A predictive analytic model for high-performance tunneling field-effect transistors approaching non-equilibrium Green's function simulations

As these As transistors are scaled to nanometer dimensions, the discreteness of the dopants becomes increasingly important. Transistors of 3 times 3 nm2 cross section contain, on average, approximately one dopant atom per nanometer of length, making any self-averaging impossible. The individual random dopants act as localized scatterers whose distribution, and therefore, impact on the electron transport, varies from device to device. This is complemented by electrostatic variation in the potential that controls the threshold voltage and the dominant current paths. The current density is greatly influenced by resonances associated with the attractive potential of the donors and screening effects. In this paper, for the first time, a full 3-D nonequilibrium Green's function (NEGF) simulation in the effective mass approximation has been used to study the influence of individual discrete donors in the source/drain on the I-V characteristics of a narrow n-channel Si nanowire transistor. We have compared devices with microscopically different configuration of dopants. The simulated variations in the I-V curves are analyzed with reference to the behavior of the transmission coefficients. We have highlighted the importance of resonance states when solving the NEGF and Poisson equations self-consistently.

Recent focus of the VLSI industry has been on performance enhancement of semiconductors by introducing alternate channel materials. In this work, we have studied electronic properties of 2 dimensional hexagonal shaped aluminum nitride (2D h-AIN) as a channel material in n-MOS transistor. With Density Functional Theory (DFT), we have calculated 2D h-AIN to understand it's electronic properties and carried out non-equilibrium Green's function (NEGF) simulations to study device performance. Our studies reveal good MOS device properties in terms of drain current (86.45 (μA/μm), transconductance (296 (iS/jim) and ON/OFF ratio (1.57 × 104), which enhances the scope of further research on 2D h-AIN FET.

Intraband source-drain tunneling is predicted to limit leakage current in sub-10 nm field-effect transistors (FETs). We use non-equilibrium Green's function simulations to study this effect in III-V multigate FETs and derive simple, accurate intraband tunneling formulas suitable for use in compact models or semiclassical device simulators. Band nonparabolicity effects are shown to be quantitatively important and incorporated using band gap scaling. We also supply a general subthreshold electrostatic model including source and drain depletion effects for analytical modeling. Our results enable rapid modeling and simulation of ultimately scaled III-V FETs for device evaluation and optimization.

We present a physics-based model for ferroelectric/negative capacitance transistors (FEFETs/ NCFETs) without an inter-layer metal between ferroelectric and dielectric in the gate stack. The model self-consistently solves 2D Poisson's equation, non-equilibrium Green's function (NEGF) based charge and transport equations, and multi-domain Landau Khalatnikov (LK) equations with the domain interaction term. The proposed simulation framework captures the variation of ferroelectric (FE) polarization (P) along the gate length due to non-uniform electric field (E) along the channel. To calibrate the LK equations, we fabricate and characterize 10nm HZO films. Based on the calibrated model, we analyze the gate/drain voltage dependence of P distribution in the FE and its effect on the channel potential and current-voltage characteristics. Our results highlight the importance of larger domain interaction to boost the benefits of FEFETs with subthreshold swing (SS) as small as ∼50mV/decade achieved at room temperature. As domain interaction increases, the characteristics of FEFETs without inter-layer metal (SS, negative drain induced barrier lowering (DIBL), negative output conductance) approach those of FEFETs with inter-layer metal.

This paper describes the point defect treatment in nanowire MOSFETs. The 3D Poisson equation is self-consistently coupled to the Schrodinger equation. We adopt the mode-space representation in which the 3D Schrodinger equation is divided into a 2D equation, including the confinement of the cross-section, and an ID equation describing the ballistic transport based on the nonequilibrium Green's function formalism (NEGF). We use the simplest form of the tight-binding theory, with one orbital per atom, and considering only the first-neighbor-interactions. In this framework, equivalent to the ellipsoidal energy band approximation, influence of point defects on electronic transport is discussed.

