Intervalley Phonon Research Articles

Stochastic simulation of electron transport in a strong electrical field in low-dimensional heterostructures

Abstract In this paper we develop a stochastic simulation algorithm for electron transport in a DA-pHEMT heterostructure. Mathematical formulation of the problem of electron gas transport in the heterostructure in the form of a coupled system of Poisson, Schrödinger and kinetic Boltzmann equations is given. A Monte Carlo model of electron transport in DA-pHEMT heterostructures which accounts for multivalley parabolic band structure, as well as relevant formulas for calculating electron scattering rates and scattering phase functions on polar optical, intervalley phonons and on impurities are developed. The results of a computational experiment involving the solution of the system of Poisson–Schrödinger–Boltzmann equations for the AlGaAs/GaAs/InGaAs/GaAs/AlGaAs heterostructure are presented. The distribution of electrons by energy subband in the main and satellite valleys and the field dependences of the electron drift velocity in each valley are calculated. It was discovered that there is no spatial transfer of electrons into wide-gap AlGaAs layers due to high barriers created by modulated-doped impurities. A comparative analysis of the electron drift velocities in the studied DA-pHEMT heterostructures and in the unstrained layer of the InGaAs is given.

Electron-phonon scattering in β -Ga2O3 studied by ultrafast transmission spectroscopy

Femtosecond pump-probe experiments in a transmission geometry were performed on Sn-doped n-type β-Ga2O3. With the pump and probe wavelengths below the bandgap, the differential transmission signal was determined by the free electron dynamics. Differential transmission decay times and their spectral dependence were used to evaluate electron-phonon scattering for polar optical (PO) and intervalley phonons. The obtained average electron-PO phonon scattering time is 4.5 ± 0.4 fs, while the electron scattering to and from the side valley is 80 ± 5 fs. The energy between the absolute and second lowest conduction band minima is estimated to be 2.6 ± 0.1 eV.

Dissipative transport and phonon scattering suppression via valley engineering in single-layer antimonene and arsenene field-effect transistors

Two-dimensional (2D) semiconductors are promising channel materials for next-generation field-effect transistors (FETs) thanks to their unique mechanical properties and enhanced electrostatic control. However, the performance of these devices can be strongly limited by the scattering processes between carriers and phonons, usually occurring at high rates in 2D materials. Here, we use quantum transport simulations calibrated on first-principle computations to report on dissipative transport in antimonene and arsenene n-type FETs at the scaling limit. We show that the widely-used approximations of either ballistic transport or simple acoustic deformation potential scattering result in large overestimation of the ON current, due to neglecting the dominant intervalley and optical phonon scattering processes. We additionally investigate a recently proposed valley engineering strategy to improve the device performance by removing the valley degeneracy and suppressing most of the intervalley scattering channels via an uniaxial strain along the zigzag direction. The method is applicable to other similar 2D semiconductors characterized by multivalley transport.

Measurement of Conduction and Valence Bands g-Factors in a Transition Metal Dichalcogenide Monolayer.

The electron valley and spin degree of freedom in monolayer transition-metal dichalcogenides can be manipulated in optical and transport measurements performed in magnetic fields. The key parameter for determining the Zeeman splitting, namely, the separate contribution of the electron and hole g factor, is inaccessible in most measurements. Here we present an original method that gives access to the respective contribution of the conduction and valence band to the measured Zeeman splitting. It exploits the optical selection rules of exciton complexes, in particular the ones involving intervalley phonons, avoiding strong renormalization effects that compromise single particle g-factor determination in transport experiments. These studies yield a direct determination of single band g factors. We measure g_{c1}=0.86±0.1, g_{c2}=3.84±0.1 for the bottom (top) conduction bands and g_{v}=6.1±0.1 for the valence band of monolayer WSe_{2}. These measurements are helpful for quantitative interpretation of optical and transport measurements performed in magnetic fields. In addition, the measured g factors are valuable input parameters for optimizing band structure calculations of these 2D materials.

