Energy Relaxation Of Hot Electrons Research Articles

Intraband carrier relaxation in mid-infrared (3–4 μm) HgCdTe based structures: Effect of the carrier heating on the operating temperatures of bulk and quantum-well lasers

In this work, we study stimulated emission (SE) at 3–4 μm wavelengths from optically pumped bulk HgCdTe and HgTe/CdHgTe quantum-well heterostructures. It is proposed that, under intense excitation of such structures, energy relaxation of hot electrons occurs mostly via electron–hole scattering, while the relaxation of hot holes is direct, phonon-mediated. By balancing carrier generation/recombination and heating/cooling processes, we outline heat-induced limits to the operating temperatures of mid-IR HgCdTe lasers. Based on the existing experimental results for the SE around 3.5 μm, we predict that lasing at this wavelength may be achieved in 2.5 μm-pumped optical converters at temperatures as high as Tmax ∼ 270 K.

Competition Pathways of Energy Relaxation of Hot Electrons through Coupling with Optical, Surface, and Acoustic Phonons

The hot electrons in carbon-based materials exhibit interesting ballistic transport behaviors for designing high-performance single-electron transistors. However, the cooling of such hot electrons back to the equilibrium state may be slowed down by the excessively populated optical phonons, thus limiting their ballistic transport. Therefore, a thorough understanding of the coupling between hot electrons and optical phonons is of critical importance. Here, by varying the thickness of a multilayer graphene film on a supporting substrate, we investigated the competition pathways of the energy relaxation of the photoinduced hot electrons through coupling with the optical, surface, and acoustic phonons. The difference in the τ2 values indicates that thickness plays an important role in the optical phonon population. For the multilayer graphene film thickness less than 3 nm, the super-collision model describes the hot electron cooling dynamics that is strongly affected by the surface phonons from the supporting substrate. As the multilayer graphene film thickness increases from 3 to 20 nm, the accumulation of the optical phonons induces a hot optical phonon effect, resulting in a bottleneck of cooling of the hot electrons. As the multilayer graphene film thickness further increases from 20 to 40 nm, a direct coupling between the hot electrons and acoustic phonons starts to dominate. The surface states of the interfaces at the inner layers of the multilayer graphene film contribute to this direct coupling as an additional cooling channel. The quantitative understanding of the energy relaxation pathways of the hot electrons offers insights into designing high-performance single-electron transistors.

Electron energy relaxation in SiGe quantum wells

In this article, we theoretically calculated the hot electron energy relaxation induced by longitudinal acoustic (LA) phonons, longitudinal optical (LO) phonons and importantly two-transverse acoustic (2TA) phonons in two-dimensional SiGe quantum wells, by incorporating dynamic screening effect in LA phonon scattering and hot-phonon effect in LO phonon scattering mechanisms. At the low-temperature regime, the ELR is found to be dominated by LA phonons and at higher temperature ELR is dominated by LO phonons. In the intermediate temperature range, 2TA phonon scattering mechanism is very important and we incorporated in our calculations. The unscreened longitudinal acoustic (LA) phonon due to deformation potential (DP) coupling is dominant over the screened acoustic piezoelectric phonon contribution. At higher temperatures, there is a crossover from ELR due to LA phonons to ELR due to longitudinal optical (LO) phonons with the cross-over temperature being about Te∼40K. The LA phonon screening effect and hot phonon effect is demonstrated to reduce ELR significantly. In the intermediate temperature range (30 K

Ultrafast transport and energy relaxation of hot electrons in Au/Fe/MgO(001) heterostructures analyzed by linear time-resolved photoelectron spectroscopy

In condensed matter, scattering processes determine the transport of charge carriers. In case of heterostructures, interfaces determine many dynamic properties like charge transfer and transport and spin current dynamics. Here we discuss optically excited electron dynamics and their propagation across a lattice-matched, metal-metal interface of single crystal quality. Using femtosecond time-resolved linear photoelectron spectroscopy upon optically pumping different constituents of the heterostructure we establish a technique which probes the electron propagation and its energy relaxation simultaneously. In our approach a near-infrared pump pulse excites electrons directly either in the Au layer or in the Fe layer of epitaxial Au/Fe/MgO(001) heterostructures while the transient photoemission spectrum is measured by an ultraviolet probe pulse on the Au surface. Upon femtosecond laser excitation, we analyze the relative changes in the electron distribution close to the Fermi energy and assign characteristic features of the time-dependent electron distribution to transport of hot and non-thermalized electrons from the Fe layer to the Au surface and vice versa. From the measured transient electron distribution we determine the excess energy which we compare with a calculation based on the two-temperature model and takes diffusive electron transport into account. On this basis we identify a transition from a super-diffusive to a diffusive transport regime to occur for a Au layer thickness of 20-30~nm.

