Intervalley Phonon Research Articles

Channel direction, effective field, and temperature dependencies of hole mobility in (110)-oriented Ge-on-insulator p-channel metal-oxide-semiconductor field-effect transistors fabricated by Ge condensation technique

This paper experimentally reports the channel direction (θ), effective field (Eeff), and temperature (T) dependencies of hole mobility in (110)-oriented 12-nm-thick accumulation mode Ge-on-insulator (GOI) p-channel metal-oxide-semiconductor field-effect transistors (pMOSFETs) fabricated by the Ge condensation technique. It is found that, the hole mobility on (110)-oriented GOI surfaces increases with the channel direction tilted from ⟨100⟩ to ⟨110⟩ direction, in contrast to (100)-oriented conventional GOI surfaces. By low temperature measurements, the extracted phonon-limited mobilities (μph) of (110)-oriented GOI surfaces along ⟨110⟩ direction occupy 2.1 and 7.1 of enhancement against (100)-oriented GOI and Si surfaces, respectively, at any T. Through physical insights into the present analyses, μph dependence on T−1.8 suggests the suppression of intervalley phonon scattering at low T as in Si. Also, μph is found to increase with Eeff, which can be regarded as an inherent property of hole mobility on (110)-oriented Ge. By further analyses base on the definition of mobility, the effective mass can be a dominant factor for the mobility anisotropy on (110)-oriented GOI pMOSFETs.

Monte Carlo Simulations of Electron Transport in In0.52Al0.48As/In0.75Ga0.25As High Electron Mobility Transistors at 300 and 16 K

We performed two-dimensional Monte Carlo (MC) simulations of 200-nm-gate InP-based In0.52Al0.48As/In0.75Ga0.25As pseudomorphic high electron mobility transistors (HEMTs) at 300 and 16 K to clarify the effect of temperature on electron transport. On decreasing the temperature, the calculated maximum transconductance gm increases from 1110 mS/mm at 300 K to 1400 mS/mm at 16 K. On the other hand, the calculated cutoff frequency fT increases from 168 GHz at 300 K to 223 GHz at 16 K. The electron velocity overshoot under the gate is enhanced by reducing the temperature. The resulting average electron velocity under the gate increases from 3.60×107 cm/s at 300 K to 5.26×107 cm/s at 16 K. The average velocity of the electrons and electron occupancy in each valley were calculated to clarify the trend of the electron velocity with temperature. We found that the intervalley phonon scattering as well as the intravalley scattering plays a very important role in determining the average electron velocity at 300 K. The contribution of the intervalley scattering to the average electron velocity is almost of the same degree as that of the intravalley scattering at 300 K.

Strain effects on three-dimensional, two-dimensional, and one-dimensional silicon logic devices: Predicting the future of strained silicon

Using a classification scheme based on carrier confinement type (electrostatic and spatial) and the degrees of freedom of the mobile carriers (3DOF, 2DOF, and 1DOF), strain effects on 3DOF to 1DOF silicon logic devices are compared from quantum confinement and device geometry perspectives. For these varied device geometries and types, the effects of strain-induced band splitting and band warping on the modification of the average conductivity effective mass and carrier scattering rates are evaluated. It is shown that the beneficial effects of strain-induced band splitting are the most effective for devices with little or no initial band splitting and become less so for devices with already large built-in band splitting. For these devices with large splitting energy, the potential for strain-induced carrier conductivity mass reduction through repopulation of lower energy bands and the suppression of optical intervalley phonon scattering are limited. On the other hand, for all devices without spatial confinement, a comparable amount of effective mass reduction occurs through favorable strain-induced band warping. Under spatial carrier confinement, much higher strain levels with respect to unconfined or electrically confined devices are required to observe strain-induced band warping in the band structure, with larger strain requirements as the confinement dimension decreases. In electrically confined volume-inversion devices, the favorable strain type required for carrier mass reduction results in increased surface scattering by bringing the carrier centroid closer to gate surfaces. However, for spatially confined volume-inversion devices, the favorable mechanical strain does not alter the carrier distribution in the device cross section. Consequently, strain is expected to be more effective in modification of low field carrier transport in electrically confined volume-inversion devices and less for spatially confined devices, with respect to conventional 2DOF planar metal-oxide-semiconductor field-effect transistors. On the other hand, for high-field quasiballistic transport, spatially confined devices, have the highest potential for strain-induced modification of device ballisticity, since the carrier backscattering ratio strongly depends on the surface roughness scattering rate at the source-end of the channel.

