A quantum correction based on Schrodinger equation applied to Monte Carlo device simulation

A full-band Monte Carlo model has been coupled to a Schrodinger equation solver to account for the size quantization effects that occur at heterojunctions, such as the oxide interface in MOS devices. The overall model retains the features of the well-developed semi-classical approach, by treating self-consistently the Schrodinger solution as a correction to the particle-based Monte Carlo. The simulator has been benchmarked by comparing results for MOS capacitors and double gate structures with a self-consistent quantum solution, showing that the proposed approach is efficient and accurate. This quantum correction methodology is extended to device simulation, by accounting for the interplay between confinement and transport through a parameter which we call "transverse" temperature. This approach appears to be valid even for nanometer-scale devices in which nonequilibrium ballistic transport is occurring. We present simulations of a 25-nm MOSFET and compare results obtained with and without the quantum correction.     

Monte Carlo simulation and measurement of nanoscale n-MOSFETs

The output characteristics of state-of-the-art n-MOSFETs with effective channel lengths of 40 and 60 nm have been measured and compared with full-band Monte Carlo simulations. The device structures are obtained by process simulation based on comprehensive secondary ion mass spectroscopy and capacitance-voltage measurements. Good agreement between the measured output characteristics and the full-band Monte Carlo simulations is found without any fitting of parameters and the on-currents are reproduced within 4%. The analysis of the velocity profiles along the channel confirms that the on-current is determined by the drift velocity in the source side of the channel. Analytic-band Monte Carlo simulations are found to involve an overestimation of the drain current in the nonlinear regime which becomes larger for increasing drain voltage and decreasing gate length. The discrepancy originates from a higher nonlinear drift velocity and a higher overshoot peak in bulk silicon which is due to differences in the band structures above 100 meV. The comparison between analytic-band and full-band Monte Carlo simulation therefore shows that the source-side velocity in the on-state is influenced by nonlinear and quasiballistic transport.     

A semi-empirical model of surface scattering for Monte Carlosimulation of silicon n-MOSFETs

A semi-empirical model of surface scattering for Monte Carlo simulation of electrons in the silicon inversion layer at 300 K is proposed. The model compares favorably with different sets of experimental electron effective mobility data over a wide range of normal electric fields, channel impurity concentrations, and substrate bias. Comparisons between Monte Carlo and drift-diffusion simulations show that the model is able to correctly predict the device termination currents in the regime where nonequilibrium transport effects are negligible. It is expected therefore that at small device lengths the Monte Carlo predictions are also quantitatively correct     

Study of Warm-Electron Injection in Double-Gate SONOS by Full-Band Monte Carlo Simulation

In this letter, we investigate warm-electron injection in a double-gate SONOS memory by means of 2-D full-band Monte Carlo simulations of the Boltzmann transport equation. Electrons are accelerated in the channel by a drain-to-source voltage $V_{rm DS}$ smaller than 3 V, so that programming occurs via electrons tunneling through a potential barrier whose height has been effectively reduced by the accumulated kinetic energy. Particle energy distribution at the semiconductor/oxide interface is studied for different bias conditions and different positions along the channel. The gate current is calculated with a continuum-based postprocessing method as a function of the particle distribution obtained from Monte Carlo simulation. Simulation results show that the gate current increases by several orders of magnitude with increasing drain bias, and warm-electron injection can be an interesting option for programming when short-channel effects prohibit the application of larger drain bias.      

Physics of Hole Transport in Strained Silicon MOSFET Inversion Layers

A comprehensive quantum anisotropic transport model for holes was used to study silicon PMOS inversion layer transport under arbitrary stress. The anisotropic band structures of bulk silicon and silicon under field confinement as a twodimensional quantum gas are computed using the pseudopotential method and a six-band stress-dependent k.p Hamiltonian. Anisotropic scattering is included in the momentum-dependent scattering rate calculation. Mobility is obtained from the Kubo–Greenwood formula at low lateral field and from the fullband Monte Carlo simulation at high lateral field. Using these methods, a comprehensive study has been performed for both uniaxial and biaxial stresses. The results are compared with device bending data and piezoresistance data for uniaxial stress, and device data from strained Si channel on relaxed SiGe substrate devices for biaxial tensile stress. All comparisons show a very good agreement with simulation. It is found that the hole band structure is dominated by 12 “wings,” where mechanical stress, as well as the vertical field under certain stress conditions, can alter the energies of the few lowest hole subbands, changing the transport effective mass, density-of-states, and scattering rates, and thus affecting the mobility.     

