Free Electron Density Research Articles

Ultra-Short Pulses Laser Heating of Dielectrics: A Semi-Classical Analytical Model

Femtosecond laser pulses are currently regarded as an emerging and promising tool for processing wide bandgap dielectric materials across a variety of high-end applications, although the associated physical phenomena are not yet fully understood. To address these challenges, we propose an original, fully analytical model combined with Two Temperatures Model (TTM) formalism. The model is applied to describe the interaction of fs laser pulses with a typical dielectric target (e.g., Sapphire). It describes the heating of dielectrics, such as Sapphire, under irradiation by fs laser pulses in the range of (1012–1014) W/cm2. The proposed formalism was implemented to calculate the free electron density, while numerical simulations of temperature field evolution within the dielectrics were conducted using the TTM. Mathematical models have rarely been used to solve the TTM in the context of laser–dielectric interactions. Unlike the TTM applied to metals, which requires solving two heat equations, for dielectrics the free electron density must first be determined. We propose an analytical model to solve the TTM equations using this parameter. A new simulation model was developed, combining the equations for non-equilibrium electron density determination with the TTM equations. Our analyses revealed the non-linear nature of the physical phenomena involved and the inapplicability of the Beer–Lambert law for fs laser pulse interactions with dielectric targets at incident laser fluences ranging from 6 to 20 J/cm2.

Engineered interface charges and traps in GaN metal-oxide-semiconductor field-effect transistors providing high channel mobility and E-mode operation

Abstract This review focuses on controlling interface charges and traps to obtain minimal channel resistance and stable enhancement-mode operation in GaN metal-oxide-semiconductor field-effect transistors. Interface traps reduce the free electron density and act as Coulomb scattering centers, thus reducing the channel mobility. Oxide traps cause instability of threshold voltage (V th) by trapping electrons or holes under gate bias. In addition, the V th is affected by the overall distribution of interface charges. The first key is a design of a bilayer structure to simultaneously obtain good insulating properties and interface properties. The other key is the optimization of post-deposition annealing to minimize oxide traps and interface fixed charges. Consequently, the gate structure of an AlSiO/AlN/p-type GaN has been designed. Reductions in V th as a result of polarization charges can be eliminated by using an m-plane trench channel, resulting in a channel mobility of 150 cm2V–1s–1 and V th of 1.3 V.

Free Electron Density Gradients Enhanced Biosensor for Ultrasensitive and Accurate Affinity Assessment of the Immunotherapy Drugs.

Accurate affinity assessments play an important role in drug discovery, screening, and efficacy evaluation. Label-free affinity biosensors are recognized as a dependable and standard technology for addressing this challenge. This study constructs a free electron density gradient-enhanced meta-surface plasmon resonance (FED-MSPR) biosensor through a finite-difference time-domain simulation model, the biosensor demonstrates superior detection performance in accurately determining affinity and kinetic rate constants. By controlling the dielectric properties of the metal on the surface of the nanocup arrays, the plasmon resonance effects are easily tuned without changing the nanostructure design. Compared with the single-layer gold chip, the triple-layer FED-MSPR chip demonstrated a four-fold improvement in resolution at the optimal resonance peak. Additionally, the sensitivity and figure of merit (FOM) of the multi-layer chip increased by 3.5 and 7.99 times, respectively. Following modification with high- and low-staggered carboxylation, the noise-signal ratio and baseline stability of the real-time kinetic curves based on these chips are significantly enhanced. The developed carboxylation FED-MSPR platform is successfully used to perform affinity assays for Adalimumab and TNF-α protein, resulting in favorable dynamic curves. These findings validate the proposed FED-MSPR biosensor platform as cost-effective, rapid, sensitive, and label-free, facilitating real-time quality control in drug development.

