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Triple heterojunction (THJ) TFETs have been proposed to resolve the low ON-current challenge of TFETs. However, the design space for THJ-TFETs is limited by fabrication challenges with respect to device dimensions and material interfaces. This work shows that the original THJ-TFET design with 12 nm body thickness has poor performance, because its sub-threshold swing is 50 mV/dec and the ON-current is only 6 $\mu A/\mu m$. To improve the performance, the doping profile of THJ-TFET is engineered to boost the resonant tunneling efficiency. The proposed THJ-TFET design shows a sub-threshold swing of 40 mV/dec over four orders of drain current and an ON-current of 325 uA/um with VGS = 0.3 V. Since THJ-TFETs have multiple quantum wells and material interfaces in the tunneling junction, quantum transport simulations in such devices are complicated. State-of-the-art mode-space quantum transport simulation, including the effect of thermalization and scattering, is employed in this work to optimize THJ-TFET design.

The triple heterojunction TFET has been originally proposed to resolve TFET's low ON-current challenge. The carrier transport in such devices is complicated due to the presence of quantum wells and strong scattering. Hence, the full band atomistic NEGF approach, including scattering, is required to model the carrier transport accurately. However, such simulations for devices with realistic dimensions are computationally unfeasible. To mitigate this issue, we have employed the empirical tight-binding mode space approximation to simulate triple heterojunction TFETs with the body thickness up to 12 nm. The triple heterojunction TFET design is optimized using the model to achieve a sub-60mV/dec transfer characteristic under realistic scattering conditions.

Quantum-Kit is a graphical desktop application for quantum circuit simulations. Its powerful, memory-efficient computational engine enables large-scale simulations on a desktop. The ability to design hybrid circuits, with both quantum and classical bits and controls, is employed to demonstrate Kitaev's approach to Shor's factorization algorithm. For the first time, Shor's factorization of a 24-bit integer is simulated with Quantum-Kit in a mere 26 minutes on a modest desktop with Intel Core i5 7400T, 2.4GHz and12GB RAM. While the largest number factorized so far has been a 20-bit integer, requiring 60 qubits and a supercomputer, the hybrid circuit functionality allows the same number to be factorized using Kitaev's trick with only 21 qubits, in 2.3 minutes, on a desktop. Furthermore, conventional Shor's algorithm for a 13-bitinteger with 39 qubits is shown to be 35x faster with Quantum-Kit., Comment: 8 pages, 6 figures

2D material based tunnel FETs are among the most promising candidates for low power electronics applications since they offer ultimate gate control and high current drives that are achievable through small tunneling distances during the device operation. The ideal device is characterized by a minimized tunneling distance. However, devices with the thinnest possible body do not necessarily provide the best performance. For example, reducing the channel thickness increases the depletion width in the source which can be a significant part of the total tunneling distance. Hence, it is important to determine the optimum channel thickness for each channel material individually. In this work, we study the optimum channel thickness for three channel materials: WSe$_{2}$, Black Phosphorus (BP), and InAs using full-band self-consistent quantum transport simulations. To identify the ideal channel thickness for each material at a specific doping density, a new analytic model is proposed and benchmarked against the numerical simulations.

In this work, vertical tunnel field-effect transistors (v-TFETs) based on vertically stacked heretojunctions from 2D transition metal dichalcogenide (TMD) materials are studied by atomistic quantum transport simulations. The switching mechanism of v-TFET is found to be different from previous predictions. As a consequence of this switching mechanism, the extension region, where the materials are not stacked over is found to be critical for turning off the v-TFET. This extension region makes the scaling of v-TFETs challenging. In addition, due to the presence of both positive and negative charges inside the channel, v-TFETs also exhibit negative capacitance. As a result, v-TFETs have good energy-delay products and are one of the promising candidates for low power applications., Comment: didn't reach to co-author agreement

Atomistic quantum transport simulation of realistically large devices is computationally very demanding. The widely used mode space (MS) approach can significantly reduce the numerical cost but good MS basis is usually very hard to obtain for atomistic full-band models. In this work, a robust and parallel algorithm is developed to optimize the MS basis for atomistic nanowires. This enables tight binding non-equilibrium Green's function (NEGF) simulation of nanowire MOSFET with realistic cross section of $\rm 10nm\times10nm$ using a small computer cluster. This approach is applied to compare the performance of InGaAs and Si nanowire nMOSFETs with various channel lengths and cross sections. Simulation results with full-band accuracy indicate that InGaAs nanowire nMOSFETs have no drive current advantage over their Si counterparts for cross sections up to about $\rm 10nm\times10nm$., Comment: 8 pages (double column), 13 figures, 1 table

