Nonequilibrium Longitudinal Optical Phonons Research Articles

Non-equilibrium longitudinal optical phonons and their lifetimes

Non-equilibrium phonons have been discussed for almost six decades. Here, the nature of the longitudinal optical mode, particularly in polar materials, is discussed along with its lifetime and bottleneck occurrences. The history of non-equilibrium phonons is discussed along with their generation by the relaxation of hot carriers. The role of inter-valley scattering and phonon lifetime is introduced along with the concept of a phonon bottleneck. Various methods of lifetime measurement are introduced. Measurements of the lifetime in a variety of semiconductor materials is reviewed and a possible scaling behavior discussed.

Optical-phonon-mediated photocurrent in terahertz quantum-well photodetectors

Strong and sharp photocurrent peak at longitudinal optical (LO) phonon frequency (8.87 THz) is found in GaAs/(Al,Ga)As terahertz quantum-well photodetectors (QWPs). Two mesa-structure terahertz QWPs with and without one-dimensional metal grating are fabricated to investigate the behavior of such photoresponse peak. The experimental and simulation results indicate that the photocurrent peak originates from a two-step process. First, at the LO phonon frequency, a large number of non-equilibrium LO phonons are excited by the incident electromagnetic field, and the electromagnetic energy is localized and enhanced in the thin multi-quantum-well layer. Second, through the Frohlich interaction, the localized electrons are excited to continuum states by absorbing the non-equilibrium LO phonons, which leads to the strong photoresponse peak. This finding is useful for exploring strong light-matter interaction and realizing high sensitive terahertz photodetectors.

Hot-electron fluctuations and transistor performance: hot-phonon effects

The frequency performance of a GaN heterostructure field-effect transistor is discussed in terms of plasmon-assisted dissipation of LO-mode heat accumulated by non-equilibrium longitudinal optical phonons (hot phonons). Hot phonons cause additional scattering of electrons and also facilitate defect formation. Plasmon–LO-phonon resonance is experimentally resolved in a wide range of experiments such as fluctuations, dissipation, hot-electron transport, transistor frequency performance, transistor reliability, and transistor phase noise.

Electron density window for best frequency performance, lowest phase noise and slowest degradation of GaN heterostructure field-effect transistors

The problems in the realm of nitride heterostructure field-effect transistors (HFETs) are discussed in terms of a novel fluctuation–dissipation-based approach impelled by a recent demonstration of strong correlation of hot-electron fluctuations with frequency performance and degradation of the devices. The correlation has its genesis in the dissipation of the LO-mode heat accumulated by the non-equilibrium longitudinal optical phonons (hot phonons) confined in the channel that hosts the high-density hot-electron gas subjected to a high electric field. The LO-mode heat causes additional scattering of hot electrons and facilitates defect formation in a different manner than the conventional heat contained mainly in the acoustic phonon mode. We treat the heat dissipation problem in terms of the hot-phonon lifetime responsible for the conversion of the non-migrant hot phonons into migrant acoustic modes and other vibrations. The lifetime is measured over a wide range of electron density and supplied electric power. The optimal conditions for the dissipation of the LO-mode heat are associated with the plasmon-assisted disintegration of hot phonons. Signatures of plasmons are experimentally resolved in fluctuations, dissipation, hot-electron transport, transistor frequency performance, transistor phase noise and transistor reliability. In particular, a slower degradation and a faster operation of GaN-based HFETs take place inside the electron density window where the resonant plasmon-assisted ultrafast dissipation of the LO-mode heat comes into play. A novel heterostructure design for the possible improvement of HFET performance is proposed, implemented and tested.

The role of the products of the decay of optical phonons

The decay of nonequilibrium longitudinal optical phonons is investigated by abandoning the usual assumption that the decay products remain in thermodynamic equilibrium. The case when only the grand-daughter modes remain in thermodynamic equilibrium is studied. The effective lifetime of the LO mode, which is the one that would be measured by experiment, is found to decrease with increasing occupancy of the LO mode.

