Electron-hole Liquid Research Articles

Coulomb resonance at the Fermi level of the electron-hole liquid in germanium

Using a modulation technique of transmitted probe light a recently predicted enhanced absorption in the electron-hole liquid is confirmed. This resonance is due to the Coulomb interaction acting resonantly at the Fermi edge. Comparison is made with calculations taking into account a screened potential, self-energy shifted bands, and warping of the valence band.

Theory of Electron–Hole Liquid in Doped Semiconductors. Application to GaP

AbstractFunctional equations for the self‐energy of an electron‐hole plasma in doped semiconductors are derived and specialized to RPA expressions. Numerical calculations are performed for doped GaP. From thermodynamical considerations a theoretical phase diagram is deduced indicating a critical point and immediately below a coexistence region of two plasma phases with finite densities. The RPA results are compared with simple analytical formulas.

Comment on "Variational Approach to the Ground State of the Electron-Hole Liquid"

A Comment on the Letter by T. Chakraborty and P. Pietilaaumlinen, Phys. Rev. Lett. 49, 1034 (1982).

Decay behaviour of high‐excitation luminescence in Gap:N II. Experimental results on the densities of the coexisting phases and the relevant recombination processes

AbstractThe radiative recombination of isoelectronic nitrogen‐doped GaP is investigated under high optical excitation at several temperatures (T = 2, 4.2, 27, and 77 K). A previously reported phase seperation is confirmed. The parameters of the electron—hole liquid and the coexisting low‐density phase are determined both from luminescence spectra and decay measurements. The dominating recombination processes for the carrier system are found to be phonon‐assisted band‐to‐band Auger recombination, phononless radiative recombination with participation of the nitrogen impurities, and phononless Auger recombination with participation of the nitrogen impurities. The respective rate coefficients are determined.

Decay behaviour of high‐excitation luminescence in GaP:N. I. Model for the decay of two coexisting phases

AbstractThe time behaviour of the radiative recombination of nitrogen‐doped GaP is investigated at pulsed intense optical excitations and low temperatures (T = 2 and 27 K). The decay behaviour of the luminescence intensities corresponding to the electron–hole liquid (EHL) and the coexisting lowdensity phase (LDP) is found for all nitrogen concentrations (nN = 2 × 1017 to 2.9 × 1018 cm−3) to be nonexponential. It is interpreted as a consequence of interactions between both coexisting phases. A model is introduced where the EHL is fed by the LDP continuously. It describes the observed decay of the luminescence very well, even for different nitrogen concentrations and different excitation intensities.

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.

Electron-hole liquid condensation: Systematics and scaling relations

Studies of electron-hole liquid (EHL) condensation in Si, in several strained Si systems, in strained Ge, and in GaP are reported, and they provide the most extensive results to date for the systematic variations with band structure of the ground state and critical properties of EHL. The ground state densities of these systems vary by a factor ∼103 and the critical temperatures by a factor ∼20. Investigations of Si with varying magnitudes of uniaxial strains provide the first systematic data for systems with significant band non-parabolicities. Based on these results proposals for scaling relations between the ground state properties and the critical points are tested, and a recently proposed set is verified in quantitative detail.

Thermodynamic properties of equilibrium and non-equilibrium plasmas in GaP

We report the first measurement of the phase diagram of electron-hole liquid (EHL) condensation for a polar compound semiconductor with indirect band structure. Above the critical point we observe an electron-hole plasma (EHP) with a density which increases with temperature. In contrast to previous results we find no evidence for a first-order Mott-transition of free excitons into this EHP.

Ground-state properties, thermodynamics and systematics of electron-hole liquid in Ge and Si under uniaxial stress

The authors present results for the ground-state and critical properties of electron-hole liquid in germanium and silicon under continuously varying stress in different symmetry directions. Comparison has been made with experimental data wherever available. The validity of scaling relations has also been examined.

Time resolved luminescence of CdS at high excitation

We report a study at low temperature of the time resolved luminescence of CdS, excited by two photon absorption. Concerning the so called EHP-LO and P bands, we confirm our results previously obtained on CdSe[1, 2]. (a) At high excitation a broad band (peak position at λ > 495 nm) occurs due to radiative recombination in an electron hole plasma, assisted by the emission of one LO phonon. (b) The simultaneous kinetics of the P line (λ ≅ 490.5 nm) and A-LO line (λ ≅ 492.5 nm) are conflicting with the interpretation of the P line as resulting of radiative exciton-exciton collisions. We interpret the P line as due to biexciton recombination. We have studied the luminescence in the ( I 2- I 1) region (486nm < λ < 490nm) at low excitation. We observe clearly the following, (a) A broad band (488 nm < λ < 490.5 nm) which corresponds to the gain observed in previous experiments of pulse and probe spectroscopy and interpreted as direct recombination in an electron hole liquid (EHL). (b) After the disappearance of the EHL band, one single line ( M D ), which shifts continuously towards the I 2 position during the time resolved kinetics. We suggest it to be connected with the high excitation effect on donor impurities (bound polyexcitons).

