Carrier Momentum Research Articles

Enhanced photoluminescence excitation in surface plasmon coupling with an InGaN∕GaN quantum well

The authors report the observation of the enhancement of photoluminescence excitation through the couplings of an InGaN∕GaN quantum well (QW) with localized surface plasmons (LSPs) and surface plasmon polaritons (SPPs), which are generated on a Ag nanostructure deposited on the SiN-coated QW epitaxial sample. At the wavelengths corresponding to the LSP modes, the excitation light is first absorbed by the LSPs. The LSP energy is then transferred into the QW such that the effective QW absorption is enhanced. Meanwhile, the application of the LSP local field to the QW may increase its absorption coefficient. Then, the coupling of the relaxed carriers with the SPPs enhances light emission that becomes stronger as temperature increases because of the increased carrier momentum.

Femtosecond carrier dynamics of InxGa1−xN thin films grown on GaN (0001): Effect of carrier-defect scattering

Ultrafast carrier dynamics in ultrathin InxGa1−xN ternary alloys were investigated in detail, using femtosecond transient differential optical absorption measurements. Measurements were performed with probing wavelengths above and below the band edge of the materials. Furthermore, we performed a structural characterization by x-ray diffraction reciprocal space maps and we found that the alloys with the higher InN mole fraction (x=0.89 and x=0.43) present large lattice mismatch-strain relaxation whereas the lower InN content alloy was fully coherent with the underlying GaN (0001) layer. Our analysis showed that the observed nonradiative carrier dynamics was strongly related with the carrier-defect scattering of the materials. Our measurements in conjunction with the numerical analysis showed that when we excite these alloys with ultrashort laser pulses the background carrier concentration for In-rich InGaN samples participates to the photoexcited carrier relaxation process via carrier momentum scattering. For the higher InN content alloys (x=0.89 and 0.43) the relaxation times were short (0.4–1.4ps) whereas for the full strained alloy (x=0.07) a slower nonradiative relaxation time (∼25ps) was observed. Finally, the energy loss rate of this material (2.05±0.10meV∕fs) as well as the optical phonon lifetime (44±2fs) were extracted.

Spin–orbit dependence on carrier momentum in (1 1 0) GaAs quantum wells

Surface acoustic waves (SAW) are employed to transport optically generated spin ensembles over distances exceeding 60 μ m in (1 1 0) GaAs quantum wells (QW). The dependence of the spin–orbit (SO) coupling on carrier momentum is investigated by using SAWs to transport spins with well-defined velocity along different directions in the QW plane. For transport along the [0 0 1] direction, the high relaxation rates for the in-plane spin component lead to fast spin decoherence under a magnetic field. For the [ 1 ¯ 1 0 ] direction, in contrast, a non-zero average value of the SO internal magnetic field retards the longitudinal spin relaxation.

Dynamics of charge current gratings generated in GaAs by ultrafast quantum interference control

Ballistic charge current gratings are induced in GaAs at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ by quantum interference of single- and two-photon absorption using noncollinearly incident 775 and $1550\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, $150\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ pulses. First-order diffraction of time-delayed $830\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, $150\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ probe pulses is used to observe carrier evolution for injected densities near ${10}^{17}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. The current grating forms electron and hole charge-density gratings during pumping, and because the pumping is uniform while the carrier density and hence electronic specific heat is not, a carrier temperature grating also forms. The peak diffraction efficiency from both grating types is only $\ensuremath{\sim}{10}^{\ensuremath{-}9}$. The temperature grating, with modulation amplitude $\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, decays through cooling in $\ensuremath{\sim}500\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$. Space-charge fields neutralize the electron and hole density gratings by the end of pumping, but nonetheless leave a neutral, electron-hole pair density grating with amplitude of $\ensuremath{\sim}{10}^{\ensuremath{-}3}$ of the injected carrier density. At the highest injected carrier densities, the pair grating amplitude builds on a few picosecond time scale before decaying by recombination and ambipolar diffusion with an $\ensuremath{\sim}15\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ time constant. A model based on continuity equations for carrier density, momentum, and energy during ballistic and drift motion is used to help interpret the experimental data. Besides qualitatively confirming the above dynamics, the model suggests that the pair grating amplitude and evolution is determined by two factors: (1) the warping or nonparabolicity of the hole bands and (2) the transfer of some electrons from the $\ensuremath{\Gamma}$-valley electron-density grating to the $L$, $X$ conduction band valleys during excitation, and their subsequent return to the $\ensuremath{\Gamma}$ valley on a few picosecond time scale.

