Polar Optical Phonon Emission Research Articles

Theoretical Prediction of Mobility Improvement in GaN-Based HEMTs at High Carrier Densities

In this article, we use a semiclassical low-field mobility modeling framework, which includes all relevant scattering mechanisms, to examine the dependence of electron mobility on 2-D electron gas (2DEG) density in previously characterized high Al-content AlGaN/gallium nitride (GaN) high electron mobility transistors (HEMTs) with and without an AlN spacer layer. Polar optical phonon (POP) scattering has previously been identified as the dominant scattering mechanism in GaN-based HEMTs at room temperature, so the analysis of POP scattering rates is of particular importance. We find that the POP-limited mobility in both structures decreases with increasing 2DEG density up to a critical density of around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${10}^{{13}}$ </tex-math></inline-formula> cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{-{2}}$ </tex-math></inline-formula> , above which we observe a significant improvement of up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${46}\%$ </tex-math></inline-formula> , contrary to the behavior typically reported for GaN HEMT structures. The POP-limited mobility increase is explained by the interplay of ground-state energy and quasi-Fermi energy within the channel, by which intrasubband POP emission within the ground state is suppressed at high 2DEG densities. This provides a universal guideline for the design and operation of GaN-based HEMTs to achieve a minimum ON-resistance in switching applications at room temperature and above.

Моделирование методом Монте – Карло кинетических явлений в твердых телах с использованием технологии параллельных вычислений OpenACC

The development of a software package using the OpenACC parallel computing technology for Monte Carlo simulation of the kinetic coefficients of homogeneous semiconductor materials is presented. The package is a set of interconnected classes, the parameters of the material and external fields are redefined in the child classes available to the user, which makes it possible to model a wide range of materials. The package allows us to use models of elastic (acoustic phonons, charged impurities) and inelastic (polar and nonpolar optical phonons) electron scattering in the single-band approximation. The use of OpenACC technology makes it possible to use both shared memory systems and hybrid systems equipped with graphics processors as a computing platform. The possibility of saving data about each particle at each time step of the simulation is provided. It allowed, in particular, to trace the dependence of the average collision frequency of the energy of charge carriers and strength of the DC electric field applied to the sample, in the beta-modification of gallium oxide, to assess the applicability of the conductivity models offered by other research groups. It is shown that the greatest contribution to the conductivity of the beta modification of gallium oxide at room temperatures is made by the scattering of electrons on polar optical phonons, and the average collision frequency, as well as the percentage of collisions of an electron with various types of inhomogeneities of the crystal lattice, weakly depend on the strength of the constant electric field. At a temperature of about 100 K, with an increase in the constant electric field applied to the sample, firstly, the proportion of scattering with the emission of polar optical phonons increases significantly and the proportion of scattering on charged impurities decreases, and secondly, the total frequency of collisions increases. This is due, on the one hand, to the heating of the electron gas by an electric field and the activation of scattering channels with the emission of a phonon at a given temperature, on the other hand, to an insufficiently rapid increase in the concentration of current carriers due to the ionization of impurities. Thanks to the Monte Carlo simulation, it was possible to directly evaluate the validity of the use of the Farvaque correction for an approximate description of the processes of inelastic electron scattering on polar optical phonons by introducing some effective relaxation time.

The effect of Auger recombination on the nonequilibrium carrier recombination rate in the InGaAsSb/AlGaAsSb quantum wells

Time dependencies of interband photoluminescence are studied in InGaAsSb/AlGaAsSb quantum well structures with various barrier materials and quantum well widths. The experimentally determined dependencies of photoluminescence intensity on the optical pumping level are compared with calculated dependencies of photoluminescence intensity on the nonequilibrium carrier concentration. Time of charge carrier trapping into quantum wells and the energy relaxation time related to the polar optical phonon emission were obtained from analysis of the photoluminescence dynamics at different optical pumping levels. The recombination rates with respect to nonradiative Shockley–Read–Hall and Auger recombination were determined. It is shown that, at certain parameter sets, resonant Auger recombination can exist in InGaAsSb/AlGaAsSb quantum well structures, which should results in the decrease of the concentration of carriers taking part in the radiative recombination.

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.

