The applications of graphene and transition metal dichalcogenides in electronics are limited by their zero-bandgap and low mobility, respectively. Here, the authors demonstrate the potential of an emerging layered material—black phosphorous—for thin film electronics and infrared optoelectronics.

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Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics

The device physics of nanoscale MOSFETs is explored by numerical simulations of a model transistor. The physics of charge control, source velocity saturation due to thermal injection, and scattering in ultrasmall devices are examined. The results show that the essential physics of nanoscale MOSFETs can be understood in terms of a conceptually simple scattering model.

Essential physics of carrier transport in nanoscale MOSFETs

There can be little doubt that the Monte Carlo method for semiconductor device simulation has enormous power as a research tool. It represents a detailed physical model of the semiconductor material(s), and provides a high degree of insight into the microscopic transport processes. However, if the authority ascribed to Monte Carlo models of devices at 1/spl mu/m feature size is to be maintained for devices below O.1/spl mu/m, modelling of the fundamental physics must be further improved. And if the Monte Carlo method is to be successful as a semiconductor device design tool, the device model must be made more realistic. Success in the industrial sector depends on this, but also on achieving fast run-times optimisation - where the scope and need for ingenuity is now greatest.

The Monte Carlo method for semiconductor device simulation

A review is given on the formation mechanisms and the properties of Si/Ge nanostructures that have been synthesized by self-assembling and self-ordering during heteroepitaxy of \mbox{silicon-germanium} alloys on single-crystal silicon substrates. The properties of electronic subbands in smooth strained Si/SiGe quantum well structures are presented as a basis for characterizing coherent Si/Ge nanostructures with free motion of carriers in a reduced number of dimensions. The low-dimensional band structure of valence band states confined in strained Si/Ge and Si/SiGe nanostructures is analysed by optical and electrical spectroscopy. The nanostructures presented were fabricated by self-assembly induced by elastic strain relaxation without applying any patterning technique. Misfit lattice strain of SiGe material deposited on Si substrates can relax by bunching of atomic surface steps with SiGe agglomeration at the step edges or by nucleation of Ge-rich islands in the Stranski-Krastanow growth mode. The size, density and composition of such Si/Ge nanostructures representing quantum wires and dots, respectively, can be tuned in a wide range by the growth parameters. Local strain fields extending into the Si host influence the nucleation and the lateral arrangement of nanostructures in subsequent layers and can be applied for self-ordering of nanostructures in the vertical as well as the lateral direction. Interband and intra-valence-band photocurrent, absorption and photoluminescence spectroscopy as well as C-V and admittance measurements reveal a consistent view of the band structure in Si/Ge quantum dot structures. This is in good agreement with model calculations based on band offsets, deformation potentials and effective electron masses known from earlier studies of Si/SiGe quantum well structures. The effective valence band offsets of hole states within Si/Ge nanostructures reach about 400?meV. Typical quantization energies of about 40?meV due to lateral confinement and Coulomb charging energies up to about 15?meV were observed for holes confined in 20?nm sized Si/Ge dots. Future applications of Si/Ge nanostructures such as photodetectors with improved performance or novel functionality are discussed.

https://iopscience.iop.org/article/10.1088/0034-4885/65/1/202/pdf

Si/Ge nanostructures

Since Stratton published his famous paper four decades ago, various transport models have been proposed which account for the average carrier energy or temperature in one way or another. The need for such transport models arose because the traditionally used drift-diffusion model cannot capture nonlocal effects which gained increasing importance in modern miniaturized semiconductor devices. In the derivation of these models from Boltzmann's transport equation, several assumptions have to be made in order to obtain a tractable equation set. Although these assumptions may differ significantly, the resulting final models show various similarities, which has frequently led to confusion. We give a detailed review on this subject, highlighting the differences and similarities between the models, and we shed some light on the critical issues associated with higher order transport models.