Electron-hole droplet transport up to near-sonic velocity in Si

In the past, several interesting effects have been observed in conducting systems where the carrier drift velocity is made to exceed the sound velocity. Nonlinear momentum damping and phonon amplification have been demonstrated in several materials (Cds,Ge,PbTe). However, high drift velocities with a high density of carriers produce immense current densities, which cause very rapid carrier and sample heating. This heating limits such transport studies to very short current pulses. In contrast, a dense, high-mobility system of photoexcited carriers in ultrapure Si allows more complete study of the near-sonic transport regime. The electron-hole liquid which condenses at low temperatures is a highly degenerate conductor. The liquid takes the form of electron-hole droplets (EHD's) of micrometer size and fixed density. The total amount of conducting volume is thus controlled by excitation level. The low carrier density (relative to a metal) and small volume of the liquid, together with the high droplet mobility, tremendously reduce the rate of sample heating by carrier-phonon scattering, compared to a normal metal. In our experiments, with $T\ensuremath{\le}2.1$ K, the electrically neutral EHD's are accelerated by a strain-induced gradient in the semiconductor energy gap ${E}_{g}(x)$. The energy shift of the recombination luminescence peak gives the motive force per pair, ${F}_{\ensuremath{\sigma}}=\ensuremath{-}\frac{d{E}_{g}}{\mathrm{dx}}$. In this paper we report basic measurements of the EHD mobility in Si. The measured drift velocity ${v}_{d}$ is found to be proportional to ${F}_{\ensuremath{\sigma}}$ as long as ${v}_{d}$ is much less than the sound velocity $S$. We further find that the momentum damping rate, ${\ensuremath{\tau}}^{\ensuremath{-}1}=\frac{{F}_{\ensuremath{\sigma}}}{m{v}_{d}}$, increases as $S$ is approached. For ${v}_{d}&lt;0.9S$ the observed damping is consistent with a theory describing the absorption and re-emission of thermal phonons (D'yakanov and Subashiev, 1978). At low velocity the observed droplet mobility exhibits the rapid $T$ dependence predicted by the Bloch conductivity theory for a degenerate Fermi liquid. The data show a saturation in ${v}_{d}$ at $0.9S$ that indicates a sharp increase in damping. The thermal-phonon scattering theory does not predict such a velocity limit. However, a "sound barrier," due to the Cherenkov-type emission of phonons when ${v}_{d}\ensuremath{\ge}S$, has been predicted. We propose that the observed velocity saturation is due to this effect.

Density Dependence of an Electron-Hole-Liquid Correlation Factor in Ge: Experiment

The first absolute measurement of the density dependence of the enhancement factor g/sub eh/(0) for the electron-hole liquid in Ge is reported. This factor g/sub eh/(0) is a measure of the electron-hole spatial correlation function, and provides a valuable and sensitive test for the predictions of various many-body approximations. A strain-confined system of electron-hole--liquid and free-excitons is used. The data reported here agree quantitatively with the results of two different many-body--theory approximations.

Variational Approach to the Ground State of the Electron-Hole Liquid

In the many-body variational approach, accurate results are obtained for the ground-state properties of the isotropic electron-hole liquid. With the increase in hole mass, the system undergoes a transition to a state with ordered heavy particles. In the case of Ge under a large [111] strain, it is predicted that the metallic state is not stable relative to free excitons. The density dependence of e-h correlation obtained here compares favorably with the experimental estimates.

Phonon spectroscopy of the electron-hole liquid in germanium

The absorption of phonons by the electron-hole liquid (EHL) in semiconductors has proven to be the principal process causing macroscopic transport of droplets of this Fermi fluid. A characterization of the absorption for frequencies of several hundred gigahertz promises to elucidate this phonon wind transport mechanism as well as test the basic theory of deformation potential scattering within a degenerate Fermi liquid. Central predictions of this theory are an absorption rate which increases linearly with frequency at low frequencies and a transparency for wave vectors greater than $2{k}_{F}$, where ${k}_{F}$ is the Fermi wave vector of the liquid. We have adapted the standard deformation potential theory to the case in which the energies are comparable to the Fermi energy and have calculated the frequency and angle dependences of the absorption by electron-hole liquid in Ge. The sharpness and position of the $2{k}_{F}$ cutoffs depend upon propagation direction and polarization. Using the method of tunnel-junction spectroscopy, we have measured the absorption of monochromatic phonons by electron-hole liquid over the frequency range 150-500 GHz. We concentrated on longitudinal phonons with $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ensuremath{\parallel}〈111〉$, the long axis of an electron energy ellipsoid. By applying an appropriate uniaxial stress to the crystal we were able to vary the population of this valley, thereby continuously tuning the predicted $2{k}_{F}$ cutoff over a factor of about 4. The resulting absorption spectra agreed with theoretical predictions, displaying for the first time the $2{k}_{F}$ cutoff for this Fermi liquid. To determine the absolute absorption length in EHL, we used a luminescence-imaging method to calibrate the volume of liquid in the path. Our measured deformation potential is smaller than that obtained for free electrons in Ge via cyclotron resonance. We interpret this reduction in electron-phonon interaction strength as due to screening within the electron-hole liquid. This interpretation is consistent with a recent theoretical calculation.