Minoritary Transport in Heavily Doped p-type InGaAs

AbstractMinoritary carrier’s transport properties are of fundamental importance in the HBT’s physics. The base transit time is a key parameter to improve microwave figure of merit. Some recent minoritary electron mobilities measurements versus acceptor doping level using magneto transport method exhibit a dramatic increase at very high majority carrier concentration. This effect has been attributed to the coupling of polar optical phonons with hole plasmons (LOPC) which controls the balance between enegy gain by electric field acceleration and energy loss by polar optical phonon emission. We present minoritary mobilities as a function of majority carrier doping calculated in the frame of electrons and holes Monte Carlo modelling including LOPC.

High-field transport in semiconductor superlattices for interacting Wannier–Stark levels

We developed a microscopic theory of electron transport in superlattices within the Wannier–Stark approach by including the interaction associated with Zener tunneling between the energy levels pertaining to adjacent quantum wells. By using a Monte Carlo technique we have simulated the hopping motion associated with absorption and emission of polar optical phonons and determined the main transport parameters for the case of a GaAs/GaAlAs structure at room temperature. Interaction between the levels is found to be responsible for a systematic increase of the level energy with respect to the bottom of the quantum well at electric fields above about 20 kV/cm. When compared with the non-interacting case, at the highest fields the average carrier energy evidences a consistent increase, which leads to a significant softening of the negative slope of both the drift velocity and diffusivity versus electric field behavior.

Monte Carlo study of terahertz generation from streaming distribution of two-dimensional electrons in a GaN quantum well

We study terahertz (THz) generation from anisotropic streaming distribution of a two-dimensional electron gas (2DEG) in a GaN/AlGaN quantum well using the ensemble Monte Carlo method. Under proper electric fields, electrons do not have enough energy for intersubband and intervalley transitions. They make nearly cyclic motion in momentum space within the first subband, which gives rise to a spindle-shaped electron distribution. This effect is improved due to large polar optical phonon energy, strong electron–phonon interaction and much sharper increase of the polar optical phonon emission rate in GaN 2DEG. We demonstrate that electrons show dynamic negative differential mobility at the transit-time frequency and its harmonics at low temperatures due to this cyclic motion. The resonant frequency can be tuned by simply varying the applied electric field. We may thus use this effect to develop voltage-tunable THz masers.

Sources of Transconductance Collapse in III–V Nitrides—Consequences of Velocity-Field Relations and Source/Gate Design

Experimental results from submicrometer devices in III-V nitride devices often exhibit a significant decrease in the transconductance when gate bias is increased. This creates new challenges for circuit design in III-V nitride technology. In this paper, we discuss possible sources of this collapse from a theoretical and computational standpoint. We find that polar optical phonon emission related velocity-field nonlinearities in 5-40 kV/cm region are the primary reason for the decrease in the transconductance. We also discuss possible solutions to this problem and examine the practicality of each solution. Shorter S/G spacing and higher doping in the source gate region are predicted to remove much of the transconductance collapse.

Exciton interaction with piezoelectric and polar optical phonons in bulk wurtzite GaN

The intrasubband transition rates of bound carriers interacting with piezoelectric and polar optical phonons in a bulk GaN lattice are presented, considering the anisotropy of the uniaxial wurtzite structure. The directional dependence of the excitonic Bohr radius has a measurable effect for both types of piezoelectric and polar optical phonon scattering. In the latter case, the anisotropy of the uniaxial crystal induces exciton scattering involving both strongly mixed transverse-like and longitudinal-like polar optical phonons. By taking into account the angular frequency dispersion of the zone centre polar optical phonons, we can relate the anisotropy of the excitonic scattering rate to a particular orientation of the transverse-like phonon wave vector with respect to the c-axis. The same effect is not as pronounced in the case of the longitudinal-like polar optical phonon emission due to the much lower anisotropy of the longitudinal-like phonon frequency branch.

