Thermal Ionization Energy Research Articles

Calculation of the Activation Energy of Electrical ε2‐Conductivity of Weakly Compensated Semiconductors

A model of tunneling (jumping) migration of charge carriers near their mobility edge in the upper band of neutral states of majority hydrogen‐like impurities is proposed to calculate the energy of thermal activation of electrical ‐conductivity of weakly compensated semiconductors. The difference from the known Hubbard model consists in the scheme of interimpurity transitions of charge carriers and in the method of calculating the position of their tunnel mobility edge. The drift mobility edge of free charge carriers corresponds to the thermal ionization energy of majority impurities , which is located near the c‐band bottom or the v‐band top in n‐ and p‐type semiconductors, respectively, and is due to the overlap of excited states of electrically neutral majority impurities. The position of the tunnel mobility edge for ‐conductivity is determined by taking into account the Coulomb interaction of the majority impurities in the charge states and . It is assumed that doping and compensating impurities form a single simple nonstoichiometric cubic lattice in a crystal matrix. The calculations of the activation energy on the insulator side of the insulator–metal concentration phase transition for weakly compensated p‐Si:B, n‐Si:P, and n‐Ge:Sb crystals quantitatively agree with known experimental data.

Electron emission from deep traps in HfO2 under thermal and optical excitation

The ratio between the energies of optical and thermal ionization depends on the defect nature and the strength of the interaction of trapped electrons with phonons. Knowing this ratio for a certain type of defect allows one to predict, e.g., thermal emission energies from the optically measured values. We present the results of direct empirical extraction of the ratio between optical and thermal electron emission energies for HfO2 bulk electron traps combined with theoretical analysis of the physical mechanism of electron transitions from the trapped state to the mobility edge. We show that, by applying different excitation mechanisms, we affect the same deep traps inside the HfO2 band gap; i.e., these traps are both optically and thermally active and are likely to have similar nature. The extracted empirical optical/thermal ionization energy ratio of 2.2±0.3 is in good agreement with the polaronic nature of the probed electron traps, as shown by the results of theoretical calculations. Our results provide experimental and theoretical methodologies for consistently linking thermal and optical ionization energies of electron traps and describing their distributions in the band gap of amorphous oxides, and can help improve modeling frameworks for reliability issues related to oxide traps. Published by the American Physical Society 2024

Two‐Photon Pumped Single‐Mode Lasing in CsPbBr3 Perovskite Microwire

AbstractAchieving high‐quality, frequency‐upconversion single‐mode lasing output is an important requirement for developing new nonlinear optoelectronic devices, such as on‐chip optical communication, nonlinear optical switches, and optical parametric amplifiers. Here, an individual CsPbBr3 microwire prepared by the anti‐solvent method is served as both gain media and microresonator to achieve two‐photon pumped frequency upconversion single‐mode lasing with the side‐mode suppression ratio of 18 dB. Meanwhile, the refractive index of orthorhombic perovskite is theoretically calculated based on first principles, and determining its square whispering‐gallery oscillation type by combining with the plane wave model and the steady‐state oscillation conditions of laser. The extracted exciton binding energy of 33.15 meV higher than the thermal ionization energy of room temperature (≈26 meV) suggests that the as‐grown CsPbBr3 microwires possess the capacity to achieve two‐photon pumped lasing output, as well further gaining deeper insights into the role of exciton‐phonon coupling in light emission.

Cobalt as a promising dopant for producing semi-insulating β-Ga2O3 crystals: Charge state transition levels from experiment and theory

Optical absorption and photoconductivity measurements of Co-doped β-Ga2O3 crystals reveal the photon energies of optically excited charge transfer between the Co related deep levels and the conduction or valence band. The corresponding photoionization cross sections are fitted by a phenomenological model considering electron–phonon coupling. The obtained fitting parameters: thermal ionization (zero-phonon transition) energy, Franck–Condon shift, and effective phonon energy are compared with corresponding values predicted by first principle calculations based on density functional theory. A (+/0) donor level ∼0.85 eV above the valence band maximum and a (0/−) acceptor level ∼2.1 eV below the conduction band minimum are consistently derived. Temperature-dependent electrical resistivity measurement at elevated temperatures (up to 1000 K) yields a thermal activation energy of 2.1 ± 0.1 eV, consistent with the position of the Co acceptor level. Furthermore, the results show that Co doping is promising for producing semi-insulating β-Ga2O3 crystals.

