Effect of Nonlinearity of the Phonon Spectrum on the Thermal Conductivity of Nanostructured Materials Based on Bi–Sb–Te

A theoretical investigation of the lattice thermal conductivity of nanostructured materials based on Bi–Sb–Te is presented. The calculations were based on relaxation time approximation and took into account both the real phonon spectra, obtained from first-principles by use of density functional theory, and the anisotropy of phonon relaxation time. Phonon relaxation time data were determined from experimental values of the lattice thermal conductivity. The decrease of the thermal conductivity caused by the nanostructure was compared with results from calculations based on the linear Debye approach. Estimation showed that phonon boundary scattering can lead to a 55% decrease of thermal conductivity for a grain size of ~20 nm in the Debye approximation. Taking the nonlinearity of the acoustic phonon spectrum into account leads to a 20% larger decrease of the thermal conductivity because of boundary scattering. The reason is that consideration of the real phonon spectrum increases the relative contribution to thermal conductivity of acoustic phonons with low frequencies that are scattered more strongly at nanograin boundaries. Similarly, estimation of lattice thermal conductivity reduction as a result of phonon scattering by nanoinclusions gave an 8% larger decrease when the real phonon spectrum was used rather than the linear Debye approximation. For such a substantial decrease of lattice thermal conductivity, the effect of the optical phonons was estimated; it was shown that optical phonons can reduce the change of thermal conductivity as a result of grain boundary scattering by no more than 10%. Finally, the minimum lattice thermal conductivity was estimated to be 0.07 W/m K because of acoustic modes (0.09 W/m K in the Debye approach) and 0.14 W/m K when the contribution of optical modes was also taken into consideration.     

The effect of acoustic phonon confinement on electron scattering in GaAs/Al<Subscript>x</Subscript>Ga<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>As superlattices

The relaxation time of quasi-two-dimensional (quasi-2D) electrons in the lowest miniband of the GaAs/Al_0.35Ga_0.65As superlattice is calculated for the case of scattering by acoustic phonons. It is shown that electron scattering is affected only slightly by the quantization of the phonon spectrum in terms of the elasticity theory. The scattering is well described based on the phonon spectrum of the bulk semiconductors that form the superlattice.     

Finite time of carrier energy relaxation as a cause of optical-power limitation in semiconductor lasers

It is shown that the reason why the maximum attainable optical power in semiconductor lasers is limited is the finite time of carrier energy relaxation via scattering by nonequilibrium optical phonons in the quantum-well active region. The power and spectral characteristics of semiconductor lasers are studied experimentally at high excitation levels (up to 100 kA/cm²) in pulsed lasing mode (100 ns, 10 kHz). As the drive current increases, the maximum intensity of stimulated emission tends to a constant value (“saturates”), and the emitted power increases owing to extension of the spectrum to shorter wavelengths. The intensity saturation is due to limitation of the rate of stimulated recombination, caused by a finite time of the electron energy relaxation via scattering by polar optical phonons. It is found that the broadening of the stimulated emission spectrum is related to an increase in carrier concentration in the active region, which enhances the escape of electrons into the waveguide layers. As the drive current increases, the carrier concentration in the waveguide reaches its threshold value and there appears an effective channel of current leakage from the active region. The experiment shows that the appearance of a band of waveguide lasing correlates with a sharp drop in the differential quantum efficiency of a semiconductor laser.     

Effect of different loss mechanisms in SiGeSn based mid-infrared laser

We have analyzed the mid-infrared SiGeSn based Barrier-Well-Barrier Heterostracture and calculated the transparency carrier density and corresponding current density for the structure. The effects of different loss mechanisms like free carrier absorption, spontaneous recombination and Auger recombination processes on the transparency current density have been examined. It is shown that, the transparency current density increases significantly with the injected carrier density. Different scattering processes like acoustic phonon scattering and intervalley optical phonon scattering are taken into consideration for this analysis of free carrier absorption mechanisms.

     

Free carrier absorption and lattice vibrational modes in bulk ZnO

The electronic properties of semiconductors are highly dependent on carrier scattering mechanisms determined by crystalline structure, band structure, and defects in the material. Experimental characteristics of lattice vibrational modes and free carrier absorption in single-crystal ZnO samples obtained from different sources are presented in this work to provide a further understanding of carrier scattering processes pertaining to electronic properties. Infrared absorption measurements indicate strong absorption peaks due to a combination of optical and nonpolar phonon modes in the 9–13 μm spectral region. The Raman spectra obtained for these samples similarly reveal the presence of these phonon modes. Infrared absorption measurements also demonstrate free carrier absorption in the 3–9 μm spectral region for higher conductivity samples, where a λ^m dependence is observed with m=2.7–3, indicating both longitudinal optical phonon scattering and ionized impurity scattering. From these results, we show that infrared absorption can be used as a routine nondestructive technique to determine the material characteristics and quality of bulk ZnO.     