Indirect Measurement of Electron Energy Relaxation Time at Room Temperature in Two-Dimensional Heterostructured Semiconductors.

Hot carriers are a critical issue in modern photovoltaics and miniaturized electronics. We present a study of hot electron energy relaxation in different two-dimensional electron gas (2DEG) structures and compare the measured values with regard to the dimensionality of the semiconductor formations. Asymmetrically necked structures containing different types of AlGaAs/GaAs single quantum wells, GaAs/InGaAs layers, or bulk highly and lowly doped GaAs formations were investigated. The research was performed in the dark and under white light illumination at room temperature. Electron energy relaxation time was estimated using two models of I-V characteristics analysis applied to a structure with n-n+ junction and a model of voltage sensitivity dependence on microwave frequency. The best results were obtained using the latter model, showing that the electron energy relaxation time in a single quantum well structure (2DEG structure) is twice as long as that in the bulk semiconductor.

Energy relaxation of quantum dot hot electrons in hybrid quantum dot—Bose–Einstein condensate system

The theory of electron energy relaxation in a hybrid structure consisting of quantum dot interacting with a two dimensional exciton gas in Bose–Einstein condensate (BEC) regime is developed. A new type of the relaxation mechanism in the presence of BEC is introduced and theoretically analyzed. It is shown that, in the first order of electron-exciton interaction, two microscopic processes of energy relaxation appear. The first one is related to the emission of a single Bogoliubov excitation (bogolon) by an electron, whereas the second process is associated with the emission of two bogolons. It is shown that the second type processes dominate in the QD electron energy relaxation.

Significant energy relaxation of quantum dot emitted hot electrons

Mesoscopic quantum dots (QDs) are ubiquitous in quantum devices as reliable sources of hot electrons. However, we have observed an unexpectedly significant energy relaxation of QD-emitted hot electrons up to $\ensuremath{\approx}55%$ of its excitation $\ensuremath{\le}1.5\phantom{\rule{4pt}{0ex}}\mathrm{meV}$ from the Fermi level. The energetics of hot electrons were obtained through transverse magnetic focusing over a few microns using both QD and quantum point contact (QPC) emitters. Unlike the QPC counterparts, QD emissions deviated substantially from Fermi gas predictions---the focusing peak appeared at lower magnetic fields, and excessive broadening was observed. The phenomenon was modeled by a capacitive interaction transferring energy from the hot electron to the QD. Model simulations reproduced the key experimental features, implying the presence of a strong yet overlooked relaxation mechanism that is intrinsic to QD emissions. Our observation calls for the prudent use of QDs as single electron sources.

Self-formation of high-field domain in epitaxial ZnO and its suppression in ZnO/MgZnO heterostructure

Microwave noise is used to study high-electric-field electronic properties of ZnO channels with electron densities in the range from 1017 to 1019 cm–3. The strong source of noise is observed to superimpose onto the standard hot-electron noise governed by the hot-electron energy relaxation. At a given current, the excess noise temperature ΔTn increases with the channel length, and values up to and above 10 000 K are reached. The steep dependence ΔTn∝I12 on the current I approximately holds for the longest channels. The source of noise in question is suppressed in ZnO epilayers at high electron densities and in a ZnO/MgZnO heterostructure with two-dimensional electron gas. The observed results are evaluated and discussed in terms of the self-formation of high field domains. The estimated domain voltage Ud increases with the current; the dependence is close to Ud∝I6. The domain self-formation is additionally confirmed by measuring the spectral density of current fluctuations; the usual hot-electron noise turns into shot noise as the current increases. The Fano factor demonstrates an increasing number of nearly ballistic electrons that traverse the self-supporting domain.

Inverse spin-Hall effect in GeSn

Due to the long spin lifetime and its optical and electrical properties, GeSn is a promising candidate for the integration of spintronics, photonics, and electronics. Here, we investigate the photoinduced inverse spin-Hall effect in a GeSn alloy with 5% Sn concentration. We generate a spin-polarized electron population at the Γ point of the GeSn conduction band by means of optical orientation, and we detect the inverse spin-Hall effect signal coming from the spin-to-charge conversion in GeSn. We study the dependence of the inverse spin-Hall signal on the kinetic energy of the spin-polarized carriers by varying the energy of the impinging photons in the 0.5–1.5 eV range. We rationalize the experimental data within a diffusion model which explicitly accounts for momentum, energy, and spin relaxation of the spin-polarized hot electrons. At high photon energies, when the spin relaxation is mainly driven by phonon scattering, we extract a spin-Hall angle in GeSn which is more than ten times larger than the one of pure Ge. Moreover, the spin–charge interconversion for electrons lying at the Δ valleys of GeSn results to be ≈4.3 times larger than the one for electrons at L valleys.