Theoretical intrinsic lifetime limit of shallow donor states in silicon

The intrinsic lifetime of the $2{p}_{0}$ shallow impurity state in silicon doped with P, As, Sb, or Bi has been computed by combining matrix elements of the electron-phonon coupling within the density-functional perturbation theory, with the envelope function approximation for the impurity wave functions. The theoretical lifetime due to the electronic interaction with intervalley phonons has been found to be 1.1 ns for P-doped silicon, and this theoretical limit is much longer than has been previously believed for the last five decades.

Saturated electron drift velocity at high electric fields in AlGaAs/GaAs/AlGaAs heterostructures

The experimental field dependences of electron drift velocity in the Al0.3Ga0.7As/GaAs quantum well (QW) have no negative slope region and saturate at electric fields in the range of 5–10 kV/cm. The saturated drift velocity in the narrow (10 nm) QW is lower and in the wide (30 nm) QW is larger than the saturated drift velocity in bulk GaAs. The enhancement of the saturated drift velocity is explained by the decrease in the equivalent intervalley and polar optical phonon scattering rates of electrons in upper valleys of a GaAs conduction band with the increase of a QW width. The calculation of these electron scattering rates shows that in AlGaAs/GaAs QW with a width larger than 10 nm, the total confined electron–phonon scattering rate is lower compared with the electron–phonon scattering rate in bulk GaAs. Correspondingly, the electron drift velocity in AlGaAs/GaAs QW is larger than in bulk GaAs at electric fields higher than 10 kV/cm. Keywords: electron drift velocity, electron–phonon scattering, AlGaAs/GaAs heterostructures

Application of the Monte Carlo Method for the Calculation of Electrical Properties, in both Wurtzite and Zinc Blende Phases, of Gallium Nitride

The gallium nitride (GaN) presents very good mechanical, chemical and physical properties, as high velocities. These properties make it more attractive for high power, temperature and frequency electronic applications.In this paper, the main electrical properties of GaN are first presented; then its advantages over the other semi-conductors are studied. In the following section; the main steps of the used method, Monte Carlo simulation, are described. The next section is concerned with a study of some electrical properties of bulk GaN. In stationary state, we calculate electron mobility according to temperature variation, and drift velocity according to electric field variation. In transient state, we calculate the electron velocity according to time variation. We consider the acoustic, piezo-electric, ionized impurities and intervalley polar optical phonon scatterings. The results we obtained are in good agreement with those obtained by other researchers in the same field.

Room temperature velocity saturation in intrinsic graphene

We report ensemble Monte Carlo (EMC) studies of velocity saturation in intrinsic graphene at room temperature. The parameters for the phonon scatterings were obtained from fitting experimental data of graphene sheets in a variety of dielectric media, in which mobilities as high as 44,000 cm2/Vs were observed at 300 K. In our work, velocity saturation was clearly observed at low carrier density (≤5×1012 cm-2). Saturation velocity as high as 5.4×107 cm/s was achieved at the lowest density (5×1011 cm-2). Only scatterings due to the acoustic phonon and the K-point intervalley optical phonon were considered in the simulation. As the density increases, the onset value increases and the saturation velocity decreases.

Electron dynamics in silicon nanowire using a Monte-Carlo method

We present a theoretical study of electron transport in silicon nanowire (SNW). A self-consistent 2D-Poisson-Schrödinger solver provides the band structure. Then, both electron velocity and low-field electron mobility along the SNW axis are computed with an ensemble Monte-Carlo method. Scattering mechanisms due to phonons (acoustic phonons, zero-order and first-order intervalley phonons) and surface roughness are taken into account. We investigate the effect of cross section size and transverse electric field on electron mobility in SNW.

Anharmonic decay of non-equilibrium intervalley phonons in silicon

We study phonons produced by transitions between the equivalent X valleys in silicon. We use the Monte Carlo method first to select stochastically the time between phonon collisions, and then to select a final-state pair of phonons from the probability distribution for anharmonic decay. Our results show that intervalley phonons decay into one near-equilibrium transverse acoustic phonon and another intermediate longitudinal phonon either on the acoustic or optical branch. This second phonon has energies between 40 and 50 meV and undergoes another decay before turning into a pair of near-equilibrium transverse acoustic phonons, presenting an additional potential bottleneck.

Transport of electrons in a GaAs quantum well in high electric fields

The rates of intrasubband and intersubband scattering of electrons by polar optical and intervalley phonons are determined in relation to the electron energy and width of a deep rectangular quantum well in GaAs. The Monte Carlo method was used to calculate the field dependences of the electron’s drift velocity in quantum wells with the width of 10, 20, and 30 nm. It is shown that the drift velocity in high electric fields in a quantum well vastly exceeds the maximum drift’s saturation velocity in the bulk material.