Photoconductivity buildup and decay kinetics in unintentionally doped β-Ga2O3

Photoconductivity transients in an unintentionally doped (UID) n-type β-Ga2O3 layer are investigated at temperatures ranging from 90 to 210 K. Illumination of the β-Ga2O3 layer with a 600 nm light pulse induces photoconductivity, which persists after the light is turned off. The origin of persistent photoconductivity (PPC) is probed using the temperature dependencies of the photoconductivity buildup and decay kinetics. Upon excitation by 600 nm light, the photoconductivity in the UID β-Ga2O3 sample is related to the photoionization of two distinct deep levels with thermal ionization energies of 1.76 ± 0.07 eV (Franck–Condon energy D FC: 0.78 ± 0.24 eV) and 2 ± 0.08 eV (D FC: 0.52 ± 0.15 eV). When the light is turned off, PPC is observed due to thermal capture barriers preventing the photo-generated electrons from relaxing back to deep levels. Capture barriers of 35 meV and 165 meV have been estimated using the temperature dependence of the PPC decay time constant. The experimentally detected deep levels are ascribed to deep donors, such as oxygen vacancies.

Estimation of Activation and Compensation Ratios in Al<sup>+</sup> Ion Implanted 4H-SiC: Comparison of Two Methodologies

Activation and compensation ratios feature the electrical doping efficiency of a semiconductor material by ion implantation. The estimation of these ratios requires a quantitative evaluation of the density of the implanted dopant in substitutional position and of the density of the compensator centers after the mandatory post implantation annealing treatment. In the case of Al+ ion implanted 4H-SiC, it is a common habit to determine acceptor density, compensator density and acceptor thermal ionization energy by fitting the curve of the drift holes temperature dependence with the charge neutrality equation. However, this strategy could lead to ambiguous results. In fact, this study shows several cases of Al+ ion implanted 4H-SiC of interest for electronic device fabrication, where at least two sets of such fitting outputs can reproduce the same experimental curve within the uncertainty of the data. Provided that a model for the carrier transport could be set-up, the contemporaneous fits of the temperature dependence of drift hole density and of drift hole mobility is proposed to alleviate the uncertainty of the estimated acceptor density, compensator density and acceptor thermal ionization energy.

Максимальная прыжковая электропроводность на постоянном токе по водородоподобным примесям в полупроводниках

A quasi-classical model for calculating DC (direct current) electrical conductivity in crystalline semiconductors with hydrogen-like impurities is developed at the transition from band conduction to impurity hopping conduction with decreasing temperature. This transition from the minimum band conductivity to the maximum hopping conductivity via impurities has the form of a characteristic ``kink'' in the temperature dependence of the electrical resistivity. The idea of the calculation is to preliminarily determine the transition temperature Tj using the standard approach within the framework of the two-band model. The shift of the top of the v-band (the bottom of the c-band) into the depth of the band gap due to the formation of a quasi-continuous band of allowed energy values from the excited states of acceptors (donors) is taken into account. This leads to a decrease in the value of a thermal ionization energy of the main shallow impurities due to a decrease in the maximum localization radius of a hole on an acceptor (an electron on a donor) with increasing impurity concentration. The values of the observed maximum hopping conductivity and drift hopping mobility corresponding to the temperature Tj are calculated. The numerical calculation within the framework of the proposed model is consistent with the known experimental data on the electrical conductivity and Hall coefficient of moderately compensated p-Ge crystals doped by neutron transmutation and non-intentionally compensated metallurgically doped n-Ge, as well as n- and p-Si crystals on the insulator side of the Mott insulator–metal concentration phase transition.

