arXiv subjects

Mark Lundstrom

Publications and source records attributed to Mark Lundstrom.

At least 19 recordsLinked to original sources

arXiv2022

A Nanometer-Thick Oxide Semiconductor Transistor with Ultra-High Drain Current

High drive current is a critical performance parameter in semiconductor devices for high-speed, low-power logic applications or high-efficiency, high-power, high-speed radio frequency (RF) analog applications. In this work, we demonstrate an In2O3 transistor grown by atomic layer deposition (ALD) at back-end-of-line (BEOL) compatible temperatures with a record high drain current exceeding 10 A/mm, the performance of which is 2-3 times better than all known transistors with semiconductor channels. A record high transconductance of 4 S/mm is also achieved among all transistors with a planar structure. It is found that a high carrier density and high electron velocity both contribute to this remarkably high on-state performance in ALD In2O3 transistors, which is made possible by the high-quality oxide/oxide interface, the metal-like charge-neutrality-level (CNL) alignment, and the high band velocities induced by the low density-of-state (DOS). Experimental Hall, I-V and split C-V measurements at room temperature confirm a high carrier density up to 6-7*10^13 /cm2 and a high velocity of about 10^7 cm/s. Ultra-thin oxide semiconductors, with a CNL located deep inside the conduction band, represent a promising new direction for the search of alternative channel materials for high-performance semiconductor devices.

cond-mat.mes-hall↗

arXiv2022

A Gate-All-Around Single-Channel In2O3 Nanoribbon FET with Near 20 mA/{\mu}m Drain Current

In this work, we demonstrate atomic-layer-deposited (ALD) single-channel indium oxide (In2O3) gate-all-around (GAA) nanoribbon FETs in a back-end-of-line (BEOL) compatible process. A maximum on-state current (ION) of 19.3 mA/{\mu}m (near 20 mA/{\mu}m) is achieved in an In2O3 GAA nanoribbon FET with a channel thickness (TIO) of 3.1 nm, channel length (Lch) of 40 nm, channel width (Wch) of 30 nm and dielectric HfO2 of 5 nm. The record high drain current obtained from an In2O3 FET is about one order of magnitude higher than any conventional single-channel semiconductor FETs. This extraordinary drain current and its related on-state performance demonstrate ALD In2O3 is a promising oxide semiconductor channel with great opportunities in BEOL compatible monolithic 3D integration.

physics.app-ph↗

arXiv2020

LanTraP: A code for calculating thermoelectric transport properties with the Landauer formalism

A code for calculating the semi-classical thermoelectric and electronic transport properties is described. It uses the Landauer transport theory, which is equivalent to the Boltzmann theory, by introducing a central quantity-the distribution of modes. Its usage enables the so-called band-counting algorithm that can speed up the calculation and offers the potential to rapidly screen DFT band structures. Good agreements are found when comparing the results obtained using band-counting and established Fourier-based interpolation methods.

cond-mat.mtrl-sci↗

arXiv2019

The use of strain and grain boundaries to tailor phonon transport properties: A first principles study of 2H-phase $CuAlO_{2}$ (Part II)

Transparent oxide materials, such as $CuAlO_{2}$, a p-type transparent conducting oxide (TCO), have recently been studied for high temperature thermoelectric power generators and coolers for waste heat. TCO materials are generally low cost and non-toxic. The potential to engineer them through strain and nano-structuring are two promising avenues toward continuously tuning the electronic and thermal properties to achieve high zT values and low cost/kW-hr devices. In this work, the strain-dependent lattice thermal conductivity of 2H $CuAlO_{2}$ is computed by solving the phonon Boltzmann transport equation with interatomic force constants extracted from first-principles calculations. While the average bulk thermal conductivity is around 32 W/(K-m) at room temperature, it drops to between 5-15 W/(K-m) for typical experimental grain sizes from 3nm to 30nm at room temperature. We find that strain can offer both an increase as well as a decrease in the thermal conductivity as expected, however the overall inclusion of small grain sizes dictates the potential for low thermal conductivity in this material.

cond-mat.mtrl-sci↗

arXiv2019

Notes on Fermi-Dirac Integrals

Fermi-Dirac integrals appear frequently in semiconductor problems, so a basic understanding of their properties is essential. The purpose of these notes is to collect in one place, some basic information about Fermi-Dirac integrals and their properties. We also present Matlab scripts that calculate Fermi-Dirac integrals (the "script F" defined by Dingle (1957)) in three different ways. The codes are available in Appendix and at the following website: "Notes on Fermi-Dirac Integrals (4th Edition)" by Raseong Kim, Xufeng Wang, and Mark Lundstrom at http://nanohub.org/resources/5475 In the 4th edition, we also provide a new table-based Matlab script (download available at https://github.com/wang159/FDIntegral_Table) that is less likely to give large errors in a wide range of input while still much faster than the rigorous numerical integration.

