Interaction between free carriers,free excitons,and electron-hole drops in germanium

Under steady-state conditions, we have observed an increase of photo-conductivity in Ge at low temperature simultaneously with radiation from electron-hole drops. A set of rate equations for a 3-phase system of carriers, free excitons and drops are used to interpret the results. Values of the exciton-recombination coefficient and the lifetimes of the three phases are determined.     

Diffusion of excitons and electron-hole drops in germanium

Diffusion of excitons and electron-hole drops is investigated in pure germanium, using a time-resolved cyclotron resonance method. The diffusion coefficient of excitons at 4.2 K is obtained to be ≈ 1000 cm²/sec. For electron-hole drops, when excitation is not so high, it is expected to be lower than ≈ 500 cm²/sec at 1.6 K.     

Formation and decay of electron-hole drops in Si

Using a single photon counting technique we were able to measure with very high time resolution the rise and decay times of the luminescence of free excitons and electron hole drops in Si. It was found that the formation and decay of droplets can be described by kinetic equations. The experimental data concerning the time behavior of the free excitons cannot be described by analogous simple kinetic equations. Therefore it is concluded that droplets are formed directly from a dense plasma rather than from a free exciton gas.     

Luminescence line shape of free excitons in pure Ge

We report luminescence experiments performed in pure Ge at low temperature. Taking into account the splitting of the ground state of free excitons in this material, we show that their emission line shape is subject to a Gaussian broadening which seems to be due to the phonon lifetime. From this study, we deduce new values of the binding energy of electron-hole drops in Ge and Si which are respectively -2 and -5.6meV.     

Auger recombination of electron-hole drops

Phonon-assisted Auger recombination is calculated for indirect band gap semiconductors in the strongly degenerate case. It follows a reciprocal lifetime τ^?1=Cn² with C=7.19×10³¹ cm⁶ sec^?1 for Si and C=2.94× 10^?31 cm⁶ sec^?1 for Ge. These results are in good agreement with experimental values of the decay of electron-hole drops. Therefore one can conclude that phonon-assisted Auger recombination is the essential nonradiative recombination process in this case.     

Radius of electron-hole drops in silicon

The radius of electron-hole drops at nucleation threshold is investigated as a function of temperature in Si using a small shift of their main luminescence line due to their surface energy. For T > 10 K, experiment and theory are consistent if we take into account a sticking coefficient (～ 4%) at the drop surface. For T ? 10 K our data indicate that the drop size is certainly small, but the measured radii are not likely. This suggests that other effects should be considered, such as the drop curvature energy for example.     

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.     

Lowest optical excitations in molecular crystals: bound excitons versus free electron-hole pairs in anthracene

By solving the Bethe-Salpeter equation for the electron-hole Green function for crystalline anthracene we find the lowest absorption peak generated by strongly bound excitons or by a free electron-hole pair, depending on the polarization direction being parallel to the short or the long molecular axis, respectively. Both excitations are shifted to lower energies by pressure. The physical difference of these excitations is apparent from the electron-hole wave functions. Our findings are a major contribution to solve the long-standing puzzle about the nature of the lowest optical excitations in organic materials.     

Size distribution of electron-hole drops in Ge

We investigate the size distribution of electron-hole drops collected in an illuminated p-n junction. The observed size distribution are of complex nature with several pronounced peaks revealing drop sizes of about 10⁸ electron-hole pairs (drop radius $\text{R ? 5}$ μm). An observed suppression of drop formation at low temperatures indicate that supersaturation effect are present.     

Luminescence of a quasi-two-dimensional electron-hole liquid and excitonic molecules in Si/SiGe/Si heterostructures upon two-electron transitions

The low-temperature photoluminescence of Si/Si_0.91Ge_0.09/Si heterostructures in the near-infrared and visible spectral ranges is investigated. For the structure in which the barrier in the conduction band formed by the SiGe layer is transparent to electron tunneling, the broad luminescence line observed in the visible range is analyzed by comparing its shape with the numerical convolution of the spectrum of near-infrared recombination radiation originating from the electron-hole liquid. The comparison demonstrates that, at high excitation levels, the visible-range emission is caused by two-electron transitions in a quasi-two-dimensional spatially direct electron-hole liquid. Furthermore, the combined analysis of the photoluminescence spectra in the near-infrared and visible ranges yields the binding energy of a quasi-two-dimensional free biexciton in the SiGe layer of these heterostructures. In the structures with a wide SiGe layer that is not tunneling-transparent to electrons, a spatially indirect (dipolar) electron-hole liquid is observed.     

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.     

Correlated ejection of electron-hole drops from a continuously generated electron-hole liquid in Ge

The photocurrent power spectra were measured in a Ge photodiode as a function of the incident optical intensity at 1.8 K and 4.3 K. The observed spectra showed a peak at low frequencies superimposed on a continuum which has a cut-off at high frequency. The interpretation of the results implies that the electron-hole drops coming from a same region of the photoexcited liquid are ejected periodically.     

