene.

Phonon limited mobility in 3D Dirac semimetal Cd3As2

We report the numerical calculations of phonon limited electron mobility, μ in Cd3As2 three dimensional Dirac semimetal using Boltzmann transport theory over a temperature range 20<T<300K. By employing the Ritz iteration technique, we have directly solved the 3D linearized Boltzmann transport equation to obtain the first order perturbation distribution function Φ−1(Ek) as a function of electron energy Ek and hence the mobility, μ. we have considered electrons scattering by acoustic phonons via deformation potential scattering and polar optical phonons. The μ due to the latter is dominating the former for T>80K, for electron concentration ne = 1x1018cm−3. Thiscrossover shifts to lower T, with decreasing ne. The calculations are qualitatively agreeing with the experimental results.

Route to High Hole Mobility in GaN via Reversal of Crystal-Field Splitting.

A fundamental obstacle toward the realization of GaN p-channel transistors is its low hole mobility. Here we investigate the intrinsic phonon-limited mobility of electrons and holes in wurtzite GaN using the abinitio Boltzmann transport formalism, including all electron-phonon scattering processes and many-body quasiparticle band structures. We predict that the hole mobility can be increased by reversing the sign of the crystal-field splitting in such a way as to lift the split-off hole states above the light and heavy holes. We find that a 2% biaxial tensile strain can increase the hole mobility by 230%, up to a theoretical Hall mobility of 120 cm^{2}/V s at room temperature and 620 cm^{2}/V s at 100K.

Phonon Limited Electron Mobility in Germanium FinFETs: Fin Direction Dependence**Supported by the National Natural Science Foundation of China under Grant Nos 61534004, 61604112 and 61622405.

We investigate the phonon limited electron mobility in germanium (Ge) fin field-effect transistors (FinFETs) with fin rotating within (001), (110), and (111)-oriented wafers. The coupled Schrödinger–Poisson equations are solved self-consistently to calculate the electronic structures for the two-dimensional electron gas, and Fermi’s golden rule is used to calculate the phonon scattering rate. It is concluded that the intra-valley acoustic phonon scattering is the dominant mechanism limiting the electron mobility in Ge FinFETs. The phonon limited electron motilities are influenced by wafer orientation, channel direction, fin thickness Wfin, and inversion charge density Ninv. With the fixed Wfin, fin directions of , and within (001), (110), and (111)-oriented wafers provide the maximum values of electron mobility. The optimized Wfin for mobility is also dependent on wafer orientation and channel direction. As Ninv increases, phonon limited mobility degrades, which is attributed to electron repopulation from a higher mobility valley to a lower mobility valley as Ninv increases.

Electron mobility limited by optical phonons in wurtzite InGaN/GaN core-shell nanowires

Based on the force-balance and energy-balance equations, the optical phonon-limited electron mobility in InxGa1-xN/GaN core-shell nanowires (CSNWs) is discussed. It is found that the electrons tend to distribute in the core of the CSNWs due to the strong quantum confinement. Thus, the scattering from first kind of the quasi-confined optical (CO) phonons is more important than that from the interface (IF) and propagating (PR) optical phonons. Ternary mixed crystal and size effects on the electron mobility are also investigated. The results show that the PR phonons exist while the IF phonons disappear when the indium composition x &amp;lt; 0.047, and vice versa. Accordingly, the total electron mobility μ first increases and then decreases with indium composition x, and reaches a peak value of approximately 3700 cm2/(V·s) when x = 0.047. The results also show that the mobility μ increases as increasing the core radius of CSNWs due to the weakened interaction between the electrons and CO phonons. The total electron mobility limited by the optical phonons exhibits an obvious enhancement as decreasing temperature or increasing line electron density. Our theoretical results are expected to be helpful to develop electronic devices based on CSNWs.