Luminescence properties of dislocations in α-Ga2O3

Abstract Dislocations in epitaxial lateral overgrown α-Ga2O3 are investigated using hyperspectral
cathodoluminescence spectroscopy. The dislocations are associated with a
reduction of self-trapped hole related luminescence (ca. 3.6 eV line) which can be
ascribed to their actions as non-radiative recombination sites for free electrons, to a
reduction in free electron density due to Fermi level pinning or to electron trapping
at donor states. An increase in the intensity of the ca. 2.8 eV and 3.2 eV lines is
observed at the dislocations, suggesting an increase in donor-acceptor pair transitions
and providing strong evidence that point defects segregate at dislocations.

Discovery of a Millisecond Pulsar Associated with Terzan 6

Observations show that globular clusters (GCs) might be among the best places to find millisecond pulsars (MSPs). However, the GC Terzan 6 seems to be an exception without any pulsar discovered, although its high stellar encounter rate suggests that it harbors dozens of them. We report the discovery of the first radio pulsar, PSR J1750–3116A, likely associated with Terzan 6 in a search of C-band (4–8 GHz) data from the Robert C. Byrd Green Bank Telescope with a spin period of 5.33 ms and dispersion measure (DM) ≃ 383 pc cm−3. The mean flux density of this pulsar is approximately 3 μJy. The DM agrees well with predictions from the Galactic free electron density model, assuming a distance of 6.7 kpc for Terzan 6. PSR J1750–3116A is likely an isolated MSP, potentially formed through dynamical interactions, considering the core-collapsed classification and the exceptionally high stellar encounter rate of Terzan 6. This is the highest radio frequency observation that has led to the discovery of a pulsar in a GC to date. While L-band (1–2 GHz) observations of this cluster are unlikely to yield significant returns due to propagation effects, we predict that further pulsar discoveries in Terzan 6 will be made by existing radio telescopes at higher frequencies.

Ultrahigh Transparent Safety Film for Spectrally Selective Photo/Electrothermal Conversion via Surface-Enhanced Plasma Resonance Dynamics.

Traditional deicing methods are increasingly insufficient for modern technologies like 5G infrastructure, photovoltaic systems, nearspace aerocraft, and terrestrial observatories. To address the challenge of combining anti-icing efficiency with operational performance, an innovative, spectrally selective, photo/electrothermic, ice-phobic film was prepared through a cost-effective mist deposition method. By manipulating the diameter ratio and density of nanowires, the local density of free electrons within this film is controlled to precisely dictate the position and intensity of surface plasmon resonance to achieve spectrally selective photo/electrothermal conversion. Additionally, the synthesized hydrophobic N-Boroxine-PDMS/SiO2 layer improves thermal stability and accelerates the deicing process. It achieves rapid deicing within 86 s under photothermal conditions and 65 s with Joule heating while maintaining high optical transmittance. The film improves the operational efficiency and thermal safety of equipment while preserving aesthetics and stability, thereby underscoring its broad suitability for advanced outdoor installations in cold environments.

New 511 keV Line Data Provide Strongest sub-GeV Dark Matter Constraints

We explore the 511 keV emission associated with sub-GeV dark matter (DM) particles that can produce electron–positron pairs and form positronium after thermalizing. We use ∼16 yr of data from the Spectrometer on INTEGRAL to constrain DM properties, including the full positron propagation and losses, and the suppression of free electron density away from the Galactic plane. We show that the predicted longitude and latitude profiles vary significantly for different DM masses, unlike previous assumptions, and obtain the strongest limits on sub-GeV DM (from the MeV to a few GeV) so far, excluding cross sections down to 〈σ v〉 ≲ 10−32 cm3 s−1 for m χ ∼ 1 MeV and 〈σ v〉 ≲ 10−26 cm3 s−1 for m χ ∼ 5 GeV and lifetimes up to τ ≳ 1029 s for m χ ∼ 1 MeV and τ ≳ 1027 s for m χ ∼ 5 GeV for the typical Navarro–Frenk–White DM profile. Our derived limits are robust within a factor of a few due to systematic uncertainties.

