Electro-thermal simulation based on coupled Boltzmann transport equations for electrons and phonons

To study the thermal effect in nano-transistors, a simulator solving self-consistently the Boltzmann transport equations for both electrons and phonons has been developed. It has been used to investigate the self-heating effects in a 20 nm-long double-gate MOSFET (Fig. 1). A Monte Carlo solver for electrons is coupled with a direct solver for the steady-state phonon transport. The latter is based on the relaxation time approximation. This method is particularly efficient to provide a deep insight of the out-of-equilibrium thermal dissipation occurring at the nanometer scale when the device length is smaller than the mean free path of both charge and thermal carriers. It allows us to evaluate accurately the phonon emission and absorption spectra in both real and energy spaces.     

Impact of the Coulomb interaction on nano-scale silicon device characteristics

Monte Carlo simulations coupled self-consistently with the three-dimensional Poisson equation are carried out under the double-gate MOSFET structures. The Coulomb force experienced by an electron inside the device is directly evaluated by performing the Monte Carlo simulations with or without the full Coulomb interaction and the Coulomb force on the channel electron corresponding to plasmon excitations is clarified. It is pointed out that the consistency of the boundary condition is achieved only if the long-range Coulomb interaction is properly taken into account, and this is crucial for predicting reliable device characteristics in ultra-small devices. The drain current and transconductance are greatly reduced if the self-consistent potential fluctuations are taken into account.     

Modeling p-channel SiGe MOSFETs by taking into account the band-structure and the size quantization effects self-consistently

The purpose of this work is to develop new approach to modeling p-channel devices using a 2D Monte Carlo transport kernel that is coupled self-consistently to a 2D Poisson equation solver and to a six-band k.p band-structure module. The need for full band solvers for hole transport is especially true in case of surface channel strained Si and buried channel strained SiGe p-MOSFETs investigated here. We have paid special attention on properly implementing and investigating the role of interface-roughness on the operation of these device structures.     

Self-Consistent Quantum Mechanical Monte Carlo MOSFET Device Simulation

We have developed a self-consistent quantum mechanical Monte Carlo device simulator that takes electron transport in quantized states into consideration. Two-dimensional quantized states in MOSFET channels are constructed from one-dimensional solutions of the Schrödinger equation at different positions along the channel, and the Schrödinger and Poisson equations are solved self-consistently in terms of electron concentration and electrostatic potential distribution. The channel electron concentration, velocity and drain currents are calculated with the one particle Monte Carlo approach incorporating the intra-valley acoustic phonon and inter-valley phonon scattering mechanisms. This simulator was applied to a 70 nm n-MOSFET transistor, and we found that current mostly flows through the lowest subband and transport is quasi-ballistic near the source junction. To quantitatively estimate the performance of advanced devices, we have developed an inversion carrier transport simulator based on a full-band model. Our simulation method enables us to evaluate device characteristics and analyze the transport properties of ultra-small MOSFETs.     

Quantum Ensemble Monte Carlo simulation of silicon-based nanodevices

A Quantum Ensemble Monte Carlo (QEMC) simulator is used to calculate electrical characteristics and transient response of actual nanotransistors: both sub-50 nm CMOS N-MOSFETs and ultrathin double gate SOI transistors have been deeply studied. Doping profiles and oxide thickness have been selected to cope with the available specifications of the ITRS Roadmap. The Quantum corrected Ensemble Monte Carlo simulator (QEMC) has been used to self-consistently solve the Boltzmann Transport and Poisson equations in actual devices. Quantum effects are included through the Multi-Valley Effective Conduction Band Edge (MV-ECBE) technique, and adequate approaches for phonon and surface roughness scattering have been developed to include the effects of carrier quantization in pseudo-2DEG simulations.     

