Transport calculationof Semiconductor Nanowires Coupled to Quantum Well Reservoirs

Semiconductor nanowires are possible candidates to replace the metal-oxide-semiconductor field-effect transistors (MOSFET) since they can act both as active devices or as device connectors. In this article, the transmission coefficients of Si and GaAs nanowires with arbitrary transport directions and cross sections are simulated in the nearest-neighbor sp³d⁵s* semi-empirical tight-binding method. The open boundary conditions (OBC) are calculated with a new scattering boundary method where a normal eigenvalue problem of reduced size is solved. Two different types of contacts are studied. In the ideal case, semi-infinite reservoirs (the source and the drain) that are the prolongation of the device are assumed. In a more realistic configuration, the active nanowire is embedded between two quantum well (QW) reservoirs. The electrical properties of the device are obtained by a non-equilibrium Green’s function (NEGF) calculation.     

Hierarchical simulation of transport in silicon nanowire transistors

We propose a very fast hierarchical simulator to study the transport properties of silicon nanowire FETs. We obtain the transverse wave functions and the longitudinal effective masses and band-edges of the lowest conduction bands from a nearest-neighbor sp ³ d ⁵ s ^* tight-binding study of an infinite nanowire with null external potential. Then we plug these parameters into a self-consistent Poisson-Schrödinger solver, using an effective mass approach and considering the bands decoupled. We apply this method, which gives quantitatively correct results with notable time savings, for the simulation of transport in two different silicon nanowire FETs.     

Electronic structure and transmission characteristics of SiGe nanowires

Atomistic disorder such as alloy disorder, surface roughness and inhomogeneous strain are known to influence electronic structure and charge transport. Scaling of device dimensions to the nanometer regime enhances the effects of disorder on device characteristics and the need for atomistic modeling arises. In this work SiGe alloy nanowires are studied from two different points of view: (1) Electronic structure where the bandstructure of a nanowire is obtained by projecting out small cell bands from a supercell eigenspectrum and (2) Transport where the transmission coefficient through the nanowire is computed using an atomistic wave function approach. The nearest neighbor sp³d⁵s^* semi-empirical tight-binding model is employed for both electronic structure and transport. The connection between dispersions and transmission coefficients of SiGe random alloy nanowires of different sizes is highlighted. Localization is observed in thin disordered wires and a transition to bulk-like behavior is observed with increasing wire diameter.     

Electronic and transport properties of silicon nanowires

The electronic, structural and transport properties of silicon nanowires have been investigated with different approaches. The Empirical Tight-Binding model (ETB) and Linear Combination of Bulk Bands (LCBB) method are used to calculate effect of quantum confinement on electronic energies, bandgap and effective masses in silicon nanowires in function of Si cell size. Both hydrogenated and SiO₂ terminated silicon surfaces are studied. Transport properties of nanowires are obtained by applying the Non-Equilibrium Green Function (NEGF) method. NEGF approach has been used to describe nanoMOSFET devices based on Silicon nanowires.     

Numerical simulation of hole transport in silicon nanostructures

In order to study the trade-off between accuracy and computational costs in p-type device simulation, we have simulated hole transport in one-dimensional Si p⁺pp⁺ structures within a nonequilibrium Green’s function formalism combining with three different types of methods for band structure calculation; an empirical sp³d⁵s* tight-binding method, k⋅p two-band approximation, and effective-mass approximation.     

Full-band particle-based simulation of 85 nm AlInSb/InSb quantum well transistors

In this work, Indium Antimonide (InSb) quantum well transistors are investigated using full-band Cellular Monte Carlo simulations. Both Depletion and Enhancement transistors are simulated, the latter being modeled using a deep recess gate. The steady-state characteristics of the devices are analyzed showing an average sub-threshold slope of 326 mV/dec and a DIBL of 569 mV/V. The small-signal behavior of the depletion and enhancement mode transistors is also investigated, and an average cut-off frequency of 380 GHz is computed. Finally, a comparison is performed between the different transistors showing all the advantages of the deep recess gate configuration such as a better sub-threshold slope and cutoff frequency.     