cond-mat.mes-hall↗

arXiv2019

Limitations of zT as a Figure of Merit for Nanostructured Thermoelectric Materials

A numerical study of thermoelectric nanocomposites is presented. Thermoelectric properties as a function of average grain size or nanoparticle density are examined by simulating the measurements as they would be done experimentally. In accordance with previous theory and experimental results, we find that the Seebeck coefficient, power factor and figure of merit, zT, can be increased by nanostructuring when energy barriers exist around the grain boundaries or embedded nanoparticles. When we simulate the performance of a thermoelectric cooler with the same material, however, we find that the maximum temperature difference is much less than expected from the given zT. The same nanocomposite without electrically active grain boundaries has a lower measured zT but a higher maximum cooling temperature. The physical reason for these results is explained. The results illustrate the limitations of zT as a figure of merit for nanocomposites with electrically active grain boundaries and suggest that the ability to enhance the electrical performance of thermoelectric materials by nanostructuring is limited.

cond-mat.mtrl-sci↗

arXiv2018

Universal Behavior of the Thermoelectric Figure of Merit, zT, vs. Quality Factor

To increase the performance of thermoelectric materials, the electronic parameters in the figure of merit must be improved. In this paper, we use full, numerical band structures and solve the Boltzmann equation in the relaxation time approximation using energy-dependent scattering times informed by first principles simulations. By varying the strength of the electron-phonon coupling or the lattice thermal conductivity, we compute the thermoelectric figure of merit, zT, vs. a generalized thermoelectric quality factor. More than a dozen different complex electronic structures are examined. Surprisingly, we find that at a given quality factor, none provides a better figure of merit than that of a material with a simple, parabolic band and acoustic deformation potential scattering. A qualitative argument for this unexpected finding is presented. This apparent universal behavior suggests that even for complex electronic band structures, the thermoelectric figure of merit depends solely on the ratio of electrical to thermal conductivity; the Seebeck coefficient and Lorenz number need not be considered. This observation should simplify the search for promising new materials, but if exceptions to this behavior can be identified, new paths for increasing thermoelectric material performance will open up.

cond-mat.mtrl-sci↗

arXiv2018

The use of strain to tailor electronic thermoelectric transport properties: A first principles study of 2H-phase CuAlO2

Using first principles calculations, the use of strain to adjust electronic transport and the resultant thermoelectric (TE) properties is discussed using 2H phase CuAlO2 as a test case. Transparent oxide materials, such as CuAlO2, a p-type transparent conducting oxide (TCO), have recently been studied for high temperature thermoelectric power generators and coolers for waste heat. Given TCO materials with relative ease of fabrication, low cost of materials, and non-toxicity, the ability to tailor them to specific temperature ranges, power needs, and size requirements, through the use of strain opens an interesting avenue. We find that strain can have a significant effect on these properties, in some cases detrimental and in others beneficial, including the potential for n-type power factors larger than the highest p-type case. The physical reasons for this behavior are explained in the terms of the thermoelectric transport distribution and the Landauer distribution of modes.

cond-mat.mtrl-sci↗

arXiv2017

On the Calculation of Lorenz Numbers for Complex Thermoelectric Materials

A first-principles informed approach to the calculation of Lorenz numbers for complex thermoelectric materials is presented and discussed. Example calculations illustrate the importance of using accurate band structures and energy-dependent scattering times. Results obtained by assuming that the scattering rate follows the density-of-states show that in the non-degenerate limit, Lorenz numbers below the commonly assumed lower limit of 2(kB/q)^2 can occur. The physical cause of low Lorenz numbers is explained by the shape of the transport distribution. The numerical and physical issues that need to be addressed in order to produce accurate calculations of the Lorenz number are identified. The results of this study provide a general method that should contribute to the interpretation of measurements of total thermal conductivity and to the search for materials with low Lorenz numbers, which may provide improved thermoelectric figures of merit, zT.

cond-mat.mtrl-sci↗

arXiv2017

Thermoelectric Band Engineering: The Role of Carrier Scattering

Complex electronic band structures, with multiple valleys or bands at the same or similar energies can be beneficial for thermoelectric performance, but the advantages can be offset by inter-valley and inter-band scattering. In this paper, we demonstrate how first-principles band structures coupled with recently developed techniques for rigorous simulation of electron-phonon scattering provide the capabilities to realistically assess the benefits and trade-offs associated with these materials. We illustrate the approach using n-type silicon as a model material and show that intervalley scattering is strong. This example shows that the convergence of valleys and bands can improve thermoelectric performance, but the magnitude of the improvement depends sensitively on the relative strengths of intra- and inter-valley electron scattering. Because anisotropy of the band structure also plays an important role, a measure of the benefit of band anisotropy in the presence of strong intervalley scattering is presented.

