Optical Phonon Emission Research Articles

Relaxation of hot electrons in a degenerate two-dimensional electron system: Transition to one-dimensional scattering

The energy relaxation channels of hot electrons far from thermal equilibrium in a degenerate two-dimensional electron system are investigated in transport experiments in a mesoscopic three-terminal device. We observe a transition from two dimensions at zero magnetic field to quasi--one-dimensional scattering of the hot electrons in a strong magnetic field. In the two-dimensional case electron-electron scattering is the dominant relaxation mechanism, while the emission of optical phonons becomes more and more important as the magnetic field is increased. The observation of up to 11 optical phonons emitted per hot electron allows us to determine the onset energy of LO phonons in GaAs at cryogenic temperatures with a high precision, $\eph=36.0\pm0.1\,$meV. Numerical calculations of electron-electron scattering and the emission of optical phonons underline our interpretation in terms of a transition to one-dimensional dynamics.

Depletion of carriers and negative differential conductivity in intrinsic graphene under a dc electric field

The heating of carriers in an intrinsic graphene under an abrupt switching off a dc electric field is examined taking into account both the energy relaxation via acoustic and optic phonons and the interband generation-recombination processes. The later are caused by the interband transitions due to optical phonon modes and thermal radiation. Description of the temporal and steady-state responses, including the nonequilibrium concentration and energy as well as the current-voltage characteristics, is performed. At room temperature, a nearly-linear current-voltage characteristic and a slowly-varied concentration take place for fields up to -- 20 kV/cm. Since a predominant recombination of high-energy carriers due to optical phonon emission at low temperatures, a depletion of concentration takes place below -- 250 K. For lower temperatures the current tends to be saturated and a negative differential conductivity appears below -- 170 K in the region of fields -- 10 V/cm.

Ultrafast nonequilibrium carrier dynamics in a single graphene layer

Nonequilibrium carrier dynamics in single exfoliated graphene layers on muscovite substrates are studied by ultrafast optical pump-probe spectroscopy and compared with microscopic theory. The very high 10-fs-time resolution allows for mapping the ultrafast carrier equilibration into a quasi-Fermi distribution and the subsequent slower relaxation stages. Coulomb-mediated carrier-carrier and carrier-optical phonon scattering are essential for forming hot separate Fermi distributions of electrons and holes which cool by intraband optical phonon emission. Carrier cooling and recombination are influenced by hot phonon effects.

Two-probe study of hot carriers in reduced graphene oxide

The energy relaxation of carriers in reduced graphene oxide thin films is studied using optical pump-probe spectroscopy with two probes of different colors. We measure the time difference between peaks of the carrier density at each probing energy by measuring a time-resolved differential transmission and find that the carrier density at the lower probing energy peaks later than that at the higher probing energy. Also, we find that the peak time for the lower probing energy shifts from about 92 to 37 fs after the higher probing energy peak as the carrier density is increased from 1.5×1012 to 3×1013/cm2, while no noticeable shift is observed in that for the higher probing energy. Assuming the carriers rapidly thermalize after excitation, this indicates that the optical phonon emission time decreases from about 50 to about 20 fs and the energy relaxation rate increases from 4 to 10 meV/fs. The observed density dependence is inconsistent with the phonon bottleneck effect.

Negative differential velocity in ultradilute GaAs1−xNx alloys

We present theoretical results on steady state characteristics in bulk GaAs1−xNx alloys (x ≤ 0.2) using the single electron Monte-Carlo method. Two approaches have been used; the first assumes a GaAs band with a strong nitrogen scattering resonance and the second uses the band anti-crossing model, in which the localized N level interacts with the GaAs band strongly perturbing the conduction band. In the first model we observe two negative differential velocity peaks, the lower one associated with nitrogen scattering while the higher one with polar optical phonon emission accounting for the nonparabolicity effect. In the second model one negative differential velocity peak is observed associated with polar optical phonon emission. Good agreement with experimental low field mobility is obtained from the first model. We also comment on the results from both Models when the intervalley Г → L transfer is accounted for.