Schottky-Barrier-Free Plasmonic Photocatalysts for Solar-Driven Ammonia Synthesis

Ammonia is not only an indispensable feedstock to produce essential industrial chemicals like fertilizers, but it is also a potential hydrogen energy carrier owing to its high energy density and hydrogen capacity. Currently, most ammonia required for humans comes from the Haber–Bosch process, which contributes more than 90% of the annual global ammonia output. However, the harsh reaction conditions of this process result in serious energy and environmental issues. According to the relevant statistics, the ammonia industry consumes about 2% of the total energy and generates about 1.6% of the total CO2 emission annually in the world.It is therefore crucial to develop a green and sustainable strategy for ammonia synthesis. Among various alternative technologies of the Haber–Bosch process, artificial photosynthesis has attracted wide research interests and has been regarded as a promising, environmentally friendly, and energy-saving process. Photocatalytic ammonia synthesis can utilize renewable solar energy to drive the reaction and operate under mild conditions, which possesses the benefits of the simple reaction system, low cost, and safety. Although numerous photocatalysts have been explored over the past several decades, their activity and efficiency have still been low and far from the practical application requirements. It is therefore a huge challenge to design efficient photocatalysts for ammonia synthesis.Localized surface plasmon resonance (LSPR) has recently drawn enormous attention. LSPR can not only endow plasmonic nanomaterials with large absorption cross-sections and intense local field enhancement but also generate energetic hot electrons and hot holes. Owing to the appealing features of LSPR, plasmonic photocatalysis has shown great potential in ammonia synthesis. Plasmonic photocatalysts are usually composed of noble metals and wide bandgap semiconductors. However, the Schottky barrier will form at the metal–semiconductor interface in such hybrid structures due to the mismatch of the band structures between plasmonic metals and semiconductors. Hence, a large portion of the hot electrons cannot cross the Schottky barrier and get lost in the metal through the recombination with the holes. To overcome the drawbacks caused by the Schottky barrier, it is strongly desirable to develop a new type of plasmonic semiconductor photocatalysts, i.e., Schottky-barrier-free plasmonic photocatalyst.The Schottky-barrier-free plasmonic photocatalysts are usually degenerately doped semiconductors containing lattice oxygen vacancies. They possess high free electron densities and strong plasmon resonance because of the high-level doping, which results in abundant hot charge carriers upon plasmon excitation. Moreover, they also have appropriate surface sites that can adsorb reactant molecules and activate them. The photogenerated plasmonic hot charge carriers can get trapped at the defect sites and thereafter drive redox reactions. Compared with traditional metal–semiconductor hybrid plasmonic photocatalysts, Schottky-barrier-free plasmonic photocatalysts enable hot charge carriers to be transported nearly freely in the material, resulting in high charge utilization and photocatalytic efficiency.We have demonstrated the synthesis of Schottky-barrier-free plasmonic MoO3−x nanospheres (NSs) with remarkably high oxygen vacancy (OV) contents by aerosol-spray. The MoO3−x NSs can achieve efficient ammonia photosynthesis through a “killing two birds with one stone” mechanism. On the one hand, the OVs can serve as chemisorption sites for N2 molecules and participate in their activation. On the other hand, the introduction of OVs generates a large number of free electrons near the conduction band, which induces a broad absorption band from the visible to the NIR region owing to the plasmon resonance. The Schottky-barrier-free nature of this plasmonic semiconductor allows free transportation of the plasmonic hot charge carriers, while the defect states introduced by the OVs can effectively trap the hot electrons to prevent rapid electron–hole recombination. As expected, the as-prepared material exhibits a superior ammonia production rate, with the highest apparent quantum efficiency (AQE) of 1.24% at 808 nm and an appreciable solar-to-ammonia conversion efficiency (SACE) of 0.057% for NH3 production. Besides MoO3−x , WO3−x is also an excellent candidate for Schottky-barrier-free plasmonic photocatalysts. We have synthesized square WO3−x nanoplates hydrothermally. The WO3-x nanoplates possess regular morphology, wide light absorption, and great ammonia production performance. Furthermore, by introducing doping elements (Mo, V, Fe, Bi) into WO3−x nanoplates, the N2 activation and dissociation can be improved by refining the defect states. The Mo-doped WO3−x nanoplates exhibit the highest ammonia production rate of 145.50 μmol g−1 h−1 with SACE of 0.011% since the Mo species can promote the chemisorption and polarization of N2 molecules and significantly reduce the reaction barrier. Notably, Mo-doped WO3−x nanoplates are a dual-function photocatalyst that can oxidize water to hydrogen peroxide in a stoichiometric ratio while synthesizing ammonia. Figure 1

Influence of Substrate-Induced Charge Doping on Defect-Related Excitonic Emission in Monolayer MoS2.

