Piezoelectric Phonons Research Articles

Energy loss in nano-dimensional wire structures due to piezoelectric interaction at low temperatures

The theory of energy loss rate of non-equilibrium electrons due to inelastic interaction with intravalley piezoelectric phonons in a nano-dimensional semiconductor wire has been developed under the condition of low lattice temperatures, without recourse to the standard approximations which are usually made when developing theories at relatively higher temperatures. Such approximations are hardly valid when the lattice temperature is low. As expected, compared to the well-known earlier results, the theory here, reveals a complex and altogether different dependence of the energy loss rate upon the carrier energy and the lattice temperature. The numerical results have been obtained for narrow channel wires of GaAs and GaN. On comparison with other available results, it is revealed that the finite energy of piezoelectric phonons and the full form of the phonon distribution bring about quite significant changes in the energy loss characteristics at low temperatures.

Hot electron transport in wurtzite-GaN: effects of temperature and doping concentration

The hot electron transport in wurtzite phase gallium nitride (Wz-GaN) has been studied in this paper. An analytical expression of electron drift velocity under the condition of impact ionization has been developed by considering all major scattering mechanisms such as deformation potential acoustic phonon scattering, piezoelectric acoustic phonon scattering, optical phonon scattering, electron-electron scattering and ionizing scattering. Numerical calculations show that electron drift velocity in Wz-GaN saturates at 1.44 × 105 m/s at room temperature for the electron concentration of 1022 m−3. The effects of temperature and doping concentration on the hot electron drift velocity in Wz-GaN have also been studied. Results show that the saturation electron drift velocity varies from 1.91 × 105–0.77 × 105 m/s for the change in temperature within the range of 10–1000 K, for the electron concentration of 1022 m−3; whereas the same varies from 1.44 × 105–0.91 × 105 m/s at 300 K for the variation in the electron concentration within the range of 1022–1025 m−3. The numerically calculated results have been compared with the Monte Carlo simulated results and experimental data reported earlier, and those are found to be in good agreement.

Local Electron Interaction with Point Defects in Sphalerite Zinc Selenide: Calculation from First Principles

The present article deals with the description of electron scattering on the different types of point defects in zinc blende ZnSe on the basis of short-range principles. The electron interaction with polar and nonpolar optical phonons, piezoelectric and acoustic phonons, neutral and ionized impurities and static strain centers is considered. The electron transition probabilities and, respectively, the kinetic coefficients in zinc selenide, were calculated using the numerical eigenfunction and self-consistent potential obtained within the ab initio density functional theory. The latter were evaluated using the projector augmented waves formalism as implemented in the ABINIT software suite. We investigated ZnSe samples with defect concentration 4.7 × 1015–1.08 × 1017 cm−3 , then calculated temperature dependencies of electron mobility and Hall factors in the range of 20–400 K. It is shown that the theoretical curves obtained in the framework of short-range scattering models much better coincide with experimental data than the curves calculated on the basis of long-range scattering models.

An analysis of phonon emission as controlled by the combined interaction with the acoustic and piezoelectric phonons in a degenerate III–V compound semiconductor using an approximated Fermi–Dirac distribution at low lattice temperatures

Compound semiconductors being piezoelectric in nature, the intrinsic thermal vibration of the lattice atoms at any temperature gives rise to an additional potential field that perturbs the periodic potential field of the atoms. This is over and above the intrinsic deformation acoustic potential field which is always produced in every material. The scattering of the electrons through the piezoelectric perturbing potential is important in all compound semiconductors, particularly at the low lattice temperatures. Thus, the electrical transport in such materials is principally controlled by the combined interaction of the electrons with the deformation potential acoustic and piezoelectric phonons at low lattice temperatures. The study here, deals with the problem of phonon growth characteristics, considering the combined scattering of the non-equilibrium electrons in compound semiconductors, at low lattice temperatures. Beside degeneracy, other low temperature features, like the inelasticity of the electron–phonon collisions, and the full form of the phonon distribution have been duly considered. The distribution function of the degenerate ensemble of carriers, as given by the heated Fermi–Dirac function, has been approximated by a simplified, well-tested model. The model which has been proposed earlier, makes it much easier to carry out analytically the integrations without usual oversimplified approximations.