Междолинные процессы релаксации состояний мелких доноров в германии

The role of the intervalley processes of electron-phonon interaction in the relaxation of excited shallow arsenic donors in germanium is analyzed. The rates of intracenter inter-valley transitions with emission of TA phonons in ger-manium are calculated in dependence on the uniaxial compression stress along {111} crystallographic direction. It is shown that inter-valley transitions to the ground state of the donor with emission of phonons can play a significant role in the relaxation of excited impurities only upon uniaxial stress of the crystal, since at zero stress, there are no exact resonances between impurity transitions and intervalley phonons. There are also transitions from highly excited states lying in a narrow band of energies (~ 0.5 meV) under very bottom of the conduction band to the first excited state 1s(3)(Г5) (in stressed germanium crystal to 1s(3)(Г3) state). The average rate of these transitions is estimated at 0.3×109 s-1.

Drift velocity in GaN semiconductors: Monte Carlo simulation and comparison with experimental measurements

Abstract Monte Carlo algorithms are developed to simulate the electron transport in semiconductors. In particular, the drift velocity in GaN semiconductors is calculated, and a comparison with experimental measurements is discussed. Explicit expressions for the scattering probabilities and distributions of the scattering angle of electrons on polar optical and intervalley phonons, and acoustic deformation potential as well are given. A good agreement of the simulation results and the experimental measurements reveals that the M-L valley is located at 0.7 eV higher than the Γ-valley. This value agrees with other experimental studies, while it is lower compared to ab initio calculations.

Power loss of hot Dirac fermions in silicene and its near equivalence with graphene

The power loss P of hot Dirac fermions through the coupling to the intrinsic intravalley and intervalley acoustic and optical phonons is analytically investigated in silicene as a function of electron temperature T e and density n s . At very low T e , the power dissipation is found to follow the Bloch–Grüneisen power-law and , as in graphene, and for 20–30 K, the power loss is predominantly due to the intravalley acoustic phonon scattering. On the other hand, dispersionless low energy intervalley acoustic phonons begin to dominate the power transfer at temperatures as low as ∼30 K, and optical phonons dominate at K, unlike the graphene. The total power loss increases with T e with a value of ∼1010 eV s−1 at 300 K, which is the same order of magnitude as in graphene. The power loss due to intravalley acoustic phonons increases with n s at higher T e , whereas due to the intervalley acoustic and optical phonons is found to be independent of n s . Interestingly, the energy relaxation time in silicene is about four times higher than that in graphene. For this reason, silicene may be superior over graphene for its applications in bolometers and calorimeters. Power transfer to the surface optical phonons is also studied as a function of T e and n s for silicene on Al2O3 substrate and it is found to be greater than the intrinsic phonon contribution at higher T e . Substrate engineering is discussed to reduce .

Influence of uniaxial stress on phonon-assisted relaxation in bismuth-doped silicon

The relaxation of electrons bound to bismuth donors in silicon and the effect of uniaxial stress have been studied using the time-resolved single color pump-probe technique. In unstressed Si:Bi, an excited 2p0 donor state is resonantly coupled with the donor 1s(A1) ground state via an intervalley f-TO optical phonon. This results in a very short lifetime (a few ps) of the excited state. Even a slight deformation of the silicon crystal leads to modification of particular interstate energies of the donor, which resolves the resonant coupling to intervalley phonons whose energies remain unchanged. We have shown that once the energy gap between the lower stress-split component of the 2p0 state and the ground state becomes less than the energy of the f-TO phonon, the relaxation of electrons from the excited state slows down to about 300 ps. The experimental data are compared with theoretical calculations of the 2p0 state relaxation rate, which are performed assuming that it is dominated by the emission of intervalley phonons.

Superconducting dome driven by intervalley phonon scattering in monolayer MoS2

We combine first-principles calculations, a three-band tight-binding model, and Bardeen–Cooper–Schrieffer theory to explore the physical mechanism for a dome-shaped dependence of superconducting transition temperature of monolayer MoS2 on electron doping concentration, which has been observed experimentally (2012 Science 338 1193). We find that in the process of doping more electrons contribute to superconducting pairing, but above some doping value the effective attractive interaction decreases so greatly that it starts to reduce the pairing strength, forming a superconducting dome. Therefore, the dome behavior can be attributed to the competition between the growing Fermi pocket (corresponding to an increase of the number of intervalley phonon scatterings) and the screened intervalley phonon scattering (corresponding to a decrease of scattering probability).