Calculation of the electron Hall mobility and Hall scattering factor in 6H-SiC

The calculated electron Hall Mobility and Hall scattering factor in n-type 6H-SiC based on numerical solutions to the Boltzmann transport equation are presented. These results were obtained by solving the Boltzmann equation exactly for the electron Hall mobility using the contraction mapping principle and the electron drift mobility with Rode’s iterative method. The relative importance of the various scattering mechanisms for these calculations is discussed, and a new set of values for the acoustic deformation potential, intervalley deformation potential, and intervalley phonon energy is found, which simultaneously fit experimental Hall mobility and Hall scattering factor data. The calculated Hall mobility and Hall scattering factor are in good agreement with experimental results. In addition, predicted values of the Hall scattering factor for various temperatures and doping concentrations are given.

Quantum cascade laser design based on impurity–band transitions of donors in Si/GeSi(111) heterostructures

The concept of quantum cascade laser based on impurity-band transitions in n-type Si/GeSi heterostructures has been analyzed. Silicon-germanium heterostructures are attractive for development of devices emitting in the terahertz spectral range, where the use of III–V compounds is limited by their reststrahlen band. The mechanism of population inversion is based on fast ionization of donor centers into continuum of the lower neighboring subband by phonon-assisted tunneling [1]. The fast tunneling is caused by hybridization between the impurity ground state and the 2D continuum in the neighboring quantum well. It is essential that the mentioned subband is closely matched with the ground state level of donor. Apopulation of the ground state therefore is smaller than that of2Dcontinuum of the higher subband. Peculiar features of silicongermanium heterostructures are related to multivalley character of the conduction band. It involves a lot of intra- and intervalley acoustical and optical phonons in tunneling and relaxation processes. The laser scheme is analyzed for n-type selectively doped Si/GeSi(111) heterostructures. The choice of the growth plane arises from two circumstances. First, the quantization effective mass, m = 0.26m0, is fairly small. This enables one to use thicker layers in heterostructures that reduces the sensitivity of the laser scheme to a dispersion of dopants through the period and to a fluctuation of heterostructure parameters. Second, build-in strain in the Si/GeSi(111) heterostructures leaves the valleys degenerate that eliminates additional relaxation channels. An undesirable impact of the remaining degeneracy is the decrease of filling factors of continuum states in the upper (working) subband. Four- and six-layer-period-superlattice cascade laser are treated. Taking into account electron heating up to 100 K amplification coefficient is of the order of 10 cm−1 for doping concentration of 5 × 1011 cm−2 per period at 24–29 μm wave lengths. Selective doping is assumed to be in the centre of a quantum well of the period. For comparison, uniform dopant distribution reduces the amplification coefficient by more than five times.

Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene

Electron-hole generation and recombination rates for intravalley and intervalley phonon scattering in graphene are presented. The transverse and the longitudinal optical phonon modes E2g modes near the zone center point contribute to intravalley interband carrier scattering. At the zone edge KK point, only the transverse optical phonon mode A 1 mode contributes significantly to intervalley interband scattering with recombination rates faster than those due to zone-center phonons. The calculated recombination times range from less than a picosecond to more than hundreds of picoseconds and are strong functions of temperature and electron and hole densities. The theoretical calculations agree well with experimental measurements of the recombination rates of photoexcited carriers in graphene.

Stress-controlled phonon-impurity resonances in terahertz silicon lasers

AbstractOptically pumped terahertz silicon lasers utilize transitions between shallow donor states at low lattice temperatures. Population inversion in these lasers is built-up due to selective relaxation routes of optically excited electrons into impurity ground state. Each relaxation step of the electron occurs under assistance of intervalley and intravalley phonons with energies approaching the particular energy gaps between interacting excited donor states. These impurity phonon interactions determine, at the end, the lifetimes of the laser levels, and, therefore, efficiency of intracenter silicon lasers. Deformation of silicon crystal is a classical example of controllable influence on energy spectrum of shallow donor levels due to specific splitting and shifts of conduction band valleys. Using moderate (up to 400 MPa) external uniaxial deformation of a crystal, one can radically modify the impurity spectra while the phononic spectra remain almost unchanged. We have demonstrated significant improvement of efficiency for intracenter silicon lasers followed by changes of lifetime for the upper and the lower laser levels due to moving the impurity levels either into or out of resonance with corresponding intervalley phonon frequencies.

Energy distributions and scattering mechanisms of carriers in diamond

Energy distributions and scattering mechanisms of carriers in CVD diamond thin films are discussed on the basis of recent experimental and theoretical studies on carrier mobility. The energy distribution of photo-excited holes has been analyzed with an ensemble Monte Carlo technique. Above 80 K, the photo-excited holes reach quasi-equilibrium with the lattice in less than 100 picoseconds, which suggests that the high mobility values of photo-excited holes so far reported cannot be attributed to the difference between the energy distribution of photo-excited holes and that of holes at the thermodynamic equilibrium. Experimental data of electron Hall mobility in the recent literature have been analyzed by an iterative technique. The fitting between the experimental and theoretical values yields a deformation potential constant of E l = 8.0 eV. Pernot et al. have analyzed the same data and obtained rather different values, E l = 17.7 eV. The discrepancy comes mostly from the difference in the method of calculating the inter-valley phonon scattering.