Electron momentum and energy relaxation rates in GaN and AlN in the high-field transport regime

Momentum and energy relaxation characteristics of electrons in the conduction band of GaN and AlN are investigated using two different theoretical approaches corresponding to two high electric-field regimes, one up to 1--2 MV/cm values for incoherent dynamics, and the other at even higher fields for coherent dynamics where semiballistic and ballistic processes become important. For the former, ensemble Monte Carlo technique is utilized to evaluate these rates as a function of electron energy up to an electric-field value of 1 MV/cm (2 MV/cm) for GaN (AlN). Momentum and energy relaxation rates within this incoherent transport regime in the presence of all standard scattering mechanisms are computed as well as the average drift velocity as a function of the applied field. Major scattering mechanisms are identified as polar optical phonon (POP) scattering and the optical deformation potential (ODP) scattering. Roughly, up to fields where the steady-state electron velocity attains its peak value, the POP mechanism dominates, whereas at higher fields ODP mechanism takes over. Next, aiming to characterize coherent dynamics, the total out-scattering rate from a quantum state (chosen along a high-symmetry direction) due to these two scattering mechanisms are then computed using a first-principles full-band approach. In the case of POP scattering, momentum relaxation rate differs from the total out-scattering rate from that state; close to the conduction-band minimum, momentum relaxation rate is significantly lower than the scattering rate because of forward-scattering character of the intravalley POP emission. However, close to the zone boundary the difference between these two rates diminishes due to isotropic nature of intervalley scatterings. Finally, a simple estimate for the velocity-field behavior in the coherent transport regime is attempted, displaying a negative differential mobility due to the negative band effective mass along the electric-field direction.

Polar optical phonon scattering and negative Krömer–Esaki–Tsu differential conductivity in bulk GaN

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.

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

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 Γ–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 ∼1 MV/cm.

Decrease of channel conductivity with increasing sheet electron concentration in modulation-doped heterostructures

The great decrease of electron mobility with increasing sheet electron concentration nS&amp;gt;5×1015 m−2 in modulation-doped Al0.25Ga0.75As/GaAs/Al0.25Ga0.75As and Al0.25Ga0.75As/In0.19Ga0.81As/GaAs quantum wells is observed experimentally. At nS&amp;gt;1016 m−2 a conductivity decreases with increasing the sheet electron concentration. The calculations of electron mobility limited by polar optical (PO) phonon scattering show that the great increase of electron intrasubband scattering by emission of PO phonons when nS exceeds 1015 m−2 is responsible for the mobility and conductivity decrease. When nS changes in the range of 1015−1017 m−2, the alternate increase and decrease of channel conductivity is observed.

Variation of transport properties along the channel of a high electron mobility transistor: a quantum influence

In the theoretical modelling of a high electron mobility transistor (HEMT), it is inherently assumed that there is little variation in quantum confinement along the channel from source to drain and therefore the transport properties are independent of the position and only dependent on the electric field along the channel. In this study, the scattering rates for bulk polar optical phonons, bulk acoustic phonons (through deformation potential) and ionized impurity scattering have been studied theoretically based on Fermi's Golden Rule as a function of position along the channel for a As/GaAs HEMT. For operation in the sub-ohmic regime, it is observed that all three mechanisms exhibit a wide variation in the rates from source to drain due to a varying degree of quantum confinement. Some of the intersubband scattering processes involving a lower and higher subband, which are present at the drain end, are absent at the source end due to the variation of energy eigenvalue differences. A quantitative variation of 10 - 50% was observed in the scattering rates at room temperature such as 1 to 1 adsorption and emission of polar optical phonons. It is important to take into account such variation in scattering rates in a complete device model.

Monte Carlo simulation of intersubband relaxation in wide, uniformly doped GaAs/AlxGa1-xAs quantum wells.

Using an ensemble Monte Carlo simulation, we have investigated intersubband relaxation of photoexcited electrons in GaAs/Al x Ga 1−x As quantum wells having a subband separation smaller than the polar optical phonon energy. Intra- and intersubband scattering through polar optical phonons, acoustic phonons, ionized impurities, and electron-electron scattering are included in the simulation. A comparison is made to recent time-resolved pump and probe experiments performed on uniformly doped samples in which good agreement between theory and experiment is obtained. Our results show that the intersubband decay of electrons from the first excited subband into the ground subband is limited by ionized impurity scattering during the photoexcitation process. Polar optical phonon emission also contributes considerably to the electron decay and occurs from the thermal tail of the heated distribution function in both subbands. Intersubband scattering by intercarrier interaction plays a lesser role for the decay. The heating of the distribution functions is due to ionized impurity intersubband scattering and electron-electron intrasubband scattering, which convert potential energy of an electron into kinetic energy. These mechanisms drive both subbands rapidly towards a single quasiequilibrium distribution with a common electron temperature and chemical potential after the pulse is over. The cooling rate of this distribution function, which governs the intersubband decay, depends initially on the energy relaxation through polar optical phonons, whereas at much longer times acoustic phonon scattering predominates. Thus, the intersubband decay of electrons is nonexponential.