Steep transistors are crucial in lowering power consumption of the integrated circuits. However, the difficulties in achieving steepness beyond the Boltzmann limit experimentally have hindered the fundamental challenges in application of these devices in integrated circuits. From a sensitivity perspective, an ideal switch should have a high sensitivity to the gate voltage and lower sensitivity to the device design parameters like oxide and body thicknesses. In this work, conventional tunnel-FET (TFET) and negative capacitance FET are shown to suffer from high sensitivity to device design parameters using full-band atomistic quantum transport simulations and analytical analysis. Although Dielectric Engineered (DE-) TFETs based on 2D materials show smaller sensitivity compared with the conventional TFETs, they have leakage issue. To mitigate this challenge, a novel DE-TFET design has been proposed and studied.

In this article, a novel two-path model is proposed to quantitatively explain sub-threshold characteristics of back-gated Schottky barrier FETs (SB-FETs) from 2D channel materials. The model integrates the 'conventional' model for SB-FETs with the phenomenon of contact gating - an effect that significantly affects the carrier injection from the source electrode in back-gated field effect transistors. The two-path model is validated by a careful comparison with experimental characteristics obtained from a large number of back-gated WSe2 devices with various channel thicknesses. Our findings are believed to be of critical importance for the quantitative analysis of many three-terminal devices with ultrathin body channels.

Low dimensional material systems provide a unique set of properties useful for solid-state devices. The building block of these devices is the PN junction. In this work, we present a dramatic difference in the electrostatics of PN junctions in lower dimensional systems, as against the well understood three dimensional systems. Reducing the dimensionality increases the depletion width significantly. We propose a novel method to derive analytic equations in 2D and 1D that considers the impact of neutral regions. The analytical results show an excellent match with both the experimental measurements and numerical simulations. The square root dependence of the depletion width on the ratio of dielectric constant and doping in 3D changes to a linear and exponential dependence for 2D and 1D respectively. This higher sensitivity of 1D PN junctions to its control parameters can be used towards new sensors., Comment: arXiv admin note: text overlap with arXiv:1611.08784

Tunneling hetero-junctions (THJs) usually induce confined states at the regions close to the tunnel junction which significantly affect their transport properties. Accurate numerical modeling of such effects requires combining the non-equilibrium coherent quantum transport through tunnel junction, as well as the quasi-equilibrium statistics arising from the strong scattering in the induced quantum wells. In this work, a novel atomistic model is proposed to include both effects: the strong scattering in the regions around THJ and the coherent tunneling. The new model matches reasonably well with experimental measurements of Nitride THJ and provides an efficient engineering tool for performance prediction and design of THJ based devices.

A high performance triple-heterojunction (3HJ) design has been previously proposed for tunneling FETs (TFETs). Compared with single heterojunction (HJ) TFETs, the 3HJ TFETs have both shorter tunneling distance and two transmission resonances that significantly improve the ON-state current ($I_{\rm{ON}}$). Coherent quantum transport simulation predicts, that $I_{\rm{ON}}=460\rm{\mu A/\mu m}$ can be achieved at gate length $Lg=15\rm{nm}$, supply voltage $V_{\rm{DD}}=0.3\rm{V}$, and OFF-state current $I_{\rm{OFF}}=1\rm{nA/\mu m}$. However, strong electron-phonon and electron-electron scattering in the heavily doped leads implies, that the 3HJ devices operate far from the ideal coherent limit. In this study, such scattering effects are assessed by a newly developed multiscale transport model, which combines the ballistic non-equilibrium Green's function method for the channel and the drift-diffusion scattering method for the leads. Simulation results show that the thermalizing scattering in the leads both degrades the 3HJ TFET's subthreshold swing through scattering induced leakage and reduces the turn-on current through the access resistance. Assuming bulk scattering rates and carrier mobilities, the $I_{\rm{ON}}$ is dropped from $460\rm{\mu A/\mu m}$ down to $254\rm{\mu A/\mu m}$, which is still much larger than the single HJ TFET case.