Non-equilibrium quantum transport theory: current and gain in quantum cascade lasers

We have developed a self-consistent non-equilibrium Green’s function theory (NEGF) for charge transport and optical gain in THz quantum cascade lasers (QCL) and present quantitative results for the I-V characteristics, optical gain, as well as the temperature dependence of the current density for a concrete GaAs/Al_.15Ga_.85As QCL structure. Phonon scattering, impurity, Hartree electron-electron and interface roughness scattering within the self-consistent Born approximation are taken into account. We show that the characteristic QCL device properties can be successfully modeled by taking into account a single period of the structure, provided the system is consistently treated as open quantum system. In order to support this finding, we have developed two different numerically efficient contact models and compare single-period results with a quasi-periodic NEGF calculation. Both approaches show good agreement with experiment as well as with one another.     

Phonon exacerbated quantum interference effects in III-V nanowire transistors

In recent years, a great deal of attention has been focused on the development of quantum wire transistors as a means of extending Moore’s Law. Here we present, results of fully three-dimensional, self-consistent quantum mechanical device simulations of InAs tri-gate nanowire transistor (NWT). The effects of inelastic scattering have been included as real-space self-energy terms. We find that the position of dopant atoms in these devices can lead a reduction in the amount of scattering the carriers experience. We find that the combination of deeply buried dopant atoms and the high energy localization of polar optical phonon processes allow devices to recover their ballistic behavior even in the presence of strong inelastic phonon processes. However, we find that dopant atoms close to the source-channel interface cause severe quantum interference effects leading to significant performance reduction.     

Self-consistent quantum transport theory: Applications and assessment of approximate models

We have implemented a fully self-consistent non-equilibrium Green’s function approach for vertical quantum transport in open quantum devices with contacts and study theoretically quantum well heterostructures, resonant tunneling diodes and quantum cascade laser structures in this formalism. We systematically investigate the role and consequences of several widely used approximations such as decoupling the equations for the scattering states and their occupation, neglect of inelastic scattering, and neglect of nonlocal scattering self-energies.     

Scaling dependence of electron transport in nano-scale Schottky barrier MOSFETs

The scaling dependence of electron transport in the double-gated Schottky barrier MOSFET (DG-SBT) below 10 nm is investigated in the framework of quantum transport theory, using non-equilibrium Green’s function method. Simulation results show that the current-voltage characteristics in ultra-small DG-SBT are characterized by both resonant and direct tunneling effects. The electron potential in the 10-nm-scale DG-SBT surrounded by Schottky barriers acts as a resonant cavity and produce a negative differential resistance due to resonant tunneling effect. While, further scaling shallows the depth of the cavity and makes it difficult to form resonance levels. Hence, at the scaling limit, direct tunneling currents simply dominate the current-voltage characteristics of DG-SBT.     

Effect of elastic processes and ballistic recovery in silicon nanowire transistors

Scaling of silicon devices is fast approaching the limit where a single gate may fail to retain effective control over the channel region. Of the alternative device structures under focus, silicon nanowire transistors (SNWT) show great promise in terms of scalability, performance, and ease of fabrication. Here we present the results of self-consistent, fully 3D quantum mechanical simulations of SNWTs to show the role of surface roughness (SR) and ionized dopant scattering on the transport of carriers. We find that the addition of SR, in conjunction with impurity scattering, causes additional quantum interference which increases the variation of the operational parameters of the SNWT. However, we also find that quantum interference and elastic processes can be overcome to obtain nearly ballistic behavior in devices with preferential dopant configurations.     

General 2D Schrödinger-Poisson solver with open boundary conditions for nano-scale CMOS transistors

Employing the quantum transmitting boundary (QTB) method, we have developed a two-dimensional Schrödinger-Poisson solver in order to investigate quantum transport in nano-scale CMOS transistors subjected to open boundary conditions. In this paper we briefly describe the building blocks of the solver that was originally written to model silicon devices. Next, we explain how to extend the code to semiconducting materials such as germanium, having conduction bands with energy ellipsoids that are neither parallel nor perpendicular to the channel interfaces or even to each other. The latter introduces mixed derivatives in the 2D effective mass equation, thereby heavily complicating the implementation of open boundary conditions. We present a generalized quantum transmitting boundary method that mainly leans on the completeness of the eigenstates of the effective mass equation. Finally, we propose a new algorithm to calculate the chemical potentials of the source and drain reservoirs, taking into account their mutual interaction at high drain voltages. As an illustration, we present the potential and carrier density profiles obtained for a (111) Ge NMOS transistor as well as the ballistic current characteristics.     