Electron transport in bulk GaAsN

We present theoretical results on the steady state characteristics of bulk GaAs1–xNx using the single electron Monte-Carlo method (x ≤ 0.4%). Two equivalent models are used. The first includes a GaAs band with a strong localized nitrogen resonance. The second model uses the band anti-crossing model, in which the localized N level interacts with the GaAs band strongly perturbing the conduction band. We obtain two negative differential velocity peaks from the first model which we associate with N scattering and polar optical phonon emission (POPem). From the second model only one peak is obtained associated with POPem. The first model gives very good agreement with experimental low field mobility. We use this model to include additional scattering resonances related with the pair and larger cluster nitrogen states. Further reduction of the mobility and convergence towards the experimental values is observed.

Heating and cooling of a two-dimensional electron gas by terahertz radiation

The absorption of terahertz radiation by free charge carriers in n-type semiconductor quantum wells accompanied by the interaction of electrons with acoustic and optical phonons is studied. It is shown that intrasubband optical transitions can cause both heating and cooling of the electron gas. The cooling of charge carriers occurs in a certain temperature and radiation frequency region where light is most efficiently absorbed due to intrasubband transitions with emission of optical phonons. In GaAs quantum wells, the optical cooling of electrons occurs most efficiently at liquid nitrogen temperatures, while cooling is possible even at room temperature in GaN heterostructures.

Channel Length Scaling in Graphene Field-Effect Transistors Studied with Pulsed Current−Voltage Measurements

We investigate current saturation at short channel lengths in graphene field-effect transistors (GFETs). Saturation is necessary to achieve low-output conductance required for device power gain. Dual-channel pulsed current-voltage measurements are performed to eliminate the significant effects of trapped charge in the gate dielectric, a problem common to all oxide-based dielectric films on graphene. With pulsed measurements, graphene transistors with channel lengths as small as 130 nm achieve output conductance as low as 0.3 mS/μm in saturation. The transconductance of the devices is independent of channel length, consistent with a velocity saturation model of high-field transport. Saturation velocities have a density dependence consistent with diffusive transport limited by optical phonon emission.

Hot-electron relaxation in ZnO films

The energy relaxation of hot electrons in ZnO films was investigated by the electric-field-dependent photoluminescence. From the high-energy tail of photoluminescence, the electron temperature of the hot electrons in ZnO was determined. Longitudinal optical phonon emission alone cannot explain the relationship between the electron temperature and the electron energy loss rate. Instead, it can be explained by a model based on a combination of both the acoustic and longitudinal optical phonon emissions.

Terahertz electromagnetic waves emitted from semiconductor investigated using terahertz time domain spectroscopy (Invited Paper)

Ultrafast electromagnetic waves radiated from semiconductor material under high electric fields and photoexcited by femtosecond laser pulses have been recorded by using terahertz time domain spectroscopy (THz-TDS). The waveforms of these electromagnetic waves reflect the dynamics of the photoexcited carriers in the semiconductor material, thus, THz-TDS provides a unique opportunity to observe directly the temporal and spatial evolutions of non-equilibrium transport of carriers within sub-picosecond time scale. We report on the observed THz emission waveforms emitted from GaAs by using a novel technology, the time domain THz electro-optic (EO) sampling, which has a bipolar feature, i.e., an initial positive peak and a subsequent negative dip that arises from its velocity overshoot. The initial positive peak has been interpreted as electron acceleration in the bottom of ?? valley in GaAs, where electrons have a light effective mass. The subsequent negative dip has been attributed to intervalley transfer from ?? to X and L valleys. Furthermore, the power dissipation spectra of the bulk GaAs in THz range are also investigated by using the Fourier transformation of the time domain THz traces. From the power dissipation spectra, the cutoff frequency for negative power dissipation (i.e., gain) under step electric field in the bulk GaAs can also be obtained. The cutoff frequency for the gain gradually increases with increasing electric fields up to 50 kV/cm and achieves saturation at approximately 1 THz at 300 K. Furthermore, based on the temperature dependence of the cutoff frequency, we find that this cutoff frequency is governed by the energy relaxation process of electrons from L to ?? valley via successive optical phonon emission.

