Ballistic Transport Model Research Articles

Diameter dependent performance of high-speed, low-power InAs nanowire field-effect transistors

The diameter dependent performance metrics of InAs nanowire (NW) field-effect transistors (FETs) are investigated using an analytical two-band model and a semiclassical ballistic transport model. The first analysis of the diameter dependence of the current, the gate delay time, the power-delay product, and the energy-delay product of InAs NW FETs, which operate in the quantum capacitance limit (QCL), are presented. Because of its small density of states, which results from the lower electron effective mass, relatively large diameter (⩽60nm) InAs NW FETs operate in the QCL. Both the energy-delay and power-delay products are reduced as the diameter is reduced, and optimum designs are obtained for diameters in the range 10–40nm. Power-delay product varies from 2×10−20to63×10−20J for all devices with a source Fermi level range 0.1–0.2eV. The gate delay time for all devices varies from 4to16fs and decreases as the NW diameter increases. Analytical expressions are derived for the key device metrics for a single-moded device and compared with the numerical results. The NW FETs provide both ultralow-power switching and high speed.

Modeling Heat Transfer in Metal Films by a Third-Order Derivative-In-Time Dissipative and Dispersive Wave Equation

The paper deals with harmonic solutions to the third-order derivative-in-time temperature equation in which θ = θ(x, t) represents a temperature field of a two-temperature model of ballistic heat transport in a metal film, and α is a nonnegative parameter; t and x denote the time and space variables, respectively. It is shown that for a suitably restricted range of the wave numbers k and of the parameter α there are three real-valued harmonic solutions θ i (i = 1, 2, 3) of equation such that θ1 represents a dissipative standing wave with a damping h 1 = h 1(k) > 0, while θ2 and θ3 are both dissipative and dispersive waves moving with the same damping h 2 = h 2(k) >0 and a velocity c = c(k) > 0 in the directions of decreasing and increasing x, respectively. Also, use of the harmonic solutions is made to obtain a closed-form transient-in-time solution to a Cauchy problem for equation in which |x| < ∞, t > 0, and α ≥ 3/2. Numerical results are included.

Conductance Asymmetry of Graphene p-n Junction

We use the nonequilibrium Green function method in the ballistic limit to provide a quantitative description of the conductance of graphene p-n junctions - an important building block for graphene electronics devices. In this paper, recent experiments on graphene junctions are explained by a ballistic transport model, but only if the finite junction transition width <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</sub> is accounted for. In particular, the experimentally observed anomalous increase in the resistance asymmetry between n-n and n-p junctions under low source/drain charge density conditions is also quantitatively captured by our model. In light of the requirement for sharp junctions in applications such as electron focusing, we also examine the p-n junction conductance in the regime where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</sub> is small and find that wave-function mismatch (so-called pseudospin) plays a major role in sharp p-n junctions.

Performance Evaluation of GaAs–GaP Core–Shell-Nanowire Field-Effect Transistors

We evaluate the performance of GaAs-GaP core-shell (C-S)-nanowire (NW) field-effect transistors by employing a semiclassical ballistic transport model. The valence-band structures of GaAs-GaP C-S NWs are calculated by using a kldrp method including the strain effect. The calculations show that the strain causes substantial band warping and pushes valence subbands to move up. We demonstrate that the on current can be enhanced with the strength of strain induced in the core, but an extremely thin equivalent oxide thickness may suppress the effect of the strain-induced current improvement. The achieved results can provide a design guide for optimizing device performance.

Tight-binding and effective mass modeling of armchair graphene nanoribbon FETs

We show that a ballistic quantum transport model based on the effective mass approximation can fairly well describe the I– V characteristics of armchair graphene nanoribbon FETs at all bias conditions, including regimes dominated by direct or band-to-band tunneling, provided first-order non-parabolic corrections be included in the simulation. This is achieved by means of an energy (position) dependent effective mass. The analysis is supported by comparisons with an atomistic tight-binding model.

Uniaxial Stress Dependence of Electrical Properties of Ulrathin Ballistic P-Type Silicon Nanotransistor

. In this paper, in order to determine whether the ballistic current enhancement saturates at very high stress level or can be further improved, the effect of uniaxial stress on the ballistic transport of the double-gated, ultrathin-body p-type silicon nanotransistor is investigated using a self-consistent device simulator, which combines the stress-dependent six-band k.p model and a semiclassical top-of-the-barrier ballistic transport model. Based on a semi-continuum atomistic lattice model, the size-dependent elastic constant correction has been for the first time coupled into this simulator. Our results presented here indicate uniaxial compressive stress at moderate levels improves ballistic performance by about 85% while uniaxial tensile stress slightly reduces ballistic drive current. Interestingly, higher compressively strained channel does not offer higher drive current. Although significant variations in the size-dependent elastic constants are found, the ballistic current shows only a small decrease after considering the elastic constant correction. Furthermore, the competition of injection velocity and carrier density related to hole effective masses is found to play a critical role in determining the performance of the nanotransistors.