Nonequilibrium optical phonon effect on high-field electron transport in InN

The effect of nonequilibrium longitudinal optical (LO) phonons on electron transport in wurtzite InN in high electric fields is studied by Monte Carlo simulations. The novel and efficient single-particle Monte Carlo method for a self-consistent simulation of nonequilibrium electron and phonon systems is developed. The effect of nonequilibrium LO phonons on electron drift velocity, valley population, and small-signal ac mobility in InN is investigated. It is found that the effect of nonequilibrium LO phonons on electron transport characteristics in InN becomes pronounced when electron density exceeds 1017 cm−3.

Non-equilibrium longitudinal and transverse optical phonons in terahertz quantum cascade lasers

We report on the experimental observation of non-equilibrium longitudinal (LO) and interface transverse-like (IF-TO) optical phonons populations associated with electron transport in resonant-phonon THz quantum-cascade lasers. The measured LO-phonon occupation numbers are in excellent agreement with the result of Monte Carlo simulations at a phonon in-plane wave number q = 4.2 × 10+4 cm−1, and they remain about 40% larger than the IF-TO ones.

Ultrafast decay of hot phonons in an AlGaN/AlN/AlGaN/GaN camelback channel

A bottleneck for heat dissipation from the channel of a GaN-based heterostructure field-effect transistor is treated in terms of the lifetime of nonequilibrium (hot) longitudinal optical phonons, which are responsible for additional scattering of electrons in the voltage-biased quasi-two-dimensional channel. The hot-phonon lifetime is measured for an Al0.33Ga0.67N/AlN/Al0.1Ga0.9N/GaN heterostructure where the mobile electrons are spread in a composite Al0.1Ga0.9N/GaN channel and form a camelback electron density profile at high electric fields. In accordance with plasmon-assisted hot-phonon decay, the parameter of importance for the lifetime is not the total charge in the channel (the electron sheet density) but rather the electron density profile. This is demonstrated by comparing two structures with equal sheet densities (1 × 1013 cm−2), but with different density profiles. The camelback channel profile exhibits a shorter hot-phonon lifetime of ∼270 fs as compared with ∼500 fs reported for a standard Al0.33Ga0.67N/AlN/GaN channel at low supplied power levels. When supplied power is sufficient to heat the electrons > 600 K, ultrafast decay of hot phonons is observed in the case of the composite channel structure. In this case, the electron density profile spreads to form a camelback profile, and hot-phonon lifetime reduces to ∼50 fs.

Ultrafast Removal of LO-Mode Heat From a GaN-Based Two-Dimensional Channel

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Dissipation of the Joule heat, accumulated in non-equilibrium longitudinal optical (LO) phonon modes, is considered in terms of LO-phonon lifetime. The dependence of the lifetime on electron density, hot-electron temperature, and supplied electric power are presented for a voltage-biased GaN-based channel with a two-dimensional electron gas (2DEG). An improved understanding of conversion of LO phonons into acoustic and other phonons is reached. A non-monotonous dependence of the lifetime on the electron density is observed. The optimal 2DEG density for ultrafast decay of the LO-mode heat is estimated and explained in terms of LO-phonon-plasmon resonance. A new limitation of the frequency performance is predicted for heterostructure field-effect transistors under the off-resonance conditions of operation. The shortest hot-phonon lifetime of <formula formulatype="inline"><tex Notation="TeX">$\sim \!\! 60\pm 20\ {\rm fs}$</tex></formula> is found, at a high level of supplied power, in nearly lattice-matched InAlN/AlN/GaN. </para>

Plasmon-enhanced heat dissipation in GaN-based two-dimensional channels

Decay of nonequilibrium longitudinal optical (LO) phonons is investigated at room temperature in two-dimensional electron gas channels confined in nearly lattice-matched InAlN/AlN/GaN structures. A nonmonotonous dependence of the LO-phonon lifetime on the supplied electric power is reported for the first time and explained in terms of plasmon–LO-phonon resonance tuned by applied bias at a fixed sheet density (8×1012 cm−2). The shortest lifetime of 30±15 fs is found at the power of 20±10 nW/electron.

