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 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 and energy relaxation 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 energy relaxation 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 power dissipation values obtained from the DC and 3DP models are in general different in the pure 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 energy relaxation: their contribution is enhanced in the pure emission process but is dramatically reduced after including the HPE. Our calculation with both phonon models has obtained a great fall in energy relaxation 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

Momentum relaxation due to polar optical phonons in AlGaN/GaN heterostructures

Using the dielectric continuum (DC) model, momentum relaxation rates are calculated for electrons confined in quasi-two-dimensional (quasi-2D) channels of AlGaN/GaN heterostructures. Particular attention is paid to the effects of half-space and interface modes on the momentum relaxation. The total momentum relaxation rates are compared with those evaluated by the three-dimensional phonon (3DP) model, and also with the Callen results for bulk GaN. In heterostructures with a wide channel (effective channel width >100 Å), the DC and 3DP models yield very close momentum relaxation rates. Only for narrow-channel heterostructures do interface phonons become important in momentum relaxation processes, and an abrupt threshold occurs for emission of interface as well as half-space phonons. For a 30-Å GaN channel, for instance, the 3DP model is found to underestimate rates just below the bulk phonon energy by 70% and overestimate rates just above the bulk phonon energy by 40% compared to the DC model. Owing to the rapid decrease in the electron-phonon interaction with the phonon wave vector, negative momentum relaxation rates are predicted for interface phonon absorption in usual GaN channels. The total rates remain positive due to the dominant half-space phonon scattering. The quasi-2D rates can have substantially higher peak values than the three-dimensional rates near the phonon emission threshold. Analytical expressions for momentum relaxation rates are obtained in the extreme quantum limits (i.e., the threshold emission and the near subband-bottom absorption). All the results are well explained in terms of electron and phonon densities of states

Negative differential resistance associated with hot phonons

We predict the existence of a hot-phonon negative differential resistance (NDR) in GaN. We show that this is a consequence of a wave-vector dependence of lifetime caused by the effect of coupled plasmon-phonons. Anti-screened long-wavelength modes have shorter lifetimes, screened shorter-wavelength modes have longer lifetimes, the boundary between them being determined by the temperature-dependent Landau damping. The higher density of screened modes means that the average lifetime is of order of the lifetime of the bare phonon. Its increase with electron temperature (field) is responsible for the NDR. We also find that the momentum relaxation rate (MRR) associated with the absorption of phonons can be negative in some circumstances, which can be seen to be a consequence of the non-uniform distribution of hot phonons in wave-vector space. We also point out that the ultra-short lifetimes sometimes deduced from experiment should more properly be regarded as electron energy- relaxation times

Measurements of Nitric Oxide During a Stratospheric Warming

The altitude distribution of NO was measured between 12 and 33 km near 54°N during the stratospheric warming of February, 1979. The NO mixing ratios were considerably smaller compared to summer conditions, especially below 23 km. The measurements are used to estimate the distribution of NO2 for comparison with ground‐based column measurements and to show that during the warming NOx is at least a factor of two lower than is observed in summer at this latitude. This reduction in NOx is shown to be consistent with a larger fraction of odd‐nitrogen existing as N2O5

Screening effects in the electron-optical phonon interaction

We show that recently reported unusual hardening of optical phonons renormalized by the electron-phonon interaction is due to the neglect of screening effects. When the electron-ion interaction is properly screened optical phonons soften in three dimension. It is important that for short-wavelength optical phonons screening is static while for long-wavelength optical phonons screening is dynamic. In two-dimensional and one-dimensional cases due to crossing of the nonperturbed optical mode with gapless plasmons the spectrum of renormalized optical phonon-plasmon mode shows split momentum dependence.Comment: 7 page

Photochemistry in the arctic free troposphere: NOx budget and the role of odd nitrogen reservoir recycling

The budget of nitrogen oxides (NOx) in the arctic free troposphere is calculated with a constrained photochemical box model using aircraft observations from the Tropospheric O3 Production about the Spring Equinox (TOPSE) campaign between February and May. Peroxyacetic nitric anhydride (PAN) was observed to be the dominant odd nitrogen species (NOy) in the arctic free troposphere and showed a pronounced seasonal increase in mixing ratio. When constrained to observed acetaldehyde (CH3CHO) mixing ratios, the box model calculates unrealistically large net NOx losses due to PAN formation (62pptv/day for May, 1-3km). Thus, given our current understanding of atmospheric chemistry, these results cast doubt on the robustness of the CH3CHO observations during TOPSE. When CH3CHO was calculated to steady state in the box model, the net NOx loss to PAN was of comparable magnitude to the net NOx loss to HNO3 (NO2 reaction with OH) for spring conditions. During the winter, net NOx loss due to N2O5 hydrolysis dominates other NOx loss processes and is near saturation with respect to further increases in aerosol surface area concentration. NOx loss due to N2O5 hydrolysis is sensitive to latitude and month due to changes in diurnal photolysis (sharp day-night transitions in winter to continuous sun in spring for the arctic). Near NOx sources, HNO4 is a net sink for NOx; however, for more aged air masses HNO4 is a net source for NOx, largely countering the NOx loss to PAN, N2O5 and HNO3. Overall, HNO4 chemistry impacts the timing of NOx decay and O3 production; however, the cumulative impact on O3 and NOx mixing ratios after a 20-day trajectory is minimal. © 2003 Elsevier Science Ltd. All rights reserved

Polar optical phonon scattering and negative Kromer-Esaki-Tsu differential conductivity in bulk GaN

Cataloged from PDF version of article.GaN is being considered as a viable alternative semiconductor for high-power solid-state electronics. This creates a demand for the characterization of the main scattering channel at high electric fields. The dominant scattering mechanism for carriers reaching high energies under the influence of very high electric fields is the polar optical phonon (POP) emission. To highlight the directional variations, we compute POP emission rates along high-symmetry directions for the zinc-blende and wurtzite crystal phases of GaN. Our treatment relies on the empirical pseudopotential energies and wave functions. The scattering rates are efficiently computed using the Lehmann-Taut Brillouin zone integration technique. For both crystal phases, we also consider the negative differential conductivity possibilities associated with the negative effective mass part of the band structure. (C) 2001 Elsevier Science B.V. All rights reserved

Comparative analysis of zinc-blende and wurtzite GaN for full-band polar optical phonon scattering and negative differential conductivity

Cataloged from PDF version of article.For high-power electronics applications, GaN is a promising semiconductor. Under high electric fields, electrons can reach very high energies where polar optical phonon (POP) emission is the dominant scattering mechanism. So, we undertake a full-band analysis of POP scattering of conduction-band electrons based on an empirical pseudopotential band structure. To uncover the directional variations, we compute POP emission rates along high-symmetry directions for the zinc-blende (ZB) crystal phase of GaN. We also compare the results with those of the wurtzite phase. In general, the POP scattering rates in the zinc-blende phase are lower than the wurtzite phase. Our analysis also reveals appreciable directional dependence, with the Gamma-L direction of ZB GaN being least vulnerable to POP scattering, characterized by a scattering time of 11 fs. For both crystal phases, we consider the negative differential conductivity possibilities driven by the negative effective mass part of the band structure. According to our estimation, for the ZB phase the onset of this effect requires fields above similar to 1 MV/cm. (C) 2000 American Institute of Physics. [S0003-6951(00)02743-1]