Study of a 50 nm nMOSFET by ensemble Monte Carlo simulationincluding a new approach to surface roughness and impurity scattering inthe Si inversion layer

A 50 nm nMOSFET has been studied by Ensemble Monte Carlo (EMC) simulation including a novel physical model for the treatment of surface roughness and impurity scattering in the Si inversion layer. In this model, we use a bulk-like phonon and impurity scattering model and surface-roughness scattering in the silicon inversion layer, coupled with the effective/smoothed potential approach to account for space quantization effects. This approach does not require a self-consistent solution of the Schrodinger equation. A thorough account of how these scattering mechanisms affect the transport transient response and steady-state regime in a 50 nm gate-length nMOSFET is given in this paper. A set of I_ds-V_ds curves for the transistor is shown. We find that the smoothing of the potential to account for quantum effects has a strong impact on the electron transport properties, both in transient and steady-state regimes. We also show results for the impact that impurity and surface-roughness scattering mechanisms have on the average velocity of the carriers in the channel and the current flowing through the device. It was found that time-scales as short as 0.1-0.2 ps are enough to reach a steady-state channel electron average velocity     

The Monte Carlo approach to transport modeling in deca-nanometer MOSFETs

In this paper, we review recent developments of the Monte Carlo approach to the simulation of semi-classical carrier transport in nano-MOSFETs, with particular focus on the inclusion of quantum-mechanical effects in the simulation (using either the multi-subband approach or quantum corrections to the electrostatic potential) and on the numerical stability issues related to the coupling of the transport with the Poisson equation. Selected applications are presented, including the analysis of quasi-ballistic transport, the determination of the RF characteristics of deca-nanometric MOSFETs, and the study of non-conventional device structures and channel materials.     

Hydrodynamic transport parameters of wurtzite ZnO from analytic- and full-band Monte Carlo simulation

Analytic-band Monte Carlo simulation of electron transport in bulk wurtzite ZnO, validated against the results of a full-band code and available experimental data, is used to determine the main parameters required by drift-diffusion and hydrodynamic models. Steady-state drift velocity, carrier temperature, energy and momentum relaxation time, noise diffusivity, and electron thermal conductivity are calculated, and their dependence on temperature and electric field or average electron energy is approximated by means of a complete set of fitting models suitable for inclusion in commercial device simulation tools.     

Ballistic Transport in InP-Based HEMTs

Ballistic transport has been of interest in semiconductor devices for quite some time, and its effect has been used to predict quite-different device performance. Here, we investigate the role of ballistic transport in a short-channel InGaAs/InAlAs HEMT through full-band cellular Monte Carlo simulations. We can examine the contrast in behavior between when scattering mechanisms are present and when they are turned off. When the scattering processes are completely removed, the output characteristics show a distinct change in behavior over all drain voltages. This result is in qualitative agreement with prior arguments, suggesting that triodelike behavior should be expected due to enhanced drain-induced barrier lowering. However, we find that explicit band-structure effects are observable in the output characteristics of the ballistic transistor. We also find that this distinctive behavior gradually disappears as scattering is turned on, particularly in the drain end of the device. We also develop a method of determining the probability that electrons pass through the gate region in a ballistic manner in the presence of realistic scattering. Even when the gate is only 10 nm long, we find that this probability is only on the order of 50% in these devices. We also examine the ballistic ratio in our device as a function of gate length.      