Electronic structure and electron mobility in Si1– xGex nanowires

We investigate the electronic structure and the electron mobility in Si1– xGex nanowires for relevant orientations (⟨001⟩, ⟨110⟩, and ⟨111⟩) and diameters up to 8 nm based on atomistic models. The calculation of the electronic structure with random distribution of alloy atoms is compared to the virtual crystal approximation. The electronic properties such as the effective mass and the character of the lowest conduction subband are linked with the strong variations of the phonon-limited electron mobility with varying Ge concentrations. The effect of alloy disorder on the mobility is also discussed.

How high can the mobility of monolayer tungsten disulfide be?

Monolayer tungsten disulfide is a very promising two-dimensional material for future transistor technology. Monolayer tungsten disulfide, owing to the unique electronic properties of its atomically thin two-dimensional layered structure, can be made into a high-performance transistor device. In this paper, we focus on band-structure and carrier mobility calculations for monolayer tungsten disulfide. We use the tight-binding (TB) method and modified effective mass approximation (MEMA) to calculate the band-structure, density of states, velocity square, and other physical quantities of monolayer tungsten disulfide. Electron mobility using the Kubo–Greenwood formula is calculated based on the TB and MEMA band model, respectively. The phonon-limited electron mobility of monolayer can be reached to ∼700 cm2/Vs. Our results help to design the future nanoelectronic devices with monolayer WS2.

The Power Law of Phonon-Limited Electron Mobility in the 2-D Electron Gas of AlGaN/GaN Heterostructure

The reduction of electron mobility in AlGaN/GaN heterostructures follows the common power law, but with an unexpectedly high power coefficient. Following the experimental verification of the unusual power-coefficient value by a different measurement method, this brief presents an analysis that identifies the temperature dependence of the effective electron mass as the responsible physical mechanism for this effect. Based on this result, the measured values of electron mobility are used to calculate the effective mass of the electrons in AlGaN/GaN heterostructures over a wide temperature range, from 25 °C to 300 °C.

Ab initiosimulation of single- and few-layerMoS2transistors: Effect of electron-phonon scattering

In this paper, we present full-band atomistic quantum transport simulations of single- and few-layer ${\mathrm{MoS}}_{2}$ field-effect transistors (FETs) including electron-phonon scattering. The Hamiltonian and the electron-phonon coupling constants are determined from ab initio density-functional-theory calculations. It is observed that the phonon-limited electron mobility is enhanced with increasing layer thicknesses and decreases at high charge concentrations. The electrostatic control is found to be crucial even for a single-layer ${\mathrm{MoS}}_{2}$ device. With a single-gate configuration, the double-layer ${\mathrm{MoS}}_{2}$ FET shows the best intrinsic performance with an ON current, ${I}_{\text{ON}}=685\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{A}/\ensuremath{\mu}\mathrm{m}$, but with a double-gate contact the transistor with a triple-layer channel delivers the highest current with ${I}_{\text{ON}}=1850\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{A}/\ensuremath{\mu}\mathrm{m}$. The charge in the channel is almost independent of the number of ${\mathrm{MoS}}_{2}$ layers, but the injection velocity increases significantly with the channel thickness in the double-gate devices due to the reduced electron-phonon scattering rates in multilayer structures. We demonstrate further that the ballistic limit of transport is not suitable for the simulation of ${MX}_{2}$ FETs because of the artificial negative differential resistance it predicts.

Electron mobility and spin lifetime enhancement in strained ultra-thin silicon films

Spintronics attracts much attention because of the potential to build novel spin-based devices which are superior to nowadays charge-based microelectronic devices. Silicon, the main element of microelectronics, is promising for spin-driven applications. Understanding the details of the spin propagation in silicon structures is a key for building novel spin-based nanoelectronic devices. We investigate the surface roughness- and phonon-limited electron mobility and spin relaxation in ultra-thin silicon films. We show that the spin relaxation rate due to surface roughness and phonon scattering is efficiently suppressed by an order of magnitude by applying tensile stress. We also demonstrate an almost twofold mobility increase in ultra-thin (001) SOI films under tensile [110] stress, which is due to the usually neglected strain dependence of the scattering matrix elements.