Many applications of transition metal dichalcogenides (TMDs) involve transfer to functional substrates that can strongly impact their optical and electronic properties. We investigate the impact that substrate interactions have on free carrier densities and defect-related excitonic (XD) emission from MoS2 monolayers grown by metal-organic chemical vapor deposition. C-plane sapphire substrates mimic common hydroxyl-terminated substrates. We demonstrate that transferring MoS2 monolayers to pristine c-plane sapphire dramatically increases the free electron density within MoS2 layers, quenches XD emission, and accelerates exciton recombination at the optical band edge. In contrast, transferring MoS2 monolayers onto inert hexagonal boron nitride (h-BN) has no measurable influence on these properties. Our findings demonstrate the promise of utilizing substrate engineering to control charge doping interactions and to quench broad XD background emission features that can influence the purity of single photon emitters in TMDs being developed for quantum photonic applications.

Excited‐State Dynamics and Optical Properties of Silica Under Ultrafast Laser Irradiation

AbstractExcited by intense infrared ultrafast light pulses, a wide bandgap material undergoes nonlinear ionization, generating a high density of free electrons in conduction states. As a result, the electronic band structure is critically modified and the bandgap shrinks. This induces rapid changes in optical properties, dramatically affecting the absorption spectrum during light coupling to the dielectric surface or during nonlinear propagation inside the bulk. This study analyzes the structural behavior and the modification of the optical properties of laser‐excited silica glass at the molecular cluster level through first‐principles simulations. Employing density functional theory and the GW approximations for band structure under nonequilibrium conditions, alongside the Bethe–Salpeter equation, the dynamics of the optical properties of fused silica are comprehensively explored. The behavior of excited fused silica in a wide photon energy range (from a few to 20 eV) is thus predicted. Laser‐induced electron excitation triggers a redistribution of charges between oxygen and silicon atoms, accompanied by a significant increase in electronic pressure, local atomic structure rearrangement, and material expansion. Molecular dynamics simulations offer a temporal perspective on the excited state dynamics, unveiling the intricate interplay between electronic and atomic effects on bandgap evolution. The analysis sheds light on excitonic resonances, intraband and interband transitions in fused silica under ultrafast laser irradiation, providing valuable insights into its excited state behavior and optical properties.

Modeling and experiment of femtosecond laser processing of micro-holes arrays in quartz

Quartz material irradiated by femtosecond laser has increasingly attracted widespread attention for the micro-fabrication of photonic devices. Mechanism exploration is beneficial for accelerating the digital progress of laser processing. However, the mechanism between femtosecond laser and quartz is complicated and needs further theoretical investigation. This paper established the theoretical model based on the ionization model with the Drude equation to study the space–time evolution of free electron density and its influence on the absorption coefficient, reflectivity, and ablation depth. In addition, we achieved a 10 × 10 micro-holes array with a pore size less than 10 μm, cone angle less than 2° in a 0.25 mm thick quartz on the condition of a laser pulse energy Ep = 3 μJ, scanning velocity v = 0.1 mm/s, and defocusing distance Δf = −0.3 mm via the bottom-up femtosecond laser processing. The work gives a new insight into further understanding the ablation mechanism of transparent materials etching by the femtosecond laser. It provides a practical technical scheme for preparing commercial quartz photonic devices.

