Piezoresistance effect in n-type silicon: from bulk to nanowires

The first order piezoresistance coefficients are examined in the n-type silicon structures with different dimensionality of electron gas: bulk crystal, quantum film (well) and quantum wire. The detail research involves quantum kinetic approach to calculation of the kinetic coefficients (conductivity, mobility, concentration) of electrons in the strained and unstrained states. As scattering system were adopted ionized impurities, longitudinal acoustic phonons and surface roughness. Detailed studies have been carried out for dependences of electron mobility and piezoresistance coefficients on confining dimensions. An alternative explanation is proposed for origin of the giant piezoresistance effect in n-type silicon nanostructures. Comparison of the obtained results shows not only qualitative but even sufficient quantitative agreement with experimental data.     

Self-Consistent Subband Structure and Mobility of Two Dimensional Holes in Strained SiGe MOSFETs

The motivation to research strained SiGe layers on relaxed silicon is to enhance the very low hole mobility observed in conventional Si MOSFETs. This is mainly due to large hole effective masses and strong surface roughness scattering. In this work, the buried SiGe quantum well, chosen as the active channel for carrier transport, enhances mobility in two ways. First, the carriers are confined in the SiGe well and are removed from the Si-SiO₂ interface, so interface roughness is not a big factor. Secondly, strained SiGe has a lower hole effective mass than unstrained Si and the mobility is expected to increase as the Ge concentration increases. We present the results of a self-consistent subband structure and low field mobility calculations for holes in a Si-SiGe heterostructure FET. Our results are in agreement with the experimental work by Garone and coworkers, indicating the validity of our model.     

Quantum kinetics approach to calculation of the low field mobility in the hole inversion layers of silicon MOSFET’s

Analytic expressions for low field mobility have been obtained in the quantized p-type inversion layers. The confining potential is approximated by a triangular quantum well. Main attention is paid to study the dependence of the hole mobility on transverse effective field at different temperatures and concentrations of the ionized impurities. Acoustic and optical phonons, charged impurities, and surface roughness have been adopted as scattering system. Theoretical considerations are based on the quantum kinetic equation and special form of the non-equilibrium distribution function (shifted Fermi distribution). Calculations show that the acoustic phonon limited mobility does not depend on the transverse effective electrical field \(E_\mathrm{eff} \) and has a temperature dependence closer to experiment than known expression for the universal mobility. At the same time, the mobility limited by scattering with optical phonons and surface roughness is proportional to \(E_\mathrm{eff} ^{-1/3}\) and \(E_\mathrm{eff} ^{-2}\), respectively. The mobility limited by scattering by ionized impurities is a weak function of the transverse effective field. Results of the calculations are compared with known experimental data.     

Piezoresistive effect in p-type silicon classical nanowires at high uniaxial strains

The longitudinal piezoresistance of the p-type silicon nanowires oriented along the 〈100〉, 〈110〉 and 〈111〉 crystallographic directions is examined at high uniaxial compressive and tensile elastic stresses ～1 GPa. The detail research on base of the six-band model of the valence band involves quantum kinetic approach to calculation of the kinetic coefficients (conductivity, mobility) in classical nanowires with diameter that is significant higher the de Broglie wavelength of the band carriers. Two mechanisms of scattering (charged impurities and longitudinal acoustic phonons) are investigated. Qualitative agreement has been reached between calculated and known experimental data. A quantitative agreement with experiment is obtained in assumption about a formation of the stress concentration (stress raisers) in regions of nanowires that are depleted by the band carriers.     

Emission and absorption of optical phonons in Multigate Silicon Nanowire MOSFETs

In this paper we study the influence of emission/absorption processes due to optical phonons on the electrical properties of multigate silicon nanowire transistors. We show that low-energy phonons reduce drain current through backscattering of carriers by emission/absorption processes while high-energy phonons redistribute the current energy spectrum along the nanowire channel through phonon emission without significantly reducing the drain current drive. The influence of emission/absorption is investigated in different multigate silicon FET structures with uniform channel, single impurity, random doping atom distribution and oxide tunnel barriers. A three-dimensional quantum mechanical device simulator based on the NEGF formalism in coupled mode-space approach is used to model electron transport in the presence of optical phonon scattering mechanism. Electron-phonon scattering is accounted for by adopting the self-consistent Born approximation and using the deformation potential theory.     