The effect of collisional broadening on Monte Carlo simulations of high-field transport in semiconductor devices

Some important consequences of the uncertainty principle on Monte Carlo simulations of very high field transport are discussed. It is shown that recent values of the phonon scattering rates reported for GaAs by Shichijo and Hess lead to an unrealistically high collisional broadening (0.3-0.6eV) of the electronic states, thus rendering questionable any attempt to relate transport properties to the band structure, and invalidating the semiclassical Boltzmann transport picture used in the Monte Carlo simulation. These considerations are important in the modeling of very high field transport properties in semiconductor devices.     

Lifetime broadening in GaAs-AlGaAs quantum well lasers

Experimental observations of spontaneous emission spectra from GaAs-AlGaAs quantum well lasers shown that spectral broadening should be included in any realistic model of laser performance. A model of the lifetime broadening due to intraband Auger processes of the Landsberg type is described and developed for the case of electron-electron scattering in a 2-D system. The model is applied to the calculation of gain and spontaneous emission spectra and gain-current relationships in short-wavelength GaAs-AlGaAs quantum well lasers, and the results are compared with those obtained using both a fixed intraband scattering time and one that varies as n^-1/2, where n is the volume injected carrier density     

Nonlinear gain coefficients in semiconductor lasers: effects ofcarrier heating

Nonlinear gain coefficients due to the effects of carrier heating are derived from the rate equations of carrier energy transfer in semiconductor lasers. We find that, in the modulation responses of semiconductor lasers, stimulated recombination heating will affect the resonant frequency and damping rate in a same form as the effects of spectral hole burning, while free carrier absorption heating will only affect the damping rate. The effects of injection heating and nonstimulated recombination heating are also discussed. The carrier energy relaxation time is calculated from first principles by considering the interactions between carriers and polar optical phonons, deformation potential optical phonons, deformation potential acoustic phonons, piezoelectric acoustic phonons. At the same time, the hot phonon effects associated with the optical phonons are evaluated because their negligible group velocity and finite decay time. We show that the carrier-polar longitudinal optical phonon interaction is the major channel of carrier energy relaxation processes for both electron and holes. We also point out the importance of the longitudinal optical phonon lifetime in evaluating the carrier energy relaxation time. Neglecting the finite decay time of longitudinal optical phonons will significantly underestimate the carrier energy relaxation time, this not only contradicts the experimental results but also severely underestimates the nonlinear gain coefficients due to carrier heating. The effects of spectral hole burning, stimulated recombination heating, and free carrier absorption heating on limiting the modulation bandwidth in semiconductor lasers are also discussed     

Calculations of the charge-carrier mobility and the thermoelectric figure of merit for multiple-quantum-well structures

The thermoelectric figure of merit of structures with multiple quantum wells (MQWs) was calculated taking into account the variations in the relaxation time of charge carriers compared to that in a bulk sample. The mechanisms of scattering by acoustic phonons, at the short-range impurity potential, and the polar scattering in the approximation of the isotropic parabolic dispersion law of the charge carriers were taken into account. The model used is based on the assumption that the phonon spectrum in the MQW structures is no different from the spectrum of the bulk crystal. In addition, the scattering is assumed to be elastic and the relaxation-time approximation was used for all three mechanisms of scattering. A comparison with the results of calculations for a bulk sample shows that the expression for thermoelectric figure of merit is exactly the same for a MQW structure as for a bulk sample if the decrease in the charge-carrier relaxation time in MQW structures is taken into account. The magnitude of the figure of merit for a MQW structure is found to be equal to that for a bulk sample if the chemical potential in each of the cases is chosen from the condition for the highest figure of merit.     

Mobility of holes in p-type silicon determined by the self-consistent method

The mobility of majority carriers is calculated in p-type silicon in the impurity concentration range from 10¹⁶ to 10²⁰ cm^?3. Taking into account the complexity of the band structure of holes and using the self-consistent model development earlier for electrons, the value of the Fermi energy and the screening length is determined. The following scattering types are considered: scattering by acoustical phonons, scattering by non-polar optical phonon and scattering by ionized impurities. The influence of interband transition of heavy and light holes on the total relaxation time is analysed. It is shown that it does not lead to essential changes in mobility. The obtained results are compared with experimental results and satisfactory agreement is found.     