Effect of spin–orbit coupling on the hot-electron energy relaxation in nanowires

The energy relaxation of hot electrons is proposed based on the spin–orbit (SO) interaction of both Rashba and Dresselhaus types with the effect of hot phonons. A continuum theory of optical phonons in nanowires taking into account the influence of confinement is used to study the hot-electron energy relaxation. The energy relaxation due to both confined (CO) and interface (IO) optical phonon emission on nanowire radius, electrical field strength, parameters of SO couplings and electron temperature is calculated. For considered values of the nanowire radius as well as other system parameters, scattering by IO phonons prevails over scattering by CO phonons. The presence of an electric field leads to the decrease of power loss in transitions between states with the same spin quantum numbers. With the increase of the electric field strength, the influence of the Dresselhaus SO interaction on the energy relaxation rate decreases. The effect of SO interaction does not change the previously obtained increasing dependence of power loss on electron temperature. The sensitivity of energy relaxation to the electric field also through the Rashba parameter allows controlling the rate of energy by electric field.

Hot electron energy relaxation time in vanadium nitride superconducting film structures under THz and IR radiation

The paper presents the experimental results of studying the dynamics of electron energy relaxation in structures made of thin (d ≈ 6 nm) disordered superconducting vanadium nitride (VN) films converted to a resistive state by high-frequency radiation and transport current. Under conditions of quasi-equilibrium superconductivity and temperature range close to critical (~ Tc), a direct measurement of the energy relaxation time of electrons by the beats method arising from two monochromatic sources with close frequencies radiation in sub-THz region (ω ≈ 0.140 THz) and sources in the IR region (ω ≈ 193 THz) was conducted. The measured time of energy relaxation of electrons in the studied VN structures upon heating of THz and IR radiation completely coincided and amounted to (2.6–2.7) ns. The studied response of VN structures to IR (ω ≈ 193 THz) picosecond laser pulses also allowed us to estimate the energy relaxation time in VN structures, which was ~ 2.8 ns and is in good agreement with the result obtained by the mixing method. Also, we present the experimentally measured volt-watt responsivity (S~) within the frequency range ω ≈ (0.3–6) THz VN HEB detector. The estimated values of noise equivalent power (NEP) for VN HEB and its minimum energy level (δE) reached NEP@1MHz ≈ 6.3 × 10–14 W/√Hz and δE ≈ 8.1 × 10–18 J, respectively.

Effect of annealing process on hot-electron energy relaxation rates in n-type modulation-doped Ga0.68In0.32N0.017As/GaAs quantum wells via deformation potential and piezoelectric scatterings

Hot electrons relax by interacting with phonons, so information about the electron-phonon interaction mechanisms are obtained by examining the cooling processes of hot electrons. In this study, the effect of annealing time on the electron temperature and energy relaxation rates in as-grown and annealed n-type modulation-doped Ga0.68In0.32N0.017As0.983/GaAs quantum well (QW) samples were investigated by comparing the relative amplitudes of Shubnikov-de Haas oscillations as a function of temperature and electric field. The samples were grown by molecular beam epitaxy (MBE) and annealed at 700 °C for 60 s and 600 s. Experiments were carried out by applying an electric field between 0.165 and 5.276 kV/m at a temperature range between 1.8 and 40 K under magnetic up to 11 T. The energy-relaxation mechanism is found to be a mixing of piezoelectric and deformation potential scatterings of hot electrons in the low-temperature regime up to 40 K electron temperature. The electron power loss by interacting with phonons is characterized with exponential term γ, which is found to be in the range from 3.42 to 4.97. The change of γ showed that the scattering mechanisms are affected by the annealing time. The piezoelectric stress constant (e14) chosen as a fit parameter in the theoretical power loss calculations, which was found between 0.129 and 0.134. The crystal quality at low temperatures has been observed to be effective on energy relaxation times.