The Interdependence of the Kinematic and Intrinsic Parameters of a HIT Cell: The Effect of Charge Carrier Mobility

This paper discusses the dependence of the kinematic and intrinsic parameters of a silicon heterojunction solar cell, highlighting mobility phenomena. First, a three-dimensional schematic of a HIT (Heterojunctions with Intrinsic Thin layer) cell is established to highlight mobility phenomena at the texturized hydrogenated indium oxide ( ) contact layer and active layers where charge carriers move. Next, mathematical equations linking the interacting physical parameters are developed, and the numerical resolution of these mathematical equations has led to results. The discussion of these results is based on charge carrier transport, more specifically the photocurrent densities of free electrons and excitons, and their contribution in terms of the photovoltaic cell's energy production efficiency.

Low-frequency conductivity of low wear high-entropy alloys

High-entropy alloys (HEAs) provide new research avenues for alloy combinations in the periodic table, opening numerous possibilities in novel-alloy applications. However, their electrical characteristics have been relatively underexplored. The challenge in establishing an HEA electrical conductivity model lies in the changes in electronic characteristics caused by lattice distortion and complexity of nanostructures. Here we show a low-frequency electrical conductivity model for the Nb-Mo-Ta-W HEA system. The cocktail effect is found to explain trends in electrical-conductivity changes in HEAs, while the magnitude of the reduction is understood by the calculated plasma frequency, free electron density, and measured relaxation time by terahertz spectroscopy. As a result, the refractory HEA Nb15Mo35Ta15W35 thin film exhibits both high hardness and excellent conductivity. This combination of Nb15Mo35Ta15W35 makes it suitable for applications in atomic force microscopy probe coating, significantly improving their wear resistance and atomic-scale image resolution.

A numerical code for the analysis of magnetic white-dwarf spectra that includes field effects on the chemical equilibrium

We present a new magnetic-atmosphere model code for obtaining synthetic spectral fluxes of hydrogen-rich magnetic white dwarfs. To date, observed spectra have been analyzed with models that neglect the magnetic field's effects on the atomic populations. In this work, we incorporate state-of-art theory in the evaluation of numerical densities of atoms, free electrons, and ions in local thermodynamical equilibrium under the action of a magnetic field. The energy distribution of atoms is rigorously evaluated for arbitrary field strength. This energy pattern includes going from tightly bound states to metastable or truly bound, highly excited states embedded in the continuum, that is, over the first Landau level. Finite nuclear mass effects and the coupling between the internal atomic structure and the motion of the atom across the magnetic field are also considered. Synthetic fluxes are generated with integrations of numerical solutions of polarized radiative transfer over the visible stellar disk using a spherical $t$-design method. The atmosphere code is tested with observations from the Sloan Digital Sky Survey for a group of known magnetic white dwarfs. Physical stellar parameters are obtained from least-squares fits to the observed energy distribution and compared with results of previous works. We show that the use of zerofield ionization equilibrium in spectral analyses can lead to underestimated effective temperatures for highly magnetic white dwarfs.

Modelling the galaxy radio continuum from star formation and active galactic nuclei in the Shark semi-analytic model

ABSTRACT We present a model of radio continuum emission associated with star formation (SF) and active galactic nuclei (AGNs) implemented in the Shark semi-analytic model of galaxy formation. SF emission includes free-free and synchrotron emission, which depend on the free-electron density and the rate of core-collapse supernovae with a minor contribution from supernova remnants, respectively. AGN emission is modelled based on the jet production rate, which depends on the black hole mass, accretion rate, and spin, and includes synchrotron self-absorption. Shark reproduces radio luminosity functions (RLFs) at $1.4\, \rm GHz$ and $150\, \rm MHz$ for 0 ≤ z ≤ 4, and scaling relations between radio luminosity, star formation rate, and infrared luminosity of galaxies in the local and distant universe in good agreement with observations. The model also reproduces observed number counts of radio sources from 150 MHz to 8.4 GHz to within a factor of 2 on average, though larger discrepancies are seen at the very bright fluxes at higher frequencies. We use this model to understand how the radio continuum emission from radio-quiet AGNs can affect the measured RLFs of galaxies. We find current methods to exclude AGNs from observational samples result in large fractions of radio-quiet AGNs contaminating the ‘star-forming galaxies’ selection and a brighter end to the resulting RLFs.We investigate how this affects the infrared-radio correlation (IRRC) and show that AGN contamination can lead to evolution of the IRRC with redshift. Without this contamination, our model predicts a redshift- and stellar mass-independent IRRC, except at the dwarf-galaxy regime.