Enhancement and spectral shift of optical gain in semiconductorsfrom non-Markovian intraband relaxation

We will investigate some aspects of the phenomenological treatment of transition (line shape) and level broadening arising from phase and energy relaxation of Bloch states, respectively. Calculating the absorption/gain via the spontaneous emission formula and performing the broadening within the latter circumvents certain artifacts for both level and transition broadening. When using k-independent relaxation times, Gaussian (non-Markovian) broadening functions are superior to Lorentzian (Markovian) ones. In contrast to transition broadening, level broadening may even enhance the gain over its whole spectral width. In contrast to Lorentzian transition broadening, Gaussian transition broadening yields a blue shift of the gain maximum. The direction and magnitude of the spectral shift arising from Gaussian level broadening depends on the degree of degeneracy of the electron and hole bands involved. The level broadening can have a significant influence on the carrier statistics, which, consequently, has to be included into a consistent treatment. Thus, the phenomenological model functions depend distinctly on which kind of relaxation process is faster, energy or phase relaxation. For GaAs-like semiconductors, the application of transition broadening-even when using the spontaneous emission formula-to cases of dominant intraband relaxation yields significant numerical deviations from the correct treatment of level broadening. Broadening the energy levels requires an additional convolution integration. We will present an approximation, which yields excellent results for the gain in GaAs-like semiconductors. This enables one to include the significant effects of level broadening without increasing the numerical effort and leads to favorable formulae for experimental data fitting and device modeling     

Analysis of Transport Parameters in an Interacting Two-Band Model with Application to p+-GaAs

We present a comprehensive derivation of the transport of holes involving an interacting two-valence-band system in terms of a generalized relaxation time approach. We solve a pair of semiclassical Boltzmann equations in a general way first, and then employ the conventional relaxation time concept to simplify the results. For polar optical phonon scattering, we develop a simple method to compensate for the inherent deficiencies in the relaxation time concept and apply it to calculate effective relaxation times separately for each band. Also, formulas for scattering rates and momentum relaxation times for the two-band model are presented for all the major scattering mechanisms for p-type GaAs for simple, practical mobility calculations. Finally, in the newly proposed theoretical framework, first-principles calculations for the Hall mobility and Hall factor of p-type GaAs at room temperature are carried out with no adjustable parameters in order to obtain a direct comparison between the theory and recent available experimental results, which would stimulate further analysis toward better understanding of the complex transport properties of the valence band. The calculated Hall mobilities show a general agreement with our experimental data for carbon doped p-GaAs samples in a range of degenerate hole densities. The calculated Hall factors show r_H = 1.25 ~ 1.75 over all hole densities (2 × 10¹⁷ ~ 1 × 10²⁰cm^??3) considered in the calculations.     

Characteristics of giant optical pulsations from ruby

A method of laser modulation is described which produces fast, intense and controllable "giant" laser pulses by "Q-modulation." In experiments with ruby, pulses of peak power up to 15 MW and of duration less than 30 nsec have been studied. The principles of the technique are outlined and early experimental results reviewed. The temporal, spectral and spatial structure of giant pulses produced from ruby by a nitrobenzene Kerr cell modulator is reported. The pulse characteristics found to date yield information about the nature of various relaxation processes in ruby and point the way to further experiments to clarify many questions which are raised. The results a) set an upper limit of 10^-7sec on the E^-→2A^-relaxation time, b) show a shortening of upper-state relaxation time by about seven times under heavy pumping, c) show relaxation of excitation taking place across the laser line in microseconds, d) show progressive spectral broadening for shorter pulses to encompass most of the fluorescent line, e) show increasing asymmetry of spectral output for faster, more intense pulses, and f) show little broadening of beam divergence over normal, but with added structure.     