Hot electron cooling in Dirac semimetal Cd3As2 due to polar optical phonons

A theory of hot electron cooling power due to polar optical phonons Pop is developed in 3D Dirac semimetal (3DDS) Cd3As2 taking account of hot phonon effect. Hot phonon distribution Nq and Pop are investigated as a function of electron temperature Te, electron density ne, and phonon relaxation time . It is found that Pop increases rapidly (slowly) with Te at lower (higher) temperature regime. Whereas, Pop is weakly decreasing with increasing ne. The results are compared with those for three-dimensional electron gas (3DEG) in Cd3As2 semiconductor. Hot phonon effect is found to reduce Pop considerably and it is stronger in 3DDS Cd3As2 than in Cd3As2 semiconductor. Pop is also compared with the hot electron cooling power due to acoustic phonons Pac. We find that a crossover takes place from Pac dominated cooling at low Te to Pop dominated cooling at higher Te. The temperature at which this crossover occurs shifts towards higher values with the increase of ne. Also, hot electron energy relaxation time is discussed. It is suggested that can be tuned to achieve faster or slower energy loss for suitable applications of Cd3As2.

Time‐Resolved Pump–Probe Measurement of Optical Rotatory Dispersion in Chiral Metamaterial

A plasmonic chiral metamaterial is fabricated from a thin Au film and exhibits static optical rotatory power (ORP) in the visible spectral range. Transient ORP is measured to clarify the temporal development of ORP using a circularly polarized light (CPL) pump beam. Three distinct transient behaviors of ORP are identified, resulting from different energy relaxation processes of hot electrons that occur during a period of a few picoseconds after pumping. Nonthermal hot electrons experience Lorentz force from an inverse Faraday effect and electron–boundary scattering, yielding a pump beam CPL helicity‐dependent transient ORP. Once hot electrons are in thermal equilibrium with the lattice, electron energy is distributed among the occupied states, as described by Fermi–Dirac statistics. Moreover, the transient ORP is independent of pump beam CPL helicity, well explained by the selection rule of electron excitation and two‐temperature model of the electron cooling process. Theoretical analysis of the transient ORP in terms of the energy relaxation of thermal hot electrons is carried out by introducing a temperature‐dependent dielectric function and finite‐difference time‐domain simulation. It is found that the magnitude of ORP at an elevated temperature is reduced to less than that at room temperature, agreeing well with the experimental observation.

Energy relaxation of hot electrons in III-N bulk materials

Energy relaxation of the hot electrons in GaN, AlN and InN is investigated and compared based on a simple analytical model with both the hot-phonon effect (HPE) and the nonparabolicity of the conduction band taken into account. The impact of the HPE on the energy relaxation time is estimated by using various optical phonon lifetimes. The calculation results show that for this group of III nitrides, the energy relaxation time first falls rapidly and then saturates with the increasing electron temperature, and is higher at a high electron density. The presence of the HPE slows down the power dissipation and increases the energy relaxation time of the hot electrons of the density 1 × 1018 cm−3 (or 1 × 1019 cm−3) by around one or two orders of magnitude at an electron temperature within 3000 K. In particular, the saturated energy relaxation times are 0.12 ps in the bulk GaN, 22 fs in AlN and 26 fs in InN for an electron density of 1 × 1018 cm−3, which imply a rather weak HPE in the AlGaN and AlInN alloys.

Energy relaxation of hot electrons by LO phonon emission in AlGaN/AlN/GaN heterostructure with in situ Si3N4 passivation

In this study, energy relaxation mechanisms of electrons in AlGaN/AlN/GaN High Electron Mobility Transistor (HEMT) structures with and without in situ Si3N4 passivation were investigated. Although the physical parameters of the samples were all different, the electron-temperature dependent power loss values were found to be identical. The study also sought to fit the current theoretical power loss in the LO-phonon regime to the experimental power-loss per carrier results. The calculated power loss offered a reasonably fit to the experimental data in the electron temperature range between 75 and 250 K.

Hot-electron energy relaxation time in Ga-doped ZnO films

Hot-electron energy relaxation time is deduced for Ga-doped ZnO epitaxial layers from pulsed hot-electron noise measurements at room temperature. The relaxation time increases from ∼0.17 ps to ∼1.8 ps when the electron density increases from 1.4 × 1017 cm−3 to 1.3 × 1020 cm−3. A local minimum is resolved near an electron density of 1.4 × 1019 cm−3. The longest energy relaxation time (1.8 ps), observed at the highest electron density, is in good agreement with the published values obtained by optical time-resolved luminescence and absorption experiments. Monte Carlo simulations provide a qualitative interpretation of our observations if hot-phonon accumulation is taken into account. The local minimum of the electron energy relaxation time is explained by the ultrafast plasmon-assisted decay of hot phonons in the vicinity of the plasmon–LO-phonon resonance.