Scattering resonances in 1D coherent transport through a correlated quantum dot: An application of the few-particle quantum transmitting boundary method

We present a method for the calculation of the scattering states of a N+1th-particle coherently interacting with N correlated particles confined in a nanostructure and placed within an open domain. The method is based on a generalization of the quantum transmitting boundary method [C. Lent and D. Kirkner, J. App. Phys. 67, 6353 (1990)]. The antisymmetry conditions of the N+1-identical particles current-carrying state results from a proper choice of the boundary conditions. As an example which is relevant to coherent electronics, we apply the method to compute the exact transmission functions and phases of an electron crossing a 1D quantum dot with zero, one or two bound electrons.     

Semiclassical transport in silicon nanowire FETs including surface roughness

In this paper we investigate the effect of surface roughness scattering on transport in silicon nanowire FETs using a deterministic Boltzmann equation solver previously developed by the authors. We first solve the coupled Schrödinger-Poisson equations to extract the subband profiles along the channel, and then address the transport problem. Some features of the low-field mobility as a function of the wire diameter and gate bias are discussed and the effect of surface roughness on the I–V characteristics is presented.     

Transport in open quantum systems: comparing classical and quantum phase space dynamics

Transport in open quantum systems is of great interest. We show that the discrete states of an open quantum system may be classified into three distinct groups, dependent upon the manner in which they influence transport when connected to an external environment. A first class of states is current-carrying states, which are naturally strongly connected to the environment. A second class of states is discrete, but stable and isolated, and thought to be the pointer states of decoherence theory. Finally, we identify backscattered states, which do not propagate through the system.     

A new approach for numerical simulation of quantum transport in double-gate SOI

Numerical simulation of nanoscale double-gate SOI (Silicon-on-Insulator) greatly depends on the accurate representation of quantum mechanical effects. These effects include, mainly, the quantum confinement of carriers by gate-oxides in the direction normal to the interfaces, and the quantum transport of carriers along the channel. In a previous work, the use of transfer matrix method (TMM) was proposed for the simulation of the first effect. In this work, TMM is proposed to be used for the solution of Schrodinger equation with open boundary conditions to simulate the second quantum-mechanical effect. Transport properties such as transmission probability, carrier concentration, and I–V characteristics resulting from quantum transport simulation using TMM are compared with that using the traditional tight-binding model (TBM). Comparison showed that, when the same mesh size is used in both methods, TMM gives more accurate results than TBM. Copyright © 2007 John Wiley & Sons, Ltd.     

锅炉与电厂管道系统应力分析关系探讨

对现行锅炉管道系统应力分析和电厂管道系统应力分析关系的处理方法进行分析,提出了联合计算、调整锅炉要求、不平衡广义力分配等改进方法。不平衡广义力分配法,力学概念清楚,操作简便,误差不到7%,比较接近联合计算的结果,推荐使用。     

Boundary conditions in TLM diffusion modelling

The connection algorithms used in transmission‐line matrix (TLM) modelling of diffusion processes for describing boundary conditions in both link‐line and link‐resistor nodal configurations have been derived. The new algorithms regarding the inhomogeneous Robin condition enhance the capability of the TLM method in simulating thermal or particle diffusion phenomena. A number of boundary treatments in the existing literature have been found to be special cases of our results. The Dirichlet‐type boundary condition is also discussed. TLM numerical results using the new algorithms, particularly with the link‐resistor model for achieving signal synchronization, are shown to be in excellent agreement with the available analytical solutions. Copyright © 2006 John Wiley & Sons, Ltd.     

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.