Hot-electron power loss in a doped GaAs/AlGaAs superlattice at intermediate temperature studied by infrared differential spectroscopy

The power loss of electrons in a strongly coupled n-type GaAs/AlxGa1−xAs superlattice is studied by analyzing the temperature and electric-field dependence of the interminiband absorption. Electrons are heated by an electric-field pulse and the resulting change of the infrared absorption spectrum is monitored by a step-scan Fourier transform spectrometer operated in a time-resolved, gated mode. The measured power loss is higher than predicted by a simple three-dimensional calculation including acoustic (deformation potential and piezoelectric) and polar-optical phonon emission. Possible explanations for this, such as relaxation via folded acoustic phonons or coupled plasmon–phonon modes, are discussed. The energy relaxation time, which can be extracted from the power balance, decreases from 300 ps at 15 K to 20 ps at 48 K.

A k.p model for hole capture into a quantum well

A k.p model for hole capture into a quantum well has been applied to the calculation of the rates for capture via phonon and alloy scattering into a 30Å In 0.7Ga 0.3As-InGaAsP quantum well, a system which is suitable for lasers operating at 1.55 μm. The well has three subbands, derived from the HH1, LH1 and HH2 zone centre states. Capture of holes into the HH2 subband is predicted to be dominated by polar optical phonon emission, whereas scattering into the other two bands proceeds mainly by non-polar optical phonon emission or alloy scattering. There is structure in the capture rate plotted as a function of the energy and in-plane wavevector of the incident hole, which is attributed to instances where incident holes in barrier states undergo strong transmission into the well region. Mixing between the quantum well subbands is important through the effect upon the density of final states in capture transitions, but is less significant with respect to its effect on the scattering matrix elements.

The theory of multiple quantum-well GaAs-AlGaAs infrared detectors

The theory of multiple quantum-well GaAs-AlGaAs IR detectors based on the principle of quantum well photoionization is presented. The expression for the photoionization probability of the symmetric quantum-well is found to be exact in the effective mass approximation. Depolarization effects in the optical absorption spectra are discussed. We demonstrate that the depolarization shift of the spectrum maximum and its broadening lead to non-monotonic dependence of the photodetector detectivity on the electron concentration in wells in the background limited IR performance condition. The optimal factor of quantum-well filling, corresponding to the maximum of detectivity is rather small, and for the photoresistor with boundary wavelength λ 1 = 10 μm, is θ =0.10. We have also performed calculations for the concentration dependence of the transition temperature for background limited IR performance and found that for optimal concentrations it is about T = 83 K (for λ 1 = 10 μm). The lifetime of non-equilibrium electrons is determined by capturing processes into the wells accompanied by emission of polar optical phonons and is τ ≅ 2 × 10 −11 s. The gain, along with the photoresistor sensitivity, is maximal for structures with a single quantum well.

Quantum well intersubband relaxation in resonant tunneling diodes and transistors

The intersubband relaxation rate due to electron-electron interaction is calculated in analytical form and compared to the intersubband relaxation rates for polar optical phonon emission and for impurity scattering. It is found that for resonant tunneling diodes biased into the second resonance, the intersubband relaxation rate due to electron-electron scattering can become comparable to that due to phonon emission and can involve subpicosecond relaxation times. Taken together, these intersubband relaxation rates are sufficiently strong to significantly reduce the gain of a resonant tunneling transistor, i.e., a device in which an ohmic contact is made to the quantum well of a resonant tunneling diode. This leads us to propose a novel device structure similar to the resonant tunneling transistor, but where the subband for base potential modulation and the subband for hot charge transfer are located at different points in the Brillouin zone. This structure has the advantage that the intersubband relaxation rate is significantly reduced due to the increased momentum exchange on intersubband scattering. A possible material system that has all the needed band lineups to implement this device structure is the GaAs/AlAs/Ge material system.