A quantum kinetic approach for calculating low-field mobility in black phosphorus crystals and multilayer phosphorene

Analytic expressions for the low-field mobility have been obtained in black phosphorus crystals and multilayer phosphorene. Acoustic and optical phonons, charged impurities and surface roughness are adopted as the scattering system. Theoretical considerations are based on a quantum kinetic equation and special form of the non-equilibrium distribution function (shifted Fermi distribution). Our calculations reveal that the hole mobility in black phosphorus crystals is limited by scattering with both acoustic and optical phonons over a wide temperature range of 10–400 K. The hole mobility in multilayer phosphorene is thus limited by impurity and optical phonon scattering in this temperature range.     

Hydrodynamic modeling of silicon quantum wires

A hydrodynamic model for silicon quantum wires is formulated by taking the moments of the multisubband Boltzmann equation, coupled to the Schr?dinger-Poisson system. Explicit closure relations for the fluxes and production terms (i.e. the moments on the collisional operator) are obtained by means of the Maximum Entropy Principle of Extended Thermodynamics, including scattering of electrons with acoustic and non-polar optical phonons. By using this model, thermoelectric effects are investigated.     

Semiclassical and Quantum Transport in Si/SiO2 Superlattices

In the last few years, many research groups have been trying to develop electroluminescent devices based on silicon. In particular, it has been shown that low-dimensional structures, such as silicon clusters, quantum wires and quantum wells, are suitable for this purpose. In this work we investigate transport properties of a particular superlattice using two approaches. The first method is a Monte Carlo simulation of electron transport in the biased superlattice. The band structure is calculated using the envelope function approximation, and the scattering mechanisms introduced in the simulator are confined optical phonons. Owing to the particularly flat band structure, drift velocities are very low, but it will be shown that a parallel component of the electric field can significantly increase the vertical drift velocity. Moreover, a superlattice based device is proposed in order to obtain high recombination efficiency. Finally, a quantum calculation is introduced, in order to describe with higher accuracy the high field transport regime.     

A deterministic study of hot phonon effects in a 2D electron gas channel formed at an AlGaN/GaN heterointerface

We investigate the hot phonon effects on the transport properties of a two-dimensional electron gas formed in an AlGaN/GaN heterostructure. For this purpose, we use a deterministic numerical scheme to solve the coupled system of Boltzmann transport equations. The envelope wave functions of the confined carriers are self-consistently calculated from the Schrödinger-Poisson system. The simulation results show that the electron drift velocity is reduced by hot phonons for moderate and high electric fields, but become enhanced for low fields. This interesting behavior is elucidated by virtue of the energy balance equation using an analytic electron temperature model. We find good agreement to experimental data when hot phonon and degeneracy effects are taken into account.     

Electron mobility in silicon and germanium inversion layers: The role of remote phonon scattering

We calculate the electron mobility in Si and Ge inversion layers in single-gate metal-oxide-semiconductor field effect transistors. Scattering with bulk phonons, surface roughness and remote phonons is included in the mobility calculations. Various high-κ dielectric materials are considered for both Si and Ge substrates. Overall, Ge outperforms Si, but in general Ge is more affected by the use of high-κ dielectrics. HfO₂ degrades the mobility substantially compared to SiO₂ for Si substrates and may prohibitively degrade performance. HfO₂ with Ge yields an improvement over Si with a mobility enhancement ≈3× at an electron sheet density of 1×10¹³ cm⁻³.     

Cross-sectional dependence of electron mobility and lattice thermal conductivity in silicon nanowires

The thermoelectric efficiency of a material depends on the ratio of its electrical and thermal conductivity. In this work, the cross-sectional dependence of electron mobility and lattice thermal conductivity in silicon nanowires has been investigated by solving the electron and phonon Boltzmann transport equations. The effects of confinement on acoustic phonon scattering (both electron–phonon and phonon–phonon) are accounted for in this study. With decreasing wire cross-section, the electron mobility shows a non-monotonic variation, whereas the lattice thermal conductivity exhibits a linear decrease. The former is a result of the decrease in intervalley and intersubband scattering due to a redistribution of electrons among the twofold-degenerate Δ₂ and fourfold-degenerate Δ₄ valley subbands when the cross-section is below 5×5 nm², while the latter is because of the monotonic increase of three phonon umklapp and boundary scattering with decreasing wire cross-section. Among the wires considered, those with a cross-section between 3×3 nm² and 4×4 nm² have the maximal ratio of the electron mobility to lattice thermal conductivity, and are expected to provide the maximal thermoelectric figure of merit.     

