Contact Block Reduction Research Articles

Numerical analysis of transmission coefficient, LDOS, and DOS in superlattice nanostructures of cubic $$\hbox {Al}_{x}\hbox {Ga}_{1-x}\hbox {N/GaN}$$ Al x Ga 1 - x N/GaN resonant tunneling MODFETs

Numerical analysis of the transmission coefficient, local density of states, and density of states in superlattice nanostructures of cubic $$\hbox {Al}_{x}\hbox {Ga}_{1-x}\hbox {N/GaN}$$AlxGa1-xN/GaN resonant tunneling modulation-doped field-effect transistors (MODFETs) using $$\hbox {next}{} \mathbf{nano}^{3}$$nextnano3 software and the contact block reduction method is presented. This method is a variant of non-equilibrium Green's function formalism, which has been integrated into the $$\hbox {next}\mathbf{nano}^{3}$$nextnano3 software package. Using this formalism in order to model any quantum devices and estimate their charge profiles by computing transmission coefficient, local density of states (LDOS) and density of states (DOS). This formalism can also be used to describe the quantum transport limit in ballistic devices very efficiently. In particular, we investigated the influences of the aluminum mole fraction and the thickness and width of the cubic $$\hbox {Al}_{x}\hbox {Ga}_{1-x}\hbox {N}$$AlxGa1-xN on the transmission coefficient. The results of this work show that, for narrow width of 5 nm and low Al mole fraction of $$x = 20\,\%$$x=20% of barrier layers, cubic $$\hbox {Al}_{x}\hbox {Ga}_{1-x}\hbox {N/GaN}$$AlxGa1-xN/GaN superlattice nanostructures with very high density of states of 407 $$\hbox {eV}^{-1}$$eV-1 at the resonance energy are preferred to achieve the maximum transmission coefficient. We also calculated the local density of states of superlattice nanostructures of cubic $$\hbox {Al}_{x}\hbox {Ga}_{1-x}\hbox {N/GaN}$$AlxGa1-xN/GaN to resolve the apparent contradiction between the structure and manufacturability of new-generation resonant tunneling MODFET devices for terahertz and high-power applications.

Analysis of ballistic transport in nanoscale devices by using an accelerated finite element contact block reduction approach

An accelerated Finite Element Contact Block Reduction (FECBR) approach is presented for computational analysis of ballistic transport in nanoscale electronic devices with arbitrary geometry and unstructured mesh. Finite element formulation is developed for the theoretical CBR/Poisson model. The FECBR approach is accelerated through eigen-pair reduction, lead mode space projection, and component mode synthesis techniques. The accelerated FECBR is applied to perform quantum mechanical ballistic transport analysis of a DG-MOSFET with taper-shaped extensions and a DG-MOSFET with Si/SiO2 interface roughness. The computed electrical transport properties of the devices obtained from the accelerated FECBR approach and associated computational cost as a function of system degrees of freedom are compared with those obtained from the original CBR and direct inversion methods. The performance of the accelerated FECBR in both its accuracy and efficiency is demonstrated.

Efficient self-consistent quantum transport simulator for quantum devices

We present a self-consistent one-dimensional (1D) quantum transport simulator based on the Contact Block Reduction (CBR) method, aiming for very fast and robust transport simulation of 1D quantum devices. Applying the general CBR approach to 1D open systems results in a set of very simple equations that are derived and given in detail for the first time. The charge self-consistency of the coupled CBR-Poisson equations is achieved by using the predictor-corrector iteration scheme with the optional Anderson acceleration. In addition, we introduce a new way to convert an equilibrium electrostatic barrier potential calculated from an external simulator to an effective doping profile, which is then used by the CBR-Poisson code for transport simulation of the barrier under non-zero biases. The code has been applied to simulate the quantum transport in a double barrier structure and across a tunnel barrier in a silicon double quantum dot. Extremely fast self-consistent 1D simulations of the differential conductance across a tunnel barrier in the quantum dot show better qualitative agreement with experiment than non-self-consistent simulations.