Monte Carlo Calculations of Energy and Drift Velocity in ZnS, ZnSe, ZnTe

A Monte Carlo simulation of high field electron transport in ZnS, ZnSe and ZnTe has been presented. The model includes a nonparabolic three valley of the conduction band. The simulation includes scattering mechanisms associated with acoustic, intervalley and polar optical phonons, as well as ionized impurity scattering and impact ionization. The inclusion of the second conduction band is found to have a significant impact on the energy distribution at fields above 100 kV/cm. The second conduction band is also important because of its effect on the impact ionization rate. The results of simulation which are drift velocity and average electron energy are presented and discussed.

Electron short-wave phonon scattering in crystals with chalcopyrite lattice

Electron short-wavelength phonon scattering is an effective channel for energy relaxation in crystals with a pseudo-direct optical gap. The equilibrium parameters of crystal structures and spectra of electrons and phonons in the ternary chalcopyrite compounds ZnSiP2 and ZnGeP2 are calculated self-consistently in good agreement with available experimental and theoretical calculations. The ab initio probabilities of phonon-assisted intervalley scattering of electrons in the conduction bands of the pseudo-direct-gap compounds ZnSiP2 and ZnGeP2 between the central Γ minima and the lowest lateral minima (valleys) at the T and N points have been calculated using the density functional perturbation theory. Electron–phonon scattering rates associated with intervalley phonons are calculated. Coupling constants for intervalley phonons in the chalcopyrite phosphides are close to their values in Si, Ge, and in the binary analog GaP.

The role of intervalley phonons in hot carrier transfer and extraction in type-II InAs/AlAsSb quantum-well solar cells

Simultaneous continuous wave (CW) photoluminescence and monochromatic current density-voltage (J-V) measurements of InAs/AlAsSb QW p-i-n diodes reveal stable hot carriers observed at relatively low power (nearly independent of power). This behavior is attributed to preferential scattering of high energy carriers to the upper satellite L- and X-valleys, which inhibits carrier thermalization via LO phonon emission. Although both high electric field and optical excitation are shown to enable stable hot carrier generation in the quantum wells (QWs), the extraction of these carriers is inhibited by the mismatch in valley degeneracy (L to Γ) across the InAs QW/n-AlInAs layers resulting in carrier localization in the QWs in the operating regime of the solar cell.

An analytical model for the electron effective mobility in a strained silicon inversion layer

An electron effective mobility analytical model without empirical parameters is investigated for the strained silicon inversion layer, which can be conveniently applied by device and circuit designers. Four kinds of scattering mechanisms, i.e., coulomb scattering, acoustic phonon scattering, intervalley phonon scattering and surface roughness scattering, are taken into account to calculate the electron mobility for the 2D (two-dimensional) inversion layer through a one-dimensional inverse transform. Considering the quantum confinement and strain effect, the valley electron occupancy variation is dissected. In regard to the Si/(001)Si1−xGex and Si/(110)Si1−xGex Si common orientation, the dependence of the electron effective mobility with various Ge content on the inversion charge density is analyzed in detail, and by means of this the mechanism of the mobility enhancement under different situations and the mobility saturation are brought to light.

Lattice scattering in n-type Ge-on-Si based on the unique dual-valley transitions