A new backscattering model giving a description of the quasi-ballistic transport in nano-MOSFET

A backscattering model suitable for compact modeling of nanoscale MOSFET is developed within the Landauer flux-scattering theory. To describe the quasi-ballistic transport, a new backscattering model based on the accurate determination of ballistic and backscattering probabilities along the channel is developed. This model is based on a careful analysis of transport in device using Monte Carlo simulation. This model allows us to display the main physical quantities along the channel and to accurately describe the quasi-ballistic transport and its effects on current-voltage characteristics.     

Numerical analysis of nonequilibrium electron transport inAlGaAs/InGaAs/GaAs pseudomorphic MODFETs

Nonequilibrium electron transport in InGaAs pseudomorphic MODFETs has been analyzed with the moment equations approach. In the model, the momentum and energy balance equations for the two-dimensional electrons in the InGaAs channel are solved with relaxation times generated from a Monte Carlo simulation. The two-dimensional electron wave functions and the quantized state energies in the InGaAs quantum well are calculated exactly from the Schrodinger equation along the direction perpendicular to the quantum well. Also included is a two-dimensional Poisson equation solver. In the calculation, all of the equations are solved iteratively until a self-consistent solution is achieved. The simulation results for a realistic device structure with a 0.5-μm recessed gate show a significant overshoot velocity of 4.5×10⁷ cm/s at a drain bias of 1.0 V. Electron temperature reaches a peak value of around 2500 K under the gate. In energy transport, the diffusive component of the energy flux is found to be dominant in the high-field region     

A drift-diffusion/Monte Carlo simulation methodology for Si1-xGex HBT design

An accurate and efficient simulation methodology for Si_1-x Ge_x HBTs is presented. A two-dimensional (2-D) drift-diffusion solver is employed for dc and ac characteristics, and one-dimensional (1-D) full-band Monte Carlo for transport in the base-collector high-electric-field region. Extrinsic parasitics are introduced as lumped circuit elements whose values are obtained from measurements and layout considerations. This approach not only reduces the computational cost of the simulation, but it also helps to differentiate the relevance of the intrinsic and extrinsic device parameters. We discuss the calibration of the simulation on a 0.25 μm process and use a 1-D regional analysis in the quasi-static approximation to identify the major source of delay. Results of the delay analysis were used to improve device performance for the 0.16 μm technology node     

Potential design and transport property of 0.1-μm MOSFET withasymmetric channel profile

This paper describes potential design and transport property of a 0.1-μm n-MOSFET with asymmetric channel profile, which is formed by the tilt-angle ion-implantation after gate electrode formation. The relation between device performance and transport property of the asymmetric 0.1-μm device is explored by Monte Carlo simulations, and measured electrical characteristics. The self-consistent Monte Carlo device simulation coupled with a process simulator reveals higher electron velocity at the source end of the channel and velocity overshoot at the source side of the channel, and the smaller high-energy tail of the distribution in the drain. This transport property creates high drain current, large transconductance, and low substrate current of the 0.1-μm n-MOSFET with asymmetric channel profile     

Full-band Monte Carlo investigation of hot carrier trends in thescaling of metal-oxide-semiconductor field-effect transistors

A full-band Monte Carlo (MC) device simulator has been used to study the effects of device scaling on hot electrons in different types of n-channel metal-oxide-semiconductor field-effect transistor (MOSFET) structures. Simulated devices include a conventional MOSFET with a single source/drain implant, a lightly-doped drain (LDD) MOSFET, a silicon-on-insulator (SOI) MOSFET, and a MOSFET built on an epitaxial layer on top of a heavily-doped ground plane. Different scaling techniques have been applied to the devices, to analyze the effects on the electric field and on the energy distributions of the electrons, as well as on drain, substrate, and gate currents. The results provide a physical basis for understanding the overall behavior of impact ionization and gate oxide injection and how they relate to scaling. The observed nonlocality of transport phenomena and the nontrivial relationship between electric fields and transport parameters indicate that simpler models cannot adequately predict hot carrier behavior at the channel lengths studied (sub-0.3-μm). In addition, our results suggest that below 0.15 μm, the established device configurations (e.g. LDD) that are successful at suppressing the hot carrier population for longer channel lengths, become less useful and their cost-effectiveness for future circuit applications needs to be reevaluated     