Feasibility, accuracy, and performance of contact block reduction method for multi-band simulations of ballistic quantum transport

Numerical utilities of the contact block reduction (CBR) method in evaluating the retarded Green’s function are discussed for 3D multi-band open systems that are represented by the atomic tight-binding (TB) and continuum k·p (KP) band model. It is shown that the methodology to approximate solutions of open systems, which has been already reported for the single-band effective mass model, cannot be directly used for atomic TB systems, since the use of a set of zinc blende crystal grids makes the inter-coupling matrix non-invertible. We derive and test an alternative with which the CBR method can be still practical in solving TB systems. This multi-band CBR method is validated by a proof of principles on small systems and also shown to work excellent with the KP approach. Further detailed analysis on the accuracy, speed, and scalability on high performance computing clusters is performed with respect to the reference results obtained by the state-of-the-art recursive Green’s function and wavefunction algorithm. This work shows that the CBR method could be particularly useful in calculating resonant tunneling features, but shows a limited practicality in simulating field effect transistors (FETs) when the system is described with the atomic TB model. Coupled to the KP model, however, the utility of the CBR method can be extended to simulations of nanowire FETs.

Simulation of quantum transport in double‐gate MOSFETs using the non‐equilibrium Green's function formalism in real‐space: A comparison of four methods

AbstractQuantum effects play an important role in determining the double‐gate (DG) MOSFETs characteristics. The non‐equilibrium Green's function formalism (NEGF) in real‐space (RS) representation provides a rigorous description of quantum transport in nanoscale devices. Unfortunately, the traditional NEGF framework has the disadvantage of being heavy in computations. Methods that reduce the computations exist in the literature like the recursive Green's Function (RGF) algorithm, the contact block reduction (CBR) method, and Gauss elimination (GE) method. Comparison of the simulation time of the traditional NEGF, the RGF algorithm, the CBR method, and the GE method was always theoretical and based on approximate estimates. In this work, we carry out a real comparison between the four methods by implementing them inside the same simulator, using them to simulate the same device dimensions and parameters on the same machine. It is demonstrated that the RGF algorithm or the GE method introduce about one order of magnitude reduction in simulation time below that traditional NEGF, whereas the CBR method yields the smallest simulation time with about two orders of magnitude reduction. Copyright © 2010 John Wiley & Sons, Ltd.

High-Order Element Effects of the Green's Function in Quantum Transport Simulation of Nanoscale Devices

High-order element (HOE) effects of the Green's function are studied by virtue of a comparative study between the recursive Green's function (RGF) method and the contact block reduction approach in double-gate metal-oxide-semiconductor field-effect transistor simulations. In general, quantum-mechanical simulations of 2-D and 3-D nanoscale devices are very computationally challenging. An efficient and widely used approach for the multidimensional problems is the RGF method. As the tridiagonal or block tridiagonal property of a self-energy matrix is exploited in the RGF method, the HOEs of the gate contact self-energy matrix are often omitted. This study on the HOE effects offers a good physical insight as well as provides a necessary measure on the applicability of the RGF method. Specifically, effects on gate current, electron density, and current density are investigated.

Ballistic quantum transport using the contact block reduction (CBR) method

The contact block reduction (CBR) method is a variant of the nonequilibrium Green’s function formalism and can be used to describe quantum transport in the ballistic limit very efficiently. We present a numerical implementation of a charge self-consistent version of the CBR algorithm. We show in detail how to calculate the electronic properties of open quantum systems such as the transmission function, the local density of states and the carrier density. Several 1D and 2D examples are provided to illustrate the key points. The CBR method is a very powerful tool to tackle the challenge of calculating transport in the ballistic limit for 3D devices of arbitrary shape and with an arbitrary number of contacts.

Simulation of the Impact of Process Variation on the Optimized 10-nm FinFET

We examined the influence of process variation on device performance of the optimized 10-nm FinFET device using a fully self-consistent quantum-mechanical transport simulator based on the contact block reduction method. Sensitivity of the on-current, leakage currents, threshold voltage, drain-induced barrier lowering, and subthreshold swing for the optimized FinFET to process variation at room temperature have been investigated. Subthreshold source-to-drain leakage current is found to be the most sensitive parameter to process variation. Gate leakage current has been analyzed for both poly-Si gates and gates with the work function of 4.35 eV. For poly-Si gates, the gate leakage is found to influence the subthreshold swing below or at a gate oxide thickness of 1 nm. Device performance has also been analyzed at ldquoslow processrdquo corner to estimate the worst case degradation in performance matrices of the considered nano-FinFET.