Strain-confined electron-hole liquid in Ge: Density variations and compressibility

We present a detailed theoretical and experimental investigation of a spatial variation in the electron-hole--pair density in the strain-confined electron-hole liquid in Ge. The density variation can be dramatic: We observed a compression of the central density by a factor of 3 for our largest drop radius, Rroughly-equal0.7 mm. Our experimental density profiles, obtained using Abel transforms of spatial luminescence profiles, are in good agreement with the theoretical predictions of approximately parabolic profiles with densities larger than the equilibrium value at the center of the drop. Our previous first-order theory has been extended to include the full density dependence of the pair free energy at finite stress and temperature. We discuss the shape and power dependence of spatial luminescence profiles and luminescence spectra, since the spatial density variation increases with drop size. We use the central densities for drop sizes ranging over an order of magnitude to measure the density dependence of the electron-hole--liquid chemical potential, providing a sensitive test of many-body theories for the correlation energy. We obtain an improved value for the isothermal compressibility of the strain-confined liquid: K/sub T/ = 0.067 +- 0.017 cm/sup 2//dyn for n = 0.47 x 10/sup 17/ cm/sup -3/, T = 1.9more » K, and -sigma = 5.5 kgf/mm/sup 2/, where kgf represents kilogram force.« less

Calculation of properties of the electron-hole liquid in uniaxially stressed Ge and Si

We present a detailed theoretical study of the stress dependence of properties of the electron-hole liquid, both at zero and finite temperatures, in $〈111〉$-stressed Ge and $〈100〉$-stressed Si. These properties include the ground-state equilibrium density, pair energy, electron and hole Fermi energies, sign of the electron-hole drop charge, luminescence linewidth, and liquid compressibility. The results are compared at $T=0$ to the calculations of Kirczenow and Singwi and at $T\ensuremath{\approx}$2 K to the available data. We discuss the possibility of a phase transition associated with the depopulation of the upper electron valleys in Ge. We also discuss methods of extrapolating from finite to infinite stress. The importance of the nonparabolicity of the valence bands is emphasized throughout. We discuss ranges of validity for a low-temperature expansion of the free energy. Results are presented for the systematic low-temperature variation of the liquid density, Fermi energy, and chemical potential and for the critical temperature and density. These theoretical results are found to be in reasonably good agreement with available data. Finally, we discuss scaling relations for combinations of electron-hole\char22{}liquid properties.

Universal behavior of exchange-correlation energy in electron-hole liquid

Exchange-correlation energy of electron-hole liquid (EHL) is shown to be independent of different band characteristics of semiconductors. A simple expression of ${\ensuremath{\epsilon}}_{\mathrm{xc}}$ for EHL in all semiconductors is given. In units of excitonic rydberg, ${\ensuremath{\epsilon}}_{\mathrm{xc}}=\frac{(a+{\mathrm{br}}_{s})}{(c+{\mathrm{dr}}_{s}+{r}_{s}^{2})}$, where $a=\ensuremath{-}4.8316$, $b=\ensuremath{-}5.0879$, $c=0.0152$, and $d=3.0426$. Ground-state and thermodynamic properties calculated with this expression are in good agreement with earlier theoretical calculations and experimental results.

Experimental determination of equilibrium constants for excitonic systems in stressed, ultrapure silicon

A basic question regarding excitonic states in semiconductors is whether the relative numbers of these particles, in spite of their finite lifetime, can be described by equilibrium thermodynamics. To answer this question we have made absolute measurements of the equilibrium constants for several excitonic systems in silicon by studying the recombination luminescence. This was accomplished by using a strain-confinement technique to determine the particle densities and by measuring the lifetimes. We find that the small mobile particles---free carriers, free excitons, and excitonic molecules---behave as an ideal gas of particles with classical equilibrium constants. The bound excitonic complexes, on the other hand, do not exhibit a classical equilibrium with free excitons in our experiments. In addition, we find that the phase transition from excitonic gas to electron-hole liquid displays a classical saturated gas density over a wide range of densities.

Theory of electron-hole liquids in two dimensions

A new theory for a two-dimensional electron-hole liquid allows the authors to give a precise evaluation of the correlation energy. An examination of the stability of electron-hole liquids based on the theory is given.

Role of Surface Structure in the Phase Separation of the Binary Electron-Hole Liquid

Microscopic calculations are presented of the surface and interface structure of the binary electron-hole liquid in $〈111〉$ -stressed Ge at $T=0$. The separation of the electron-hole droplet into two coexisting phases is found to have a surface precursor. The phase separation is predicted to occur without any nucleation process or hysteresis effects even though the phase transition is first order. Perfect wetting between the two liquid phases is predicted. Experimental implications are discussed.