Alloy scattering and high field transport in ternary and quaternary III–V semiconductors

A technique is described for the estimation of the influence of random potential alloy scattering on the high field transport properties of quaternary III–V semiconductors obtained by Monte Carlo simulation. The approach is based on an extension of a theoretical model for scattering in the ternary alloys. The magnitude of the scattering potential is an important parameter in alloy scattering, and three proposed models for calculating this potential are discussed. These are the energy bandgap difference, the electron affinity difference, and the heteropolar energy difference for the appropriate binary compounds.The technique is used in the Monte Carlo method to study the influence of alloy scattering on the transport properties of III–V quaternary alloys. The results of this study are used in a device model to estimate device parameters for FETs.     

Simulation of quantum effects along the channel of ultrascaledSi-based MOSFETs

Quantum transport simulations, including phase-breaking scattering, are used to observe the transition from classical to quantum transport in ultrascaled Si and SiGe heterostructure MOSFETs in order to gauge the potential effectiveness of semiclassical and pure phase-coherent quantum transport models as this transition is approached. It is shown that semiclassical models of transport along the length of the channel (as opposed to normal to the channel, where the importance of quantum mechanical effects has long been recognized) may remain reliable for channel lengths down to roughly 10 nm and perhaps beyond, and likely more reliable at this point than phase-coherent quantum transport simulations even when much of the transport is coherent/ballistic. As coherent transport effects within the channel eventually do become significant for ballistic carriers, the phase-breaking scattering rate, itself, also becomes a nonlocal function of the carrier's kinetic energy placing further demands on simulation. Simulations also reaffirm that for injection into the channel, the modeling of quantum transport effects such as tunneling, particularly in Si-SiGe heterostructure MOSFET's, will be important in much longer devices. However, even for this purpose it may not be possible to neglect the effects of inelastic scattering that can provide additional tunneling "paths."     

Quantum-aperture formation in a quasi-ballistic MESFET by neutron irradiation

The effect of neutron irradiation with a fluence reaching 5 × 10¹⁵ cm^?2 on a quasi-ballistic MESFET is studied theoretically and experimentally. A marked improvement is observed in the device performance; it is attributed to quantum effects. The experimental results are interpreted by the Monte Carlo simulation of defect formation and carrier transport in the channel of irradiated devices. It is shown that the positive effect of irradiation may be linked to the transformation of the channel into a set of quantum-size gaps (short quantum wires) between radiation-defect clusters. The higher degree of control over the drain current should result from the influence of the gate voltage on the gap diameter (and hence on the electron energy levels associated with the gaps).     

Simulation of Schottky barrier MOSFETs with a coupled quantuminjection/Monte Carlo technique

A full-band Monte Carlo device simulator has been used to analyze the performance of sub-0.1 μm Schottky barrier MOSFETs. In these devices, the source and drain contacts are realized with metal silicide, and the injection of carriers is controlled by gate voltage modulation of tunneling through the source barrier. A simple model treating the silicide regions as metals, coupled with an Airy function approach for tunneling through the barrier, provides injecting boundary conditions for the Monte Carlo procedure. Simulations were carried out considering a p-channel device with 270 Å gate length for which measurements are available. Our results show that in these structures there is not a strong interaction with the oxide interface as in conventional MOS devices and carriers are injected at fairly wide angles from the source into the bulk of the device. The Monte Carlo simulations not only give good agreement with current-voltage (I-V) curves, but also easily reproduce the subthreshold behavior since all the computational power is devoted to simulation of channel particles. The simulations also clarify why these structures exhibit a large amount of leakage in subthreshold regime, due to both thermionic and tunneling emission. Computational experiments suggest ways to modify the doping profile to reduce to some extent the leakage