Monte Carlo simulation of low-field mobility in strained double gate SOI transistors

Electron transport in strained double gate silicon on insulator transistors has been studied by Monte Carlo method. Poisson and Schroedinger equations have been self-consistently solved in these devices for different silicon layer thicknesses both for unstrained and strained silicon channels. The results show that the strain of the silicon layer leads to a larger population of the no-primed subbands, thus decreasing the average conduction effective mass. However, strain also contributes to a larger confinement of the charge close to the two Si/SiO₂ interfaces, thus weakening the volume inversion effect, and limiting the potential increase of the phonon limited mobility.     

Boundary conditions with Pauli exclusion and charge neutrality: application to the Monte Carlo simulation of ballistic nanoscale devices

Electron transport becomes (quasi-) ballistic for nanoscale devices with active regions smaller than 20 nm. Under these conditions, the current and the noise are mainly determined by the electron injection process. Thus, the numerical simulation of these small devices can be very sensible to the boundary conditions (BC). In this work, we present a novel BC for (time-dependent) particle simulators that fulfill Fermi statistics and charge neutrality at the contacts. Monte Carlo simulations of a nanometric two-terminal device using a traditional injection model and the novel model presented in this work are compared.     

BioMOCA: A Transport Monte Carlo Model for Ion Channels

Ion channels are proteins that form natural water-filled nanotubes in the membranes of all biological cells. They regulate ion transport in and out of the cell thereby maintaining the correct internal ion composition that is crucial to cell survival and function. Every channel carries a strong permanent charge, which plays a critical role in the conduction mechanisms of the open channel. Many channels can selectively transmit or block a particular ion species and most have switching properties similar to electronic devices. These device-like features are appealing to the electronics community for their possible application in the design of novel bio-devices. Here we describe a three-dimensional (3-D) transport Monte Carlo ion channel simulation, BioMOCA, based on the approach taken in semiconductor device simulations. Since ion diameters are comparable with channel dimensions a physical model of the volume of the ions must also be included.     

Thirty Years of Monte Carlo Simulations of Electronic Transport in Semiconductors: Their Relevance to Science and Mainstream VLSI Technology

We review briefly some aspects of the history of Monte Carlo simulations of electronic transport in semiconductors. In the early days their heavy computational cost rendered them suitable only to study problems of pure physics, as simpler models provided the answers necessary to design ‘electrostatically good’ devices. Now that scaling has taken another meaning (i.e., looking for alternative materials, crystal orientations, device geometries, etc.), Monte Carlo simulations may gain popularity once more, since they allow an efficient and reliable evaluation of speculative ideas. We show examples of both aspects of the results of Monte Carlo work.     

Use of density gradient quantum corrections in the simulation of statistical variability in MOSFETs

With the scaling of field-effect transistors to the nanometre scale, it is well recognised that TCAD simulations of such devices need to account for quantum mechanical confinement effects. The most widely used method to incorporate quantum effects within classical and semi-classical simulators is via density gradient quantum corrections. Here we present our methodologies for including the density gradient method within our Drift-Diffusion and Monte Carlo simulators and highlight some of the additional benefits that this provides when dealing with the charge associated with random discrete dopants.     

Comparison Between Non-Equilibrium Green's Function and Monte Carlo Simulations for Transport in a Silicon Quantum Wire Structure

We present comparisons of simulations conducted with non-equilibrium Green's functions and Monte Carlo approaches. As prototype, we consider an idealized silicon quantum wire structure, consisting of a conduction channel of rectangular cross-section, terminated by two contacts. The Monte Carlo model treats the particles as semi-classical, but distributed over up to seven subbands and with scattering model similar to the one used for the Green's functions model. Results for drift velocity under various field conditions agree very closely using the two techniques, suggesting that particle simulation may continue to be a useful physical investigation tool at the nanoscale with an appropriate introduction of the most important quantum features of the transport.     

