Atomistic Quantum Transport Simulations Research Articles

<italic>Ab Initio</italic> Simulation of Band-to-Band Tunneling FETs With Single- and Few-Layer 2-D Materials as Channels

Full-band atomistic quantum transport simulations based on first principles are employed to assess the potential of band-to-band tunneling FETs (TFETs) with a 2-D channel material as future electronic circuit components. We demonstrate that single-layer (SL) transition metal dichalcogenides are not well suited for TFET applications. There might, however, exist a great variety of 2-D semiconductors that have not even been exfoliated yet; this paper pinpoints some of the most promising candidates among them to realize highly efficient TFETs. SL SnTe, As, TiNBr, and Bi are all found to ideally deliver ON-currents larger than 100{\mu}A/{\mu}m at 0.5-V supply voltage and 0.1 nA/{\mu}m OFF-current value. We show that going from single to multiple layers can boost the TFET performance as long as the gain from a narrowing bandgap exceeds the loss from the deteriorating gate control. Finally, a 2-D van der Waals heterojunction TFET is revealed to perform almost as well as the best SL homojunction, paving the way for research in optimal 2-D material combinations.

Atomistic Tight-Binding Study of Contact Resistivity in Si/SiGe PMOS Schottky Contacts

The metal-semiconductor contact resistivity has started to play a critical role for the overall device performance as Si is reaching 10-nm size ranges. The International Technology Roadmap for Semiconductors (ITRS) target predicts a requirement of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-9</sup> Ω·cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> by 2023 which has been a challenging target to achieve. This paper explores the impact of doping concentration, Schottky barrier height, strain, and SiGe mole fraction on the resistivity of Si/SiGe p-type metal-oxide semiconductor (PMOS) contacts with 20-band atomistic tight binding quantum transport simulations. Commonly used simple effective mass approximation models are shown to overestimate the resistivity values. The predicted model results are compared with experimental data and the device parameters needed to achieve 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-9</sup> Ω·cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> are identified.

Switching Mechanism and the Scalability of Vertical-TFETs

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.

Sensitivity Challenge of Steep Transistors

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.

Robust mode space approach for atomistic modeling of realistically large nanowire transistors

Nanoelectronic transistors have reached 3D length scales in which the number of atoms is countable. Truly atomistic device representations are needed to capture the essential functionalities of the devices. Atomistic quantum transport simulations of realistically extended devices are, however, computationally very demanding. The widely used mode space (MS) approach can significantly reduce the numerical cost, but a 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 engineering-level, reliable tight binding non-equilibrium Green's function simulation of nanowire metal-oxide-semiconductor field-effect transistor (MOSFET) with a realistic cross section of 10 nm × 10 nm using a small computer cluster. This approach is applied to compare the performance of InGaAs and Si nanowire n-type MOSFETs (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 10 nm × 10 nm.

The Potential of Phosphorene Nanoribbons as Channel Material for Ultrascaled Transistors

Transport properties of realistic phosphorene nanoribbons (PNRs) with edge defects are studied by using statistical atomistic quantum transport simulations. Regarding the impact of nanoribbon width downscaling and increasing of edge defect percentage, we show that PNRs exhibit qualitatively similar behavior of the ON- and OFF-state conductance, and of the ON–OFF conductance ratio as graphene nanoribbons (GNRs). However, we demonstrate that PNRs are superior to GNRs in terms of the absolute values of the conductance parameters, and that PNRs are much more immune to edge defects than their graphene counterparts. This paper identifies PNRs as a more promising channel material than GNRs for the extremely scaled postsilicon transistor technology.

Assessment of Germanane Field-Effect Transistors for CMOS Technology

Using self-consistent atomistic quantum transport simulations, the device characteristics of n-type and p-type germanane (GeH) field-effect transistors (FETs) are evaluated. While both devices exhibit near-identical off-state characteristics, n-type GeH FET shows ~40% larger on current than the p-type counterpart, resulting in faster switching speed and lower power-delay product. Our benchmark of GeH FETs against similar devices based on 2D materials reveals that GeH outperforms MoS2 and black phosphorus in terms of energy-delay product (EDP). In addition, the performance of GeH-based CMOS circuit is analyzed using an inverter chain. By engineering power supply voltage and threshold voltage simultaneously, we find the optimal operating condition of GeH FETs, minimizing EDP in the CMOS circuit. Our comprehensive study, including material parameterization, device simulation, and circuit analyses, demonstrates significant potential of GeH FETs for 2D-material CMOS circuit applications.