Hot electron energy relaxation in lattice-matched InAlN/AlN/GaN heterostructures: The sum rules for electron-phonon interactions and hot-phonon effect

Using the dielectric continuum (DC) and three-dimensional phonon (3DP) models, energy relaxation (ER) of the hot electrons in the quasi-two-dimensional channel of lattice-matched InAlN/AlN/GaN heterostructures is studied theoretically, taking into account non-equilibrium polar optical phonons, electron degeneracy, and screening from the mobile electrons. The electron power dissipation (PD) and ER time due to both half-space and interface phonons are calculated as functions of the electron temperature Te using a variety of phonon lifetime values from experiment, and then compared with those evaluated by the 3DP model. Thereby, particular attention is paid to examination of the 3DP model to use for the hot-electron relaxation study. The 3DP model yields very close results to the DC model: With no hot phonons or screening, the power loss calculated from the 3DP model is 5% smaller than the DC power dissipation, whereas slightly larger 3DP power loss (by less than 4% with a phonon lifetime from 0.1 to 1 ps) is obtained throughout the electron temperature range from room temperature to 2500 K after including both the hot-phonon effect (HPE) and screening. Very close results are obtained also for ER time with the two phonon models (within a 5% of deviation). However, the 3DP model is found to underestimate the HPE by 9%. The Mori-Ando sum rule is restored by which it is proved that the PD values obtained from the DC and 3DP models are in general different in the spontaneous phonon emission process, except when scattering with interface phonons is sufficiently weak, or when the degenerate modes condition is imposed, which is also consistent with Register's scattering rate sum rule. The discrepancy between the DC and 3DP results is found to be caused by how much the high-energy interface phonons contribute to the ER: their contribution is enhanced in the spontaneous emission process but is dramatically reduced after including the HPE. Our calculation with both phonon models has obtained a great fall in ER time at low electron temperatures (Te < 750 K) and slow decrease at the high temperatures with the use of decreasing phonon lifetime with Te. The calculated temperature dependence of the relaxation time and the high-temperature relaxation time ∼0.09 ps are in good agreement with experimental results.

Energy relaxation and separation of a hot electron-hole pair in organic aggregates from a time-dependent wavepacket diffusion method.

The time-dependent wavepacket diffusive method [X. Zhong and Y. Zhao, J. Chem. Phys. 138, 014111 (2013)] is extended to investigate the energy relaxation and separation of a hot electron-hole pair in organic aggregates with incorporation of Coulomb interaction and electron-phonon coupling. The pair initial condition generated by laser pulse is represented by a Gaussian wavepacket with a central momentum. The results reveal that the hot electron energy relaxation is very well described by two rate processes with the fast rate much larger than the slow one, consistent with experimental observations, and an efficient electron-hole separation is accomplished accompanying the fast energy relaxation. Furthermore, although the extra energy indeed helps the separation by overcoming the Coulomb interaction, the width of initial wavepacket is much sensitive to the separation efficiency and the narrower wavepacket generates the more separated charges. This behavior may be useful to understand the experimental controversy of the hot carrier effect on charge separation.

Energy relaxation of hot electrons in Si-doped GaN

Energy relaxation of the hot electrons in Si-doped bulk GaN is studied theoretically, taking into account non-equilibrium polar optical phonons, electron degeneracy, and screening from the mobile electrons. The electron power dissipation and energy relaxation time are calculated as functions of the electron temperature Te, the hot-phonon effect (HPE) is examined by varying the optical phonon lifetime values, and the results are compared with previous calculations for typical GaN-based heterostructures. Particular attention is paid to the distinct temperature Te dependences of the power loss and the energy relaxation time τE at the low and high electron temperatures. At low electron temperatures (Te<500 K), the exponential rise of phonon generation number, fast weakened screening and HPE result in a rapid increase of power loss and sharp drop of relaxation time with Te. At high electron temperatures (Te>1500 K), the power loss increases slowly with Te due to the decrease in phonon generation rate, and the temperature-dependence of the energy relaxation time depends on the polar optical phonon lifetime—saturation in energy relaxation occurs when the phonon lifetime increases or varies little with Te. Our calculated temperature dependences of the energy relaxation time are in good agreement with experimental findings [Liberis et al., Appl. Phys. Lett. 89, 202117 (2006); Matulionis et al., Phys. Status Solidi C 2, 2585 (2005)]. With no HPE, the electron energy relaxation is much faster in bulk GaN (τE∼ several tens femtoseconds) than in the GaN-based heterostructures. However, stronger hot-phonon re-absorption occurs in bulk GaN due to rapid polar-optical phonon emission compared to phonon decay. Therefore, including HPE yields very close power loss and energy relaxation times in bulk and heterostructures with similar densities of electrons (τE∼ several tenths of a picosecond). Transparent expressions for energy relaxation are obtained in the Boltzmann approximation, which are very useful for resolving the temperature dependences of the energy relaxation in the low- and high-Te regions.