Two-dimensional Electron-hole Plasma Research Articles

Two-Dimensional Electron-Hole Plasma in Colloidal Quantum Shells Enables Integrated Lasing Continuously Tunable in the Red Spectrum.

Combining integrated optical platforms with solution-processable materials offers a clear path toward miniaturized and robust light sources, including lasers. A limiting aspect for red-emitting materials remains the drop in efficiency at high excitation density due to non-radiative quenching pathways, such as Auger recombination. Next to this, lasers based on such materials remain ill characterized, leaving questions about their ultimate performance. Here, we show that colloidal quantum shells (QSs) offer a viable solution for a processable material platform to circumvent these issues. We first show that optical gain in QSs is mediated by a 2D plasma state of unbound electron-hole pairs, opposed to bound excitons, which gives rise to broad-band and sizable gain across the full red spectrum with record gain lifetimes and a low threshold. Moreover, at high excitation density, the emission efficiency of the plasma state does not quench, a feat we can attribute to an increased radiative recombination rate. Finally, QSs are integrated on a silicon nitride platform, enabling high spectral contrast, surface emitting, and TE-polarized lasers with ultranarrow beam divergence across the entire red spectrum from a small surface area. Our results indicate QS materials are an excellent materials platform to realize highly performant and compact on-chip light sources.

Heat capacity of nonequilibrium electron-hole plasma in graphene layers and graphene bilayers

We analyze the statistical characteristics of the quasi-nonequilibrium two-dimensional electron-hole plasma in graphene layers (GLs) and graphene bilayers (GBLs) and evaluate their heat capacity.The GL heat capacity of the weakly pumped intrinsic or weakly doped GLs normalized by the Boltzmann constant is equal to $c_{GL} \simeq 6.58$. With varying carrier temperature the intrinsic GBL carrier heat capacity $c_{GBL}$ changes from $c_{GBL} \simeq 2.37$ at $T \lesssim 300$~K to $c_{GBL} \simeq 6.58$ at elevated temperatures. These values are markedly differentfrom the heat capacity of classical two-dimensional carriers with $c = 1$. The obtained results can be useful for the optimization of different GL- and GBL-based high-speed devices.

Theoretical analysis of injection driven thermal light emitters based on graphene encapsulated by hexagonal boron nitride

We develop the device model for the proposed injection (electrically) driven thermal light emitters (IDLEs) based on the vertical hexagonal boron nitride layer/graphene layer/ hexagonal boron nitride layer (hBNL/GL/hBNL) heterostructures and analyze their dynamic response. The operation of the IDLEs is associated with the light emission of the hot two-dimensional electron-hole plasma (2DEHP) generated in the GL by both the lateral injection from the side contacts and the vertical injection through the hBNL (combined injection) heating the 2DEHP. The temporal variation of the injection current results in the variation of the carrier effective temperature and their density in the GL leading to the modulation of the output light. We determine the mechanisms limiting the IDLE efficiency and the maximum light modulation frequency. A large difference between the carrier and lattice temperatures of the IDLEs with an effective heat removal enables a fairly large modulation depth at the modulation frequencies about dozen of GHz in contrast to the standard incandescent lamps. We compare the IDLEs with the combined injection under consideration and IDLEs using the carrier Joule heating by lateral current. The obtained results can be used for the IDLE optimization.

Multiple graphene-layer-based heterostructures with van der Waals barrier layers for terahertz superluminescent and laser diodes with lateral/vertical current injection

We analyze terahertz superluminescent and laser diodes using the injection pumping in the multiple graphene-layer (GL)/van der Waals barrier layers (BLs) heterostructures. The operation of such terahertz radiation sources is associated with the interband transitions in the gapless GLs under the population inversion leading to the GL negative dynamic conductivity. These devices use the lateral injection of holes and vertical injection of electrons. Such an injection might have advantages over the lateral injection of the bipolar carriers. Due to relatively large conduction band offsets at the GL-BL interface, the population inversion at the vertical injection can be markedly hampered by the injection current heating of the two-dimensional electron-hole plasma in the GLs. We show that doping GLs and/or BLs can substantially diminish the carrier heating promoting the interband population. Numerical analysis assumed the BL material parameters of MoS2 and WSe2 and showed the feasibility of such terahertz radiation sources.

