Electron-hole Liquid Research Articles

Electron-hole liquid in the hexaborides

We investigate the energetics of the electron-hole liquid in stoichiometric divalent metal hexaborides. The ground state energy of an electron-hole plasma is calculated using RPA and Hubbard schemes and compared to the binding energy of a single exciton. Intervalley scattering processes play an important role in increasing this binding energy and stabilizing a dilute Bose gas of excitons.

Nature of the low-temperature anomalies in the physical properties of the intermediate-valent compound SmB6

The transport properties (Hall coefficient, thermopower, and resistivity) of high-quality single-crystal samples of the classical mixed-valent compound SmB6 are investigated over a broad temperature range (1.6–300 K) in magnetic fields up to 45 T for the first time following the quasioptical measurements in the 0.6–4.5 meV frequency range [B. Gorshunov, N. Sluchanko, A. Volkov et al., submitted to Phys. Rev. B (1998)]. Measurements in the intrinsic conduction region permit determination of the gap width Eg≈20 meV and evaluation of the behavior of the mobility and concentration of light and heavy charge carriers, as well as the temperature dependence of the carrier relaxation time, in samarium hexaboride. The results of experimental investigations in the “impurity” conduction region (Eex≈3.5 meV) are discussed within the Kikoin-Mishchenko exciton-polaron model of charge fluctuations. Arguments supporting the formation of a metallic state with an electron-hole liquid in SmB6 at liquid-helium temperatures are presented.

Luminescence due to electron-hole condensation in silicon-on-insulator

We show that photoluminescence from a thin silicon-on-insulator (SOI) layer with a thickness of about 0.1 μm excited by ultraviolet (UV) light originates from the recombination of electrons and holes in their condensed phase. The UV excitation increases the density of electrons and holes in the SOI layer, since the UV light is predominantly absorbed in that layer and the excited carriers cannot diffuse into the base wafer because of the presence of a buried oxide layer which acts as a diffusion barrier. As a result, a characteristic “condensate luminescence” is emitted from the SOI layer. The spectral shape of the condensate luminescence agrees with the calculated shape using convolution of the occupied electron and hole densities of states. A systematic spectral change induced by the variation of excitation intensity and the sample temperature is consistently explained by the phase diagram of the electron-hole system in Si which consists of free exciton (FE), electron-hole plasma (EHP), and electron-hole liquid (EHL). The phase transition from FE to EHP or that from FE to EHL is observed with increasing excitation intensity, according to whether the temperature is higher or lower than the critical temperature of EHL. These results confirm for us that the condensate luminescence in the SOI layer is due to the recombination of electrons and holes in their condensed phase.

Photoluminescence Due to Degenerate Electron-Hole System in Silicon-on-Insulator Wafers under Ultraviolet Light Excitation

Photoluminescence (PL) spectroscopy has been used for characterization of silicon-on-insulator (SOI) wafers with SOI thickness of 75 nm fabricated by separation by implanted oxygen (SIMOX) technique. While PL signals from the substrate were dominant under conventional visible light excitation, a characteristic broad line was observed under ultraviolet (UV) light excitation throughout our temperature range between 4.2 to 70 K. The spectral distribution of the characteristic line agreed with calculated shape using convolution of the occupied electron and hole densities of states. This agreement can be regarded as strong evidence for formation of degenerate electron-hole systems, electron-hole liquid and electron-hole plasma, in the SOI layer. The detection of luminescence due to these systems allows us to suggest that relief of crystalline damage in the SOI layer induced by oxygen implantation and improvement of quality of interfaces between the SOI layer and oxide layers are efficiently achieved in the present low dose SIMOX process with an internal thermal oxidation.

Luminescence optical spectra of stressed Ge in a strong magnetic field: electron-hole liquid or biexcitons?

We discuss the nature of the unknown line recently observed by Timofeev and Chernenko in the luminescence spectra of stressed Ge in a strong magnetic field [JETP Lett. 61 (1995) 617] as a biexcitonic line. The optical spectra of a semiconductor are considered for different magnetic field strengths on the basis of the solution describing the interaction of hydrogen-like excitons. The possibility of electron-hole liquid formation is also considered.