Approaching Optimal Characteristics of 10-nm High-Performance Devices: A Quantum Transport Simulation Study of Si FinFET

We utilized a fully self-consistent quantum mechanical simulator based on the contact block reduction (CBR) method to optimize a 10 nm FinFET device and meet the International Technology Roadmap for Semiconductors (ITRS) projections for double-gate high-performance logic technology devices. We found that the device ON-current approaching the value projected by the ITRS can be obtained using a conventional unstrained Si channel and a SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gate insulator. We also performed a detailed analysis of the gate leakage under different bias conditions. Our simulation results show that the quantum mechanical effects significantly enhance the intrinsic switching speed of the device. In our simulations, quantum confinement in both the gates and the channel has been taken into account self-consistently. The obtained theoretical value of the intrinsic switching speed for the considered FinFET device exceeds the ITRS-projected value.

3D NEGF quantum transport simulator for modeling ballistic transport in nano FinFETs

Quantum effects play a dominant role in many of the state-of-the-art small size structures for which the applicability of the standard well-developed engineering tools based on a semi-classical transport description is very limited or even impossible. There are a number of methods developed by solid state theorists over the last several decades to address the issue of quantum transport. Among the most commonly used in nanostructure calculations schemes are the Wigner-function approach, the Pauli master equation, and the non-equilibrium Green's functions (NEGF). The growing popularity of the latest (sometimes referred to as the Keldysh or the Kadanoff-Baym) formalism is conditioned by its sound conceptual basis for the development of the new class of quantum transport simulators. We demonstrate in this work that the key to the successful application of the NEGF formalism to the 3D quantum transport problem in semiconductor nanostructures is the numerical efficiency of the contact block reduction (CBR) method. We also present some very important results from the 3D FinFET analysis, such as the importance of the third gate.

Fully 3D self-consistent quantum transport simulation of Double-gate and Tri-gate 10 nm FinFETs

We utilize a fully self-consistent 3D quantum mechanical simulator based on the Contact Block Reduction (CBR) method to investigate the effects of fin height and unintentional dopant on the device characteristics of a 10-nm FinFET device. The per-fin height off-current is found to be relatively insensitive to fin height while the corresponding per fin height on-current may significantly depend on fin height due to the stronger confinement with decreasing fin height. Also gate leakage is found to show similar behavior as device on-current with decreasing fin height. Tri-gate (TG) FinFET is found to show better performance compared to Double-gate (DG) FinFET, with the exception of gate leakage current. Simulation results show that an unintentional dopant within the channel can significantly alter device characteristics depending on its position and applied biases. In addition, the effects of unintentional dopant are found to be stronger at high drain bias than at low drain bias.

Influence of interface roughness on quantum transport in nanoscale FinFET

The authors utilize a fully quantum mechanical transport simulator based on the contact block reduction method to investigate the influence of interface roughness in nanoscale FinFET devices. In this work we treat interface roughness by creating a random deviation at the ideal Si∕SiO2 interface in real space and then solving the quantum transport problem fully self-consistently with the gates for the resulting device potential. We study the influence of interface roughness on device capacitance, drain current, and gate leakage for different regimes of operation. Our simulation results show that gate leakage is significantly affected by surface roughness, even though the average oxide thickness remains approximately the same. On the other hand, the on current is comparatively less sensitive to the interface roughness for FinFET devices with a narrow fin width. Furthermore, we find that the interface roughness significantly affects both the intrinsic switching speed and, especially, the cutoff frequency of FinFET with a narrow fin thickness.

Assessment of the CBR Quantum Transport Simulator on Experimentally Fabricated Nano-FinFET

We have utilized fully self-consistent quantum mechanical simulator based on Contact Block Reduction (CBR) method, to simulate experimentally fabricated 10nm FinFET device. A series of simulations have been performed with varying S/D extension length and doping profile to match the experimental data. The simulation results have been found to be in good agreement with the experimental data in the subthreshold regime. Small signal analysis has been performed to extract device capacitances and to compare the intrinsic propagation delay to that of the experimental device.