Compact Modeling Source-to-Drain Tunneling in Sub-10-nm GAA FinFET With Industry Standard Model

We present a compact model for source-to-drain tunneling current in sub-10-nm gate-all-around FinFET, where tunneling current becomes nonnegligible. Wentzel–Kramers–Brillouin method with a quadratic potential energy profile is used to analytically capture the dependence on biases in the tunneling probability expression and simplify the equation. The calculated tunneling probability increases with smaller effective mass and with increasing bias. We at first use the Gaussian quadrature method to integrate Landauer’s equation for tunneling current computation without further approximations. To boost simulation speed, some approximations are made. The simplified equation shows a good accuracy and has more flexibility for compact model purpose. The model is implemented into industry standard Berkeley Short-channel IGFET Model-common multi-gate model for future technology node, and is validated by the full-band atomistic quantum transport simulation data.

Assessment of High-Frequency Performance Limit of Black Phosphorus Field-Effect Transistors

Recently, gigahertz frequencies have been reported with black phosphorus (BP) field-effect transistors (FETs), yet the high-frequency performance limit has remained unexplored. Here we project the frequency limit of BP FETs based on rigorous atomistic quantum transport simulations and the small-signal circuit model. Our self-consistent nonequilibrium Green’s function (NEGF) simulation results show that semiconducting BP FETs exhibit clear saturation behaviors with the drain voltage, unlike zero-bandgap graphene devices, leading to >10 THz frequencies for both intrinsic cutoff frequency ( ${f}_{T}$ ) and unity power gain frequency ( ${f} _{{\mathsf {max}}}$ ). To develop keen insight into practical devices, we discuss the optimization of ${f} _{T}$ and ${f} _{{\mathsf {max}}}$ by varying various device parameters such as channel length ( ${L} _{{\mathsf {ch}}}$ ), oxide thickness, device width, gate resistance, contact resistance, and parasitic capacitance. Although extrinsic ${f}_{T}$ and ${f} _{{\mathsf {max}}}$ can be significantly affected by the contact resistance and parasitic capacitance, they can remain near THz frequency range ( ${f} _{T} = \mathsf {900}$ GHz; ${f} _{{\mathsf {max}}} = \mathsf {1.2}$ THz) through proper engineering, particularly with an aggressive channel length scaling ( ${L} _{{\mathsf {ch}}} \approx \mathsf {10}$ nm). Our benchmark against the experimental data indicates that there still exists large room for optimization in fabrication, suggesting further advancement of high-frequency performance of state-of-the-art BP FETs for the future analog and radio-frequency applications.

Transport in vertically stacked hetero-structures from 2D materials

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 1000µA/µm with VDD = 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.

Performance Limit Projection of Germanane Field-Effect Transistors

Here we explore the performance limit of monolayer germanane (GeH) field-effect transistors (FETs). We first plotted an electronic band structure of GeH using density functional theory and then tight-binding parameters were extracted. Device characteristics of GeH FETs are investigated using rigorous self-consistent atomistic quantum transport simulations within tight-binding approximations. Our simulation results indicate that GeH FETs can exhibit exceptional on-state device characteristics, such as high $\text{I}_{\textit {on}}$ (>2 mA/ $\mu \text{m}$ ) and large $\text{g}_{m}$ (~7 mS/ $\mu \text{m}$ ) with $\text{V}_{\textit {DD}} = 0.5$ V due to the very light effective mass of GeH (0.07m0), while maintaining excellent switching characteristics (SS ~64 mV/dec). We have also performed a scaling study by varying the channel length, and it turned out that GeH FET can be scaled down to ~14-nm channel without facing significant short channel effects but it may suffer from large leakage current at the channel length shorter than 10 nm. Finally, we have benchmarked GeH FET against MoS2 counterpart, exhibiting better suitability of GeH device for high-performance applications compared with MoS2 transistors.