Maximum hopping direct current conductivity via hydrogen-like impurities in semiconductors

A quasi-classical model for calculating DC (direct current) electrical conductivity in crystalline semiconductors with hydrogen-like impurities is developed at the transition from band conduction to impurity hopping conduction with decreasing temperature. This transition from the minimum band conductivity to the maximum hopping conductivity via impurities has the form of a characteristic "kink" in the temperature dependence of the electrical resistivity. The idea of the calculation is to preliminarily determine the transition temperature Tj using the standard approach within the framework of the two-band model. The shift of the top of the v-band (the bottom of the c-band) into the depth of the band gap due to the formation of a quasi-continuous band of allowed energy values from the excited states of acceptors (donors) is taken into account. This leads to a decrease in the value of a thermal ionization energy of the majority shallow impurities due to a decrease in the maximum localization radius of a hole on an acceptor (an electron on a donor) with increasing impurity concentration. The values of the observed maximum hopping conductivity and drift hopping mobility corresponding to the temperature Tj are calculated. The numerical calculation within the framework of the proposed model is consistent with the known experimental data on the electrical conductivity and Hall coefficient of moderately compensated p-Ge crystals doped by neutron transmutation and non-intentionally compensated metallurgically doped n-Ge, as well as n- and p-Si crystals on the insulator side of the Mott insulator--metal concentration phase transition. Keywords: bulk crystals of germanium and silicon, hydrogen-like acceptors and donors, holes and electrons, band and hopping motion of charge carriers.

Site occupancy and luminescence of Ce3+-doped NaK2Li[Li3SiO4]4: A first-principles study

The observed photoluminescent properties of Ce3+-doped NaK2Li[Li3SiO4]4 suggest the importance and potential of this phosphor in practical applications. It is noted that only half of the Na+ and Li + sites in the Na/Li channel are found to be occupied in the host and two sets of different luminescent Ce3+ centers are observed. In this work, first-principles calculations are performed to resolve the site occupancy of Ce3+ by taking experimental synthesis conditions into consideration. The formation energy results show that Ce3+ prefers to replace the Na atom in the Na/Li channel than K atom in the K channel, whilst the cation vacancies VLi, VNa and VK are formed as charge compensation. Besides, a large amount of Ce4+ would be present. Based on the obtained excitation and emission energies, the Stokes shifts, and the 5d crystal-field splitting, the luminescent center with a larger red-shift of the emission wavelength is assigned as Ce at the Na site, and the other center is assigned as Ce at the K site. The energy level structures of Ce occupying a certain site (Na site or K site) with different local environments differ slightly, thus the broadening of the spectra can be interpreted. Furthermore, we provide an explanation on the excellent thermal stability of this phosphor based on the large energy barrier for the 5d-4f crossover point and the large 5d thermal ionization energy. To sum up, the insights gained in this work deepen our understanding on the luminescent properties of Ce3+-doped NaK2Li[Li3SiO4]4 in which some of the host cation sites are partially occupied.

Curie–Weiss behavior of the low-temperature paramagnetic susceptibility of semiconductors doped and compensated with hydrogen-like impurities

For the first time, a quantitative model of the Curie–Weiss behavior of a low-temperature paramagnetic susceptibility of electrically neutral donors in n-type diamagnetic covalent semiconductors is proposed. The exchange interaction between nearest two neutral donors was calculated with the use of the Heitler–London model. In this model, we take into account the change in the thermal ionization energy of donors due to the shift of the bottom of the conduction band to the bandgap with doping and compensation. The energy of the exchange spin–spin interaction between electrons localized on donors is calculated as a function of the donor concentration and the degree of their compensation by acceptors. The broadening of the donor band due to the Coulomb interaction of the nearest impurity ions was taken into account. We considered crystals of n-type germanium doped with arsenic up to the concentration close to the insulator–metal phase transition (Mott transition) and compensated with gallium. The compensation ratio K is the ratio of the concentration of compensating acceptors KN to the concentration of doping donors N. The model predicts a change in the sign of the Curie–Weiss temperature from minus to plus (a transition from the antiferromagnetic to ferromagnetic local ordering of electron spins on donors) for K ≈ 0.15–0.3, reaching its maximum positive values of ≈1.3 K for K ≈ 0.5 with the following decrease (a transition to paramagnetism) for K > 0.85. The calculated behavior of the paramagnetic susceptibility of donors is consistent with the experimental data for compensated n-Ge:As,Ga samples close to the Mott transition.