Transient optical properties change and dense plasma dynamics during water breakdown induced by ultrashort laser pulses

We propose a nonlinear transient coupling model to study the plasma dynamics during the interaction between ultrashort laser pulses and water. We conduct a quantitative characterization of the transient optical properties, energy deposition, and dense plasma dynamics in water with near-infrared ultrashort laser pulses by simulating the spatiotemporal coupling of the laser field with the plasma while calculating the time-varying relative permittivity. The results show that the free electron density in the dense plasma exceeds ≈1.0×1026 m−3, the plasma will move in the reverse direction of the laser pulse propagation, and the velocity is related to the incident laser intensity. An empirical model is established to quantify this reverse movement of dense plasma in the laser field taking into account the energy deposition. We also validate our coupling model by comparing the breakdown thresholds with experimental results and find excellent agreement.

Landau damping effects on dust ion-acoustic solitary waves in a nonthermal pair-ion plasma

The Landau damping effects on the nonlinear propagation of dust ion-acoustic solitary waves (DIASWs) are studied in an electron-free unmagnetized collisionless dusty pair-ion plasma. The two species of nonthermal ions (positive and negative) are described by the kinetic Vlasov equations, whereas the massive charged dust grains form only the background plasma. Using the multi-scale reductive perturbation technique generalized for the applications to the Vlasov equation, we derive a modified Korteweg–de Vries (KdV) equation that governs the evolution of DIASWs with the effects of linear resonance, in particular, linear Landau damping. The properties of the phase velocity and the Landau damping rate of DIASWs are studied with the effects of positive and negative-ion nonthermality parameters ( α p , α n ), the ratios of the positive to negative ion masses (m) and temperatures (T) as well as the dust to negative-ion number density ratio (δ). It is found that, depend on the degree of positive to negative ion mass ratios (m), both of damped and growing oscillations occur in a collisionless dusty pair-ion plasma due to the resonance phenomena between the wave and the nonthermal particles of the system. The properties of the decay rates of the amplitude of the KdV soliton with a small effect of Landau damping are also studied with the above system of parameters. The results may be useful for understanding the localization of solitary pulses and associated resonance damping and/or growing oscillations of the wave in laboratory and space plasmas, in which the number density of free electrons is much smaller than that of ions and highly charged heavy, micron seized dust grains.

Defect Passivation of 2D Semiconductors by Fixating Chemisorbed Oxygen Molecules via h-BN Encapsulations.

Hexagonal boron nitride (h-BN) is a key ingredient for various 2D van der Waals heterostructure devices, but the exact role of h-BN encapsulation in relation to the internal defects of 2D semiconductors remains unclear. Here, it is reported that h-BN encapsulation greatly removes the defect-related gap states by stabilizing the chemisorbed oxygen molecules onto the defects of monolayer WS2 crystals. Electron energy loss spectroscopy (EELS) combined with theoretical analysis clearly confirms that the oxygen molecules are chemisorbed onto the defects of WS2 crystals and are fixated by h-BN encapsulation, with excluding a possibility of oxygen molecules trapped in bubbles or wrinkles formed at the interface between WS2 and h-BN. Optical spectroscopic studies show that h-BN encapsulation prevents the desorption of oxygen molecules over various excitation and ambient conditions, resulting in a greatly lowered and stabilized free electron density in monolayer WS2 crystals. This suppresses the exciton annihilation processes by two orders of magnitude compared to that of bare WS2. Furthermore, the valley polarization becomes robust against the various excitation and ambient conditions in the h-BN encapsulated WS2 crystals.