Comparison of Double-Gate MOSFETs and FinFETs with Monte Carlo Simulation

A full-band Monte Carlo simulator has been used to analyze and compare the performance of n-channel double-gate MOSFETs and FinFETs. Size quantization effects were accounted for by using a quantum correction based on Schrödinger equation. FinFETs are a variation of typical double-gate devices with the gate surrounding the channel on three sides. From our simulations, we observed that the quantization effects in double-gate devices are less significant as compared to bulk MOSFETs. The total sheet charge density drops only slightly as the depletion of charge at the interface is counterbalanced by the increased volume inversion effect. We also observed an appreciable drop in average velocity distribution when quantum corrections were applied. For FinFETs, the fin extension lengths on either side of the gate affect the device performance significantly. These underlap regions have low carrier concentration and behave as large resistors. The current drops non-linearly with increasing fin extension lengths.     

On the Electron Transient Response in a 50 nm MOSFET by Ensemble Monte Carlo Simulation in Presence of the Smoothed Potential Algorithm

The inclusion of a smoothed potential algorithm within the Ensemble Monte Carlo method (EMC) to account for quantization effects in the inversion layer of a silicon n-MOSFET has been discussed by several authors. Most of the data reported deal with steady state terminal current, transconductance, and capacitance. Within this approach, the electric field acting on each particle is computed from the smoothed potential, which introduces a potential barrier underneath the gate region that pushes the carriers away from the interface, thus accounting for space quantization effects. However, in the EMC method, the electric field at the interface is also used to compute the displacement charge/current during the transient regime. In the implementation of the smoothed potential algorithm, care must be taken when computing this component of the total gate charge. We distinguish between two differently computed electric fields, one from the smoothed potential used for the charge transport and the other one computed from the real potential, as obtained from the solution of Poisson's equation, and used for the displacement charge. We propose this procedure in order to properly include space quantization effects, and at the same time avoid the inaccuracy introduced by the smoothed potential in the displacement charge.     

Energy transport model with full band structure for GaAs electronic devices

Electronic band structure is incorporated into a versatile energy transport model that treats heat flow between mobile electron ensembles with the thermodynamic identity for ideal gases instead of an electron thermal conductivity. This alleviates the closure issue common to thermal conductivity models and is amenable to different forms of charge gas transport. This flexibility allows the model to accommodate band dispersions typical of semiconductors. A simulation scheme and the device equations for a generalized band structure are presented. The model is then implemented for GaAs using a band structure calculated with the empirical pseudopotential method. Comparisons to Monte Carlo for certain bulk GaAs test cases indicate that the model may capture hot electron effects with sufficient accuracy and reduced computational cost suitable for larger scale device simulation and design.     

A Non Perturbative Model of Surface Roughness Scattering for Monte Carlo Simulation of Relaxed Silicon n-MOSFETs

In the present paper the problem of interface roughness scattering is treated non-perturbatively by incorporating the effects of scattering as a boundary condition for the Boltzmann transport equation (BTE). This provides a basis for the development of a semi-classical model of the interface roughness scattering mechanism applicable to the Monte Carlo (MC) simulations of electron transport in the Si n-MOSFET. The model is based on the Boltzmann-Fuchs method for the solution of the BTE. This method has shown to be computationally efficient and is naturally suited to the semi-classical spirit of the BTE and its direct solution via the MC method.     

Influence of constant electric field on circular photogalvanic effect in material with Rashba Hamiltonian

An appearance of a direct current perpendicularly to a constant component of an electric field in material with Rashba Hamiltonian under the influence of an elliptically polarized wave is investigated in one-subband approximation. On its physical nature this effect is close to a circular photogalvanic effect on intraband transitions. The effect is studied on the base of two approaches: investigations of Boltzmann kinetic equation in a constant collision frequency approximation and semiclassical Monte Carlo simulations, which immediately takes into account microscopic processes of charge carriers scattering on optical and acoustical phonons. Monte Carlo modelling allows us to determine a mean relaxation time and its dependencies on electric field strengths and on the energy of optical phonons. On the base of these estimations a possibility of using a constant relaxation time approximation is justified. It is confirmed that the main contribution to the effects of transverse rectification is made by inelastic scattering of electrons on optical phonons. A comparison of results of Monte Carlo simulations and calculations on the base of a constant collision frequency approximation is presented.