cond-mat.mtrl-sci↗

arXiv2016

Role of photon recycling in perovskite solar cells

Nearly perfect photon recycling helped GaAs cells achieve the highest efficiency ever reported for a solar cell. Recent reports of photon recycling in perovskite solar cells suggest that, once optimized, it may as well achieve GaAs-like performance. In this paper, we show that GaAs and perovskite cells recycle photons in different ways. First, although bare-perovskite has been shown to have lifetimes (~1us) in the radiative limit, non-radiative recombination at the transport layers restricts the solar cell operation far below the "photon-recycling" regime. GaAs cells have no such limitation. Second, even if the transport layers were optically and electrically perfect, the poor mobility of the perovskite layer would still restrict the optimum thickness ~1um. Thus, a very high quality mirror (reflectivity >96%) is required to utilize photon-recycling. The mirror reflectivity restriction was far more relaxed for the thicker (~2-3um) GaAs cells. Therefore, a nontrivial co-optimization of device geometry, mirror reflectivity, and material choice is necessary for achieving highest theoretical efficiency anticipated for perovskite cells.

cond-mat.mes-hall↗

arXiv2016

Thermal Transport at the Nanoscale - A Fourier's Law vs. Phonon Boltzmann Equation Study

Steady-state thermal transport in nanostructures with dimensions comparable to the phonon mean-free-path is examined. Both the case of contacts at different temperatures with no internal heat generation and contacts at the same temperature with internal heat generation are considered. Fourier's Law results are compared to finite volume method solutions of the phonon Boltzmann equation in the gray approximation. When the boundary conditions are properly specified, results obtained using Fourier's Law without modifying the bulk thermal conductivity are in essentially exact quantitative agreement with the phonon Boltzmann equation in the ballistic and diffusive limits. The errors between these two limits are examined in this paper. For the four cases examined, the error in the apparent thermal conductivity as deduced from a correct application of Fourier's Law is less than 6%. We also find that the Fourier's Law results presented here are nearly identical to those obtained from a widely-used ballistic-diffusive approach, but analytically much simpler. Although limited to steady-state conditions with spatial variations in one dimension and to a gray model of phonon transport, the results show that Fourier's Law can be used for linear transport from the diffusive to the ballistic limit. The results also contribute to an understanding of how heat transport at the nanoscale can be understood in terms of the conceptual framework that has been established for electron transport at the nanoscale.

cond-mat.mes-hall↗

arXiv2016

Gate-Tunable and Thickness-dependent Electronic and Thermoelectric Transport in few-layer MoS2

Over the past few years, there has been a growing interest in layered transition metal dichalcogenides (TMD) such as molybdenum disulfide (MoS2). Most studies so far have focused on the electronic and optoelectronic properties of single-layer MoS2, whose band structure features a direct bandgap, in sharp contrast to the indirect bandgap of thicker MoS2. In this paper, we present a systematic study of the thickness-dependent electrical and thermoelectric properties of few-layer MoS2. We observe that the electrical conductivity () increases as we reduce the thickness of MoS2 and peaks at about two layers, with six-time larger conductivity than our thickest sample (23-layer MoS2). Using a back-gate voltage, we modulate the Fermi energy () of the sample where an increase in the Seebeck coefficient () is observed with decreasing gate voltage () towards the subthreshold (OFF state) of the device, reaching as large as in a four-layer MoS2. While previous reports have focused on a single-layer MoS2 and measured Seebeck coefficient in the OFF state, which has vanishing electrical conductivity and thermoelectric power factor (), we show that MoS2-based devices in their ON state can have as large as in the two-layer sample. The increases with decreasing thickness then drops abruptly from double-layer to single-layer MoS2, a feature we suggest as due to a change in the energy dependence of the electron mean-free-path according to our theoretical calculation. Moreover, we show that care must be taken in thermoelectric measurements in the OFF state to avoid obtaining erroneously large Seebeck coefficients when the channel resistance is very high. Our study paves the way towards a more comprehensive examination of the thermoelectric performance of two-dimensional (2D) semiconductors.

cond-mat.mes-hall↗

arXiv2016

Some Useful Relations for Analyzing Nanoscale MOSFETs Operating in the Linear Region