Electron trapping in ferroelectric HfO2

Charge trapping study at 300 and 77 K in ferroelectric (annealed Al- or Si-doped) and nonferroelectric (unannealed and/or undoped) ${\mathrm{HfO}}_{2}$ films grown by atomic layer deposition reveals the presence of ``deep'' and ``shallow'' electron traps with volume concentrations in the ${10}^{19}\text{\ensuremath{-}}{\mathrm{cm}}^{\ensuremath{-}3}$ range. The concentration of deep traps responsible for electron trapping at 300 K is virtually insensitive to the oxide doping by Al or Si but slightly decreases in films crystallized by high-temperature annealing in oxygen-free ambient. This behavior indicates that the trapping sites are intrinsic and probably related to disorder in ${\mathrm{HfO}}_{2}$ rather than to the oxygen deficiency of the film. Electron injection at 77 K allowed us to fill shallow electron traps energetically distributed at \ensuremath{\sim}0.2 eV. These electrons are mobile and populate states with thermal ionization energies in the range \ensuremath{\sim}0.6--0.7 eV below the ${\mathrm{HfO}}_{2}$ conduction band (CB). The trap energy depth and marginal sensitivity of their concentration to crystallization annealing or film doping with Si or Al suggests that these traps are associated with boundaries between crystalline grains and interfaces between crystalline and amorphous regions in ${\mathrm{HfO}}_{2}$ films. This hypothesis is supported by density functional theory calculations of electron trapping at surfaces of monoclinic, tetragonal, and orthorhombic phases of ${\mathrm{HfO}}_{2}$. The calculated trap states are consistent with the observed thermal ionization (0.7--1.0 eV below the ${\mathrm{HfO}}_{2}$ CB) and photoionization energies (in the range of 2.0--3.5 eV below the ${\mathrm{HfO}}_{2}$ CB) and support their intrinsic polaronic nature.

Localization by an external magnetic field of electrons on the ions of hydrogen-like donors in non-degenerate semiconductors

In the quasi-classical approximation of quantum mechanics a model for the localization of conduction electrons on the ions of hydrogen-like donors in an external magnetic field was developed. The thermal ionization energy of donors in lightly doped and moderately compensated crystals of gallium arsenide and indium antimonide of n-type was calculated depending on the induction of the external magnetic field. In contrast to the known theoretical works (which use variational methods for solving the Schrödinger equation), a simple analytical expression is proposed for the ionization energy of the donor in the magnetic field, which quantitatively agrees with the known experimental data. It is shown that the magnitude of the magnetic field induced by the orbital motion of the electron around the ion core of the donor is negligible compared to the external field and does not contribute to the ionization energy of donors.

Phonon-assisted electron tunneling between traps in silicon oxide films treated in hydrogen plasma

The charge transport in thin thermal silicon oxide films treated in electron cyclotron resonance hydrogen plasma at different exposure times was investigated. X-ray photoelectron studies show that such treatment leads to the oxygen deficiency of the films. It was established that the treatment of the films in plasma leads to an increase of their conductivity by a factor of about 102. The film charge transport properties were studied at different temperatures and analyzed within four theoretical dielectric conductivity models. It was found that the charge transport mechanism is described by Fowler-Nordheim model in the initial silicon oxide and by the model of phonon-assisted electron tunneling between neutral traps after the treatment in hydrogen plasma. The thermal trap ionization energy value (Wt = 1.6 eV) measured from transport experiments is in agreement with that obtained from ab initio calculations for the oxygen vacancy (Si-Si bond) in SiO2.