Low dimensional material systems provide a unique set of properties useful for solid-state devices. The building block of these devices is the PN junction. In this work, we present a dramatic difference in the electrostatics of PN junctions in lower dimensional systems, as against the well understood three dimensional systems. Reducing the dimensionality increases the fringing fields and depletion width significantly. We propose a novel method to derive analytic equations in 2D and 1D that considers the impact of neutral regions. The analytical results show an excellent match with both the experimental measurements and numerical simulations. The square root dependence of the depletion width on the ratio of dielectric constant and doping in 3D changes to a linear and exponential dependence for 2D and 1D respectively. This higher sensitivity of 1D PN junctions to its control parameters can be used towards new sensors., Comment: 4 pages, 6 figures

In this work, the transport of tunnel field-effect transistor (TFET) based on vertically stacked hereto-structures from 2D transition metal dichalcogenide (TMD) materials is investigated by atomistic quantum transport simulations. WTe2-MoS2 combination was chosen due to the formation of a broken gap hetero-junction which is desirable for TFETs. There are two assumptions behind the MoS2-WTe2 hetero-junction tight binding (TB) model: 1) lattice registry. 2) The $S-Te$ parameters being the average of the $S-S$ and $Te-Te$ parameters of bilayer MoS2 and WTe2. The computed TB bandstructure of the hetero-junction agrees well with the bandstructure obtained from density functional theory (DFT) in the energy range of interest for transport. NEGF (Non-Equilibrium Green$'$s Function) equations within the tight binding description is then utilized for device transfer characteristic calculation. Results show 1) energy filtering is the switching mechanism; 2) the length of the extension region is critical for device to turn off; 3) MoS2-WTe2 interlayer TFET can achieve a large on-current of $1000 \mu A/\mu m$ with $V_{DD} = 0.3V$, which suggests interlayer TFET can solve the low ON current problem of TFETs and can be a promising candidate for low power applications., Comment: 2016 ICPS proceeding

Thickness engineered tunneling field-effect transistors (TE-TFET) as a high performance ultra-scaled steep transistor is proposed. This device exploits a specific property of 2D materials: layer thickness dependent energy bandgap (Eg). Unlike the conventional hetero-junction TFETs, TE-TFET uses spatially varying layer thickness to form a hetero-junction. This offers advantages by avoiding the interface states and lattice mismatch problems. Furthermore, it boosts the ON-current to 1280$\mu A/\mu m$ for 15nm channel length. TE-TFET shows a channel length scalability down to 9nm with constant field scaling $E = V_{DD}/L_{ch}= 30V/nm$. Providing a higher ON current, phosphorene TE-TFET outperforms the homojunction phosphorene TFET and the TMD TFET in terms of extrinsic energy-delay product. In this work, the operation principles of TE-TFET and its performance sensitivity to the design parameters are investigated by the means of full-band atomistic quantum transport simulation., Comment: 6 figures

Scaling transistors' dimensions has been the thrust for the semiconductor industry in the last 4 decades. However, scaling channel lengths beyond 10 nm has become exceptionally challenging due to the direct tunneling between source and drain which degrades gate control, switching functionality, and worsens power dissipation. Fortunately, the emergence of novel classes of materials with exotic properties in recent times has opened up new avenues in device design. Here, we show that by using channel materials with an anisotropic effective mass, the channel can be scaled down to 1nm and still provide an excellent switching performance in both MOSFETs and TFETs. In the case of TFETs, a novel design has been proposed to take advantage of anisotropic mass in both ON- and OFF-state of the TFETs. Full-band atomistic quantum transport simulations of phosphorene nanoribbon MOSFETs and TFETs based on the new design have been performed as a proof.