Monte Carlo analysis of terahertz oscillations of photoexcited carriers in GaAsp−i−nstructures

Pulsed terahertz emission from the electron-hole plasma excited by a femtosecond optical pulse in GaAs $p\text{\ensuremath{-}}i\text{\ensuremath{-}}n$ structures is studied by Monte Carlo simulations. The conduction band composed from $\ensuremath{\Gamma}$, $L$, and $X$ valleys, and the valence band composed from heavy, light, and split-off subbands, are considered in the simulations. The Pauli exclusion principle and the intercarrier scattering between electrons and holes are taken into account self-consistently with the time- and position-dependent carrier density and momentum distribution. Good agreement between Monte Carlo results and experimental data is obtained. The simplified hydrodynamic model of the transient dynamics of the photoexcited carriers is suggested. The proposed model accurately reproduces Monte Carlo results when the excitation is considered to be spatially uniform.

Terahertz investigation of high quality indium nitride epitaxial layers

AbstractWe report on the optical characterization of InN layers in the THz range and magnetic fields up to 13 T. The results are interpreted using the dielectric function formalism, with contributions of cyclotron resonance, phonons, plasmons and helicon wave excitations. We show how THz radiation transmission measurements can provide an optical contactless method of determining the quality (carrier density and momentum scattering rate) in the InN layers. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Pure spin current gratings in semiconductors generated by quantum interference

We demonstrate that the quantum mechanical interference between the probability amplitudes for the two-photon absorption of a fundamental (1.55 μm)∼150 fs pulse and for the one-photon absorption of a noncollinearly propagating second-harmonic (775 nm) pulse can create transient, ballistic, purely spin-polarized current gratings in bulk GaAs at room temperature. For fundamental and second-harmonic pulses having orthogonal linear polarizations, two periodically modulated ballistic spin-polarized current gratings are injected that have opposite spins and opposite propagation directions at each point along the grating. Consequently, there is no initial modulation of the charge current, carrier population, or net spin. Before the carrier momentum relaxes, the transport associated with these spin currents forms two oppositely spin-polarized population gratings that are exactly out of phase spatially and that decay by electronic spin diffusion in a time of 3.2 ps. In addition, charge density gratings are directly produced by the quantum interference process, and they decay by ambipolar diffusion and recombination (∼17.6 ps). The polarization selection rules and sample orientation are used to separate the contributions of the current and density gratings.

Two-dimensional hydrodynamic model including inertia effects in carrier momentum for power millimetre-wave semi-conductor devices

A two dimensional-hydrodynamic model is carried out to predict the performance of short gate length power field effect transistors based on III–V semi-conductor systems. The model is based on the conservation equations, deduced from the Boltzmann transport equation, solved in their whole form by taking temporal and spatial variations in carrier momentum into account. This model is well suited to get accurate predictions for power devices having various gate recess topologies. Results are performed for devices with different gate lengths and compared with those obtained from simplified models. For gate lengths shorter than 0.5 μm, a drop in the overshoot velocity phenomenon involves a better estimation of the characteristics of the device.

A method to reduce small-angle scattering in Monte Carlo device analysis

Ionized-impurity scattering is an anisotropic process showing a high preference for small scattering angles. In a Monte Carlo simulation of a semiconductor device many small angle scattering events have to be processed, although the contribution of these events to carrier momentum relaxation is small. A new method is presented which reduces the amount of small-angle scattering very effectively. In the simulation an isotropic process is used which yields the same momentum relaxation time as the anisotropic process. A theoretical analysis based on the Boltzmann equation is carried out. Monte Carlo calculations are performed over a wide range of doping concentrations, lattice temperatures and electric fields. No systematic difference is found in the results from the anisotropic and the isotropic scattering models. For a given accuracy, the reduction of needed scattering events and free flights can be more than one order of magnitude at low and medium doping concentrations.

Role of interlayer coupling in the superconducting state of layered cuprate superconductors

The role of interlayer coupling in the superconducting state of high- T c layered cuprate systems has been studied using one-band two-layer tight binding Hamiltonian with intra- and interlayer attractive interactions. The expressions of charge carrier (hole) density and momentum dependent energy-gap function are derived on the basis of BCS-type pairing in narrow band within Hubbard-III like decoupling approximations. The hole density and generalized gap-parameter are found to be dependent on the interlayer interactions. It is found that for a two layer per unit cell cuprate systems there is a contribution in the hole density due to interlayer interactions and numerical analysis shows that change in the holes between the cuprate planes depends on the magnitude of interlayer hopping element and superconducting transition temperature.