Several equations used to model and characterize the linear region IV characteristics of nanoscale field-effect transistors are derived. The meaning of carrier mobility at the nanoscale is discussed by defining two related quantities, the apparent mobility and the ballistic mobility. The validity of Matthiessen's Rule for relating the apparent ability to the ballistic and diffusive mobilities is examined. Other questions that arise in the analysis and characterization of nanoscale field-effect transistors are also discussed. These notes are intended to pull together in one place some key equations needed to analyze the linear region performance of nanoscale MOSFETs and to point out some errors in previous publications.

cond-mat.mes-hall↗

arXiv2016

Modeling ballistic effects in frequency-dependent transient thermal transport using diffusion equations

Understanding ballistic phonon transport effects in transient thermoreflectance experiments and explaining the observed deviations from classical theory remains a challenge. Diffusion equations are simple and computationally efficient but are widely believed to break down when the characteristic length scale is similar or less than the phonon mean-free-path. Building on our prior work, we demonstrate how well-known diffusion equations, namely the hyperbolic heat equation and the Cattaneo equation, can be used to model ballistic phonon effects in frequency-dependent periodic steady-state thermal transport. Our analytical solutions are found to compare excellently to rigorous numerical results of the phonon Boltzmann transport equation. The correct physical boundary conditions can be different from those traditionally used and are paramount for accurately capturing ballistic effects. To illustrate the technique, we consider a simple model problem using two different, commonly-used heating conditions. We demonstrate how this framework can easily handle detailed material properties, by considering the case of bulk silicon using a full phonon dispersion and mean-free-path distribution. This physically transparent approach provides clear insights into the nonequilibrium physics of quasi-ballistic phonon transport and its impact on thermal transport properties.

cond-mat.mes-hall↗

arXiv2015

A Simple Boltzmann Transport Equation for Ballistic to Diffusive Transient Heat Transport

Developing simplified, but accurate, theoretical approaches to treat heat transport on all length and time scales is needed to further enable scientific insight and technology innovation. Using a simplified form of the Boltzmann transport equation (BTE), originally developed for electron transport, we demonstrate how ballistic phonon effects and finite-velocity propagation are easily and naturally captured. We show how this approach compares well to the phonon BTE, and readily handles a full phonon dispersion and energy-dependent mean-free-path. This study of transient heat transport shows i) how fundamental temperature jumps at the contacts depend simply on the ballistic thermal resistance, ii) that phonon transport at early times approach the ballistic limit in samples of any length, and iii) perceived reductions in heat conduction, when ballistic effects are present, originate from reductions in temperature gradient. Importantly, this framework can be recast exactly as the Cattaneo and hyperbolic heat equations, and we discuss how the key to capturing ballistic heat effects is to use the correct physical boundary conditions.

cond-mat.mes-hall↗

arXiv2015

Steady-State Heat Transport: Ballistic-to-Diffusive with Fourier's Law

It is generally understood that Fourier's law does not describe ballistic phonon transport, which is important when the length of a material is similar to the phonon mean-free-path. Using an approach adapted from electron transport, we demonstrate that Fourier's law and the heat equation do capture ballistic effects, including temperature jumps at ideal contacts, and are thus applicable on all length scales. Local thermal equilibrium is not assumed, because allowing the phonon distribution to be out-of-equilibrium is important for ballistic and quasi-ballistic transport. The key to including the non-equilibrium nature of the phonon population is to apply the proper boundary conditions to the heat equation. Simple analytical solutions are derived, showing that i) the magnitude of the temperature jumps is simply related to the material properties and ii) the observation of reduced apparent thermal conductivity physically stems from a reduction in the temperature gradient and not from a reduction in actual thermal conductivity. We demonstrate how our approach, equivalent to Fourier's law, easily reproduces results of the Boltzmann transport equation, in all transport regimes, even when using a full phonon dispersion and mean-free-path distribution.

cond-mat.mes-hall↗

arXiv2013

Engineering Nanowire n-MOSFETs at Lg < 8 nm

As metal-oxide-semiconductor field-effect transistors (MOSFET) channel lengths (Lg) are scaled to lengths shorter than Lg<8 nm source-drain tunneling starts to become a major performance limiting factor. In this scenario a heavier transport mass can be used to limit source-drain (S-D) tunneling. Taking InAs and Si as examples, it is shown that different heavier transport masses can be engineered using strain and crystal orientation engineering. Full-band extended device atomistic quantum transport simulations are performed for nanowire MOSFETs at Lg<8 nm in both ballistic and incoherent scattering regimes. In conclusion, a heavier transport mass can indeed be advantageous in improving ON state currents in ultra scaled nanowire MOSFETs.

cond-mat.mes-hall↗