Tunneling field-effect transistors (TFETs) based on 2D materials are promising steep sub-threshold swing (SS) devices due to their tight gate control. There are two major methods to create the tunnel junction in these 2D TFETs: electrical and chemical doping. In this work, design guidelines for both electrically and chemically doped 2D TFETs are provided using full band atomistic quantum transport simulations in conjunction with analytic modeling. Moreover, several 2D TFETs' performance boosters such as strain, source doping, and equivalent oxide thickness (EOT) are studied. Later on, these performance boosters are analyzed within a novel figure-of-merit plot (i.e. constant ON-current plot)., Comment: 5 pages, 8 figures

2D transition metal dichalcogenides (TMDs) have attracted a lot of attention recently for energy-efficient tunneling-field-effect transistor (TFET) applications due to their excellent gate control resulting from their atomically thin dimensions. However, most TMDs have bandgaps (Eg) and effective masses (m*) outside the optimum range needed for high performance. It is shown here that the newly discovered 2D material, few-layer phosphorene, has several properties ideally suited for TFET applications: 1) direct Eg in the optimum range ~1.0-0.4 eV, 2) light transport m* (0.15m0), 3) anisotropic m* which increases the density of states near the band edges, and 4) a high mobility. These properties combine to provide phosphorene TFET outstanding ION 1 mA/um, ON/OFF ratio~1e6, scalability to 6 nm channel length and 0.2 V supply voltage, thereby significantly outperforming the best TMD-TFETs in energy-delay products. Full-band atomistic quantum transport simulations establish phosphorene TFETs as serious candidates for energy-eficient and scalable replacements of MOSFETs.

In this work, an analytic model is proposed which provides in a continuous manner the current-voltage characteristic (I-V) of high performance tunneling field-effect transistors (TFETs) based on direct bandgap semiconductors. The model provides closed-form expressions for I-V based on: 1) a modified version of the well-known Fowler-Nordheim (FN) formula (in the ON-state), and 2) an equation which describes the OFF-state performance while providing continuity at the ON/OFF threshold by means of a term introduced as the "continuity factor". It is shown that traditional approaches such as FN are accurate in TFETs only through correct evaluation of the total band bending distance and the "tunneling effective mass". General expressions for these two key parameters are provided. Moreover, it is demonstrated that the tunneling effective mass captures both the ellipticity of evanescent states and the dual (electron/hole) behavior of the tunneling carriers, and it is further shown that such a concept is even applicable to semiconductors with nontrivial energy dispersion. Ultimately, it is found that the I-V characteristics obtained by using this model are in close agreement with state-of-the-art quantum transport simulations both in the ON- and OFF-state, thus providing validation of the analytic approach., Comment: 9 pages, 6 figures

The main promise of tunnel FETs (TFETs) is to enable supply voltage ($V_{DD}$) scaling in conjunction with dimension scaling of transistors to reduce power consumption. However, reducing $V_{DD}$ and channel length ($L_{ch}$) typically deteriorates the ON- and OFF-state performance of TFETs, respectively. Accordingly, there is not yet any report of a high perfor]mance TFET with both low V$_{DD}$ ($\sim$0.2V) and small $L_{ch}$ ($\sim$6nm). In this work, it is shown that scaling TFETs in general requires scaling down the bandgap $E_g$ and scaling up the effective mass $m^*$ for high performance. Quantitatively, a channel material with an optimized bandgap ($E_g\sim1.2qV_{DD} [eV]$) and an engineered effective mass ($m*^{-1}\sim40 V_{DD}^{2.5} [m_0^{-1}]$) makes both $V_{DD}$ and $L_{ch}$ scaling feasible with the scaling rule of $L_{ch}/V_{DD}=30~nm/V$ for $L_{ch}$ from 15nm to 6nm and corresponding $V_{DD}$ from 0.5V to 0.2V., Comment: 4 pages, 5 figures

Self-assembled quantum dots (QDs) are highly strained heterostructures. the lattice strain significantly modifies the electronic and optical properties of these devices. A universal behavior is observed in atomistic strain simulations (in terms of both strain magnitude and profile) of QDs with different shapes and materials. In this paper, this universal behavior is investigated by atomistic as well as analytic continuum models. Atomistic strain simulations are very accurate but computationally expensive. On the other hand, analytic continuum solutions are based on assumptions that significantly reduce the accuracy of the strain calculations, but are very fast. Both techniques indicate that the strain depends on the aspect ratio (AR) of the QDs, and not on the individual dimensions. Thus simple closed form equations are introduced which directly provide the atomistic strain values inside the QD as a function of the AR and the material parameters. Moreover, the conduction and valence band edges $E_{C/V}$ and their effective masses $m^*_{C/V}$ of the QDs are dictated by the strain and AR consequently. The universal dependence of atomistic strain on the AR is useful in many ways; Not only does it reduce the computational cost of atomistic simulations significantly, but it also provides information about the optical transitions of QDs given the knowledge of $E_{C/V}$ and $m^*_{C/V}$ from AR. Finally, these expressions are used to calculate optical transition wavelengths in InAs/GaAs QDs and the results agree well with experimental measurements and atomistic simulations., Comment: 14 pages, 7 figures