How the carrier momentum influences the polarization properties of a vertical-cavity semiconductor laser

By taking carrier momentum into account, we present an extension of the commonly used model that describes the polarization properties of vertical-cavity surface-emitting lasers (VCSEL's). We study how this modifies the polarization dependence of the gain saturation, and introduce the role of the crystalline symmetry of the semiconductor material. On a macroscopic level we show that a limited number of parameters is sufficient to describe fully the polarization properties of the VCSEL. On a microscopic level we show how the magnitudes of these parameters are determined by the dependence of the interband-transition dipole matrix element on the relative orientation of the carrier momentum and optical polarization. It turns out to be essential that the component of the carrier momentum in the plane of the quantum well is non-negligible. Furthermore, the relaxation rates of the carrier momentum and carrier spin are crucial in determining the magnitude of the polarization effects. Inclusion of the carrier momentum changes the interpretation of experimental results on the polarization of VCSEL's, and makes it possible to understand experimental results that were until now unexplained.

Probing ultrafast carrier and phonon dynamics in semiconductors

Over the past 2 decades there has been tremendous advancements in the field of ultrafast carrier dynamics in semiconductors. The driving force behind this movement other than the basic fundamental interest is the direct application of semiconductor devices and the endless need for faster response and faster processing of information. To improve and develop microelectronics devices and address these needs, there must be a basic understanding of the various dynamical processes in the semiconductors which have to be studied in detail. Therefore, the excitation of semiconductors out of their equilibrium and the subsequent relaxation processes with various rates has become a key area of semiconductor research. With the development of lasers that can generate pulses as short as a few femtoseconds the excitation and subsequent probing of semiconductors on an ultrashort timescale have become routine. Processes such as carrier momentum randomization, carrier thermalization, and energy relaxation have been studied in detail using excite-and-probe novel techniques. This article reviews the status of ultrafast carrier and phonon dynamics in semiconductors. Experimental techniques such as excite-and-probe transmission, time-resolved up-conversion luminescence, and pump-probe Raman scattering along with some of the significant experimental findings from probing semiconductors are discussed. Finally, a selfconsistent theoretical model, which correlates the carrier and phonon dynamics in germanium on an ultrashort time scale, is described in detail.

Memory effect for polarization of pump light in optically pumped vertical-cavity semiconductor lasers

We report that the polarization of the emission of an optically pumped vertical-cavity surface-emitting laser (VCSEL) is sensitive to the polarization state of the pump light. By measuring this memory effect for circularly polarized pump light, we determine the normalized relaxation rate of the carrier spin, /spl Gamma//sub s/, which is a vital parameter in current theoretical models of VCSEL polarization. We find /spl Gamma//sub s/=300/spl plusmn/150, a value which is significantly larger than previously estimated. We also observe a memory effect for the orientation of linearly polarized pump light. This signals that, apart from the carrier spin, the VCSEL polarization is also determined by the carrier momentum.

Injection-level dependence of charge carrier mobility in high-injection plasma

The contradictions between results of commonly used charge carrier transport equations resulting from electron-hole scattering on the one hand and experimental data concerning transport coefficients in an electron-hole plasma on the other are pointed out. To resolve them, the influence of the injection level on the transfer of charge carrier momentum to the phonon system is investigated. The effective momentum transfer mobility for electrons and holes is derived, taking into account the indirect influence of electron-hole scattering on the momentum transfer to acoustical and high-energetic phonons in silicon. The result of the calculation is compared with measurements, and an analytical fitting formula for the implementation of the injection dependent phonon scattering into device simulators is presented.

Carrier spillover at 300, 195, and 77 K in InGaAs and GaAs single quantum wells

The carrier recombination rates in GaAs and strained InGaAs–GaAs single-quantum-well lasers of varying well width and potential depth, respectively, have been measured at 300, 195, and 77 K. For the InGaAs quantum wells (QWs), the carrier lifetime saturates at high inversion, with both the Shockley–Read (SR) lifetime and the saturation lifetime showing substantial reductions with decreasing temperature. The large reduction in the SR lifetime may be attributed to the increased effectiveness of acceptor ions as trap sites, due to the reduced carrier momentum at lower temperature. In a similar vein, the saturation lifetime is also reduced, due to the enhanced carrier confinement in the QW, brought about by the decrease in the carrier thermalization. For the GaAs QWs at 300 K, the saturation lifetime decreases as the well width is increased. The recombination rate law of bulk material is inadequate to predict the recombination rates in these QWs. Consequently, a local recombination model has been developed which accurately predicts the observed lifetime saturation behavior as a function of well width, potential depth, and temperature. Further, T0 of 95 and 162 K are calculated for the shallow and deep QW lasers, respectively. This calculation suggests that it is the temperature dependence of the differential gain that is the dominant factor in setting the temperature sensitivity of the InGaAs QW lasers.