Ultrafast Electronic Dynamics in Unipolar n-Doped InGaAs–GaAs Self-Assembled Quantum Dots

The dynamics of electron capture and relaxation in an n-doped quantum-dot (QD) infrared detector structure are studied directly in the time domain using ultrafast intraband-pump-interband-probe differential transmission spectroscopy. Femtosecond midinfrared pulses are used to excite electrons from the doped QDs into the conduction band continuum, and the complete electron distribution functions are monitored as a function of time using an interband probe. Because only electrons are excited and no holes are present, the electron-hole scattering which dominates the relaxation in bipolar systems is not present, and the measurement yields the electron dynamics exclusively. Excitation-dependent electron capture times were measured from 40 to <10 ps with increasing pump intensity. Intradot inter-level relaxation times were observed to be ~100 ps, driven by Auger-type electron-electron scattering. Nanosecond-scale dynamics in the n=1 state were also observed and attributed to transport effects. Our results indicate that the phonon bottleneck in the QDs is circumvented by Auger scattering; nevertheless, the electron dynamics in the unipolar device are found to be slower than those observed in bipolar systems, which confirms the significance of the holes in the carrier relaxation in bipolar devices. The results also support the improved operation of QD infrared photodetectors relative to quantum-well-based devices     

Negative electron diffusivity in high electric fields

The prediction that the electron diffusivity may be negative in high electric fields under some conditions has been examined starting from the Boltzmann equation and assuming a Maxwellian distribution function. It is found that the diffusion constant is positive for predominant acoustic phonon, polar optical phonon or impurity atom scattering. But the constant may be negative when effects of nonparabolicity are important and energy relaxation is limited by non-polar optical phonon scattering but the momentum relaxation is dominated by impurity atom scattering. Calculations with the parameter values of InSb, silicon and germanium show that only in materials like germanium at low temperatures of about 27 K the diffusion constant may be negative for impurity concentrations of 10¹⁷–10¹⁸ cm^?3.     

Comparison between the relaxation time approximation and the Boltzmann collision operator for simulation of dissipative electron transport in resonant tunnelling diodes

Carrier scattering in the Wigner formalism has been introduced for the simulation of dissipative electron transport in resonant tunnelling diodes. Two approaches have been considered: the relaxation time approximation and the Boltzmann collision operator. The relaxation time and transition rates have been evaluated and have been introduced in the discretized version of the Liouville equation to obtain the Wigner distribution function and the current density. Not only phonon scattering, but also ionized impurity scattering has been accounted for in both approaches. We have compared the two scattering models on the basis of the I–V characteristics which have been simulated under various temperature and doping conditions. The results clearly reveal a lower current peak in the Boltzmann collision operator approach. Since the results of both approaches are divergent and since no clear computation advantages are obtained from the relaxation time approximation, we prefer the use of the more realistic Boltzmann collision operator for the simulation of dissipative electron transport in resonant tunnelling diodes.     

Raman scattering in InP doped by Be<Superscript>+</Superscript>-ion implantation

InP (100) crystals implanted with Be⁺ ions with an energy of 100 keV and doses of 10¹³–10¹⁵ cm^–2 are studied by Raman spectroscopy before and after thermal annealing at temperatures of 300–850°C. It is found that, as the implanted ion dose is increased, the surface region of InP is partially amorphized; in this case, spectral lines related to longitudinal lattice vibrations exhibit a shift to lower frequencies and inhomogeneous broadening, which is indicative of the formation of a nanocrystalline phase. Thermal annealing results in recovery of the crystal structure of InP. At annealing temperatures of >700°C, scattering at phonon–plasmon coupled modes is detected in the Raman spectra. This is attributed to electrical activation of the impurity. From the frequency of the phonon–plasmon mode, the concentration of heavy holes is estimated in the context of the model of a two-oscillator dielectric function.     

Theory of the two-photon absorption-fluorescence method of pulsewidth measurement

A three-level model of a two-photon absorber is set up, and the response of the system to a pulsed excitation is calculated, including the effects of homogeneous and inhomogeneous broadening. The results are applied to the two-photon absorption-fluorescence (TPF) mesurement technique and it is shown that the larger of the two broadening mechanisms sets an upper limit to the spectral width of pulses, for which an unambiguous interpretation of the TPF display can be made. Effects that occur when this condition is violated are discussed.     

Effects of carrier heating on laser dynamics-a Monte Carlo study

The static and dynamic properties of semiconductor quantum-well (QW) lasers have traditionally been analyzed by using rate equations that couple cold carriers to photons in the lasing cavity. This assumption of cold carriers, however, has often been disputed because it does not account for heating due to carrier relaxation, hot phonon effects, and spectral hole burning. All these processes affect laser performance significantly by modifying the gain because gain depends on carrier temperature as well as spectral broadening. In this paper, we study the carrier dynamics of QW lasers using a Monte Carlo method and conclude that hot carrier effects in semiconductor lasers are important and need to be considered for the analysis and design of semiconductor lasers