Saturation of interband absorption in graphene

The transient response of an intrinsic graphene, which is caused by the ultrafast interband transitions, is studied theoretically for the range of pumping correspondent to the saturated absorption regime. Spectral and temporal dependencies of the photoexcited concentration as well as the transmission and relitive absotption coefficients are considered for mid-IR and visible (or near-IR) spectral regions at different durations of pulse and broadening energies. The characteristic intencities of saturation are calculated and the results are compared with the experimental data measured for the near-IR lasers with a saturable absorber. The negative absorption of a probe radiation during cascade emission of optical phonons is obtained.

Optical transitions and energy relaxation of hot carriers in Si nanocrystals

Dynamics of hot carriers confined in Si nanocrystals is studied theoretically using atomistic tight binding approach. Radiative, Auger-like, and phonon-assisted processes are considered. The Auger-like energy exchange between electrons and holes is found to be the fastest process in the system. However, the energy relaxation of hot electron-hole pair is governed by the single optical phonon emission. For a considerable number of states in small nanocrystals, single-phonon processes are ruled out by energy conservation law.

Temperature dependence of inverse population on intracenter transitions of shallow impurity centers in semiconductors

Analysis of the main factors of the temperature dependence of inverse population on shallow-impurity transitions in semiconductors is carried out in the context of the four-level inversion scheme: the population of the lower state of the laser transition by heating from the ground state and a decrease in the population of the long-lived impurity state due to thermal ionization and an increase in the rate if direct recombination to the ground state with optical-phonon emission occurs. The temperatures at which these factors become substantial are determined. It is shown that thermal ionization from the long-lived state is the major factor determining the temperature quenching of stimulated emission upon shallow-donor transitions in silicon.

Energy Loss of the Electron System in Individual Single-Walled Carbon Nanotubes

We characterize the energy loss of the nonequilibrium electron system in individual metallic single-walled carbon nanotubes at low temperature. Using Johnson noise thermometry, we demonstrate that, for a nanotube with Ohmic contacts, the dc resistance at finite bias current directly reflects the average electron temperature. This enables a straightforward determination of the thermal conductance associated with cooling of the nanotube electron system. In analyzing the temperature- and length-dependence of the thermal conductance, we consider contributions from acoustic phonon emission, optical phonon emission, and hot electron outdiffusion.

The prediction of the effective charge number in single-walled carbon nanotubes using Monte Carlo simulation

The ensemble Monte Carlo simulation is used to calculate the electron-wind forces per unit length of single-walled carbon nanotubes under an electric field applied through the nanotube axis. The electronic system and the ionic system are decoupled from each other. The rate of momentum transferred from the electronic system to the ionic system in the form of the emission or absorption of longitudinal acoustic and longitudinal optical phonons is calculated stochastically to determine the electron-wind forces. Complete unabridged energy and phonon dispersion relations are included in order to obtain more accurate results. The effect of the temperature and the electric field magnitude on the induced forces is also taken into account. Results are compared with a prediction based on quantum mechanical integral form that calculates the electron occupation probability based on a modified Fermi–Dirac distribution. Results show a quantitative agreement between the two methods, however, the method proposed in here we believe is more accurate, because it does not make simplifications for the electron occupation probability as in the modified Fermi–Dirac distribution.