Complementary-metal-oxide-semiconductor (CMOS) transistors have been commonly employed in the electronics industry for the past decades thank to their excellent scalability, low cost, and high performance. The semiconductor industry follows the Moore’s law which predicts that the number of transistors in an integrated circuit (IC) approximately doubles every two years. High packing density enables more logic circuits to be fabricated on a given IC chip area which lowers the cost per function. However, exponential growth of the number of transistors per IC chip leads to a drastic increase in the power density. Basically, power consumption of an IC can be categorized into two components: active power (PActive ) and passive power (PPassive ). PActive is given by αfCVDD 2 , where α is the activity factor, f is the operating frequency, C is the load capacitance, and VDD is the power supply voltage. PPassive is the power dissipation of transistors that are at the OFF state. Its magnitude is proportional to the product of OFF state current (IOFF ) and VDD . With the shrinking of physical dimensions of CMOS devices into sub-10 nanometer regime, direct source to drain tunneling and gate leakage can significantly increase the IOFF , which in turn increases the static power. In other words, power consumption has imposed a serious issue for advanced technology nodes. Since both active and passive powers are strongly dependent on the VDD , one effective way to reduce the power consumption is to scale down the VDD . The threshold voltage (VTH ) of the conventional MOSFETs needs to be reduced so that the same ION can be sustained at reduced VDD . However, decreasing VTH without scaling the subthreshold swing (S) will result in a high IOFF . This causes high passive power consumption. In the conventional MOSFET, the high energy electrons following the Fermi-Dirac distribution contribute to the subthreshold current which sets the lower limit of the subthreshold swing. Thus, a steeper switching characteristic is required in order to retain the same ION and IOFF when VDD is reduced. In this context, tunneling field-effect transistors (TFET) based on band-to-band tunneling (BTBT) is a promising candidate to overcome the 60mV/dec swing limitation at room temperature faced in conventional MOSFETs. Although a steeper switching characteristic can be achieved in TFETs, the ION of TFETs is still too low to satisfy the drive current requirement for low power application projected by the International Technology Roadmap for Semiconductors (ITRS). The performance of TFET can be enhanced via a few innovations, such as the employment of direct band gap materials, heterostructures with staggered band alignments, and inventive device structure designs. Recent advancements in TFET shows that enhancement in TFET is attained when the BTBT direction is aligned to the gate induced electric field, so-called vertical TFET (VTFET). This is due to the greater efficiency of the gate to control the band bending. In this work, we investigate the performance of the vertical TFET based on group IV and III-V materials. The vertical TFET considered is the Electron-Hole Bilayer TFET. The device Hamiltonians for all channel materials are constructed based on the full-band sp3d5s*tight-binding (TB) model. The atomistic TB model offers a realistic calculation which captures the properties of nano-scale structures more accurately. The carrier transport of VTFET is calculated using a quantum simulator based on the formalism of non-equilibrium Green’s function (NEGF). Subsequently, the atomic charge obtained from NEGF is coupled with the Poisson solver to solve for the atomic potential self-consistently. The optimization of VTEFT is carried out in terms of ON-current and subthreshold swing. The materials considered consist of silicon, germanium, and indium antimonide, and hetero-structures from III-V semiconductors. The effects of the device geometries, such as the length of overlap (LOV ) and underlap (LUN ) regions, are studied in order to provide insights in enhancing the electrical performance of VTFETs. Our study shows that heterojunction consisting of GaSb (source) and InAs (drain) offers higher current than that of Si homojunction. The electrical performance of VTEFT is further benchmarked with that of the conventional lateral PIN structure. In conclusion, this work presents the challenges and key design considerations of VTEFT.

In this paper, we present a full 3-D real-space quantum-transport simulator based on the Green's function formalism developed to study nonperturbative effects in ballistic nanotransistors. The nonequilibrium Green function (NEGF) equations in the effective mass approximation are discretized using the control-volume approach and solved self-consistently with the Poisson equation in order to obtain the electron and current densities. An efficient recursive algorithm is used in order to avoid the computation of the full Green function matrix. This algorithm, and the parallelization scheme used for the energy cycle, allow us to compute very efficiently the current-voltage characteristic without the simplifying assumptions often used in other quantum-transport simulations. We have applied our simulator to study the effect of surface roughness and stray charge on the I<sub>D</sub>-V<sub>G</sub> characteristic of a 6-nm Si-nanowire transistor. The results highlight the distinctly 3-D character of the electron transport, which cannot be accurately captured by using 1-D and 2-D NEGF simulations, or 3-D mode-space approximations.