High-Speed and Low-Power Performance of n-type InSb/InP and InAs/InP Core/Shell Nanowire Field Effect Transistors for CMOS Logic Applications

AbstractThe performance metrics of highly scaled n-type InSb/InP and InAs/InP core/shell nanowire (NW) field-effect transistors (FETs) are theoretically investigated using an 8-band k•p model and a semiclassical ballistic transport model. We present the ON-current, the intrinsic cut-off frequency, the gate-delay time, the power-delay product, and the energy-delay product of NWFETs with two NW diameters of 10 nm and 12 nm, which operate in the quantum capacitance limit. We compare the results to the numbers predicted or projected for other materials and dimensionalities and find good agreement. Within a source Fermi energy range of 0.1 – 0.3 eV for all devices, the ON-current varies from 7 – 58 μA, the intrinsic cut-off frequency ranges from 8 – 15 THz, the power-delay product varies from 2×10-20 – 9.7×10-19 J, the gate-delay time varies from 2 – 19 fs, and the energy-delay product ranges from 7×10-35 – 1×10-32 Js. These NWFETs, thus, provide both ultra-low power switching and high-speed.

Characteristic Features of 1-D Ballistic Transport in Nanowire MOSFETs

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, we theoretically investigate characteristic features of 1-D, ballistic transport in nanowire (NW) MOSFETs. An analytic model at <formula formulatype="inline"><tex Notation="TeX">$T= 0$</tex></formula> K is first derived using the top-of-the-barrier ballistic transport model. When the drain voltage is low, this model shows that the drain current increases stepwise with increasing gate voltage, and the transconductance vs. gate voltage displays spikes. These features are the most evident signatures of 1-D transport. Next, we examine the finite-temperature performance numerically and show how <formula formulatype="inline"><tex Notation="TeX">$I$</tex></formula>-<formula formulatype="inline"><tex Notation="TeX">$V$</tex></formula> characteristics change as device parameters and temperature are varied. Finally, recently reported silicon NW gate-all-around MOSFETs are analyzed with our model. We show that some quantum features of these experiments can be explained with our simple, ballistic model. This approach may be a possible tool for subband spectroscopy and device performance assessment. </para>

Dimensionality in metal-oxide-semiconductor field-effect transistors: A comparison of one-dimensional and two-dimensional ballistic transistors

One-dimensional (1D) and two-dimensional (2D) metal-oxide-semiconductor field-effect transistors are compared using an approach based on the top-of-the-barrier ballistic transport model. The results for model devices show that 1D and 2D transistors behave quite similarly if the electrostatics is assumed to be perfect. Distinctive features of 1D transport are difficult to observe at room temperature. The effects of band structure on I-V and C-V characteristics of Si and InAs nanowire transistors are also examined using the sp3d5s* tight-binding model. It is found that band structure effects in 1D transistors are most distinctively reflected in the drain current versus gate bias or transconductance versus gate bias for low drain bias at low temperatures. Some effects may also be observed in nanowire C-V characteristics.

Sub-100 Nanometer Channel Length Ge/Si Nanowire Transistors with Potential for 2 THz Switching Speed

Ge/Si core/shell nanowires (NWs) are attractive and flexible building blocks for nanoelectronics ranging from field-effect transistors (FETs) to low-temperature quantum devices. Here we report the first studies of the size-dependent performance limits of Ge/Si NWFETs in the sub-100 nm channel length regime. Metallic nanoscale electrical contacts were made and used to define sub-100 nm Ge/Si channels by controlled solid-state conversion of Ge/Si NWs to NiSixGe y alloys. Electrical transport measurements and modeling studies demonstrate that the nanoscale metallic contacts overcome deleterious short-channel effects present in lithographically defined sub-100 nm channels. Data acquired on 70 and 40 nm channel length Ge/Si NWFETs with a drain-source bias of 0.5 V yield transconductance values of 78 and 91 microS, respectively, and maximum on-currents of 121 and 152 microA. The scaled transconductance and on-current values for a gate and bias voltage window of 0.5 V were 6.2 mS/microm and 2.1 mA/microm, respectively, for the 40 nm device and exceed the best reported values for planar Si and NW p-type FETs. In addition, analysis of the intrinsic switching delay shows that terahertz intrinsic operation speed is possible when channel length is reduced to 70 nm and that an intrinsic delay of 0.5 ps is achievable in our 40 nm device. Comparison of the experimental data with simulations based on a semiclassical, ballistic transport model suggests that these sub-100 nm Ge/Si NWFETs with integrated high-kappa gate dielectric operate near the ballistic limit.

