Multi-subband Monte Carlo Simulations Research Articles

Systematic Modeling of Electrostatics, Transport, and Statistical Variability Effects of Interface Traps in End-of-the-Roadmap III–V MOSFETs

Thanks to their superior transport properties, indium gallium arsenide (InGaAs) metal–oxide–semiconductor field-effect transistors (MOSFETs) constitute an alternative to conventional silicon MOSFETs for digital applications at ultrascaled nodes. The successful integration of this technology is challenged mainly by the high defect density in the gate oxide and at the interface with the semiconductor channel, which degrades the electrostatics and could limit the potential benefits over Si. In this work, we: 1) establish a systematic modeling approach to evaluate the performance degradation due to interface traps in terms of electrostatics and transport of InGaAs dual-gate ultrathin body (DG-UTB) FETs and 2) investigate the effects of random interface-trap concentration as another roadblock to the scaling of the technology, due to statistical variability of the threshold voltage. Variability is assessed with a Technology CAD (TCAD) simulator calibrated against multi-subband Monte Carlo (MSMC) simulations. The modeling approach overcomes the TCAD limitations when dealing with ultrathin channels (i.e., below 5 nm) without altering crucial geometrical parameters that would compromise the dependability of the variability analysis. Our results indicate that interface-trap fluctuation becomes comparable with the other variability sources dominating the total variability when shrinking the device dimensions, thus contrasting the trend of reduced variability with scaling. This, in turn, implies that interface and border traps may strongly limit the benefits of InGaAs over Silicon if not effectively reduced by gate process optimization.

Quasi-Ballistic $\Gamma $ - and L-Valleys Transport in Ultrathin Body Strained (111) GaAs nMOSFETs

We carefully scrutinize the potential of ultrathin body strained (111) GaAs MOSFETs to achieve better performance than other GaAs-based channel FETs at scaled channel length and with relaxed thickness requirements, thanks to L-valleys enhanced density-of-states (DoS) and carrier transport. Calibrated multi-subband Monte Carlo simulations including scattering provide the modeling framework necessary for accurate simulations. The results show that L-valley-enhanced transport most likely will not yield the ${I}_{\rm{\scriptscriptstyle ON}}$ and switching time improvements observed in simple ballistic simulations, even if considering the ideal material properties and purely phonon scattering limited transport. In fact, the increased DoS and inversion charge at the virtual source provided by the L-valleys in the strained material is counterbalanced by an increased phonon scattering rate and reduced carrier velocity.

A multi-subband Monte Carlo study on dominance of scattering mechanisms over carrier transport in sub-10-nm Si nanowire FETs.

Dominance of various scattering mechanisms in determination of the carrier mobility is examined for silicon (Si) nanowires of sub-10-nm cross-sections. With a focus on p-type channels, the steady-state hole mobility is studied with multi-subband Monte Carlo simulations to consider quantum effects in nanoscale channels. Electronic structures of gate-all-around nanowires are described with a 6-band k · p model. Channel bandstructures and electrostatics under gate biases are determined self-consistently with Schrödinger-Poisson simulations. Modeling results not only indicate that the hole mobility is severely degraded as channels have smaller cross-sections and are inverted more strongly but also confirm that the surface roughness scattering degrades the mobility more severely than the phonon scattering does. The surface roughness scattering affects carrier transport more strongly in narrower channels, showing ∼90 % dominance in determination of the mobility. At the same channel population, [110] channels suffer from the surface roughness scattering more severely than [100] channels do, due to the stronger corner effect and larger population of carriers residing near channel surfaces. With a sound theoretical framework coupled to the spatial distribution of channel carriers, this work may present a useful guideline for understanding hole transport in ultra-narrow Si nanowires.

The impact of interface states on the mobility and drive current of [formula omitted] semiconductor n-MOSFETs

Accurate Schrödinger-Poisson and Multi-Subband Monte Carlo simulations are used to investigate the effect of interface states at the channel-insulator interface of In0.53Ga0.47As MOSFETs. Acceptor states with energy inside the conduction band of the semiconductor can explain the dramatic Fermi level pinning observed in the experiments. Our results show that these states significantly impact the electrical mobility measurements but they appear to have a limited influence on the static current drive of short channel devices.

Simulation of low Schottky barrier MOSFETs using an improved Multi-subband Monte Carlo model

We present a simple and efficient approach to implement Schottky barrier contacts in a Multi-subband Monte Carlo simulator by using the subband smoothening technique to mimic tunneling at the Schottky junction. In the absence of scattering, simulation results for Schottky barrier MOSFETs are in agreement with ballistic Non-Equilibrium Green’s Functions calculations. We then include the most relevant scattering mechanisms, and apply the model to the study of double gate Schottky barrier MOSFETs representative of the ITRS 2015 high performance device. Results show that a Schottky barrier height of less than approximately 0.15eV is required to outperform the doped source/drain structure.