InAlN-barrier HFETs with GaN and InGaN channels

Advantages and drawbacks of InN-containing GaN-based heterostructure field-effect transistors (HFETs) are reviewed. The main attention is paid to fundamental processes and experimental observations associated with hot-electron transport in two-dimensional electron gas (2DEG) channels subjected to high electric fields. Complementary information is obtained from fluctuations. When interface roughness and alloy scattering are minimized, an important transport limitation originates from additional scattering of hot electrons by non-equilibrium longitudinal optical (LO) phonons (hot phonons) governed by the hot-phonon temperature and the hot-phonon decay into acoustic phonons. The ultrafast decay is observed for high supplied power where the hot-phonon lifetime of ∼60 fs is found. The optimal 2DEG density for the fastest decay of hot phonons is estimated and associated with LO-phonon–plasmon resonance. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Investigation of hot electrons and hot phonons generated within an AlN/GaN high electron mobility transistor

We review our recent results obtained on an AlN/GaN-based high-electron-mobility transistor. The temperature of the electrons drifting under a relatively-high electric field is significantly higher than the lattice temperature (i.e., the hot electrons are generated). These hot electrons are produced through the Fröhlich interaction between the drifting electrons and long-lived longitudinal-optical phonons. By fitting electric field vs. electron temperature deduced from the measurements of photoluminescence spectra to a theoretical model, we have deduced the longitudinal-optical-phonon emission time for each electron is to be on the order of 100 fs. We have also measured the decay time constant for LO phonons to be about 4.2 ps. An electric field present in a GaN/AlN heterostructure can bring both the first-order and second-order Raman scattering processes into strong resonances. The resonant Stokes and anti-Stokes Raman scattering results in the increase and decrease of non-equilibrium longitudinal-optical phonon temperatures, respectively. Moreover, the phonon temperature measured from the Raman scattering is increased with an applied electric field at a much higher rate than the lattice temperature due to the presence of field-induced non-equilibrium longitudinal-optical phonons.

GaN-based two-dimensional channels: hot-electron fluctuations and dissipation

Ultrafast electronic and phononic processes are investigated in voltage-biased GaN-basedtwo-dimensional channels of interest for heterostructure field-effect transistors. Theaccumulation of non-equilibrium longitudinal optical phonons (hot phonons) is treated forAlGaN/GaN, AlGaN/AlN/GaN, AlGaN/GaN/AlN/GaN, and AlInN/AlN/GaN structuresin terms of the hot-phonon temperature and hot-phonon lifetime. The hot-phononeffect on hot-electron energy relaxation and hot-phonon number relaxation isextracted from an experimental investigation of hot-electron fluctuations and powerdissipation. The measured equivalent hot-phonon temperature is nearly equalto the hot-electron temperature. The hot-phonon lifetime varies in the rangefrom 150 to 800 fs and depends on electron density, temperature, and suppliedelectric power. The experimental dependence of the hot-phonon lifetime on thehot-phonon mode occupancy is unique—neither Raman optical-photon scattering noroptical-phonon-assisted intersubband absorption has, as yet, provided any experimentaldata of this sort.

Stokes and anti-Stokes resonant Raman scatterings from biased GaN/AlN heterostructure

An electric field present in a GaN/AlN heterostructure can bring both the first-order and second-order Raman scattering processes into strong resonances. The resonant Stokes and anti-Stokes Raman scatterings result in the increase and decrease in nonequilibrium longitudinal-optical phonon temperatures, respectively. Moreover, the phonon temperature measured from the Raman scattering is increased with an applied electric field at a much higher rate than the lattice temperature due to the presence of field-induced nonequilibrium longitudinal-optical phonons.

Hot-Electron Transport, Noise and Power Dissipation in GaN Channels at High Density of Electrons

The experimental results on transport, noise, and dissipation of electric power for voltage-biased Si-doped GaN channels are compared with those of Monte Carlo simulation. The measured dissipated power shows a stronger hot-phonon effect than the simulated one. On the other hand, the experimental results on the electron drift velocity at high electric fields show a weaker hot-phonon effect as compared with the simulated one. The misfit can be reduced if a conversion of the friction-active nonequilibrium longitudinal optical phonons into the friction-passive longitudinal optical phonons is considered.