Phonons in Wurtzites, Fullerenes, and Nanotubes

The applicability of the dielectric and elastic continuum models for describing phonons in nanostructures is discussed. As an example, properties of confined, interface and propagating modes in wurtzite quantum-confined structures are described theoretically in terms of the dielectric continuum model and Loudon's model for uniaxial semiconductors. As a second example, dimensionally-confined acoustic phonon modes of fullerenes and carbon nanotubes will be described in terms of the elastic continuum model.     

Subthreshold Mobility Extraction for SOI-MESFETs

Mobility calculation is a difficult task due to the stochastic nature of the particles in a device. This is especially true for a device operated in the sub-threshold region because the transport is a combination of diffusion and drift albeit diffusion dominated. As a result, one can calculate the mobility based on the drift and the diffusion techniques for a device operated in the subthreshold regime. We have developed a transport model, based on the solution of the Boltzmann Transport Equation, for modeling n-channel silicon-on-insulator (SOI) MOSFETs and MESFETs using the Ensemble Monte Carlo technique. All relevant scattering mechanisms for the silicon material system have been included in the model. The model is used to calculate both the diffusion coefficient and the drift based mobility and the results are compared with available experimental values. The mobility of the equivalent SOI MESFET device is a factor of 3–5 times higher than that of the MOSFET in the sub-threshold regime.     

Monte Carlo study of electron transport in strained silicon inversion layers

The effect of degeneracy both on the phonon-limited mobility and the effective mobility including surface-roughness scattering in unstrained and biaxially tensile strained Si inversion layers is analyzed. We introduce a new method for the inclusion of the Pauli principle in a Monte Carlo algorithm. We show that incidentally degeneracy has a minor effect on the bulk effective mobility, despite non-degenerate statistics yields unphysical subband populations and an underestimation of the mean electron energy. The effective mobility of strained inversion layers slightly increases at high inversion layer concentrations when taking into account degenerate statistics.     

Joule heating and phonon transport in silicon MOSFETs

This work examines the generation of heat in silicon MOSFETs using self-consistent Monte Carlo device simulation with full electron bandstructure and a full phonon dispersion computed from the Adiabatic Bond Charge model. We devise an efficient algorithm for the inclusion of full phonon dispersion in order to account for anisotropy and details of heat transport with great accuracy. We compute the density-of-states (DOS) and the lattice thermal energy numerically and use them to generate maps of local temperatures in a representative small-channel MOSFET device. Our results show that most heat is dissipated in the form of optical g-type phonons in a small region in the drain, and that the heat flows in a preferred direction aligned with the flow of the electron current. We also show that the distribution of generated phonons in energy closely follows the phonon DOS.     

Modeling of some electrical parameters of a MOSFET under applied uniaxial stress

A semi analytical model describing the bulk mobility for electrons in strained-Si layers as a function of applied uniaxial strain applied at the gate has been developed in this paper. The uniaxial stress has been applied through the silicon nitride cap layer. The effects of uniaxial stress are understood on all the three components of mobility i.e. phonon, columbic and surface roughness mobility. The results show that the electron mobility is a strong rising function of applied uniaxial strain. Flatband voltage, Depletion Charge density, Inversion charge density, Energy gap and Effective surface electrical field have been analytically modeled. There is a sharp increase in the vertical electrical field and inversion charge density and decrease in the energy gap, depletion charge density and the flatband voltage when the uniaxial stress is applied. The electron mobility results have also been compared with the experimentally reported results and show good agreement.     

Thermoelectric properties of silicon nanostructures

Semiconductor nanostructures are promising candidates for efficient thermoelectric energy conversion, with applications in solid-state refrigeration and power generation. The design of efficient semiconductor thermocouples requires a thorough understanding of both charge and heat transport; therefore, thermoelectricity in silicon-based nanostructures requires that both electronic and thermal transport be treated on an equal footing. In this paper, we present semiclassical simulation of carrier and phonon transport in ultrathin silicon nanomembranes and gated nanoribbons. We show that the thermoelectric response of Si-membrane-based nanostructures can be improved by employing the anisotropy of the lattice thermal conductivity, revealed in ultrathin Si due to boundary scattering, or by using a gate to provide additional carrier confinement and enhance the thermoelectric power factor.     

Acoustic phonon modulation and electron�Cphonon interaction in?semiconductor slabs and nanowires

The acoustic phonon modulation (confinement) in semiconductor nanostructures and their interaction with electrons are reviewed. Special emphasis will be placed on free-standing and layered slabs, as well as nanowires. Analysis includes acoustic phonon dispersion relations, displacement wave functions, amplitudes, form factor, electron-phonon scattering rate, and electron mobility.