Negative Terahertz Conductivity at Vertical Carrier Injection in a Black-Arsenic-Phosphorus–Graphene Heterostructure Integrated With a Light-Emitting Diode

We propose and analyze the heterostructure comprising a black-arsenic-phosphorus layer (b-As $_{1-x}$ P $_{x}$ L) and a graphene layer (GL) integrated with a light-emitting diode (LED). The integrated b-As $_{1-x}$ P $_{x}$ L-GL-LED heterostructure can serve as an active part of the terahertz (THz) laser using the interband radiative transitions in the GL. The feasibility of the proposed concept is enabled by the combination of relatively narrow energy gap in the b-As $_{1-x}$ P $_{x}$ L and the proper band alignment with the GL. The operation of the device in question is associated with the generation of the electron-hole pairs by the LED emitted near-infrared radiation in the b-As $_{1-x}$ P $_{x}$ L, cooling of the photogenerated electrons and holes in this layer, and their injection into the GL. Since the minimum b-As $_{1-x}$ PL energy gap is smaller than the energy of optical phonons in the GL, the injection into the GL can lead to a relatively weak heating of the two-dimensional electron-hole plasma (2D-EHP) in the GL. At the temperatures somewhat lower than the room temperature, the injection can cool the 2D-EHP. This is beneficial for the interband population inversion in the GL, reinforcement of its negative dynamic conductivity, and the realization of the optical and plasmonic modes lasing supporting the new types of the THz radiation sources.

Negative terahertz conductivity and amplification of surface plasmons in graphene–black phosphorus injection laser heterostructures

We propose and evaluate the heterostructure based on the graphene-layer (GL) with the lateral electron injection from the side contacts and the hole vertical injection via the black phosphorus layer (PL) (p$^+$PL-PL-GL heterostructure). Due to a relatively small energy of the holes injected from the PL into the GL (about 100 meV, smaller than the energy of optical phonons in the GL which is about 200 meV), the hole injection can effectively cool down the two-dimensional electron-hole plasma in the GL. This simplifies the realization of the interband population inversion and the achievement of the negative dynamic conductivity in the terahertz (THz) frequency range enabling the amplification of the surface plasmon modes. The later can lead to the plasmon lasing. The conversion of the plasmons into the output radiation can be used for a new types of the THz sources.

Exciton/Free-Carrier Plasma in GaN-Based Quantum Wells: Scattering and Screening

The degree of ionisation of a two-dimensional electron-hole plasma is calculated in the low-density (Boltzmann) limit. The electron-hole interaction is considered for all states: optically active and inactive, bound and unbound. The theory is applied to exciton/free-carrier plasma in GaN-based quantum wells at room temperature.

Ionization degree of the electron-hole plasma in semiconductor quantum wells

The degree of ionization of a nondegenerate two-dimensional electron-hole plasma is calculated using the modified law of mass action, which takes into account all bound and unbound states in a screened Coulomb potential. Application of the variable phase method to this potential allows us to treat scattering and bound states on the same footing. Inclusion of the scattering states leads to a strong deviation from the standard law of mass action. A qualitative difference between mid- and wide-gap semiconductors is demonstrated. For wide-gap semiconductors at room temperature, when the bare exciton binding energy is of the order of T, the equilibrium consists of an almost equal mixture of correlated electron-hole pairs and uncorrelated free carriers.

Pattern formation under bistable electro-optical absorption in quantum wells: I

We have formulated and analysed a model of transverse self-sustained pattern formation in a photoexcited and voltage-biased quantum well (QW) structure. Our model explains the formation of patterns of quasi-neutral two-dimensional electron-hole plasma whose intrinsic bistability was shown in recent experiments. A number of patterns containing regions with different spreading of the electron and hole wave functions and different densities of the two-dimensional electron-hole plasma have been found by using a nonlinear interband light-absorption model. When the transverse extent of the QW layer is large in comparison with the pattern characteristic transverse length scale (of the order of the two-dimensional plasma ambipolar diffusion length), most patterns consist of wide plateaus with high (low) plasma density and relatively narrow domains with low (high) density.

Pattern formation under bistable electro-optical absorption in quantum wells: II

In the first part of this work (Bonilla L L, Kochelap V A and Velasco C A 1999 J. Phys.: Condens. Matter 11 6395) we formulated and analysed a model of transverse self-sustained pattern formation in a photoexcited and voltage-biased quantum well (QW) structure. Our model explained the formation of patterns of quasi-neutral two-dimensional electron-hole plasma whose intrinsic bistability was shown in recent experiments. We found patterns containing regions with different spreading of the electron and hole wave functions and different densities of the two-dimensional electron-hole plasma. In this second part we extend our results to QWs with finite transverse dimension. We will show that the boundary conditions at the edges of the QW layer control the behaviour of the patterns. We will study the stability of the patterns and will show its strong dependence on the boundary conditions. A linear stability criterion for these patterns is presented and compared with numerical simulations.