Diminution of impact ionization rate of charge carriers in semiconductors due to acoustic phonon scattering

The effects of acoustic phonon scattering on the impact ionization rate of charge carriers in a semiconductor have been studied in this paper. The inelastic interactions of charge carriers with both deformation and piezoelectric acoustic phonons have been considered. An analytical expression of impact ionization rate has been developed by considering all possible types of inelastic collision mechanisms such as acoustic phonon scattering, optical phonon scattering, and inter-carrier scattering prior to the ionizing collision. The said expression has been used to calculate the impact ionization rate of electrons and holes in 4H-SiC as functions of electric field and doping concentration at room temperature. Numerical results show that the ionization rate of charge carriers deteriorates significantly due to the interactions of those with acoustic phonons. This deterioration is found to be more pronounced in hot carriers. The numerical results calculated from the present model have been compared with the ionization rate data calculated numerically using an earlier developed analytical expression of ionization rates, which does not take into account the acoustic phonon-scattering events. The calculated results have also been compared with earlier reported experimental data. It is observed that the numerical results obtained from the present model are in better agreement with the experimental results.

Many-body effects in doped graphene on a piezoelectric substrate

We investigate the many-body properties of graphene on top of a piezoelectric substrate, focusing on the interaction between the graphene electrons and the piezoelectric acoustic phonons. We calculate the electron and phonon self-energies as well as the electron mobility limited by the substrate phonons. We emphasize the importance of the proper screening of the electron-phonon vertex and discuss the various limiting behaviors as a function of electron energy, temperature, and doping level. The effect on the graphene electrons of the piezoelectric acoustic phonons is compared with that of the intrinsic deformation acoustic phonons of graphene. Substrate phonons tend to dominate over intrinsic ones for low doping levels at high and low temperatures.

Heating of carriers as controlled by the combined interactions with acoustic and piezoelectric phonons in degenerate III-V semiconductors at low lattice temperature

In compound semiconductors which lack inversion symmetry, the combined interaction of the electrons with both acoustic and piezoelectric phonons is dominant at low lattice temperatures (~ 20K). The field dependence of the effective electron temperature under these conditions, has been calculated by solving the modified energy balance equation that takes due account of the degeneracy. The traditionally used heated Fermi-Dirac (F.D.) function for the non-equilibrium distribution function is approximated by some well tested model distribution. This makes it possible to carry out the integrations quite easily and, thus to obtain some more realistic results in a closed form, without taking recourse to any oversimplified approximations. The numerical results that follow for InSb, InAs and GaN, from the present analysis, are then compared with the available theoretical and experimental data. The degeneracy and the piezoelectric interaction, both are seen to bring about significant changes in the electron temperature characteristics. The scope for further refinement is discussed.

Piezoelectric interaction in controlling the effective electron temperature and the non-ohmic mobility characteristics in GaN and other III–V compounds at low lattice temperature

In a compound semiconductor that lacks inversion symmetry, the free electrons interact simultaneously with the piezoelectric and acoustic phonons. This combined interaction principally controls the electrical transport at low lattice temperatures. Again, at low temperatures, the electrons in some of the compounds may be significantly perturbed for comparatively low fields, say, even for a fraction of a Vcm−1 or so, which effectively seems to be high enough, and the material exhibits electrical nonlinearity. Such a perturbed ensemble then attains a field dependent effective electron temperature Te, which exceeds the lattice temperature TL. The relative importance of the piezoelectric interaction in controlling the field dependence of the effective electron temperature, and therefrom, the non-ohmic mobility characteristics have been analyzed here under the condition of low lattice temperature. The numerical results obtained for InSb, InAs, and GaN are studied in detail. When compared with the experiments, the results here seem to give the same qualitative picture with respect to the variation of the non-ohmic mobility with the electric field for the indium compounds. The results, being interesting, stimulate further work in the same field.

The local electron interaction with crystal defects in wurtzite CdS

AbstractIn the present paper the interaction of electrons with different types of defects with the potential of the limited action radius – polar and nonpolar optical phonons, piezoelectric and acoustic phonons, static strain centers, ionized and neutral impurities – in cadmium sulfide is considered. The dopant concentration in observed CdS crystals was in the limits of 5.5×1015 ÷ 1.1×1019 cm‐3. The dependences of the electron mobility and Hall factor on temperature in the interval 10 ÷ 400 K are investigated. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Density Dependence of Electron Spin Relaxation Time in GaA

The electron density dependence of the electron spin relaxation time in a system of electrons interacting with phonons through phonon-modulated spin-orbit coupling was calculated using the formula for electron spin resonance derived by the projection-reduction method. The electron spin relaxation time in GaAs increased with increasing electron density, and the electron density was found to affect the electron spin relaxation differently according to temperature. The electron spin in GaAs was relaxed mainly by optical phonon scattering at high electron densities and piezoelectric phonon scattering at relatively low electron densities.

