Electron-hole Droplets In Ge Research Articles

Effect of deep impurity of recombination lifetime of a large electron-hole drop in strained germanium

Lifetime shortening of a large electron-hole drop in zinc-doped Ge is reported by using time-resolved photoluminescence technique. The lifetime decreases remarkably with the concentration of a double acceptor Zn up to ∼10 16 cm −3. This makes a striking contrast to the result by Chen et al. for ordinary electron-hole droplets in Ge doped with shallow impurities. Additional information from microwave Alfvén wave dimensional resonance of a large drop is also presented.

Interaction of phonons with the electron-hole liquid

Three new experiments are described which quantify the interaction of high-frequency phonons with the electron-hole liquid. Drift measurements in Si have determined the mobility of electron-hole droplets (EHD) and shown a temperature dependence of the electron-phonon scattering rate which is characteristic of a degenerate Fermi fluid. The drift velocity of EHD strongly saturates at near-sonic velocities, suggesting a Cherenkov-like phonon emission. Phonon spectroscopy in the 150–500 GHz range has determined the dynamic deformation potential and demonmstrated the predicted 2kF-cutoff in the absorption of phonons by EHD in Ge. Time-resolved luminescence imaging has revealed an interesting phonon-wind-induced anisotropy in a cloud of electron-hole droplets which is produced by intense pulsed-laser excitation of Ge.

Time-resolved images of electron-hole droplets produced by intense pulsed-laser excitation of germanium

We have examined the spatial evolution of electron-hole droplets in Ge created in Ge by an intense pulse of 100 ns duration. The resulting electron-hole droplet cloud is remarkably different in anisotropy and size from a CW-excited cloud, providing new insights into the droplet transport process. Sharp anisotropies and prolonged expansion of the cloud imply a localized phonon source which exists for 1–2 micros after the laser pulse.

Momentum damping time and phonon-wind force for electron-hole droplets in Ge

Momentum damping time and phonon-wind force for electron-hole droplets in Ge

Interaction of electron-hole droplets in Ge with dislocations

We report the discovery of a strong interaction between electron-hole droplets and dislocation lines in ultrapure Ge. The normal, phonon wind produced, flow pattern of droplets is strongly perturbed by the presence of even a single dislocation line. Intense droplet luminescence is observed within about 50 μm of the defect and the droplet flux passing through this region is greatly attenuated. Several possible mechanisms for this surprisingly large interaction range are examined.

The phonon wind and distribution of electron-hole droplets in Ge

Intensity contour maps of electron-hole droplet luminescence in Ge reveal a striking evolution of the droplet cloud shape with radial distance from the excitation point. A calculation of the phonon wind force which includes anisotropies in phonon absorption and phonon focusing explains the general features of the cloud. The data and calculations indicate a strong attenuation of the LA phonon flux due to absorption by droplets.

Role of thermalization phonons in producing the electron-hole droplet cloud

Abstract The phonon wind which generates the characteristics cloud of electron-hole droplets in Ge cannot be composed solely of phonons produced via Auger recombination in drops. The nearly constant droplet density in the cloud and the rapid expansion of the cloud both point to an extra source of phonons spatially localized near the crystal surface and formed during the initial thermalization of hot carriers. Most experiments, including recent measurements of droplet velocities, are consistent with about 10–20% of the wind phonons being of thermalization origin.

Line shapes for electron-hole plasmas in semiconductors. I. The heavy-hole to spin-orbit split-band transitions in electron-hole droplets in Ge

We report details of a new theory for the luminescence and absorption line shapes of electron-hole plasmas in semiconductors. The theory includes the physical processes which lead to the creation of single-plasmon or particle-hole pairs. It is the extension to line-shape problems of the random-phase approximation which has been successful for the thermodynamic properties of electron-hole liquids. Extensive calculations are presented and compared to experiments on the cross section for absorption due to heavy-hole to spin-orbit split-band transitions in electron-hole droplets in Ge. Good agreement with the observed broad line shape is obtained when details of the valence-band structure of Ge are included. In an appendix, we present an analysis of the dielectric function in the spherical model for the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ valence-band Hamiltonian of diamond and zinc-blende semiconductors for finite spin-orbit splitting.