High-doping induced Urbach tails and band gap narrowing play a significant role in determining the performance of tunneling devices and optoelectronic devices such as tunnel field-effect transistors (TFETs), Esaki diodes and light-emitting diodes. In this work, Urbach tails and band gap narrowing values are calculated explicitly for GaAs, InAs, GaSb and GaN as well as ultra-thin bodies and nanowires of the same. Electrons are solved in the non-equilibrium Green's function method in multi-band atomistic tight binding. Scattering on polar optical phonons and charged impurities is solved in the self-consistent Born approximation. The corresponding nonlocal scattering self-energies as well as their numerically efficient formulations are introduced for ultra-thin bodies and nanowires. Predicted Urbach band tails and conduction band gap narrowing agree well with experimental literature for a range of temperatures and doping concentrations. Polynomial fits of the Urbach tail and band gap narrowing as a function of doping are tabulated for quick reference.

The sixth interdisciplinary conference 'Progress in Non-equilibrium Green's Functions' (PNGF6) took place at Lund University, Sweden, on 17-21 August 2015. The conference was attended by 60 scientists, from Europe and overseas, sharing an interest in Green's function methods and/or non-equilibrium phenomena. At the conference, 34 invited and contributed talks were given, together with a poster session with 17 contributions. As its predecessors (Rostock 1999, Dresden 2002, Kiel 2005, Glasgow 2009, Jyväskylä 2012) did, the conference succeeded in gathering different communities for the exchange of recent developments and results. Among the topics of the conference, we mention approaches for strongly correlated systems, improvements of existing perturbative many-body schemes, electron-phonon/-photon interactions in time-dependent treatments, numerical scalability of NEGF approaches, connections with other non-equilibrium methods and concrete physical applications. For the latter, we mention quantum transport, semiconductor kinetics, multiply excited states in atoms and ions, nuclear reactions, high energy physics, quantum cascade lasers, strongly correlated model systems, graphene-nanostructures, optoelectronics, superconductors, spin-dynamics, photovoltaics, excitations in atoms and ions and time-resolved spectroscopy. The present volume contains 20 articles from participants of PNGF6, devoted to these topics.Compared to previous conferences, a completely novel and successful aspect of PNGF6 was the participation of experimentalists among the invited speakers, to establish a connection between emerging experimental techniques (for example, time-dependent spectroscopies) and the theoretical NEGF community. As at the previous PNGF conferences, the atmosphere was friendly and exciting at the same time, favoring vivid and stimulating discussions among experienced scientists, young researchers and students.The conference would not have been possible without financial support from the Swedish VR and from the "Christian-Albrechts-Universität-Kiel via the Kiel nano- and surface- science center (KinSis). Particular thanks go to Katarina Lindqvist, the administrator at the division of Mathematical Physics in Lund, who provided assistance in many different matters, in particular in making the conference unfold very smoothly. We also acknowledge the contributors to this volume for their papers and all the referees of the manuscripts.Finally, we are glad to announce that the seventh conference 'Progress in Nonequilibrium Green's Functions' (PNGF7) is organized by Andrea Marini and Gianluca Stefanucci, and it will take place in August 2018 in Rome, Italy. Arrivederci in Roma!

Aided by density functional theory with nonequilibrium Green's functions simulations, the thermoelectric (TE) properties of nanoporous carbon nanotube junctions formed by covalently binding carbon nanotubes via benzene bridges with either meta‐ or para‐connections are investigated. The results show that the TE performances of meta‐connected nanoporous carbon nanotube junctions are significantly improved due to the influence of destructive quantum interference (DQI) effect. Moreover, the TE properties of meta‐connected carbon nanotube junctions can be further improved by substitution of nitrogen atom and gate voltage. The reason is that the quantum interference patterns can be transformed from DQI to constructive quantum interference (or Fano resonance). The theoretical analysis shows that the TE figure of merit (ZT) for meta‐connected carbon nanotube junctions at room temperature is close to 0.5 near the Fermi level, ≈20 times higher than that of the perfect carbon nanotube junction. These results reveal that quantum interference effect can indeed be used to enhance the TE performance of molecular junctions.