Contact correlations of charged fermions in two dimensions and the electron-hole plasma lifetime in semiconductor quantum wells

We consider a multicomponent ensemble of charged fermions which are constrained to move on the plane. By just retaining particle-particle ladder diagrams in Goldstone's expression for the energy shift and approximating the kernel of the resultant integral equation, we obtain for this system an analytical Yasuhara-like formula for the contact pair correlations that includes screening effects. An undesirable pseudo-screening due to the kernel approximation is overcome by adding a corrective term into the integral equation. In particular, we use the case in which the system has only two species of opposite charge to model a quantum well as a two-dimensional electron-hole plasma. The electron-hole correlation at contact so calculated is taken as the enhancement factor in the photoluminescence from the quantum well and it is checked against available experimental data for the density dependence of the electron-hole plasma lifetime.

On the gain mechanism in GaN based laser diodes

We investigate the gain mechanism in a current GaN based laser diode design using the variable stripe length method and optical nanosecond excitation. The combination of absorption measurements, gain spectra and photoluminescence excitation data allows us to understand the fundamental mechanisms responsible for gain in these devices. We conclude that optical amplification is due to a conventional two-dimensional electron-hole plasma in contrast to the spontaneous emission mechanism in similar light emitting diode structures.

Exchange carrier-carrier scattering of spin-polarized two-dimensional electron-hole plasma: Monte Carlo study

Thermalization of near-bandgap excited electron-hole (e-h) plasma in an intrinsic GaAs quantum well is studied by Monte Carlo simulation. Carrier-carrier interaction is treated as two-particle e-e, e-h and h-h collisions due to screened Coulomb interaction. The indistinguishability of two colliding electrons (holes) is included by taking into account the exchange e-e (h-h) scattering between the electrons (holes) of like spin. The model is modified to the case of spin-polarized (SP) e-h plasma. We show that the thermalization of the SP plasma is several limes slower than the thermalization of the spin-randomized plasma, when the density of photoexcited e-h pairs is 3*1011cm-2. The effect is due to the exchange e-e (h-h) scattering, which significantly weakens the direct Coulomb scattering in the dense SP plasma. This yields a chance to observe the exchange experimentally.

Effects of nonparabolicity on collective intersubband excitations.

We have used inelastic light scattering to study the collective charge- and spin-density excitations associated with electronic intersubband transitions in GaSb-AlSb superlattices. The density of the photoexcited two-dimensional electron-hole plasma was controlled by varying the incident laser power. A comparison of experiment with detailed calculations of the response functions shows that the noparabolicity of the conduction band must be properly included in order to yield quantitative agreement. It is found that nonparabolicity, in addition to decreasing the resonance energies of the collective excitations, provides a mechanism for observing single-particle excitations at q=0.

Time-resolved Raman scattering in GaAs quantum wells.

We employ a picosecond--time-resolved Raman-scattering technique to investigate the dynamics of two-dimensional electron-hole plasma confined to a multiple--quantum-well structure composed of layers of GaAs and (GaAl)As. The lifetime and the intersubband scattering time of the electrons photoexcited on the lowest electronic subbands are determined separately. Calculation of the rate of intersubband scattering by longitudinal-acoustical phonons successfully accounts for the observation of relatively long-lived electrons on the second subband of a 215-A\r{} multiple--quantum-well structure.

Effect of a strong magnetic field on the relaxation of a hot 2-D electron-hole plasma studied with picosecond photoluminescence

We present time-energy resolved picosecond photoluminescence measurements on a two-dimensional electron-hole plasma in a strong magnetic field. The temporal evolution of the temperature T e,h , the density n e,h and the Landau level broadening parameter Δ dre determined. At B=20T the cooling rate of the e-h plasma is increased by a factor of 7 with respect to B=0T.

Light Scattering by Photoexcited Two-Dimensional Electron Plasma in GaAs-(AlGa) As Heterostructures

We report resonant inelastic light scattering by photoexcited electrons in GaAs-(AlGa)As multiple quantum-well heterostructures and find that a variable-density two-dimensional electron-hole plasma is created in a controlled manner. The energy levels and collective electron-electron and electron-phonon interactions were studied for carrier densities as high as \ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}${10}^{12}$ ${\mathrm{cm}}^{\ensuremath{-}2}$. Charge neutrality is preserved in each quantum well. Complex collective interactions occur among modes involving transitions between quantum-well states.