Phonon lifetime and acoustic attenuation due to phonon-assisted Auger recombination in electron-hole drops in Ge

The phonon lifetime due to the phonon-assisted Auger recombination in electron-hole droplets is calculated and from that the attenuation coefficient is deduced. Numerical estimates are made for electron-hole droplets in Ge. The lifetime of the phonon is estimated to be of the order of 10-3s and the attenuation coefficient of the order of 10-4 cm-1.

Formation of the electron-hole droplet cloud in germanium

We describe luminescence imaging experiments that probe the nature of the phonon wind which transports electron-hole droplets in Ge. The participation of non-equilibrium phonons emanating near the excitation region is supported by: (a) sharp features in the droplet spatial distribution (b) a dependence of the average cloud density on the excitation photon energy, and (c) a rapid initial buildup of the cloud.

Size effects in small electron-hole drops

The self-consistent formulation of density functional theory is used to calculate the single-particle properties of electron-hole droplets in Ge with between 10 and 120 pairs. Results are presented for the recombination luminescence lineshape, the electron and hole density profiles and the work function. As in the physics of the nucleus there are strong effects associated with the filling of the various electron and hole shells. In particular, the luminescence line narrows and oscillates as N decreases for a drop with less than 120 pairs. If N = 70 the width is 70% of the bulk value; while for N = 50 it is 80%. The density profiles and work functions for different N are rather varied and show very strong shell effects.

Time-resolved recombination luminescence spectra from “hot” and “cold” carriers in electron-hole droplets in stressed Ge

Time-resolved measurements are presented which further support the presence of “hot” electrons in electron-hole droplets in Ge under 〉111〈 stress. The results are used to discuss the decay mechanisms of “hot” electrons and the possibility of phase separation of “hot” and “cold” electrons in an electron-hole droplet.

Inter-Valence-Band Absorption in Electron-Hole Droplets

The broad line shape for absorption due to transitions between heavy-hole and spin-orbit bands in electron-hole droplets in Ge is explained. The calculation uses multiple-scattering concepts to remove the divergences of ordinary perturbation expansions in the dynamical Coulomb interaction. The absorption resembles the free-hole theory at low frequencies, is sensitive to both band anisotropy and screening approximations at intermediate frequencies, and is independent of screening at high frequencies.

Alfvén-wave oscillations in a sphere, with applications to electron-hole drops in Ge

The problem of Alfven-wave oscillations in an anisotropic sphere is studied, and two solutions are presented. Our solution is exact, involving an expansion of the current inside the sphere in a series of orthonormal modes. The second is approximate, based on a perturbation expansion of the induced fields and currents in powers of the radius. The approximate solution can be applied to a material having a completely general conductivity tensor, while the exact solution is restricted to situations of high symmetry. As an illustration of these solutions, the resonant power absorption by electron-hole droplets in Ge is calculated explicitly. Size-dependent resonances, for which the resonant field increases with the drop radius, have been observed experimentally. The present calculation shows that such resonances occur both in the magnetic- and electric-dipole absorption, with the magnetic-dipole absorption being most intense for the drop sizes and frequencies under consideration, particularly for small drops. From the approximate solution, it is found that certain of the resonances can have a very strong dependence on the orientation of the magnetic field with respect to the crystal axes, similar to cyclotron resonance of an electron in Ge. As a second application of these results, the transition from Alfvenmore » waves (in a material having equal numbers of electrons and holes) to helicon waves (only one carrier type) is studied, using the approximate solution only. The ''elimination'' of one carrier type can be accomplished by increasing its mass, decreasing its concentration, or increasing its collision rate. The Alfven-to-helicon transitions are quite different in each of these three cases, and examples of intermediate states are presented.« less