We propose broadband quantum cascade detectors based on a dual-upper-state active region design. The dual-upper-state concept is known to produce broad gain in quantum cascade lasers and is also expected to provide a wide spectral response for quantum cascade detectors. Compared with quantum cascade detectors employing a bound-to-bound design, dual-upper-state devices are anticipated to exhibit broader bandwidth and can achieve higher responsivity. To validate this, we designed and fabricated quantum cascade detectors for each mid-wave (∼5 μm) and long-wave (∼10 μm) infrared regions, implementing anti-crossed dual-upper states in the main absorbing transition. At 300 K, the fabricated devices exhibited responsivities of ∼13.5 mA/W at λpeak ∼5.1 μm and ∼7.1 mA/W at λpeak ∼10 μm. The measured relative bandwidth of the devices Δλ/λcenter are approximately ∼20.8% and ∼21.1%. These results indicate that the dual-upper-state not only enables a wide spectral response but also may provide enhanced responsivity. The experimental findings are further supported by non-equilibrium Green's function simulations. Overall, our results highlight the potential of the dual-upper-state approach for broadband, high-performance infrared detection.

Two-dimensional (2D) polymeric carbon nitride (PCN) materials have drawn broad attention as promising candidates for photocatalytic hydrogen evolution. However, it remains a significant challenge to simultaneously improve the visible light absorption, separation of photogenerated carriers, and activity. Herein, alkali metals doping PCN (e.g., C6N6 and C2N) are systematically investigated based on density functional theory. Different from the conventional notion of doping atoms as active sites, the actual active site is the intrinsic pyridine nitrogen surrounding the alkali metal. Compared to the change of Gibbs free energy value of −0.45 eV (−0.60 eV) for pristine C6N6 (C2N), Li or Cs doped PCN decreases to −0.03 eV (−0.10 eV) or 0.06 eV (−0.11 eV), respectively, benefitting from the adjustment of the 3p electronic state occupation for N atoms by charges transfer from alkali metal. Meanwhile, Li or Cs doping not only broadens the absorption of visible light by narrowing the band edge position but also promotes the separation of photogenerated electrons and holes by regulating their spatial separation, which is further confirmed by significant photocurrents for Li or Cs doped PCN based on nonequilibrium Green's function simulation. Our work could provide interesting insights into the mechanistic understanding and the highly efficient design of PCN materials in photocatalysis.

The recent advancement in the fabrication of narrow graphene nanoribbon with smooth edges has catalyzed the growth of nanoribbon based transistors. Motivated by these advances, we suggest bilayer graphene nanoribbon tunnel field-effect transistors (BLGNR-TFETs) for low voltage digital and analog applications. The device performance is analyzed by quantum transport simulation, based on self-consistent solutions of two-dimensional Poisson's equation and nonequilibrium Green's function formalism. The results indicate that the use of BLGNR-TFET instead of monolayer graphene nanoribbon TFET with very narrow width, increases the ON current and reduces the intrinsic device delay without lowering the ON/OFF current ratio. The BLGNR-TFET for analog/RF applications has provided higher intrinsic gain at very narrow ribbon width; however, very narrow width reduces the cutoff frequency. Furthermore, RF figure of merits are investigated in the presence of external parasitics.

We discuss within the nonequilibrium Green's function formalism the self-consistent Born approximation of the electronic self-energy for concurrent coupling of charge carriers to photons and phonons. The expansion of the charge carrier Green's function is shown to provide a description for a range of physical processes with relevance for the photovoltaic device operation, such as indirect optical transitions, thermally assisted photocarrier escape from quantum wells or phonon-mediated interband transfer in tunnel junctions. The nonequilibrium Green's function picture of these processes is reviewed with focus on the evolution of the system towards the steady state in the convergence of the self-consistency iteration process and on the impact of inelastic scattering on device operation.

We present a detailed simulation study on the current-voltage characteristics of ballistic graphene nanoribbon (GNR) tunneling FETs of different widths with varying temperatures and channel length. Our model uses the self-consistent nonequilibrium Green's function and the quasi-2-D Poisson solver with the material details of the GNRs modeled by the uncoupled mode space Dirac equation. We find that, in general, the GNR tunneling FETs from the 3 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> + 1 family have better <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON</sub> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OFF</sub> characteristics than those from the 3 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> family due to smaller effective masses of the former. A lower drain doping concentration relative to that of the source enhances the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON</sub> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OFF</sub> . Most significantly, we find that a higher doping concentration at the source enhances <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON</sub> but degrades the subthreshold swing (SS). As a function of temperature, the SS shows highly nonlinear behaviors. In terms of intrinsic delay and power-delay product, the GNR tunneling FETs show very promising scaling behaviors and can be optimized to meet the International Technology Roadmap for Semiconductors roadmap requirements through adjustment in doping concentrations and other parameters.