Silicon-based light emitting materials and devices with high efficiency are inarguably the most challenging elements in silicon (Si) photonics. Band-gap engineering approaches, including tensile strain and n-type doping, utilized for tuning germanium (Ge) to an optical gain medium have the potential for realizing monolithic optoelectronic integrated circuit. While previous experimental research has greatly contributed to optical gain and lasing of Ge direct-gap, many efforts were made to reduce lasing threshold, including the understanding of high efficiency luminescence mechanism with tensile strain and n-type doping in Ge. This paper focuses on the theoretical analysis of lattice scattering in n-type Ge-on-Si material based on its unique dual-valley transition for further improving the efficiency luminescence of Ge direct-gap laser. Lattice scattering of carriers, including inter-valley and intra-valley scattering, influence the electron distribution between the direct valley and indirect L valleys in the conduction of n-type Ge-on-Si material. This behavior can be described by theoretical model of quantum mechanics such as perturbation theory. In this paper, the lattice scatterings of intra-valley scattering in valley and L valleys, and of inter-valley scattering between the direct valley and L valleys in the n-type Ge-on-Si materials are exhibited based on its unique dual-valley transition by perturbation theory. The calculated average scattering times for phonon scattering in the cases of valley and L valleys, and for inter-valley optical phonon scattering between valley and L valleys are in agreement with experimental results, which are of significance for understanding the lattice scattering mechanism in the n-type Ge-on-Si material. The numerical calculations show that the disadvantaged inter-valley scattering of electrons from the direct valley to indirect L valleys reduces the electrons dwelling in the direct valley slightly with n-type doping concentration, while the strong inter-valley scattering from the indirect L valleys to indirect valleys increases electrons dwelling in the direct valley with n-type doping concentration. The competition between the two factors leads to an increasing electrons dwelling in the direct valley with n-type doping in a range from 1017 cm-3 to 1019 cm-3. That the electrons in the indirect L valleys are transited into the direct valley by absorbing inter-valley optical phonon modes is one of the effective ways to enhance the efficiency luminescence of Ge direct-gap laser. The results indicate that a low-threshold Ge-on-Si laser can be further improved by engineering the inter-valley scattering for enhancing the electrons dwelling in the valley.

A Silicon Ratchet to Produce Power from Below‐Bandgap Photons

AbstractThis paper computationally demonstrates a new photovoltaic mechanism that generates power from incoherent, below‐bandgap (THz) excitations of conduction band electrons in silicon. A periodic sawtooth potential, realized through elastic strain gradients along a 100 nm thick Si slab, biases the oscillatory motion of excited electrons, which preferentially jump and relax into the adjacent period on the right to generate a net current. The magnitude of the ratchet current increases with photon energy (20, 50, and 100 meV) and irradiance (≈MW cm−2), which control the probability of photon scattering, and peaks as a function of the well depth of the ratchet potential, and the dominant mode of energy loss (the 62 meV intervalley phonon). The internal power conversion efficiency of the ratchet has a maximum of 0.0083% at a photon energy of 100 meV, due to inefficiencies caused by isotropic scattering. This new photovoltaic mechanism uses wasted below‐bandgap absorptions to enhance the directional diffusion of charge carriers and could be used to augment the efficiency of traditional photovoltaics.

Specific features of electron scattering in uniaxially deformed n-Ge single crystals in the presence of radiation defects

ABSTRACTTemperature dependencies for concentration of electrons and the Hall mobility for unirradiated and irradiated by the flow of electrons single crystals , with the energy of , for different values of uniaxial pressures along the crystallographic directions , and are obtained on the basis of piezo-Hall effect measurements. Non-typical growth of the Hall mobility of electrons for irradiated single crystals in comparison with unirradiated with the increasing of value of uniaxial pressures along the crystallographic directions (for the entire range of the investigated temperatures) and (to temperatures ) has been revealed. Such an effect of the Hall mobility increase for uniaxially deformed single crystals is explained by the reduction of gradients of a resistance as a result of reduction in the amplitude of a large-scale potential with deformation and concentration of charged A-centers in the process of their recharge by the increasing of uniaxial pressure and consequently the probability of scattering on these centers. Theoretical calculations for temperature dependencies of the Hall mobility for uniaxially deformed single crystals in terms of the electrons scattering on the ions of shallow donors, acoustic, optical and intervalley phonons, regions of disordering and large-scale potential is good conformed to the corresponding experimental results at temperatures T<220 K for the case of uniaxial pressures along the crystallographic directions and and for temperatures when the uniaxial pressure is directed along the crystallographic directions . The mechanism of electron scattering on a charged radiation defects (which correspond to the deep energy levels of A-centers) ‘is turned off’ for the given temperatures due to the uniaxial pressure. Reduction of the Hall mobility in transition through a maximum of dependence with the increasing temperature for cases of the uniaxial deformation of the irradiated single crystals along the crystallographic directions and is explained by the deforming redistribution of electrons between the minima of conduction band of germanium with different mobility.