Excitons in Semiconductor–Dielectric Nanostructures

Confinement in nanostructures with (some of the) linear dimensions small compared to the exciton radius provides a possibility of enhancement of both the binding energy and the oscillator strength of excitons. Moreover in such structures the possibility arise of controlling the strength of Coulomb interaction, responsible for binding of electron and hole to the exciton, by combining materials for the structure with essentially different values of dielectric constants. Transformations of Wannier-Mott excitons which are dependent on both of these factors — confinement geometry and dielectric constants ratio —, their optical manifestations and similar trends in many body phenomena, including electron–hole liquid formation, will be discussed.

Stabilization of electron-hole liquid in uniaxially strained germanium in a strong magnetic field

Luminescence spectra of uniaxially and uniformly strained high-purity germanium crystals at liquid-helium temperatures in a magnetic field of up to 14 T have been investigated. In strongly strained Ge crystals, a new line has been detected on the low-energy side of the excitonline in magnetic fields higher than 4 T. Studies of this line’s characteristics as functions of pressure, temperature, and magnetic field have led us to conclude that its presence is due to recombination of electron-hole pairs in an electron-hole liquid. The experimental data suggest that the metallic electron-hole liquid is stabilized in a strong magnetic field. By approximating the shape of the newly detected line using the model of metallic electron-hole liquid, we have obtained the electron-hole liquid density n EHL(B) and Fermi energies E Fe,h of electrons and holes. The liquid binding energy o as a function of magnetic field has been estimated.

Magnetically stabilized electron-hole liquid in indium antimonide

Luminescence spectra of sufficiently pure n-type indium antimonide crystals (ND−NA=(1–22)·1014 cm−3) in a magnetic field of up to 56 kOe, at temperatures of 1.8–2 K, and high optical pumping densities (more than 100 W/cm2) have been studied. More evidence of the existence of electron-hole liquid stabilized by magnetic field has been obtained, and its basic thermodynamic parameters as functions of magnetic field have been measured. When the magnetic field increases from 23 to 55.2 kOe, the liquid density increases from 3.2·1015 to 6.7·1015 cm−3, the binding energy per electron-hole pair rises from 3.0 to 5.2 meV, and the binding energy with respect to the ground exciton level (work function of an exciton in the liquid) rises from 0.43 to 1.2 meV.

High Density Excitation Effect of the Indirect Band Luminescence in Thallous Halides*

A broad band luminescence is observed at the indirect gap region in highly purified TlBr and TlCl crystals under high density excitation. From the analysis of the line shape, power dependence, lifetime and some characteristic features of the luminescence, it is discussed the possibility that the luminescence is associated with an LA-phonon assisted indirect recombination (X 6 + -R 6 - ) of electron-hole liquid (EHL). Equilibrium density, binding energy and other parameters of EHL are estimated and it is presumed that the hole-phonon scattering is dominant in their recombination process.

Density and binding energy of magnetically stabilized electron-hole liquid in indium antimonide

Main thermodynamic parameters of magnetic-field-stabilized electron-hole liquid (EHL) in indium antimonide are determined as a function of magnetic field strength from the shape and spectral position of its luminescence line. It is found, that in the stability region of the liquid phase (H> 20 kOe) the EHL experiences self-compressing with the rise of magnetic field, and the binding energy per pair of particles, measured from the ground exciton level (work function) increases significantly. In the field range from 23 to 55.2 kOe the liquid density grows linearly from 3.5·10 15 to 7.3·10 15 cm −3, and the work function increases from 0.36 to 1.2 meV with the increase of magnetic field strength.

Time-resolved study of electron-hole plasmas near the liquid-gas critical point in Si: Evidence for a second condensed phase.