Constructing heterostructure by co-doping of Ta5+ and F− with carbon nanotubes to improve kinetic properties of Na3V2(PO4)3

The advancement of Na3V2(PO4)3 has been impeded by its subpar kinetic characteristics, resulting in suboptimal electrochemical performance. In this case, a dual modification strategy involving Ta and F co-doping is employed, along with the incorporation of carbon nanotubes (CNTs), is introduced. Notably, the substitution of high-valence Ta5+ for V3+ ions induces an n-type doping effect, thereby increasing the density of free electrons and enhancing electrochemical performance. Moreover, Ta5+ possesses a comparatively larger ionic radius than V3+, which enhances the ease of Na+ transport, leading to an increased rate of ionic diffusion. Furthermore, Ta5+ ions play a crucial role in reinforcing the crystal structure, thereby strengthening the stability of the NVP system. Importantly, during the high-temperature calcination process, the reduction of carbon results in the conversion of Ta5+ to Ta3+, forming a novel conductive TaN phase through its reaction with N2. This TaN phase, known for its high conductivity, intercalates into the NVP bulk as interlayers, forming beneficial grain boundaries. Thanks to this unique TaN//NVP heterojunction, the migration of Na+ ions is notably accelerated along the grain boundaries rather than within the NVP bulk. The introduction of F contributes to reducing the grain size of active particles, consequently shortening the pathways for Na+ migration and improving kinetic properties. Moreover, the presence of carbon layers and the encapsulation of CNTs collaboratively construct a highly conductive cross-linking network, elevating both electronic conductivity and mitigating NVP particle aggregation during high-temperature sintering. Consequently, the modified NVTPF0.07/@CNTs sample exhibits outstanding performance in both half and full cells, underscoring its substantial potential for application in the field of sodium-ion batteries.

New Critical Density in Metal-Insulator Transition, obtained in n(p)- Type Degenerate [ InAs1-xPx(Sbx), GaTe1-xAsx(Sbx,Px), CdTe1-xSx(Sex)]-Crystalline Alloys, 0≤x≤1, being just That of Carriers Localized in Exponential

By basing on the same physical model and treatment method, as used in our recent works [1, 2], for GaAs1-xTex(Sbx,Px) -crystalline alloys, 0≤x≤1 , we will investigate the critical impurity density in the metal-insulator transition (MIT), obtained now in n(p)-type degenerate X(x)=[InAs1-xPx(Sbx), GaTe1-xAsx(Sbx,Px), CdTe1-xSx(Sex)]- crystalline alloys, being due to the effects of the size of donor (acceptor) d(a)-radius, rd(a), and the x- concentration, assuming that all the impurities are ionized even at T=0 K. In such n(p)-type degenerate X(x)= -crystalline alloys, we will determine:
 (i)-the critical impurity density NCDn(CDp)(rd(a), x) in the MIT, as given in Eq. (8), by using an empirical Mott parameter Mn(p)=0.25, and
 (ii)-the density of electrons (holes) localized in the exponential conduction (valence)-band tails (EBT), NEBTCDn(CDp)(rd(a),x), as given in Eq. (26), by using our empirical Heisenberg parameter, Hn(p)=0.47137, as given in Eq. (15), suggesting that: for given rd(a) and x, NEBTCDn(CDp)(rd(a),x)=NCDn(CDp)(rd(a),x) obtained with a precision of the order of 2.91x10-7, as observed in Tables 2-8.
 In other words, such the critical d(a)-density NCDn(CDp)(rd(a),x) is just the density of electrons (holes) localized in the EBT, NEBTCDn(CDp)(rd(a),x).
 So, if denoting the total impurity density by N, the effective density of free electrons (holes), N* given in the parabolic conduction (valence) band of the n(p)-type degenerate - crystalline alloy, can thus be defined by: N*(N,rd(a),x)=N-NCDn(NDp)=N-NEBTCDn(CDp) , as that given in compensated crystals, needing to determine various optical, electrical, and thermoelectric properties in such n(p)-type degenerate X(x)-crystalline alloys, as those studied in n(p)-type degenerate crystals [3-7].