Two deterministic approaches to topography evolution

We discuss two deterministic approaches to model free-molecular transport and reaction inside features on patterned wafers during thermal deposition processes. One approach that has been widely used to model chemical vapor deposition processes, which are largely steady state at the equipment scale, is based upon the ballistic transport and reaction model (BTRM). The major computational burden in BTRM based codes is usually computing the geometry-defined matrix of transmission probabilities; each element of which is used to determine what fraction of material leaving one point on the surface goes to each other point. This computation scales quadratically in the size of the discretizations, but is done in parallel. The second approach to modeling transport and reaction in the free-molecular flow regime is based on the kinetic transport and reaction model (KTRM). The KTRM starts from the Boltzmann equation and is particularly appropriate for processes operated under transient conditions at the reactor scale; e.g., atomic layer deposition. The KTRM is computationally expensive; models in three spatial dimensions require the discretization of the three spatial dimensions, three velocity dimensions, and time for transient studies. The spatial mesh scales with the third power of the system size, for the same resolution. The KTRM is implemented in parallel.

Full-band study of current across silicon nanowire transistors

The authors report an atomistic study of the ballistic current through silicon nanowire metal-oxide-semiconductor transistors. A self-consistent quantum ballistic transport model is used to calculate the current in gate-all-around nanowire transistors, taking into account the full-band structure of the quantum wire with a sp3 tight-binding approach. The authors demonstrate the occurence of an optimal wire cross section for which the on-state/off-state current ratio is maximum, a result which cannot be obtained in a standard bulk effective mass description.

Performance Analysis of a Ge/Si Core/Shell Nanowire Field-Effect Transistor

We ana/lyze the performance of a recently reported Ge/Si core/shell nanowire transistor using a semiclassical, ballistic transport model and an sp3d5s* tight-binding treatment of the electronic structure. Comparison of the measured performance of the device with the effects of series resistance removed to the simulated result assuming ballistic transport shows that the experimental device operates between 60 and 85% of the ballistic limit. For this approximately 15 nm diameter Ge nanowire, we also find that 14-18 modes are occupied at room temperature under ON-current conditions with ION/IOFF = 100. To observe true one-dimensional transport in a 110 Ge nanowire transistor, the nanowire diameter would have to be less than about 5 nm. The methodology described here should prove useful for analyzing and comparing on a common basis nanowire transistors of various materials and structures.

Spin transport at interfaces in magnetic multilayers

We report systematic measurements of resistance dependence on the angle between the magnetizations in magnetic multilayers at 4.2K, with varied configurations and thickness of one of the layers. Our results fall within a wide range of theoretical predictions based on the ballistic or diffusive transport models of the interface. We obtain a small but finite penetration depth of transverse spin current into the ferromagnets by using a diffusive transport model. We also show that the data for trilayers with the smallest thickness of one of the ferromagnetic layers are inconsistent with the existing models.

Improvement of current-control induced by oxide notch in very short field-effect transistor

A two-dimensional quantum ballistic transport model based on the nonequilibrium Green’s function formalism has been used to theoretically investigate the effects induced by an oxide notch in a very short (7 nm) thin-film metal-oxide-semiconductor field-effect transistor. Our investigation shows that a well adjusted notch permits an improvement of on-off current ratio Ion∕Ioff of about 244% with no detrimental change in the drive current Ion. This remarkable result is explained by a nontrivial influence of notch on conduction-band structure in thin film. Therefore, a well optimized notch seems to be a good solution to have a much better control of short channel effects in transistor where the transport has a strong quantum behavior.

Detailed Modeling of Sub-100-nm MOSFETs Based on SchrÖdinger DD Per Subband and Experiments and Evaluation of the Performance Gap to Ballistic Transport

We analyze in detail the requirements for the detailed physical modeling of nanoscale MOSFETs and show that Schro/spl uml/dinger drift-diffusion per subband simulations are adequate for the inverse modeling of bulk-Si MOSFETs with gate length down to 40 nm (channel length down to 26 nm) from their dc electrical characterization. We show that a proper treatment of quantum effects both in the channel and in the polysilicon gate through the direct solution of Schro/spl uml/dinger equation, and a transport model based on two-dimensional subbands are required for accurate and-after calibration-predictive modeling. The model is included in the NANOTCAD2D code (Curatola and Iannaccone, 2003). We also evaluate the performance gap to ballistic transport, by comparing the experiments with simulations based on a fully ballistic transport model on the devices structures extracted with the inverse modeling procedure.