SA-phonon-assisted cyclotron resonance via two-photon process in graphene on GaAs substrate

The phonon-assisted cyclotron resonance (PACR) effect in a single-layer graphene on a GaAs substrate are theoretically studied via one and two-photon absorption processes. The result is limited by the combined interaction of the extrinsic potential of piezoelectric surface acoustic phonons of the substrate (PA) and of the intrinsic deformation potential of acoustic phonons of graphene (DA). The two-photon absorption process gives a significant contribution to magneto-optical absorption coefficient compared to one-photon process. It is shown that in the regime of low magnetic fields and temperatures the PA phonons dominate the magneto-optical absorption coefficient and half-width at half-maximum (HWHM). This finding would be useful to examine in subsequent research about HWHM in graphene. The present results have also demonstrated that the optical properties of graphene on a GaAs substrate can be controlled via extrinsic piezoelectric coupling.

Peculiarities of magnetoresistance in InSb whiskers at cryogenic temperatures

The study of the magnetoresistance in InSb whiskers with an impurity concentration in the vicinity to the metal-insulator phase transition, at low temperature range 4.2–77K, and in fields, with induction up to 14T, was conducted. The presence of Shubnikov-de Haas oscillations in both transverse and longitudinal magnetoresistance was observed. The following parameters of InSb whiskers were defined: period of oscillations 0.1Т−1, cyclotron effective mass of electrons mс≈0.14mо, concentration of charge carriers 2.3×1017сm−3, g-factor g*≈30 and Dingle temperature ТD=14.5K. To determine the nature of crystal defects, the electron scattering processes on the short-range potential, caused by interaction with polar and nonpolar optical phonons, piezoelectric and acoustic phonons, static strain centers and ionized impurities in n-InSb whiskers, with defect concentration 2.9×1017cm−3, are considered. The temperature dependences of electron mobility in the range 4.2–500K were calculated.

Piezoelectric scattering limited mobility as controlled by the transverse component of the phonon wave vector in quantum layers at low temperatures

Theory of the momentum relaxation time of the carriers and of their ohmic mobility in a quantum well in a non-degenerate compound semiconductor has been developed for interaction with piezoelectric phonons at low temperatures. The calculations have been made without taking recourse either to the Kawaji's traditional model of interaction with only the in-plane component of the phonon wave vector or to the equipartition approximation for the phonon population. The numerical results obtained for inversion layers in GaAs and CdS describe how significantly does the consideration of the transverse component of the phonon wave vector in the light of the Ridley's momentum conservation approximation or of the true phonon distribution bring in significant changes in the transport characteristics compared to what the traditional approximations predict.

Electron spin relaxation in two polymorphic structures of GaN

The relaxation process of electron spin in systems of electrons interacting with piezoelectric deformation phonons that are mediated through spin–orbit interactions was interpreted from a microscopic point of view using the formula for the electron spin relaxation times derived by a projection-reduction method. The electron spin relaxation times in two polymorphic structures of GaN were calculated. The piezoelectric material constant for the wurtzite structure obtained by a comparison with a previously reported experimental result was . The temperature and magnetic field dependence of the relaxation times for both wurtzite and zinc-blende structures were similar, but the relaxation times in zinc-blende GaN were smaller and decreased more rapidly with increasing temperature and magnetic field than that in wurtzite GaN. This study also showed that the electron spin relaxation for wurtzite GaN at low density could be explained by the Elliot–Yafet process but not for zinc-blende GaN in the metallic regime.

Calculation of the electron spin relaxation times in InSb and InAs by the projection-reduction method

The electron spin relaxation times in a system of electrons interacting with piezoelectric phonons mediated through spin-orbit interactions were calculated using the formula derived from the projection-reduction method. The results showed that the temperature and magnetic field dependence of the relaxation times in InSb and InAs were similar. The piezoelectric material constants obtained by a comparison with the reported experimental result were Ppe=4.0×1022 eV/m for InSb and Ppe=1.2×1023 eV/m for InAs. The result also showed that the relaxation of the electron spin by the Elliot-Yafet process is more relevant for InSb than InAs at a low density.

Electron scattering on the short-range potential of the crystal lattice defects in ZnO

The processes of electron scattering on a short-range potential caused by interaction with polar and nonpolar optical phonons, piezoelectric and acoustic phonons, static strain, and neutral and ionized impurities in wurtzite n-ZnO with impurity concentration ∼1 × 1017 cm−3 are considered. The temperature dependences of electron mobility and Hall factor in the range 15/550 K are calculated.