Thermal ionization energy of hydrogen-like impurities in semiconductor materials

In the work the dependence of the thermal ionization energy of hydrogen-like donors and acceptors on their concentration in n- and p-type semiconductors is analyzed analytically and numerically. The impurity concentrations and temperatures at which the semiconductors are on the insulator side of the concentration insulator – metal phase transition (Mott transition) are considered. It is assumed that impurities in the crystal are distributed randomly (according to Poisson), and their energy levels are distributed normally (according to Gauss). In the quasi-classical approximation, it is shown, for the first time, that the decrease in the ionization energy of impurities mainly occurs due to the joint manifestation of two reasons. Firstly, from the excited states of electrically neutral impurities, a quasicontinuous band of allowed energy values is formed for c-band electrons in an n-type crystal (or for v-band holes in a p-type crystal). This reduces the energy required for the thermally activated transition of electron from the donor to the c-band (for the transition of the hole from the acceptor to the v-band). Secondly, from the ground (unexcited) states of impurities a classical impurity band is formed, the width of which at low temperatures is determined only by the concentration of impurity ions. In moderately compensated semiconductors (when the ratio of the concentration of minority impurities to the concentration of majority impurities is less than 50 %) the Fermi level is located closer to the edge of the band of allowed energy values than the middle of the impurity band, that issue reduces thermal ionization energy of impurities from states in the vicinity of the Fermi level (transition of electron from a donor to the c-band, or hole from an acceptor to the v-band). Previously, these two causes of decrease in the thermal ionization energy due to increase in the concentration of impurities were considered separately. The results of calculations according to the proposed formulas are quantitatively agree with the known experimental data for a number of semiconductor materials (germanium, silicon, diamond, gallium arsenide and phosphide, silicon carbide, zinc selenide) with a moderate compensation ratio.

Thermal ionization energy of hydrogen-like impurities in semiconductor materials

Thermal ionization energy of hydrogen-like impurities in semiconductor materials

Influence of Charge Transport Layers on Capacitance Measured in Halide Perovskite Solar Cells

Summary Capacitance-based techniques have been used to measure the electrical properties of halide perovskite solar cells (PSCs) such as defect activation energy and density, carrier concentration, and dielectric constant, which provide key information for evaluating the device performance. Here, we show that capacitance-based techniques cannot be used to reliably analyze the properties of defects in the perovskite layer or at its interface, because the high-frequency capacitance signature is due to the response of charge carriers in the hole-transport layer (HTL). For HTL-free PSCs, high-frequency capacitance can be considered as the geometric capacitance for analyzing the dielectric constant of the perovskite layer because there is no trapping and de-trapping of charge carriers in the perovskite layer. We further find that the low-frequency capacitance signature can be used to calculate the activation energy of the ionic conductivity of the perovskite layer, but the overlapping effects with charge transport materials must be avoided.

Enhanced thermal quenching characteristic via carbon doping in red‐emitting CaAlSiN3:Eu2+ phosphors

AbstractEnhancing thermal quenching characteristic of phosphor for use in high power white‐light‐emitting diodes (wLEDs) is a significant materials challenge. To achieve this goal, a series of red‐emitting carbidonitride phosphors Ca0.992AlSiN3 − 4/3xCx:0.008Eu2+ have been synthesized by high‐temperature solid‐state reaction method. Crystal structure, luminescence properties, and thermal quenching process are investigated. The location of carbon in the lattice is proved by the Raman spectra. The preferential crystallographic site of carbon is validated by the first‐principles density functional theory calculations combining the Rietveld refinement. With carbon doping from x = 0 to x = 0.24, the emission spectra are blue‐shifted from 656.8 to 650.2 nm, and the fitted lifetime of Eu2+ decreases from 775.3 to 721.7 ns. Replacing nitrogen by carbon enhances thermal quenching characteristic by 8.9% at 300°C. Carbon doping enlarges the thermal ionization energy barriers (EdC) which is calculated at great length, and suppresses thermal ionization process. A wLED fabricated by the combination of a blue chip with the as‐synthesized red phosphor and LuAG: Ce3+ green phosphor shows a high color rendering indexes (Ra = 95.9 and R9 = 92). The promising application of Ca0.992AlSiN3 − 4/3xCx:0.008Eu2+ phosphor for wLEDs is proved by all results above.

