Drops In Ge Research Articles

The plasma resonance of electron-hole drops in uniaxially stressed germanium

The far infrared absorption spectrum of electron-hole drops in Ge under uniaxial stress S ≤ 20 kg/mm2 is studied. Large variations in positions and lineshape are observed for different stress values and direction of polarization of the infrared electric field with respect to the stress direction. A sharp decrease in the plasma frequency occurs at S ~ 3 kg/mm2, reflecting the change in occupancy of the conduction band valleys. The density of the fluid, n, as a function of [111] stress is obtained from the fit of the experimental results to a theory with the band structure modified by stress.

Multichannel time-resolved measurement in far-infrared magnetoabsorption

A drastic innovation has been achieved in the time-resolved far-infrared magnetooptics by introducing multichannellisation of the delay time. The key section of the new system utilises a digital boxcar unit connected with a common personal computer. Making use of a test pattern signal by magneto-plasma absorption of electron-hole drops in Ge, an eight channel performance over the time window of 100 μs is demonstrated.

Role of Free Electrons and Holes in the Exciton Condensation Process in Semiconductors

AbstractAn experimental study of hysteresis in the luminescence of electron—hole drops in Ge upon the action of a magnetic field is presented. In the magnetic field the free electron and hole flows onto a drop decrease. This results in an increase of the nucleation rate of the drops and also the decrease of the drop radius. The principal experimental results are: 1) The threshold phase diagram obtained in the presence of magnetic field is different from that for H = 0; 2) the new hysteresis loop is found on varying the magnetic field; 3) the contribution from free carrier current in the stationary drop radius is determined and it follows that the value of the cross‐section for the exciton formation process is of the order of 2 × 10−11 cm2.

Non-isothermal nucleation of electron-hole drops in Ge

The delay effect of electron-hole drop nucleation caused by the presence of free carriers (electrons and holes) has been discovered in Ge. The phenomenon is discussed in the model of non-isothermal nucleation.

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.

Radius-independent resonances in electron-hole drop magnetoplasmas

We discuss theoretically the microwave and far-infrared spectra which exist in the parameter ranges appropriate to small electron-hole drops in Ge when they are located in a dc magnetic field. Our examination employs the perturbation-theory results of Ford, Furdyna, and Werner, which rigorously describe the interaction of a small gyrotropic sphere with external time-varying electric and magnetic fields. We consider only the two high-symmetry orientations of the dc magnetic field, parallel to the [100] axis of Ge and parallel to the [111] axis of Ge, for which the electron-hole magnetoplasma in Ge is described by a dielectric tensor of a form amenable to the perturbation theory. The theory predicts several radius-independent electric and magnetic resonances. In parameter ranges appropriate to compensated electron-hole drops in Ge, we find that the positions of all resonances are functions only of the various carrier effective masses and ratios of the concentrations of the different carriers. The intensities of the electric resonances are inversely proportional to the electron carrier concentration and vary as the cube of sphere radius and the fourth power of frequency. The intensities of the magnetic resonances are directly proportional to the electron carrier concentration and vary with the fifth power of radius and the square of frequency. We find that two additional electric resonances can occur when the electron-hold drop is uncompensated. The positions of these resonances depend directly upon the difference in the electron and hole carrier densities.

Electron-hole drops in Ge at high magnetic fields

Light scattering near the focal point of excitation reveals a distribution of electron-hole drop radii, r ≈ 7–60 μm, independent of B up to 15 T. Small radii r ≈ 0.15 μm are determined from magneto-photoconductivity measurements. Electron-hole drop luminescence from valleys of light cyclotron mass are found for B ∥ [111], [110] with B ⪆ 12 T.

Discovery of the Immobility of Electron-Hole Drops in Ge at Low Excitation

Using a new experimental technique based on the hysteresis effect, the spatial distribution of a localized packet of electron-hole drops in a spatially uniform free-exciton gas near threshold is measured for times approx. 10/sup 4/ sec. No significant motion is found, determining an upper limit D or approx. = 5 meV.