On the origin of the mobility reduction in n- and p-metal–oxide–semiconductor field effect transistors with hafnium-based/metal gate stacks

We examine the mobility reduction measured in hafnium-based dielectrics in n- and p-MOSFETs by means of extensive comparison between accurate multi-subband Monte Carlo simulations and experimental data for reasonably mature process technologies. We have considered scattering with remote (soft-optical) phonons and remote Coulomb interaction with single layers and dipole charges. A careful examination of model assumptions and limitations leads us to the conclusion that soft optical phonon scattering cannot quantitatively explain by itself the experimental mobility reduction reported by several groups for neither the electron nor the hole inversion layers. Experimental data can be reproduced only assuming consistently large concentrations of Coulomb scattering centers in the gate stack. However, the corresponding charge or dipole density would result in a large threshold voltage shift not observed in the experiments. We thus conclude that the main mechanisms responsible for the mobility reduction in MOSFETs featuring Hafnium-based high-κ dielectric have not been completely identified yet. Additional physical mechanisms that could reconcile simulations with experimental results are suggested and critically discussed.

Applicability of Macroscopic Transport Models to Decananometer MOSFETs

We perform a comparative study of various macroscopic transport models against multisubband Monte Carlo (MC) device simulations for decananometer MOSFETs in an ultra-thin body double-gate realization. The transport parameters of the macroscopic models are taken from homogeneous subband MC simulations, thereby implicitly taking surface roughness and quantization effects into account. Our results demonstrate that the drift-diffusion (DD) model predicts accurate drain currents down to channel lengths of about 40 nm but fails to predict the transit frequency below 80 nm. The energy-transport (ET) model, on the other hand, gives good drain currents and transit frequencies down to 80 nm, whereas below 80 nm, the error rapidly increases. The six moments model follows the results of MC simulations down to 30 nm and outperforms the DD and the ET models.

Failure of the Scalar Dielectric Function Approach for the Screening Modeling in Double-Gate SOI MOSFETs and in FinFETs

This paper shows that modeling of the screening effect based on the scalar dielectric function (SDF) fails in double-gate (DG) MOS transistors and in FinFETs. This leads to simulation results inconsistent with the experiments, especially at high channel inversion densities where the mobility is limited by the surface roughness scattering. These results suggest that one should not use the SDF to model transport in DG silicon-on-insulator MOSFETs or FinFETs, but rather resort to the full tensorial dielectric function. This paper clearly identifies, using multi-subband Monte Carlo simulations as well as analytical derivations for the screened matrix elements of the surface roughness scattering, the simplifying assumptions in the derivation of the SDF that do not hold in a DG MOSFET.

An improved empirical approach to introduce quantization effects in the transport direction in multi-subband Monte Carlo simulations

In this paper we propose and validate a simple approach to empirically account for quantum effects in the transport direction of MOS transistors (i.e. source and drain tunneling and delocalized nature of the carrier wavepacket) in multi-subband Monte Carlo simulators, that already account for quantization in the direction normal to the semiconductor-oxide interface by solving the 1D Schrödinger equation in each section of the device. The model has been validated and calibrated against ballistic non-equilibrium Green's function simulations over a wide range of gate lengths, voltage biases and temperatures. The proposed model has just one adjustable parameter and our results show that it can achieve a good agreement with the NEGF approach.

Electrical excitation of surface phonon-polaritons in III-V heterostructures: A Monte Carlo study

The surface phonon polaritons (SPP) excitation by hot electrons of an appropriate two-dimensional gas could make possible to implement an opto-electronic device emitting around 10 THz. To quantitatively assess the SPP emission by inter-subband electron relaxation in a GaAs/AlGaAs quantum well, accurate electron/SPP scattering rates have been included in a particle Multi-Subband Monte Carlo (MSMC) simulator. Our results suggest some possible optimizations to enhance the SPP emission in order to design new Tera-Hertz sources.

Semiclassical Modeling of Quasi-Ballistic Hole Transport in Nanoscale pMOSFETs Based on a Multi-Subband Monte Carlo Approach

This paper presents a new self-consistent multi-subband Monte Carlo (MSMC) simulator designed to investigate quasi-ballistic transport in nanoscale pMOSFETs. The simulator is 2-D in real space and k-space, and an accurate analytical model of the warped hole energy dispersion is adopted. The effects of the hole gas degeneracy are naturally included by accounting for the Pauli's exclusion principle. The simulator is implemented by resorting to original solutions for handling the hole-free flights consistently with the complicated energy dispersion. A detail description of the formulation of the scattering rates used in the simulator and a comparison to calculations based on a k middot p quantization model are given. Upon an appropriate calibration, the new MSMC tool can accurately reproduce the experimental data for low field mobility, and it can be used for the analysis of the semiballistic transport regime in nanoscale pMOSFETs. Preliminary results for the ballistic ratios BR in double-gate silicon-on-insulator pMOSFETs show that the BR in pMOS are not much worse than in nMOS transistors.