Optical Properties of Manufactured III-Vs and II-VIs Short Wavelength Laser Structures

We focus on most commonly used epitaxial growth techniques of quantum wells (QWs) and study the single electron transitions within the QW laser structures made with II-VIs (e.g. CdSe/ZnSe) and III-Vs (e.g. GaN/AlN), considering only emission of longitudinal optical (LO) phonons. Two different approaches have been employed in order to describe the initial electron wavefunctions in the continuum energy spectrum: the width of the barrier region is a) small b) large, relative to the electron mean free path. For the LO phonons, we have used the bulk phonon approximation and the dielectric continuum (DC) model to study the lattice dynamics in the crystal. Our theoretical models show that the scattering times for II-VIs are very short comparing to the III-Vs semiconductor (except the V-III nitrides) laser structures and highlight that the size of the well is of special importance for the laser operation. Keywords: MBE, MOCVD, large energy gaps, capture velocity, optical phonons, LED

Transient magnetoresponse of photoexcited electrons: Negative cyclotron absorption and evolution of Faraday angle

The transient magnetooptical response of electrons with partly inverted initial distribution produced by an ultrashort optical pulse near the optical phonon energy is studied theoretically. Transient cyclotron absorption and Faraday rotation of polarization plane are considered for bulk semiconductors (GaAs, InAs, and InSb) as well as for a GaAs-based quantum well. Damping of the response due to electron momentum relaxation associated with elastic scattering from acoustic phonons is taken into account in calculations, as well as the evolution of the electron distribution due to quasi-elastic energy relaxation at acoustic phonons and effective inelastic transitions accompanied by spontaneous emission of optical phonons. Nonstationary negative absorption in the cyclotron resonance conditions and peculiarities of Faraday rotation of the polarization plane associated with partial inversion of the initial distribution are considered. The possibility of transient enhancement of the probe field under cyclotron resonance conditions is indicated.

Simplified theory of carrier back-scattering in semiconducting carbon nanotubes: A Kane’s model approach

We present a simplified yet analytical formulation of the carrier backscattering coefficient for zig-zag semiconducting single walled carbon nanotubes under diffusive regime. The electron-phonon scattering rate for longitudinal acoustic, optical, and zone-boundary phonon emissions for both inter- and intrasubband transition rates have been derived using Kane’s nonparabolic energy subband model. The expressions for the mean free path and diffusive resistance have been formulated incorporating the aforementioned phonon scattering. Appropriate overlap function in Fermi’s golden rule has been incorporated for a more general approach. The effect of energy subbands on low and high bias zones for the onset of longitudinal acoustic, optical, and zone-boundary phonon emissions and absorption have been analytically addressed. 90% transmission of the carriers from the source to the drain at 400 K for a 5 μm long nanotube at 105 V m−1 has been exhibited. The analytical results are in good agreement with the available experimental data.

Phonon-Assisted Electroluminescence from Metallic Carbon Nanotubes and Graphene

We report on light emission from biased metallic single-wall carbon nanotube (SWNT), multiwall carbon nanotube (MWNT) and few-layer graphene (FLG) devices. SWNT devices were assembled from tubes with different diameters in the range 0.7-1.5 nm. They emit light in the visible spectrum with peaks at 1.4 and 1.8 eV. Similar peaks are observed for MWNT and FLG devices. We propose that this light emission is due to phonon-assisted radiative decay from populated pi* band states at the M point to the Fermi level at the K point. Since for most carbon nanotubes as well as for graphene the energy of unoccupied states at the M point is close to 1.6 eV, the observation of two emission peaks at approximately 1.6 +/- approximately 0.2 eV could indicate radiative decay under emission or absorption of optical phonons, respectively.

Terahertz current oscillations assisted by optical phonon emission in GaN n+nn+ diodes: Monte Carlo simulations

Under certain conditions, plasma instabilities associated with streaming motion of carriers taking place in n+nn+ diodes can lead to current oscillations. The origin of the phenomenon, known as optical phonon transit time resonance, is characterized by a frequency related to the transit time between consecutive optical phonon emissions by electrons along the active region of the diode. By means of Monte Carlo simulations, the possibility to obtaining current oscillations in GaN n+nn+ diodes is analyzed. The optimum conditions for the onset of such mechanism are investigated: applied bias, temperature, doping, and length of the active n region. Simulations show that current oscillations at frequencies in the terahertz range can be obtained at very low temperatures. Moreover, by choosing the appropriate applied voltage and length of the n region, some degree of tunability can be achieved for frequencies close to the plasma frequency of the n region of the n+nn+ diode.