Spin susceptibility and electron-phonon coupling of two-dimensional materials by range-separated hybrid density functionals: Case study ofLixZrNCl

We investigate the capability of density functional theory (DFT) to appropriately describe the spin susceptibility, $\chi_s$, and the intervalley electron-phonon coupling in Li$_x$ZrNCl. At low doping, Li$_x$ZrNCl behaves as a two-dimensional two-valley electron gas, with parabolic bands. In such a system, $\chi_s$ increases with decreasing doping because of the electron-electron interaction. We show that DFT with local functionals (LDA/GGA) is not capable of reproducing this behavior. The use of exact exchange in Hartree-Fock (HF) or in DFT hybrid functionals enhances $\chi_s$. HF, B3LYP, and PBE0 approaches overestimate $\chi_s$, whereas the range-separated HSE06 functional leads to results similar to those obtained in the random phase approximation (RPA) applied to a two-valley two-spin electron gas. Within HF, Li$_x$ZrNCl is even unstable towards a ferromagnetic state for $x<0.16$. The intervalley phonons induce an imbalance in the valley occupation that can be viewed as the effect of a pseudomagnetic field. Thus, similarly to what happens for $\chi_s$, the electron-phonon coupling of intervalley phonons is enhanced by the electron-electron interaction. Only hybrid DFT functionals capture such an enhancement and the HSE06 functional reproduces the RPA results presented in M. Calandra {\it et al.} [Phys. Rev. Lett. {\bf 114}, 077001 (2015)]. These results imply that the description of the susceptibility and electron-phonon coupling with a range-separated hybrid functional would be important also in other two-dimensional weakly doped semiconductors, such as transition-metal dichalcogenides and graphene.

Hot carrier and hot phonon coupling during ultrafast relaxation of photoexcited electrons in graphene

We study, by means of a Monte Carlo simulator, the hot phonon effect on the relaxation dynamics in photoexcited graphene and its quantitative impact as compared with considering an equilibrium phonon distribution. Our multi-particle approach indicates that neglecting the hot phonon effect significantly underestimates the relaxation times in photoexcited graphene. The hot phonon effect is more important for a higher energy of the excitation pulse and photocarrier densities between 1 and 3 × 1012 cm−2. Acoustic intervalley phonons play a non-negligible role, and emitted phonons with wavelengths limited up by a maximum (determined by the carrier concentration) induce a slower carrier cooling rate. Intrinsic phonon heating is damped in graphene on a substrate due to the additional cooling pathways, with the hot phonon effect showing a strong inverse dependence with the carrier density.

Very large strain gauges based on single layer MoSe2 and WSe2 for sensing applications

Here, we propose a strain gauge based on single-layer MoSe2 and WSe2 and show that, in these materials, the strain induced modulation of inter-valley phonon scattering leads to large mobility changes, which in turn result in highly sensitive strain gauges. By employing density-functional theory bandstructure calculations, comprehensive scattering models, and the linearized Boltzmann equation, we explain the physical mechanisms for the high sensitivity to strain of the resistivity in single-layer MoSe2 and WSe2, discuss the reduction of the gauge factor produced by extrinsic scattering sources (e.g., chemical impurities), and propose ways to mitigate such sensitivity degradation.

Impact of non uniform strain configuration on transport properties for FD14+ devices

As device dimensions are scaled down, the use of non-geometrical performance boosters becomes of special relevance. In this sense, strained channels are proposed for the 14nm FDSOI node. However this option may introduce a new source of variability since strain distribution inside the channel is not uniform at such scales. In this work, a MS-EMC study of different strain configurations including non-uniformities is presented showing drain current degradation because of the increase of intervalley phonon scattering and the subsequent variations of transport effective mass and drift velocity. This effect, which has an intrinsic statistical origin, will make necessary further optimizations to keep the expected boosting capabilities of strained channels.