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A review of hydrodynamic and energy-transport models for semiconductor device simulation

Hierarchical Device Simulation

Introduction References Semiclassical Transport Theory The Boltzmann Transport Equation * Balance Equations * The Microscopic Relaxation Time * Fluctuations in the Steady-State * References The Monte-Carlo Method Basic Monte-Carlo Methods * The Monte-Carlo Solver of the Boltzmann Equation * Velocity Autocorrelation Function * Basic Statistics * Convergence Estimation * References Scattering Mechanisms Phonon Scattering * Alloy Scattering * Impurity Scattering * Impact Ionization by Electrons * Surface Roughness Scattering * References Full-Band Structure Basic Properties of the Band Structure of Relaxed Silicon * Basic Properties of the Band Structure of Strained SiGe * k-Space Grid * Calculation of the Density of States * Mass Tensor Evaluation * Particle Motion in Phase-Space * Selection of a Final State in k-Space * References Device Simulation Device Discretization * Band Edges * Poisson Equation * Self-Consistent Device Simulation * Nonlinear Poisson Equation * Nonself-Consistent Device Simulation * Statistical Enhancement * Terminal Current Estimation * Contact Resistance * Normalization of Physical Quantities * References Momentum-Based Transport Models The Hydrodynamic Model * Small-Signal Analysis * Noise Analysis * The Drift-Diffusion Model * Transport and Noise Parameter Simulation * References Stochastic Properties of Monte-Carlo Device Simulations Stochastic Error * In-Advance CPU Time Estimation * References Results N+ NN+ and P+ PP+ Structures * MOSFETs * SiGe HBTs Subject Index

Hierarchical Device Simulation: The Monte-Carlo Perspective

Classical semiconductor equations are based on the thermal equilibrium approximation. Limitations introduced by this approximation for the 2-D numerical modeling of n-channel silicon submicrometer MOS transistors are investigated. It is shown that the classical equations are accurate for predicting drain current for devices with effective channel lengths as small as 0.3 mu m. However, accurate substrate current modeling requires a more detailed level of simulation even for devices with longer channel lengths. The solution of the energy conservation equation is discussed. >

The influence of the thermal equilibrium approximation on the accuracy of classical two-dimensional numerical modeling of silicon submicrometer MOS transistors

The full-band Monte Carlo technique is currently the most accurate device simulation method, but its usefulness is limited because it is very CPU intensive. This work describes efficient algorithms in detail, which raise the efficiency of the full-band Monte Carlo method to a level where it becomes applicable in the device design process beyond exemplary simulations. The k-space is discretized with a nonuniform tetrahedral grid, which minimizes the discretization error of the linear energy interpolation and memory requirements. A consistent discretization of the inverse mass tensor is utilized to formulate efficient transport parameter estimators. Particle scattering is modeled in such a way that a very fast rejection technique can be used for the generation of the final state eliminating the main cause of the inefficiency of full-band Monte Carlo simulations. The developed full-band Monte Carlo simulator is highly efficient. For example, in conjunction with the nonself-consistent simulation technique CPU times of a few CPU minutes per bias point are achieved for substrate current calculations. Self-consistent calculations of the drain current of a 60 nm-NMOSFET take about a few CPU hours demonstrating the feasibility of full-band Monte Carlo simulations. key words: silicon, full-band Monte Carlo, microscopic relax-

https://www.nst.ing.tu-bs.de/publikationen/public/jung99.pdf

Efficient Full-Band Monte Carlo Simulation of Silicon Devices

Ohmic minority and majority drift mobilities as well as saturation velocities are reported for unstrained and strained Si/sub 1-x/Ge/sub x/ alloys up to z=0.31. The electron-transport model is verified by measurements of the in-plane majority drift mobility in strained Si/sub 1-x/Ge/sub x/ samples for various dopant and Ge concentrations. Saturation velocities are determined by full-band Monte Carlo simulations. There is no substantial decrease in the mobility perpendicular to the Si/SiGe interface for doping concentrations above 10/sup 19/ cm/sup -3/ and growing x. In contrast, the saturation-drift velocity is strongly reduced with x.

Bernd Meinerzhagen

Papers

Hierarchical Device Simulation

Hierarchical Device Simulation: The Monte-Carlo Perspective

The influence of the thermal equilibrium approximation on the accuracy of classical two-dimensional numerical modeling of silicon submicrometer MOS transistors

Efficient Full-Band Monte Carlo Simulation of Silicon Devices

Low- and high-field electron-transport parameters for unstrained and strained Si/sub 1-x/Ge/sub x/