Acoustic phonon scattering by electron–hole droplets in Ge. II. Total scattering rate and anisotropy of scattering, as reflected in the shape of a droplet cloud

AbstractThe pair‐phonon scattering rate is calculated for carriers inside an electron–hole drop in Ge. The calculation includes effects due to screening, electron mass anisotropy, and sound velocity anisotropy. The net scattering time is shorter by about a factor of two than found in previous calculations. A very similar integral occurs in calculating the force of the ‘phonon wind’ on the cloud of droplets. Using a simple model, this integral can explain the anisotropic shape of the cloud observed experimentally by Greenstein and Wolfe. The calculation accounts for both the broad lobes observed along 〈111〉 axes and the sharp flares along 〈100〉 axes (the latter due to a focusing of the phonons in Ge).

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

Time and spatially resolved absorption at 3.4 μm in highly excited germanium

We report on a study of the spatial distribution of electron-hole drops in Ge at 2 and 4.6\ifmmode^\circ\else\textdegree\fi{}K, using 3.4-\ensuremath{\mu}m intervalence-band absorption. We find that the cloud of electron-hole drops produced at 2\ifmmode^\circ\else\textdegree\fi{}K decays nearly uniformly. At 4.6\ifmmode^\circ\else\textdegree\fi{}K, decay near the edge of the crystal and at the boundary between the cloud and bulk Ge is more rapid than in the middle of the cloud. The rapid decay near the crystal edge is interpreted in terms of surface recombination of excitons. The results are found to support qualitatively the previously proposed cloud model for decay.

Theory of magnetostriction of electron-hole drops in Ge

A large mass of electron-hole liquid ($\ensuremath{\gamma}$ drop) formed in a strain-induced potential well in Ge is known to distort its shape significantly in a magnetic field $B\ensuremath{\gtrsim}1$ kG. It is shown in this paper that the shape change can be understood in detail as due to a "recombination current" of electron-hole pairs needed to replace those pairs which recombine in the drop volume. The Lorentz force deflects this current and produces a macroscopic dipole current loop inside the drop. The drop then changes shape to minimize its total energy, including magnetic, strain, and surface energies. While the drop usually flattens along the field direction, both para- and diamagnetic effects (elongated drops) are found to be possible, depending on excitation conditions, in accord with experiment. Similar effects are predicted to occur in small drops in unstrained Ge. This paper presents a magnetohydrodynamic theory of the magnetostriction which takes into account density variations which occur in the strain well and in high magnetic fields. A simpler theory is given for the special case in which the drop may be considered incompressible (small drops and moderate fields). Effects of carrier mass anisotropy and fluid viscosity are taken into consideration.

Temperature dependence of the radius of electron-hole drops in Ge : B. Grossman, K. L. Shaklee and M. Voos. Solid St. Commun.23, 271 (1977)

Temperature dependence of the radius of electron-hole drops in Ge : B. Grossman, K. L. Shaklee and M. Voos. Solid St. Commun.23, 271 (1977)

Magnetostriction of an electron‐hole drop in Ge

AbstractBy infrared imaging the shape of a strain‐confined electron‐hole drop in germanium is measured in an applied magnetic field, H ≦ 22 kOe. A considerable distortion from sphericity is observed for all field orientations and stress geometries studied. It is found that in most cases the drop flattens along the field direction. For II ‖〈111〉‖ (applied stress) the drop shape depends markedly on the position of the light excitation spot on the crystal. The dimension parallel to the field decays more rapidly than the perpendicular dimension. The data strongly support a dynamic interpretation in which the recombination currents of electrons and holes give rise to the field‐induced distortion.

Temperature dependence of the radius of electron-hole drops in Ge

The temperature dependence of the radius of electron-hole drops in Ge is determined from measurements of the number of particles in the drops using the p-n junction technique. The drop radius is found to increase from 5.5μ at 1.7 K to 10μ at 3.2 K for an excitation intensity of 160 mWatt/mm 2. As a function of excitation level at 1.8 K the drop radius is found to increase from 2.9μ at 8 mWatt/mm 2 to 6.5μ at 300 mWatt/mm 2. Our data are compared to results available in this field.