Infrared absorption and scattering by electron-hole droplets in Ge

The scattering and absorption of fat-infrared radiation by electron-hole liquid droplets in Ge is calculated using Mie theory. These processes show a strong resonance at ${\ensuremath{\omega}}_{0}\ensuremath{\approx}\frac{{\ensuremath{\omega}}_{p}}{\ensuremath{\surd}3}$ [here ${\ensuremath{\omega}}_{p}$ is the plasmon frequency of the electron-hole liquid (EHL)]. The line shape of the resonance is determined primarily by three factors: (i) interband transitions from the heavy- to light-hole bands; (ii) the finite quasiparticle lifetime; and (iii) the size of the droplets. Assuming droplets with radii $R$, of approximately 1 \ensuremath{\mu}m, and taking the first two effects into account by means of the dielectric constant, we obtain good fits to the currently available experimental data. From the data we conclude that density of the EHL is 2.2 \ifmmode\times\else\texttimes\fi{} ${10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ at 1.5\ifmmode^\circ\else\textdegree\fi{}K, and that the EHL has an effective quasiparticle lifetime $\ensuremath{\tau}\ensuremath{\approx}0.33$ me${\mathrm{V}}^{\ensuremath{-}1}$. Finally, we discuss the line shapes of large droplets ($R>2$ \ensuremath{\mu}m). Comparison of our calculations with the experimental data of Timusk and Silin leads to the conclusion that large radius droplets, $R=8$ \ensuremath{\mu}m, occur in Sb-doped Ge.

Recombination Luminescence from "Hot" Carriers in Electron-Hole Droplets in Stressed Ge

We have observed luminescence lines from "hot" free excitons and from recombination of "hot" electrons within electron-hole droplets in Ge under uniform $〈111〉$ uniaxial stress. Our results suggest that both "hot" and "cold" electrons coexist in the same electron-hole droplets. We have also measured the total lifetime of the hot electrons, which is in good agreement with intervalley relaxation by electron-electron scattering.

Phonon damping of the electron-hole droplet motion

We report on a study of phenomena limiting the motion of electron-hole droplets in Ge. The role of screening of the carrier-phonon interaction in the droplet by the carriers making up the droplet is examined using a Hartree approximation. We consider damping of the droplet motion for droplet velocities both greater and less than the sound velocity.

Capillary-Wave Resonances of Electron-Hole Droplets

We have studied in the gigahertz range the ultrasonic attenuation by electron-hole droplets in Ge as function of their size. A broad bump is attributed to the resonant excitation of nonresolved capillary modes. From a detailed analysis of the line shape we derive a value of 3\ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$ erg/${\mathrm{cm}}^{2}$ for the surface tension of droplets. This is the first mechanical measurement of this quantity.

Mott transition of the electron-hole liquid in Ge

A treatment is given of the Mott transition of a gas of excitons in equilibrium with electron-hole droplets in Ge. We find that transition occurs near 4K. We can come to no firm conclusion whether the Mott transition is a first-order transition separate from the liquid-gas transition, as has been suggested.

Collision broadening in the exciton gas outside the electron-hole droplets in Ge

A broadening of both the recombination luminescence and absorption spectra of indirect excitons in Ge is observed. This broadening is found to be density dependent consistent with an exciton-exciton collision process. An effective exciton collision radius of 220 \ifmmode\pm\else\textpm\fi{} 80 \AA{} is measured in agreement with theoretical estimates. Density-modulated absorption spectra also indicate an apparent red shift of the exciton energy at high carrier densities. A detailed analysis of the exciton line shape leads to a better understanding of the thermodynamics of the coexisting electron-hole liquid and exciton gas, provides improved values of the binding energy, $\ensuremath{\varphi}=1.8\ifmmode\pm\else\textpm\fi{}0.2$ meV, and the ground-state energy per pair, ${E}_{G}=\ensuremath{-}5.9\ifmmode\pm\else\textpm\fi{}0.3$ meV, and gives the most nearly complete description of the gas-liquid phase boundary. The complications due to density gradients which arise from surface excitation with be briefly discussed.