A bilayer graphene based electrostatically doped tunnel field-effect transistor (BED-TFET) is proposed in this work. Unlike graphene nanoribbon TFETs in which the edge states deteriorate the OFF-state performance, BED-TFETs operate based on different bandgaps induced by vertical electric fields in the source, channel, and drain regions without any chemical doping. The performance of the transistor is evaluated by self-consistent quantum transport simulations. This device has several advantages: 1) ultra-low power (VDD=0.1V), 2) high performance (ION/IOFF>104), 3) steep subthreshold swing (SS<10mv/dec), and 4) electrically configurable between N-TFET and P-TFET post fabrication. Here, the operation principle of the BED-TFET and its performance sensitivity to the device design parameters are studied., Comment: 4 pages, 6 figures in 2016 Journal of the Electron Device Society

The dielectric engineered tunnel field-effect transistor (DE-TFET) as a high performance steep transistor is proposed. In this device, a combination of high-k and low-k dielectrics results in a high electric field at the tunnel junction. As a result a record ON-current of about 1000 uA/um and a subthreshold swing (SS) below 20mV/dec are predicted for WTe2 DE-TFET. The proposed TFET works based on a homojunction channel and electrically doped contacts both of which are immune to interface states, dopant fluctuations, and dopant states in the band gap which typically deteriorate the OFF-state performance and SS in conventional TFETs., Comment: 3 pages, 3 figures

A new compact modeling approach is presented which describes the full current-voltage (I-V) characteristic of high-performance (aggressively scaled-down) tunneling field-effect-transistors (TFETs) based on homojunction direct-bandgap semiconductors. The model is based on an analytic description of two key features, which capture the main physical phenomena related to TFETs: 1) the potential profile from source to channel, and 2) the elliptic curvature of the complex bands in the bandgap region. It is proposed to use 1D Poisson's equations in the source and the channel to describe the potential profile in homojunction TFETs. This allows to quantify the impact of source/drain doping on device performance, an aspect usually ignored in TFET modeling but highly relevant in ultra-scaled devices. The compact model is validated by comparison with state-of-the-art quantum transport simulations using a 3D full band atomistic approach based on Non-Equilibrium Green's Functions (NEGF). It is shown that the model reproduces with good accuracy the data obtained from the simulations in all regions of operation: the on/off states and the n/p branches of conduction. This approach allows calculation of energy-dependent band-toband tunneling currents in TFETs, a feature that allows gaining deep insights into the underlying device physics. The simplicity and accuracy of the approach provides a powerful tool to explore in a quantitatively manner how a wide variety of parameters (material-, size- and/or geometrydependent) impact the TFET performance under any bias conditions. The proposed model presents thus a practical complement to computationally expensive simulations such as the 3D NEGF approach., Comment: 31 pages, 6 figures

In this letter, it is shown that the existing scaling theories for chemically doped transistors cannot be applied to the novel class of electrically doped 2D transistors and the concept of equivalent oxide thickness (EOT) is not applicable anymore. Hence, a novel scaling theory is developed based on analytic solutions of the 2D Poisson equation. Full band atomistic quantum transport simulations verify the theory and show that the critical design parameters are the physical oxide thickness and distance between the gates. Accordingly, the most optimized electrically doped devices are those with the smallest spacing between the gates and the thinnest oxide, and not the smallest EOT., Comment: 3 pages, 2 Figures

A detailed theoretical study of the optical absorption in self-assembled quantum dots is presented in this paper. A rigorous atomistic strain model as well as a sophisticated electronic band structure model are used to ensure accurate prediction of the optical transitions in these devices . The optimized models presented in this paper are able to reproduce the experimental results with an error less than 1$\%$. The effects of incident light polarization, alloy mole fraction, quantum dot dimensions, and doping have been investigated. The in-plane polarized light absorption is more significant than the perpendicularly polarized light absorption. Increasing the mole fraction of the strain controlling layer leads to a lower energy gap and larger absorption wavelength. Surprisingly, the absorption wavelength is highly sensitive to changes in the dot diameter, but almost insensitive to changes in the dot height. This unpredicted behavior is explained by sensitivity analysis of different factors which affect the optical transition energy.