At low temperatures and sufficient densities, free excitons in Si and Ge undergo simultaneous gas-liquid and insulator-metal transitions into droplets of electron-hole liquid. Some previous theoretical and experimental studies have suggested that, under certain values of density and temperature, there may be separate metal-insulator and liquid-gas transitions. In the present paper, we examine the difficult transcritical region for electron-hole liquid formation in unstressed Si using time- and space-resolved photoluminescence spectroscopy. Using the latest models for the luminescence of electron-hole plasma and small excitonic complexes (EC's), we have succeeded in characterizing the complicated luminescence spectra both above and below the liquid-gas critical temperature [${\mathit{T}}_{\mathit{c}}$(LG)\ensuremath{\approxeq}24.5 K] with a relatively small number of free parameters. Near the liquid-gas critical point the luminescence spectra are analyzed as contributions from four lines: the high-density electron-hole liquid (EHL), a lower-density electron-hole plasma (EHP), free excitons (FE's), and excitonic complexes. After a sufficient thermalization time, the temperature of all phases settles to a value indistinguishable from the lattice temperature. The line shapes of FE's and EC's are calculated using previously established parameters. Using the latest band-renormalization theory, the pair density of the plasma phases (EHL and EHP) determines both the position and the shape of the spectrum.Therefore the analysis of these complex spectra is reduced to five free parameters: A single parameter describing the intensity of the FE line (the intensity of the EC line shape is linked to that of the FE using an experimentally determined scaling relation), the intensities of the two plasma components EHL and EHP, and the pair densities of these two plasmas. These parameters are sufficient to characterize the spectra over a wide range of particle density and temperature. The EHP density obtained in this way is remarkably independent of temperature and particle density, providing evidence for a second condensed phase of electron-hole plasma. The condensed liquid has a density of about one-tenth that of the ground-state electron-hole liquid and is observed both above and below the EHL critical temperature. An excitonic phase diagram for silicon is described which includes two condensed plasmas. A triple point at 18.5 K is observed where the electron-hole liquid coexists with the lower-density condensed plasma (CP) and excitonic gas. Above this temperature the CP is observed at all temperatures up to a second critical point at 45\ifmmode\pm\else\textpm\fi{}5 K. We also consider the hypothesis that the extra luminescence attributed to the CP is instead due to large excitonic complexes. Using the recently determined binding energies of large excitonic complexes and the measured gas volume, we conclude that the density of these species is too small to account for the observed luminescence.

The electron-hole plasma and liquid in confined semiconductor systems

Time-resolved luminescence spectroscopy is used to investigate the properties of the electron-hole plasma and liquid in low-dimensional semiconductors. A density-dependent band gap renormalization is found in GaAs/AlGaAs quantum-well wires and compared to available theories. The formation of a fog of electron-hole droplets surrounded by a low-density exciton gas occurs in type-II (3 1 1) quantum-well wire superlattices. The condensation of the quantum-confined droplets as well as some properties of the plasma are influenced by the presence of disorder.

Equilibrium density of an electron-hole liquid in a strong magnetic field: A possibility of phase separation.

The ground state of a model electron-hole liquid (EHL) in a strong magnetic field is investigated. In the regime when only a few Landau subbands are occupied the complex behavior of the equilibrium density leads to a possibility of phase separation. At certain magnetic-field strengths the EHL ground-state energy plotted as a function of the density has two local minima corresponding to two phases with different numbers of Landau subbands occupied. As a result the equilibrium density of EHL will have strong discontinuities as a function of the magnetic field, occurring whenever the relative strength of those minima changes. In a nonequilibrium system, such as a real electron-hole droplet, both phases may be present simultaneously. We discuss several luminescence and infrared absorption experiments, and suggest that they indicate such a phase separation.

Observation of Excitonic n-Strings In A Quasi-one-Deviensional Charge-Transfer Crystal

ABSTRACTCollective excitations, such as plasmons, rotons, electron-hole liquid, and excitonic Molecules, have been extensively studied in condensed Matter.1 Wannier excitons in inorganic semiconductors are bound by the exchange interactions between two electrons of the exciton, and the bound state of More than two excitons is not possible. We demonstrate here a new type of collective excitations,2 bound states of Multiple charge-transfer (CT) excitons. Coulomb interactions in one dimension are shown to bind a train of several (More than two) CT excitons. Experimental evidence for these new type of elementary excitations is reported in a quasi-one-dimensional CT crystal of anthracene PMDA. High density excitation by femtosecond light pulses generates Multi-exciton chains, which we refer to as excitonic n-strings with n = 1, 2, 3, etc., along the stack axis of the crystal. Both the n = 2 excitonic string (biexciton) and the n = 3 string (tri-exciton) are observed. This report provides evidence for an n > 2 exciton chain in this system.2 The stability of the n-string exciton is supported by our theoretical calculations based on the extended Hubbard Hamiltonian in one dimension.