Electron transfer between heterogeneous lanthanides in BaF2 crystals

Forward electron photo-transfer and reverse thermal transfer between divalent and trivalent heterogeneous lanthanides in barium fluoride crystals has been studied using optical absorption. In crystals activated by two heterogeneous lanthanides and grown in reducing conditions, one of the lanthanides becomes bivalent whereas the other lanthanide remains trivalent. Illumination of the crystal in the ultraviolet bands led to the transfer of electrons from divalent lanthalides (Eu, Yb, Sm) to trivalent ions (Ho, Nd, Dy, Tm, Sm, Yb). The thermal ionization energies to the conduction band of created lanthanides are determined from the thermal bleaching curves of absorption bands. The experimental energies are compared with the estimated energies of the Dorenbos model.

Electronic Structure of Tantalum Oxide with Oxygen Vacancy and Polyvacancy, Oxygen Interstitial, Tantalum Interstitial and Tantalum Substituting Oxygen

The electronic properties of Ta2O5 are limited by its defects. The defects are problem if Ta2O5 is used in DRAM or as a blocking layer in a flash charge trapping memory (CTM), because it leads to a high conductivity via the traps and the threshold voltage instability. On the contrary, the high defects concentration opens the possibility of using Ta2O5 as a storage medium in the CTM [1] and resistive random-access memory (ReRAM) [2]. The aim of the study is the investigation of the electronic structure of O vacancy (VO), O polyvacancy, interstitial O and Ta atoms, O-to-Ta substitution in Ta2O5 to clarify the trap nature responsible for the charge localization and transport. The simulations carried out for the λ-Ta2O5 [3] 168-atom supercell in terms of the DFT in Quantum-ESPRESSO code. The calculated bandgap of λ-Ta2O5 is 4.2 eV. All types of native defects, except for the O interstitial, form defect states into the λ-Ta2O5 bandgap. The value of trap thermal ionization energy 0.5 eV are comparable to the experimental ones 0.7-0.8 eV [4], and optical trap energy 0.9 eV for the VO indicate that the VO in Ta2O5 can act as the charge trap, and participate in charge transport. The width of density of states defect peaks indicate the charge localization in space. The electron localization on the VO in Ta2O5 is due to the polaronic effect. The negative charge distributed between the nearest Ta atoms and it reflects the bonding character of the Ta orbitals charge density. Its allows us to conclude that the chains of closely located oxygen vacancies in TaOx can act as a conductive shunt and participate in the resistive switching. Each subsequent O vacancy forms near the already existing one, and no more than 2 removed O atoms, related to Ta atom. The O polyvacancy forms a filled defective band in Ta2O5 bandgap. The work is supported by the Russian Science Foundation grant #17-72-10103. [1] K. Hota, F.H. Alshammari, K. N. Salama et. al, Acs. Appl. Mater. Inter. 9, 21856 (2017). [2] M. Kim, S.R. Lee, S. Kim, M. Chang et. al, Adv. Funct. Mater. 25, 1527 (2015). [3] H. Lee, J. Kim, S.J. Kim et. al, Phys. Rev. Lett. 110, 235502 (2013). [4] V. Egorov, D.S. Kuzmichev, P.S. Chizhov et. al, Acs. Appl. Mater. Inter. 9, 13286 (2017). Figure 1

Oxygen Polyvacancies as Conductive Filament in Zirconia: First Principle Simulation

The atomic and electronic structure of oxygen vacancy and polyvacancy in the cubic, tetragonal and monoclinic zirconium oxide were investigated using quantum-chemical density functional theory simulation. It is shown that the neutral oxygen vacancy in crystalline zirconia can act as electron and hole trap. An electron added to ZrO2 structure with the oxygen monovacancy has a bonding charge density character. The defect levels position as well as thermal and optical trap ionization energies are consisted with the previously defined experimentally values. Each subsequent vacancy is formed near the already existing one, and no more than 2 removed oxygen atoms are related to Zr atom. The levels from oxygen polyvacancies are distributed in the bandgap preferentially localized close to the monovacancy level. The ability of oxygen vacancy chain in crystalline ZrO2 to act as a conductive filament is discussed.