Multi-Subband Monte Carlo simulations of [formula omitted] degradation due to fin thickness fluctuations in FinFETs

The impact of fin thickness nonuniformities on carrier transport in n-type FinFETs is analyzed with a Multi-Subband Monte Carlo technique, which allows for an accurate description of the quasi-ballistic transport taking place in short channel devices and which comprises the dominant scattering mechanisms as well as a semi-empirical technique to handle quantization effects in the transport direction. We found that the impact of channel thickness discontinuity on the on-current is larger when the nonuniformities are located close to the Virtual Source of the device. Furthermore, the sensitivity of the on-current to thickness nonuniformity is essentially the same when considering devices with different crystal orientations. Comparison with drift-diffusion simulations reveals substantial differences in the predicted trends of the sensitivity of the drain current to thickness fluctuations in these nanoscale devices.

On the Apparent Mobility in Nanometric n-MOSFETs

This letter investigates the definition and determination of mobility in nanometric metal-oxide-semiconductor transistors by means of multisubband Monte Carlo simulations. Our results clearly show that the transport in nano-MOSFETs, even for very small VDS, is far from being uniform and local. Consequently, the apparent mobility extracted from the experiments is a channel-length-dependent quantity, which is only partly related to the uniform transport mobility. Our study comprises both the electrical and magnetoresistance mobility.

A new analytical model for the energy dispersion in two-dimensional hole inversion layers

This paper presents an analytical model for the energy dispersion of 2D hole inversion layers. In our approach, the energy dispersion along a few principal directions is described according to a conventional non-parabolic model. Then the angular dependence of the energy to wavevector relation is approximated with an analytical expression that has no fitting parameters. The overall model represents an analytical, non-parabolic and anisotropic description of the hole energy dispersion in inverted layers and it is tuned by comparisons with a quantization model based on the k · p method. The computational efficiency of the model presented in this work is suitable for its implementation in a multi-subband Monte Carlo simulator.

Microscopic theory of quantum-cascade lasers

We review and discuss the first fully three-dimensional study of non-equilibrium carrier dynamics governing semiconductor-based intersubband optoelectronic devices, such as quantum-cascade lasers. First, a multisubband Monte Carlo simulation scheme in a kinetic Boltzmann-like approach is presented. Then, its generalization into a density-matrix quantum-transport formalism is discussed. This allows us to directly access microscopic key features of the electron relaxation dynamics (without resorting to phenomenological parameters) as well as to investigate the nature, coherent versus incoherent, of charge injection/transport processes. Applications to state-of-the-art mid-infrared quantum-cascade lasers and novel far-infrared emitters are reviewed. The extremely good agreement between theoretical results and experimental findings demonstrates that our approach is a valid and predictive tool for the understanding of charge transport in these quantum devices.

Microscopic modelling of semiconductor‐based quantum devices: a predictive simulation strategy

AbstractWe review and discuss the first fully three‐dimensional study of non‐equilibrium carrier dynamics governing semiconductor‐based intersubband optoelectronic devices like, e.g., quantum‐cascade lasers. First, a multisubband Monte Carlo simulation scheme in a kinetic Boltzmann‐like approach is presented. Then, its generalisation into a density‐matrix quantum‐transport formalism is discussed. This allows us to directly access microscopic key‐features of the electron relaxation dynamics (without resorting to phenomenological parameters) as well as to investigate the nature, coherent vs incoherent, of charge injection/transport processes. Besides providing a quantitative investigation into the operation of these devices, our kinetic analysis can indeed serve as a predictive tool for the evaluation of new designs and strategies. Applications are presented concerning quantum‐cascade devices, both state‐of‐the‐art mid‐infrared lasers as well as novel Thz emitters.

Femtosecond optical absorption measurements of electron-phonon scattering in GaAs quantum wells

We present a combined experimental and theoretical investigation of intra- and intersubband carrier relaxation in GaAs/AlAs quantum wells following femtosecond laser excitation at low density. Time-resolved optical absorption has been measured using 125 fs pulses from a tunable Ti:sapphire laser which allows carriers to be excited preferentially into different subbands. The experiments have been analyzed using a multi-subband Monte Carlo simulation which contains all the important scattering mechanisms. Electron-phonon scattering rates obtained from dielectric continuum theory have been used, and we find excellent agreement with the experiment. The dominance of interface phonons in intrasubband relaxation is confirmed.