Quantum Transport Simulation of Experimentally Fabricated Nano-FinFET

We have utilized the contact-block-reduction (CBR) method, which we extended to allow a charge self-consistent scheme, to simulate experimentally fabricated 10-nm-FinFET device. The self-consistent CBR simulator has been modified to simulate devices with channels along arbitrary crystallographic orientation. A series of fully quantum-mechanical transport simulations has been performed. First, the fin extension length and doping profile have been calibrated to match the experimental data. The process control window for the threshold voltage as a function of fin extension has been extracted for the considered device. Then, a set of transfer characteristics and gate leakage currents have been calculated for different drain voltages. The simulation results have been found to be in good agreement with the experimental data in the subthreshold regime. The device turn-off and turn-on behavior has been examined for different fin widths: 12 (experimental), 10, 8, and 6 nm. Finally, the subthreshold slope degradation at high temperatures has been studied

Self-consistent treatment of quantum transport in 10 nm FinFET using Contact Block Reduction (CBR) method

A fully quantum mechanical approach must be utilized to investigate the characteristics of nanoscale semiconductor devices and capture the essential physics with high accuracy. In this work a very efficient quantum mechanical transport simulator based on Contact Block Reduction (CBR) method is used to analyze the behavior of 10 nm FinFET device in the quasi-ballistic regime of operation. Simulation results depict the transformation of multiple channels into a single merged channel across the fin as the fin width is reduced gradually. Also we observe that short channel effects can be minimized by reducing the fin thickness, which is evident from the device transfer characteristics for different fin thickness presented in this paper. A comparison of simulation results with the available experimental data is presented. An optimized 10 nm gate length FinFET structure is suggested.

Ballistic Quantum-Mechanical Simulation of 10nm FinFET Using CBR Method

Simulating nanoscale devices with high accuracy, particularly towards 10nm feature sizes, requires highly efficient fully quantum mechanical simulators. In this work fully quantum mechanical simulator based on Contact Block Reduction (CBR) method has been used to investigate the behaviour of 10nm FinFET device in the ballistic regime of operation. Simulation results show the transformation from multiple channels into a single merged channel as the fin width is reduced gradually. Also we observe that short channel effects can be minimized by reducing the fin width which is evident from the device transfer characteristics presented in this paper.

Contact block reduction method for ballistic transport and carrier densities of open nanostructures

A method is presented for quantum-mechanical ballistic transport calculations of realistic two- and three-dimensional open devices that may have any shape and any number of leads. Observables of the open system can be calculated with an effort comparable to a single calculation of a suitably defined closed system. The method is based on a previously developed scheme for calculating transmission functions, the contact block reduction method, and is shown to be applicable to the density matrix, the density of states, and the local carrier density. The electronic system may be characterized by a single or multiband Hamiltonian. We illustrate the method for the four-band GaAs hole transport through a two-dimensional three-terminal T-junction device and for the electron tunneling through a three-dimensional InAs quantum dot molecule embedded into an InP heterostructure.

Contact block reduction method and its application to a 10 nm MOSFET device

With the scaling of semiconductor devices to nano-size dimensions, gate lengths reach their physical limits of 8–15 nm. In such devices, a variety of undesirable effects begin to be prominent, including gate leakage, discrete impurity effects and source-to-drain tunnelling. To address the issue of source-to-drain tunnelling we apply to a prototypical 10 nm MOSFET device a novel highly efficient method, termed contact block reduction (CBR) method. It has been reported recently [1] that the CBR method allows us to calculate the ballistic current (transmission function) through an arbitrarily shaped, multi-terminal two- or three-dimensional device. Here we show that in the ballistic case the density matrix of the open device can be computed using the same method. This opens a possibility for an efficient fully quantum-mechanical self-consistent calculation within the ballistic limit.

Prediction of a realistic quantum logic gate using the contact block reduction method

We present a theoretical study of the realization of a quantum logic gate based on a laterally structured high mobility GaAs/AlGaAs 2DEG. The I–V characteristics exhibit a pronounced switching behaviour which demonstrates that quantum logic gates can be fabricated and operated experimentally. The calculations have been performed with the recently developed contact block reduction method. We show that this method can be readily extended to multi-band k ⋅ p-Hamiltonians while retaining its efficiency.

Electron Density Calculation Using the Contact Block Reduction Method

A novel efficient method to calculate the ballistic quantum transport in two or three dimensional multi-terminal devices of arbitrary geometry, potential profile and number of leads has been presented. In this work we show that the method termed contact block reduction (CBR) allows calculation of not only the transmission function, but the electron density and density matrix of the device as well. The calculation costs are mainly determined by the size of the contact boundaries of the device.