Theoretical Study of Carrier Transport in Silicon Nanowire Transistors Based on the Multisubband Boltzmann Transport Equation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We study electronic transport in silicon nanowire transistors at room temperature based on the self-consistent numerical solution of the multisubband Boltzmann transport equation and Poisson equation. The SchrÖdinger equation with nonparabolic corrections is solved in order to obtain the multisubband structure. Relevant microscopic scattering mechanisms due to acoustic and intervalley phonons, surface roughness, and ionized impurities are included in the simulation. A flux-conserving discretization scheme based on the uniform total energy grid is employed to avoid excessive numerical diffusion originating from the conventional kinetic-energy-based upwind scheme. We report an interesting kink behavior in the output characteristics and study the electron energy distribution inside the transistor as a function of bias conditions and scattering mechanisms. </para>

Electron transport in silicon nanowires: The role of acoustic phonon confinement and surface roughness scattering

We investigate the effects of electron and acoustic phonon confinements on the low-field electron mobility of thin, gated, square silicon nanowires (SiNWs), surrounded by SiO2. We employ a self-consistent Poisson–Schrödinger–Monte Carlo solver that accounts for scattering due to acoustic phonons (confined and bulk), intervalley phonons, and the Si/SiO2 surface roughness. The wires considered have cross sections between 3×3 and 8×8 nm2. For larger wires, the dependence of the mobility on the transverse field from the gate is pronounced, as expected. At low transverse fields, where phonon scattering dominates, scattering from confined acoustic phonons results in about a 10% decrease in the mobility with respect to the bulk phonon approximation. As the wire cross section decreases, the electron mobility drops because the detrimental increase in both electron-acoustic phonon and electron-surface roughness scattering rates overshadows the beneficial volume inversion and subband modulation. For wires thinner than 5×5 nm2, surface roughness scattering dominates regardless of the transverse field applied and leads to a monotonic decrease in the electron mobility with decreasing SiNW cross section.

Relaxation of excited donor states in silicon with emission of intervalley phonons

The process of low-temperature relaxation of excited states of Group V donors in silicon due to coupling of electrons bound at Coulomb centers with intervalley phonons is analyzed. The rate of transitions from the 2p 0 state to the group of 1s(E, T 2) states with emission of the intervalley acoustic phonons LA-g and TA-f is calculated for the phosphorus, antimony, arsenic, and bismuth donors. It is shown that the TA-f phonons make a substantial contribution to nonradiative decay of the 2p 0 state that controls the stimulated infrared emission of the phosphorus and antimony donors in silicon.

Phonon confinement and electron transport in GaAs-based quantum cascade structures

We present a detailed investigation of the effects that optical-phonon confinement has on the electronic transport properties of GaAs-based midinfrared multiple-quantum-well (MQW) quantum cascade lasers (QCLs). The macroscopic dielectric continuum model is used to describe the interface (IF) and confined (CF) optical phonon modes. Dispersions of the IF modes are obtained by using the transfer matrix method with periodic boundary conditions. Normalization coefficients of the IF and CF potentials are derived in detail for MQW structures consisting of arbitrary combinations of binary and ternary alloys. Interstage and intrastage scattering rates due to all the IF and CF modes are calculated for both Γ- and X-valley electrons. The IF and CF scattering processes, in addition to the electron-electron and intervalley phonon scattering, are fully incorporated into the multivalley Monte Carlo simulation of a deep-active-well 6.7μm GaAs-based MQW QCL. At both 77K and room temperature, we find that phonon confinement enhances the electron-polar optical phonon scattering rates to a relatively small extent and induces minor corrections to the current, population inversion, and the electronic temperature with respect to the results obtained in the bulk-phonon approximation. Therefore, the bulk-phonon approximation in transport simulations of GaAs-based QCLs remains valuable due to its simplicity and high accuracy.

Phonon scattering of hot electrons in intense mid‐infrared laser fields

AbstractWe calculated intravalley and intervalley phonon scattering rates of accelerated electrons under intense midinfrared laser fields. We extended the Keldysh theory, which assumes oscillatory motion of Bloch electrons driven by intense laser fields, to phonon scattering of electrons in semiconductors. We find that phonon emission is possible even if the initial electron energy is less than the phonon energy due to multi‐photon absorption processes. We also find that the scattering rates increase with electric field strength and wavelength. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)