Isotope effect in Ge: a photoluminescence study

Edge photoluminescence data (0.69–0.75 eV) at low temperatures (T = 1.8 and 4.2 K were obtained in three isotope enriched Ge crystals ( M=70.1 , 73.95 and 75.62) and a natural one ( M=72.59 ). We observed the energy shifts of the bound exciton, phonon assisted electron-hole liquid and free exciton recombination luminescences as a function of the mean isotope mass. The results are in good agreement with both theoretical estimates using a rigid-ion pseudopotential and some existing experimental information.

Pairing ground states in fermion systems: A static method.

We present a static recursive method that can straightforwardly be applied to variational treatments of canonical many-body systems whose ground states generally exhibit pairing or higher clustering correlations. We illustrate the utility of the method by applying it to an electron system with pairing interactions where we obtain, as expected, a smooth transition between a Bose condensate of tightly bound electron pairs and a superconducting ground state. The method also reproduces the mean-field results for the electron-hole liquid problem as well as the antiferromagnetic insulator ground state of the Hubbard model but in a simpler way. We give a nontrivial application to a model of dense molecular hydrogen consisting of condensed generalized molecules. We show that the effective interaction between identical particles is of such a form that the state undergoes a dielectric catastrophe at a certain finite density. The competition between this abrupt transition and a smooth transition of atomic pairs in the spinless and translationally invariant version of the problem is also discussed.

Electron-hole liquid in germanium under high stress.

The properties of the electron-hole liquid (EHL) in Ge are examined as a function of uniaxial 〈111〉 stress with use of spectral and temporal measurements of the electron-hole--recombination luminescence. We are the first to observe the EHL phase in the high-stress limit (\ensuremath{\sigma}\ensuremath{\gtrsim}70 kgf/${\mathrm{mm}}^{2}$, where 1 kgf/${\mathrm{mm}}^{2}$==10 MPa) at T=2 K, based on fits to calculated spectral line shapes. The dependence of the measured EHL densities on uniaxial 〈111〉 stress agrees well with that predicted by sophisticated many-body calculations. Measurements of the EHL lifetime are also reported for uniaxial 〈111〉 stresses from 5.6 to 23.9 kgf/${\mathrm{mm}}^{2}$. The density dependence of the EHL lifetime indicates a constant value for the electron-hole enhancement factor, ${g}_{\mathrm{eh}}$(0), for electron-hole--pair densities>3.5\ifmmode\times\else\texttimes\fi{}${10}^{16}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. This result disagrees with theoretical predictions, but is consistent with experimental results reported by others.

Electron-hole liquids and band-gap renormalization in short-period semiconductor superlattices.

In short-period superlattices, excited electrons and holes are subject to a one-dimensional perturbation with spatial dimension comparable to the bulk excitonic radius and strength comparable to the bulk excitonic binding energy. We study the stability of the electron-hole liquid and band-gap renormalization as a function of the perturbing potentials (band offsets) using the density-functional approach. We find that there is no universal band-gap renormalization in superlattices, that type-II staggered superlattices are the best candidates for observing the electron-hole liquid, and that a luminescence line in these systems should show a blue shift at intermediate electron-hole densities due to a positive differential band-gap renormalization.

Electron-hole liquid and two-dimensional electron gas in layered group A3B6semiconductors

Electron-hole liquid and two-dimensional electron gas in layered group A³B⁶semiconductors

Steady-state and transient nucleation of a new phase in a first-order transition

Examples of crystallization of glasses and of the condensation of excitons to form an electron-hole liquid in germanium are used to study the kinetics of nucleation of a new phase. There are considerable advantages in tackling such model systems rather than other systems undergoing a first-order phase transition. Attention is drawn to two different nucleation regimes: transient and quasisteady-state. Special consideration is given to nucleation in an open system from which nuclei of the new phase may be removed rapidly as a result of diffusion or drift to absorbing walls. In such cases very strong supersaturation may be reached and the threshold of the appearance of a new phase may be independent of temperature.