Modeling of a ferromagnetic two-dimensional electron gas device

We present a realistic modeling of ballistic electron transport in a hybrid ferromagnetic (FM) two-dimensional electron gas (2DEG) device, consisting of an FM gate on an AlGaAs-GaAs or AlSb-InAs high electron mobility transistor (HEMT) heterostructure. The carriers within the 2DEG are spin-polarized by a combination of magnetic and electrostatic barriers. The magnetic barriers are supplied by a composite FM gate, consisting of two domains made of magnetically hard and soft materials. This gate arrangement breaks the antisymmetry of the fringe B field, and results in a finite spin polarization of the 2DEG current. The B field strength is calculated by considering the pole strength at the gate surfaces and domain boundary, and is significantly weaker than normally assumed. We obtain parameters such as the electrostatic barrier height, Fermi level, and carrier concentration within the 2DEG by a finite-element Poisson calculation, which is self-consistent with the Fermi-Dirac distribution. We calculate the transmission probability and conductance through the 2DEG from these parameter values, assuming a single particle effective mass Hamiltonian and purely ballistic transport. We show that the spin polarization ratio P/sub G/ is extremely sensitive to the gate bias and HEMT doping concentration. However, the maximum P/sub G/ is extremely low for AlGaAs-GaAs (0.003%) and even for AlSb-InAs (0.12%) devices, despite a large Lande g factor. These values are many orders of magnitude smaller than previous predictions of close to 100% polarization, obtained by using simpler models.

Lorentz magnetoresistance of thin films in the presence of surface scattering and domain structures

A modeling of ballistic electronic transport in thin films with diffuse surface scattering in the presence of a magnetic domain structure is performed. The conductance is obtained from the diffusive mean-square displacement of the conductance electrons. Lorentz magnetoresistance (LMR) effects for several domain structures are simulated and compared to corresponding experiments. We conclude that there is no reason to assume an intrinsic domain-wall resistance (DWR) in pure iron and cobalt films in order to explain experimental results. More generally, simulation results indicate that additional LMR related to the domain structure is best understood in terms of three separate effects, which all scale with the LMR of the homogenously magnetized film.

Subband decomposition approach for the simulation of quantum electron transport in nanostructures

The modeling of ballistic quantum transport in ultimate size semiconductor devices usually involves a self-consistent solution between the Schrödinger and the Poisson equations. In the 2D or 3D real space, this procedure requires huge computer resources to obtain the I– V characteristics. The general approach proposed in this article relies on the decomposition of the wave function on subband eigenfunctions, which account for the confinement of the electrons in the whole structure. The method can be applied to study large 2D and 3D real systems with a drastic reduction of the numerical cost, since the dimension of the transport problem for the Schrödinger equation is now reduced in real space. The results obtained for the 2D nanoscale MOSFETs show the efficiency of the algorithm and allow to estimate the effects of the coupling between the subbands. The asymptotic approach of the subband decomposition is also presented for devices showing a strong confinement for the electron gas as the 3D electron waveguide devices.

Three-dimensional deposition topography simulation based on new combinations of flux distribution and surface representation algorithms

The development of a full three-dimensional (3-D) deposition topography simulator is indispensable to the precise estimation of thin film deposition topography on asymmetric deposition geometries. In this study, we expand the application range of the equi-volume rate model (EVRM), a cell-based surface representation algorithm for full 3-D topography simulation, into rigorous flux distribution algorithms such as the Monte Carlo method (MCM) and the ballistic transport and reaction model (BTRM). A new full 3-D deposition topography simulation is conducted based on the new combinations of flux distribution and surface representation algorithms. To ensure the effectiveness of our simulation, we conduct numerous simulations for various deposition geometries with varying sticking coefficients and directionality factors. We also compare the simulation results of MCM-EVRM and BTRM-EVRM versions. From the viewpoint of precise simulated topography, a particle-based MCM has better suitability to a cell-based EVRM than a flux-based BTRM. In addition, from the viewpoint of computational time, the MCM-EVRM method is apt for the complex geometries and for the deposition processes of high sticking coefficient; such as physical vapor deposition and plasma enhanced chemical vapor deposition. In the other hand, the BTRM-EVRM method is suitable for the simple geometries and for the processes of low sticking coefficient such as chemical vapor deposition.