A widely used technique to mitigate the gate leakage in the ultra-scaled metal oxide semiconductor field effect transistors (MOSFETs) is the use of high-k dielectrics, which provide the same equivalent oxide thickness (EOT) as $\rm SiO_2$, but thicker physical layers. However, using a thicker physical dielectric for the same EOT has a negative effect on the device performance due to the degradation of 2D electrostatics. In this letter, the effects of high-k oxides on double-gate (DG) MOSFET with the gate length under 20 nm are studied. We find that there is an optimum physical oxide thickness ($\rm T_{OX}$) for each gate stack, including $\rm SiO_2$ interface layer and one high-k material. For the same EOT, $\rm Al_2O_3$ (k=9) over 3 $\rm\AA$ $\rm SiO_2$ provides the best performance, while for $\rm HfO_2$ (k=20) and $\rm La_2O_3$ (k=30), $\rm SiO_2$ thicknesses should be 5 $\rm\AA$ and 7 $\rm\AA$, respectively. The effects of using high-k oxides and gate stacks on the performance of ultra-scaled MOSFETs are analyzed. While thin oxide thickness increases the gate leakage, the thick oxide layer reduces the gate control on the channel. Therefore, the physical thicknesses of gate stack should be optimized to achieve the best performance., Comment: 5 pages

In this work, the performance of Tunnel Field-Effect Transistors (TFETs) based on two-dimensional Transition Metal Dichalcogenide (TMD) materials is investigated by atomistic quantum transport simulations. One of the major challenges of TFETs is their low ON-currents. 2D material based TFETs can have tight gate control and high electric fields at the tunnel junction, and can in principle generate high ON-currents along with a sub-threshold swing smaller than 60 mV/dec. Our simulations reveal that high performance TMD TFETs, not only require good gate control, but also rely on the choice of the right channel material with optimum band gap, effective mass and source/drain doping level. Unlike previous works, a full band atomistic tight binding method is used self-consistently with 3D Poisson equation to simulate ballistic quantum transport in these devices. The effect of the choice of TMD material on the performance of the device and its transfer characteristics are discussed. Moreover, the criteria for high ON-currents are explained with a simple analytic model, showing the related fundamental factors. Finally, the subthreshold swing and energy-delay of these TFETs are compared with conventional CMOS devices., Comment: 7 pages, 8 figures. The revised version is uploaded

Thermal properties are of great interest in modern electronic devices and nanostructures. Calculating these properties is straightforward when the device is made from a pure material, but problems arise when alloys are used. Specifically, only approximate bandstructures can be computed for random alloys and most often the Virtual Crystal Approximation (VCA) is used. Unfolding methods [T. B. Boykin, N. Kharche, G. Klimeck, and M. Korkusinski, J. Phys.: Condens. Matt. 19, 036203 (2007).] have proven very useful for tight-binding calculations of alloy electronic structure without the problems in the VCA, and the mathematical analogy between tight-binding and valence-force-field approaches to the phonon problem suggest they be employed here as well. However, there are some differences in the physics of the two problems requiring modifications to the electronic structure approach. We therefore derive a phonon alloy bandstructure (vibrational mode) approach based on our tight-binding electronic structure method, modifying the band-determination method to accommodate the different physical situation. Using the method, we study In$_x$Ga$_{1-x}$As alloys and find very good agreement with available experiments., Comment: Main paper with attached supplemental material

We have developed a simulation system for nanoscale high-electron mobility transistors, in which the self-consistent solution of Poisson and Schr\"odinger equations is obtained with the finite element method. We solve the exact set of nonlinear differential equations to obtain electron wave function, electric potential distribution, electron density, Fermi surface energy and current density distribution in the whole body of the device. For more precision, local dependence of carrier mobility on the electric field distribution is considered. We furthermore compare the simulation to a recent experimental measurement and observe perfect agreement. We also propose a graded channel design to improve the transconductance and thereby the threshold frequency of the device., Comment: 8 pages, 19 figures