Piezoelectric surface acoustical phonon amplification in graphene on a GaAs substrate

We study the interaction of Dirac Fermions in monolayer graphene on a GaAs substrate in an applied electric field by the combined action of the extrinsic potential of piezoelectric surface acoustical phonons of GaAs (piezoelectric acoustical (PA)) and of the intrinsic deformation potential of acoustical phonons in graphene (deformation acoustical (DA)). We find that provided the dc field exceeds a threshold value, emission of piezoelectric (PA) and deformation (DA) acoustical phonons can be obtained in a wide frequency range up to terahertz at low and high temperatures. We found that the phonon amplification rate RPA,DA scales with TBGS−1 (S=PA,DA), TBGS being the Block−Gru¨neisen temperature. In the high-T Block−Gru¨neisen regime, extrinsic PA phonon scattering is suppressed by intrinsic DA phonon scattering, where the ratio RPA/RDA scales with ≈1/n, n being the carrier concentration. We found that only for carrier concentration n≤1010cm−2, RPA/RDA>1. In the low-T Block−Gru¨neisen regime, and for n=1010cm−2, the ratio RPA/RDA scales with TBGDA/TBGPA≈7.5 and RPA/RDA>1. In this regime, PA phonon dominates the electron scattering and RPA/RDA<1 otherwise. This study is relevant to the exploration of the acoustic properties of graphene and to the application of graphene as an acoustical phonon amplifier and a frequency-tunable acoustical phonon device.

Electron spin relaxation times by piezoelectric and polar optical phonon scattering in GaAs

The electron spin relaxation times by piezoelectric and polar optical phonon scattering in GaAs are calculated using the formula derived from the projection-reduction method. The temperature, magnetic field, and electron density dependences of the relaxation time are investigated. The electrons are found to be scattered mostly by piezoelectric phonons at low temperatures and polar optical phonons at high temperatures. The electron density affects the magnetic field dependence of the relaxation time at low temperatures but have only slight affects at high temperatures.

Piezoelectric interaction in quantum wires at low temperatures

The theory of piezoelectric scattering rate and of the corresponding zero-field mobility in quantum wires has been developed under the condition of low temperature when the well known approximations of the traditional theory are hardly valid. The scattering rate and the mobility characteristics thus revealed from the present analysis are quite complex and significantly different from what the traditional theory predicts. The numerical results obtained for narrow channel wires of GaAs and ZnO, show how do the finite energy of the piezoelectric phonons and the full form of the phonon distribution bring about quite significant changes in the transport characteristics at low temperatures.

Effect of temperature on the transconductance of AlGaN/GaN high electron mobility transistors (HEMT)

An analytical-numerical model for the electronic current of two dimensional quantum well AlGaN/GaN in high electron mobility transistors has been developed in this paper that is capable of accurately predicting the effect of temperature on the electronic current of two dimensional quantum well and transconductance . Salient futures of the model are incorporated of fully and partially occupied sub-bunds in the interface quantum well .In addition temperature dependent of band gap , quantum well electron density , threshold voltage, mobility of electron , dielectric constant , polarization induce charge density in the device are also take in to account . In order to obtain accurate values for the Fermi energy, the energies of quantized levels within the two dimensional electron gas (2DEG), the occupancy of the various sub-bands, the intrasub-band and intersub-band coupling coefficients (Hmn) for the two dimensional electron gas in AlGaN/GaN heterostructures; both the Schrodinger and Poisson equations must be solved self-consistently. This has been achieved by solving Schrodinger’s equation and simultaneously taking into account the electrostatic potential obtained from Poisson’s equation, as well as the image and exchange-correlation potentials using Numerov’s numerical method. In the self-consistent calculation, the nonlinear formulism of the polarization–induced field as a function of Al mole fraction in AlmGa1-mN/GaN heterostructures has been assumed, as well as taking in to account all fully and partially–occupied sub-bands within the interface two dimensional electron gas potential well [1, 2]. Using such an approach, it is possible to calculate the two dimensional electron mobility taking into account the combined contributions from each of the individual electron scattering mechanisms. At high temperature (T ≥ 300K), inelastic polar optical phonon scattering dominates over all other scattering mechanisms. In the linearized Boltzmann equation, the different scattering rates can be separated in to two type: (i) elastic scattering du to acoustic and piezoelectric phonons, ionized impurities and interface roughness, etc., and (ii) inelastic scattering due to polar optical phonons in order to take in to consideration all scattering mechanism in the mobility calculation, it is solve numerically using an iterative