Ground state energy of small electron-hole drops

The ground state energy of small electron-hole drops is calculated for droplets ranging in size from 10 to 10,000 pairs. A new value for the bending energy of $\text{1.1×10}{}^{\mathrm{?10}}\text{erg}\text{cm}$ is derived. We also give a simple highly accurate formula for the total energy per pair. The surface energy is extracted from the total energy and found to agree well with a previous self-consistent calculation. The density at the center of the drop remains essentially constant over the entire range of N, indicating that the drop is not dramatically compressed by the surface tension.     

Luminescence of impurity-bound excitons in corundum

The luminescence characteristics of M ³⁺: Al₂O₃ crystals, where M ³⁺ stands for an isoelectronic cation impurity with a filled electron shell, namely, Sc³⁺, Y³⁺, or La³⁺, were studied. The luminescence of excitons bound (BE) to these impurities was detected. The position of the BE energy states at the long-wavelength absorption edge as a function of the M ³⁺ ionic radius was established. The energies of the long-wavelength BE creation threshold and of the maximum of the BE luminescence band were approximated empirically by third-order polynomials of the Toyozawa polynomial type, which describes electron-phonon interaction. The energy and spatial structure of the BE was found to be similar to that of a self-trapped exciton (STE). The BE and STE states are separated by an energy barrier, and energy transfer from the STE to BE is frozen at low temperatures.     

Luminescence of excitons in single-crystal garnets

Comparative studies of the luminescence of Y₃Al₅O₁₂:Ce and Lu₃Al₅O₁₂:Ce single-crystal films and their volume analogues—Y₃Al₅O₁₂ and Y₃Al₅O₁₂:Ce single crystals, excited by synchrotron radiation with energy E=120–150 eV, have been performed. The films were grown from melt-solution by liquid-phase epitaxy and the crystals were grown from melt. The single-crystal films and single crystals studied are characterized by different degrees of structural order, in particular, different concentrations of substitutional defects of the Y _Al ³⁺ and LU _Al ³⁺ types. It was ascertained that the bands at 260 and 250 nm in the intrinsic luminescence spectra of Y₃Al₅O₁₂:Ce and Lu₃Al₅O₁₂:Ce single-crystal films and single crystals are due to the emission of self-trapped excitons. The luminescence band with λ_max=300 nm and τ=0.36 μs, which is present in the luminescence spectrum of single crystals and absent in the spectra of single-crystal films, is due to the recombination of electrons with holes localized at Y _Al ³⁺ centers. It is shown that an efficient energy transfer by excitons to activator ions occurs in Y₃Al₅O₁₂ and Lu₃Al₅O₂ single-crystal films doped with Ce³⁺ ions.     

Motion of electron-hole drops in low magnetic fields

The effect of magnetic fields on the motion of electron-hole drops in germanium is studied. A non-uniform strain is used to provide a known and controllable driving force for drop motion in the sample plane. Contrary to the results of earlier experiments in which drop motion was normal to the sample plane, the results are consistent with conventional models of drop-phenomenon interaction and weak magnetic fields have no observable effects on this motion.     

Explosive instabilities in electron-hole drops under microwave radiation

We consider the Kroemer experiments on explosive instabilities in EHD in Ge in the light of an extension of the Altukhov theory to encompass general values of ωτ and of the ratio of drop radius to rf penetration depth. We suggest that the drops were heated above their critical temperature, but by a monotonic path.     

Net negative charge of electron-hole drops in germanium

The giant fluctuating photocurrent has been observed in highly excited germanium samples with ohmic contacts at 1.6 K. From the observation of this fluctuating photocurrent spike with varying static electric field, it is found that the electron-hole drop is negatively charge as a whole.     

Luminescence from compressed electron-hole plasma in germanium

We have studied the luminescence spectra from compressed electron-hole plasma in pure germanium. The spectra show a satisfactory thermalization of the charge carriers and lead to a reasonable value of the compressibility. These features encourage to further experimental efforts in the studies of the Mott transition in highly excited semiconductors.     

Luminescence of direct-and indirect-gap electron-hole plasma in TlBr

Luminescence of TlBr crystals highly excited by a nanosecond pulsed-dye laser (3.4 eV) at the bath temperature ∼ 8.5 K was studied. Two emission lines labeled A (∼ 2.98 eV) and B (∼ 2.62 eV) were found, which show typical behavior of the electron-hole plasma recombination radiation. The A-line is assigned to the recombination of e-h pairs in the direct gap (X⁺₆−X^-₃) and the B-line to the simultaneous recombination in the indirect gap (X⁺₆−R^-₆). Condensation of carriers into an electron-hole liquid was not observed.