Strain-confined electron-hole liquid in germanium

Previous experiments in pure germanium at low temperatures have shown that high densities of photo-produced electron-hole pairs condense into a metallic liquid phase---typically manifested as small electron-hole droplets (EHD). The energy, pair density, and lifetime of an EHD can be significantly modified by applying a stress to the crystal. Due to the lowering of the indirect band edge with strain, droplets, free excitons, and carriers are accelerated in a strain gradient approximately towards a point of maximum shear strain. We show that by appropriately stressing a crystal, it is possible to create inside the crystal a shear strain maximum, i.e., a potential well, into which droplets, excitons, and carriers are attracted, causing them to coalesce into a macroscopic mass of electron-hole liquid with diameter up to a millimeter. Using the known deformation potentials and anisotropies of germanium, we calculate numerically the stress tensor, the band-edge shift, and the electron-hole liquid energy vs position in an inhomogeneously stressed crystal. We report photographic data on large drops in Ge and compare these data to the strain theory. A two-dimensional numerical calculation is in essential agreement with the observed drop locations. Due to the anisotropy of the band-edge shift with strain, we find that it is possible to form one, two, or four electron-hole drops beneath the stress contact area by applying stress along $〈111〉$, $〈110〉$, and $〈100〉$ crystal axes, respectively. In addition we have observed birefringence patterns in these same crystals which yield strain distributions in accord with the above theory and photographic data. Theoretical calculations of the birefringence also agree with observations. Thus the macroscopic features (i.e., position, shape, and number) of the large strain-confined drops can be understood in terms of the known deformation properties of germanium.

Rapid formation kinetics of a long-lived electron-hole drop in Ge under pulsed excitation : J. E. Furneaux, J. P. Wolfe and C. D. Jeffries. Solid-St. Commun.20, 317 (1976)

The photodegradation of anthracene (Ant) and benz[a]anthracene (BaA) were studied in air-equilibrated hexane, methanol and pure water solutions in the absence and presence of phenolic compounds (4-methylcatechol, guaiacol and syringol). In the absence of phenolic compound, the pseudo first-order degradation rate constants of Ant and BaA increased with the polarity of solvent, demonstrating the influence of solvent effects on the photoreactivity. The differences can be attributed to factors such as the proton donating potential of the solvent, and the formation potentials of PAH radical cation and hydroxyl radical in solvent. In the presence of phenolic compound, Ant and BaA photodegradation rates were accelerated in hexane and methanol while inhibited in water solutions. Photodegradation kinetics of the phenolic compounds were also measured; and visible colored products were observed in all three solvents. The observed accelerations of Ant and BaA photodecay in the presence of the phenolic compounds can be explained by energy transfer from the phenolic compound to PAH, phenolic hydrogen abstraction by excited PAH and more reactive radical formation from the phenolic compound. However, the inhibition effects of Ant and BaA photodecay in water were more influenced by the quenching of photo-produced reactive oxygen species (ROS) by the phenolic compound and/or its photoproducts. The results indicate that the photodegradation of PAHs will be highly dependent on the aerosol water content. i.e., the chemical composition of the environmental aerosols.

Determination of nonradiative decay rate in electron-hole drops in Ge at 1.6°K

We show that microwave photoconductivity measurements of optically excited carriers in Ge at 1.6°K can be used to determine the importance of nonradiative recombination within electron-hole liquid drops. Our results show that the nonradiative lifetime is 80 μsec from which we calculate a radiative efficiency of 0.5 ± 0.1 for the condensed phase.

Rapid formation kinetics of a long-lived electron-hole drop in Ge under pulsed excitation

The buildup of a large long-lived electron-hole drop in stressed Ge is studied using its Alfvén wave resonances. This microwave method permits rapid time resolution of the formation process after a short intense (100 nsec, 7 W) laser excitation pulse. A delay of about 1 μsec is observed before the drop radius rapidly increases from zero to ∼ 100 μm within the next μsec. This is consistent with the interpretation that the photo-produced electron-hole pairs are quickly accelerated to the strain-induced potential minimum which is well within the crystal.

Investigation of the shape of a cloud of electron-hole droplets in germanium

Absorption and scattering of light are used to investigate a cloud of electron-hole drops in Ge at 2\ifmmode^\circ\else\textdegree\fi{}K. We find a drop size of 2 \ensuremath{\mu}m, from light scattering; and use an Abel transform to unfold the absorption data and obtain a complete droplet density map. The cloud is distinctly nonspherical. The droplet penetration in a direction perpendicular to the surface of excitation is 1.5 times greater than that in a parallel direction. This result is discussed in terms of alternative models for cloud formation.