Atomistic quantum transport simulation of multilayer phosphorene nanoribbon field effect transistors

Few-layer black phosphorus is a semiconductor material, where its allotrope is called phosphorene; a new two-dimensional material which is discovered in 2014. In this paper, first we use the tight-binding method to implement a matrix representation for single-layer and multilayer structures of phosphorene nanoribbon (PNR) to define the Hamiltonian of the system. Second, we investigate the band structure and the band gap of multilayer PNRs. The band gap of armchair PNRs with 16 atoms across the width of PNR for single-layer, bilayer, and three-layer structures are obtained as 1.899, 1.224, and 0.937eV, respectively. Third, we use the atomistic description of structure to simulate the performance characteristics of single and multilayer PNR field effect transistors (PNRFETs) by employing the non-equilibrium Green's function (NEGF) formalism. Based on the properties of the material and device structures, Id-Vgs, Id-Vds characteristics, energy band diagram in the channel, and ION/IOFF are analyzed. The ON to OFF current ratio for single-layer, bilayer, and three-layer PNRFETs are increasing when the channel length increases from 5nm to 15nm. The current ratio for single-layer increases from 1277 for Lch=5nm to 216.7×106 for Lch=15nm. The ION/IOFF in single-layer PNRFET is higher in comparison with those values in bilayer and three-layer PNRFETs due to very small off-current in the single-layer PNRFET which in turn resulted from its larger band gap. The results show that the performance of PNRFET changes significantly depending on the number of phosphorene layers and the length of the channel of device.

Aharonov-Bohm effect in monolayer phosphorene nanorings

This work presents theoretical demonstration of Aharonov-Bohm (AB) effect in monolayer phosphorene nanorings (PNR). Atomistic quantum transport simulations of PNR are employed to investigate the impact of multiple modulation sources on the sample conductance. In presence of a perpendicular magnetic field, we find that the conductance of both armchair and zigzag PNR oscillate periodically in a low-energy window as a manifestation of the AB effect. Our numerical results have revealed a giant magnetoresistance (MR) in zigzag PNR (with a maximum magnitude approaching two thousand percent). It is attributed to the AB effect induced destructive interference phase in a wide energy range below the bottom of the second subband. We also demonstrate that PNR conductance is highly anisotropic, offering an additional way to modulate MR. The giant MR in PNR is maintained at room temperature in the presence of thermal broadening effect.

Scalable GaSb/InAs Tunnel FETs With Nonuniform Body Thickness

GaSb/InAs heterojunction tunnel field-effect transistors are strong candidates in building future low-power integrated circuits, as they could provide both steep subthreshold swing and large ON-state current ($I_{\rm{ON}}$). However, at short channel lengths they suffer from large tunneling leakage originating from the small band gap and small effective masses of the InAs channel. As proposed in this article, this problem can be significantly mitigated by reducing the channel thickness meanwhile retaining a thick source-channel tunnel junction, thus forming a design with a non-uniform body thickness. Because of the quantum confinement, the thin InAs channel offers a large band gap and large effective masses, reducing the ambipolar and source-to-drain tunneling leakage at OFF state. The thick GaSb/InAs tunnel junction, instead, offers a low tunnel barrier and small effective masses, allowing a large tunnel probability at ON state. In addition, the confinement induced band discontinuity enhances the tunnel electric field and creates a resonant state, further improving $I_{\rm{ON}}$. Atomistic quantum transport simulations show that ballistic $I_{\rm{ON}}=284$A/m is obtained at 15nm channel length, $I_{\rm{OFF}}=1\times10^{-3}$A/m, and $V_{\rm{DD}}=0.3$V. While with uniform body thickness, the largest achievable $I_{\rm{ON}}$ is only 25A/m. Simulations also indicate that this design is scalable to sub-10nm channel length.

Thickness Engineered Tunnel Field-Effect Transistors Based on Phosphorene

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.