Non-equilibrium carrier transport in the base of heterojunction bipolar transistors

The conventional drift-diffusion equation is inadequate to analyze ballistic effects. In most device analysis, thermoelectric effects associated with gradients in the carrier temperature are assumed to be small. The base thickness dependence of current gain as a result of non-equilibrium transport of electrons in the base was experimentally shown by many researchers. We present a simulation to analyze the electron transport in the base region of an HBT based on the carrier density balance, momentum balance, and energy balance equations. Transistors with base thickness of 1000 Å and 2500 Å are investigated. Simulation results of electron transport in the base region indicates that tunneling electrons give rise to unique transport characteristics in the base of HBTs. The density profile is found as a result of transition from ballistic to diffusive transport in the base region. The range of observed non-equilibrium transport and the carrier density and temperature profiles in the base region are functions of average momentum and energy relaxation times. The non-equilibrium effects are shown to exist up to 1000 Å in the base region of HBTs. The simulation results are in good agreement with experimental data.

Temperature- and carrier-density-dependent electron tunneling kinetics in (Ga,In)As/(Al,In)As asymmetric double quantum wells

We present a detailed investigation of electron tunneling in (Ga,In)As/(Al,In)As asymmetric double quantum wells as a function of different excitation and temperature conditions. We show that tunneling dynamics depend strongly on the initial carrier temperature and momentum. For example, electron and hole tunneling out of the narrow well is complete at low temperature. However at room temperature carriers do not exhibit any tunneling kinetics. We propose a simple kinetic model which describes the observed population dynamics at different carrier densities, temperatures, and excitation conditions.

Evolution of non-equilibrium electron distribution functions at hydrodynamic scales in multi-valley semiconductors

The concept of the physical evolution process for the distribution function is used to derive a non-equilibrium hydro-kinetic transport theory. The hydro-kinetic distribution that is interpolated between the kinetic and hydrodynamic levels is introduced to elucidate the physics of evolution for the distribution. The evolution scales of the distribution are decomposed into characteristic scales of hydrodynamic parameters, such as carrier density, energy and momentum characteristic times. The coarseness of the hydro-kinetic distribution function is determined by scales of the chosen hydrodynamic parameters. The hydro-kinetic distribution is used to close the infinite set of moments and to determine the rate coefficients in the closed set of hydrodynamic equations. In this paper, the hydro-kinetic distribution at the energy characteristic scale is applied to study evolution of the electron energy/momentum distribution and transport parameters, including inter-valley transfer, in GaAs subjected to a fast varying electric field. Monte Carlo (MC) simulations are also included to illustrate the difference between evolution scales of the kinetic and tepsilon -scale hydro-kinetic distributions. The study indicates that the electron distribution is strongly dependent on the mean energy but weakly on the average momentum. In GaAs subjected to a rapid increase in field, effects of the momentum dependence is enhanced only near the peak of strong velocity overshoot, such as the overshoot in the Gamma valley. The Gamma -valley energy scale hydro-kinetic (energy dependent) distribution thus appreciably deviates from the kinetic distribution near the peak of strong overshoot. As a result, the hydro-kinetic model leads to a smaller overshoot in the Gamma valley than the Me method. In the case of less pronounced velocity overshoot, the energy scale hydro-kinetic distribution can reasonably follow the evolution scale of the kinetic distribution function.

Formulation of a tail electron hydrodynamic model based on Monte Carlo results

In this paper, the Monte Carlo method is applied to uniform and n/sup +/-n/sup -/-n/sup +/ structures of silicon to study the behavior of tail electrons and to develop a new set of hydrodynamic equations based on tail electron statistics. Each term in these equations is calibrated under both nonhomogeneous and homogeneous electric fields. Terms associated with surface integral of the carriers and carrier momentum over an iso energy surface: (/spl Escr/=/spl Escr//sub th/) are introduced. The new tail electron hydrodynamic model yields the density (n/sub 2/) and the average energy (w/sub 2/) of tail electrons and is shown to predict hot electron effects accurately.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

K-space carrier dynamics in GaAs

We investigate the k-space scattering dynamics of carriers in GaAs by measuring the transient relaxation of an anisotropic population produced by a linearly polarized 9 femtosecond infrared pulse. The redistribution of carrier momentum is shown to occur in the first tens of femtoseconds after excitation, and the relaxation times are found to vary with carrier density, from 25 to 60 fs for a carrier density range from 8×1017 to 8×1016 cm−3. Our results indicate that carrier momentum is rapidly redistributed via carrier–carrier scattering, and the nature of the density dependence suggests that the scattering is mediated by a screened Coulomb interaction between the carriers.