Monte Carlo evaluation of an analytical model for nonequilibrium-phonon-induced electron velocity saturation in GaN

The ensemble Monte Carlo method is used to solve the Boltzmann equation for electrons together with the equation for phonons treated in the relaxation-time approximation. The effect of nonequilibrium longitudinal optical phonons on hot-electron energy distribution, mean energy, drift velocity and power dissipation is considered for bulk GaN subjected to electric fields in a range up to 100 kV cm−1. In particular, the suppression of the high-energy tail of the hot-electron distribution due to the phonon accumulation is resolved. The results of the simulation are compared with those obtained within the recently proposed analytical model for the saturation of electron drift velocity at high electric fields. The saturated velocity decreases as the electron gas density increases. Values around 107 cm s−1 are reached at an electric field of 100 kV cm−1 for an electron gas density of 1018 cm−3. The analytically obtained results are in a better agreement with those of Monte Carlo simulation if the electron gas density is higher and the electric field is stronger.

Hot-Electron Transport and Noise in GaN Two-Dimensional Channels for HEMTs

Accumulation of non-equilibrium longitudinal optical (LO) phonons (termed hot phonons) is considered as a possible cause for limitation of frequency of operation of GaN-based high-electron-mobility transistors (HEMTs). The experimental data on noise temperature of hot electrons at a microwave frequency as a function of supplied electric power is used to extract information on hot phonons: the hot-phonon lifetime, the equivalent hot-phonon temperature, the effective occupancy of hot-phonon states involved into electron-LO-phonon interaction. The possible ways for controlling the hot-phonon effect on electron drift velocity through variation of electron density, channel composition, and hot-phonon lifetime are discussed. The expected dependence of hot-electron drift velocity on hot-phonon lifetime is confirmed experimentally. A self-consistent explanation of different frequency behaviour of InP-based and GaN-based HEMTs is obtained from a comparative study of hot-phonon effects.

Hot‐electron microwave noise and power dissipation in AlGaN/AlN/GaN channels for HEMTs

Dependence of hot-electron noise temperature on supplied electric power is measured at room temperature for an AlGaN/AlN/GaN channel with a two-dimensional electron gas (1 × 1013 cm–2). The results are interpreted in an electron-temperature approximation for a 5-subband model with electron-gas degeneracy taken into account. The fitting is obtained when non-equilibrium (hot) longitudinal optical (LO) phonons are taken into account. The estimated effective occupancy of the involved LO-phonon states exceeds the equilibrium one more than 30 times at 2000 K electron temperature. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Detection of non‐equilibrium longitudinal optical phonons in InN and its consequences

Picosecond Raman spectroscopy has been used to study properties of non-equilibrium longitudinal optical phonons in a high quality, single crystal wurtzite structure InN sample. Our experimental results show that the bandgap of InN cannot be around 1.89 eV; but are consistent with a bandgap of around 0.8 eV. Our results provide a concrete evidence that 0.8 eV-luminescence observed recently in InN cannot be due to deep level radiative emission in InN. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Hot-phonon effect on power dissipation in a biasedAlxGa1−xN∕AlN∕GaNchannel

The Monte Carlo simulation of hot-electron energy dissipation is carried out for a biased $\mathrm{Al}\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$ channel. The conduction band profile and electron wave functions are calculated through self-consistent solution of Poisson and Schr\"odinger equations. Nonelastic scattering of electrons on acoustic phonons and nonequilibrium longitudinal optical (LO) phonons is included. The nonequilibrium LO phonons are treated in terms of hot-phonon lifetime. The dependence of electron temperature and dissipated power on the applied electric field is obtained from the Monte Carlo simulation. The experimental results on noise temperature and current as functions of electric field strength applied along the channel are presented, and the dependence of the supplied electric power on the inverse electron temperature is evaluated. The best agreement between the Monte Carlo results and the experimental data is obtained for the hot-phonon lifetime ${\ensuremath{\tau}}_{\mathrm{ph}}=1\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$.