Design of High-Performance InAs–Si Heterojunction 2D–2D Tunnel FETs With Lateral and Vertical Tunneling Paths

Double-gate tunneling FETs (TFETs) exploiting the 2D density-of-state switch are studied. A full-band and atomistic quantum transport simulator based on the sp3d5s* tight-binding model is used to solve the quantum transport problem taking into account both lateral and vertical band-to-band tunneling paths. The tunneling paths are identified by means of the calculation of the electron and hole generation rates. They are computed with an in-house tool based on the Flietner imaginary dispersion and a non-local path band-to-band tunneling model. First, a InGaAs electron–hole bilayer TFET is investigated. It is found that the suppression of lateral tunneling components is crucial to obtain a steep slope in this device. On the other hand, the presence of both tunneling components can boost the ON-current of TFETs. The latter can be achieved by implementing an InAs–Si heterostructure as 2D–2D TFET. Such a combination offers a device solution with both steep subthermal subthreshold swing and high ON-current. In the best case of an extremely thin InAs–Si 2D–2D TFET, the minimal swing would be SS = 28 mV/decade and the ON-current would reach 240 $\mu \text{A}/\mu \text{m}$ .

Design Rules for High Performance Tunnel Transistors From 2-D Materials

Tunneling field-effect transistors (TFETs) based on 2-D materials are promising steep sub-threshold swing devices due to their tight gate control. There are two major methods to create the tunnel junction in these 2-D TFETs: 1) electrical and 2) chemical doping. In this paper, design guidelines for both electrically and chemically doped 2-D TFETs are provided using full band atomistic quantum transport simulations in conjunction with analytic modeling. Moreover, several 2-D TFETs' performance boosters such as strain, source doping, and equivalent oxide thickness are studied. Later on, these performance boosters are analyzed within a novel figure-of-merit plot (i.e., constant ON-current plot).

Saving Moore's Law Down To 1 nm Channels With Anisotropic Effective Mass.

Scaling transistors’ dimensions has been the thrust for the semiconductor industry in the last four 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 1 nm and still provide an excellent switching performance in phosphorene nanoribbon MOSFETs. To solve power consumption challenge besides dimension scaling in conventional transistors, a novel tunnel transistor is proposed which takes advantage of anisotropic mass in both ON- and OFF-state of the operation. Full-band atomistic quantum transport simulations of phosphorene nanoribbon MOSFETs and TFETs based on the new design have been performed as a proof.

Few-layer Phosphorene: An Ideal 2D Material For Tunnel Transistors

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* (0.15 m0), 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 ~ 106 for a 15 nm channel and 0.5 V supply voltage, thereby significantly outperforming the best TMD-TFETs and CMOS in many aspects such as ON/OFF current ratio and energy-delay products. Furthermore, phosphorene TFETS can scale down to 6 nm channel length and 0.2 V supply voltage within acceptable range in deterioration of the performance metrics. Full-band atomistic quantum transport simulations establish phosphorene TFETs as serious candidates for energy-efficient and scalable replacements of MOSFETs.

Design strategy of two-dimensional material field-effect transistors: Engineering the number of layers in phosphorene FETs

Thickness or the number of layers in 2D semiconductors is a key parameter to determine the material's electronic properties and the overall device performance of 2D material electronics. Here, we discuss the engineering practice of optimizing material and device parameters of phosphorene field-effect transistors (FETs) by means of self-consistent atomistic quantum transport simulations, where the impacts of different numbers of phosphorene layers on various device characteristics are explored in particular, considering two specific target applications of high-performance and low-power devices. Our results suggest that, for high-performance applications, monolayer phosphorene should be utilized in a conventional FET structure since it can provide the equally large on current as other multilayer phosphorenes (Ion &amp;gt; 1 mA/μm) without showing a penalty of relatively lower density of states, along with favorableness for steep switching and large immunity to gate-induced drain leakage. On the other hand, more comprehensive approach is required for low-power applications, where operating voltage, doping concentration, and channel length should be carefully engineered along with the thickness of phosphorene in tunnel FET (TFET) structure to achieve ultra-low leakage current without sacrificing on current significantly. Our extensive simulation results revealed that either bilayer or trilayer phosphorene can provide the best performance in TFET with the maximum Ion/Ioff of ∼2 × 1011 and the subthreshold swing as low as 13 mV/dec. In addition, our comparative study of phosphorene-based conventional FET and TFET clearly shows the feasibility and the limitation of each device for different target applications, providing irreplaceable insights into the design strategy of phosphorene FETs that can be also extended to other similar layered material electronic devices.