Multiphonon Mechanism Research Articles

Carrier capture at the SiO2–Si interface: A physical model

The carrier (electron and hole) capture cross section of defects at the SiO2–Si interface is measured using trap-fill time in gigahertz charge-pumping experiment. The ability to use a highly asymmetric rectangular wave with very fast rise and fall times in our charge-pumping experiment greatly simplified data interpretation. Trap-fill times of less than or equal to 0.7ns are found for both electrons and holes. The corresponding capture cross section of 10−15cm2 or larger for both electron and hole cannot be explained by the usual multiphonon emission mechanism. A modified cascade capture model involving the strained Si–Si bonds around the Pb center is proposed to explain the large capture cross sections.

Electrical characterization of alpha radiation-induced defects in p-GaAs grown by metal-organic chemical-vapor deposition

Investigations of the alpha particle irradiation-induced defects in low-pressure metal-organic chemical-vapor deposition grown p-GaAs have been carried out. By employing deep-level transient spectroscopy, at least seven radiation-induced deep-level defects have been observed in the lower half of the band gap in the temperature range of 12−475 K. Double-correlation deep-level transient spectroscopy measurements show three prominent levels: two known radiation-induced levels namely, Hα1 and Hα5, and one inadvertent center HSA, present before irradiation, to exhibit a significant dependence of thermal emission rate on the junction electric field. For Hα1 and HSA the field-enhanced emission data are well fitted with a Poole-Frenkel model, using a three-dimensional square-well potential with radius r=3.2 and 1.43 nm, respectively. The field effect for Hα5 has been explained by a square-well potential in combination with a phonon-assisted tunneling process. Detailed data on the carrier capture cross section for all three levels have been obtained. The hole capture cross section for the levels Hα1 and Hα5 are found to be temperature independent, while for HSA, the hole capture data show a dependence on temperature. The dependence of hole capture cross section of HSA on temperature has been explained in terms of multiphonon capture mechanism, yielding a capture barrier of 0.13 eV and σ(∞)=1.5×10−14 cm2. These analyses lead us to conclude that the levels Hα1 and HSA are associated with a charged center, while the level Hα5 is most likely a substitutional defect in GaAs.

Electronic properties of interstitial iron and iron-boron pairs determined by means of advanced lifetime spectroscopy

As dissolved iron is one of the most common lifetime-killing contaminants in silicon, its coexisting defect configurations, interstitial iron (Fei) and iron-boron pairs (FeB), are investigated on an intentionally iron-contaminated silicon sample by means of temperature-dependent lifetime spectroscopy (TDLS) and injection-dependent lifetime spectroscopy (IDLS). In good agreement with the literature, the study identifies the known Fei donor level at Et−EV=(0.394±0.005)eV and determines its symmetry factor as k=σn∕σp=51±5, which is an order of magnitude lower than expected from the literature. Using the well-confirmed k factor, the poorly confirmed electron-capture cross section is redetermined as σn=(3.6±0.4)×10−15cm2 at 300K. In addition, the observed exponential σ(T) dependence identifies the multiphonon emission mechanism as the dominant capture mechanism for electrons with an activation energy E∞=0.024eV. Concerning the defect related to the iron-boron pair, the study unambiguously identifies the deep FeB acceptor level as the dominant FeB recombination center. While the known average value EC−Et=(0.26±0.03)eV for the energy level is well confirmed, the symmetry factor is determined as k=0.45, which represents an intermediate value among the scattered results from the literature. Additional spectroscopic information from the defect transformation allows both capture cross sections of the FeB defect to be determined (σn=2.5×10−15cm2 and σp=5.5×10−15cm2). Being suggested as a fingerprint of iron in the literature, the crossover position of the Fei- and FeB-dominated IDLS curves (at 300K) is experimentally proved to be doping dependent which is accurately predicted on the basis of the extracted set of Fei and FeB defect parameters. An additional fingerprint of iron is found by the qualitative change of the TDLS curve upon illumination and its S-like shape under dark conditions, which represents a robust criterion for unambiguous identification of iron in silicon. As the most sensitive technique to detect and determine an iron contamination in silicon heavily relies on the Fei and FeB defect parameters, the spectroscopic results are of special practical importance.

The luminescence decay-time of Mn2+ activated calcite

Luminescence decay time data are presented for 17 samples of synthetic calcite and a natural calcite between room temperature and approximately 15 K. The majority of the samples have Mn concentration in the range 0.0001–0.01 atoms per formula unit (apfu). Their spectra are consistent with a single exponential decay. It was necessary to use a “stretched” exponential to obtain adequate fits to the spectra of two samples having Mn concentrations of 0.036 and 0.091 apfu. The decay time at room temperature ranges from approximately 40–57 ms. At low temperature the corresponding range is 51–120 ms, indicating that thermal quenching of the decay time takes place. The decay time is dependent on the concentration of Mn, reaching a maximum (at both room- and low-temperature) in the range 0.001–0.003 apfu. The composition dependence is greater at low temperature. The results are discussed in terms of the Mott-Seitz and multiphonon mechanisms of thermal quenching. It is concluded that the latter provides a better fit to the data and is more consistent with models of the luminescence process in calcite:Mn.

Judd–Ofelt analysis of spectroscopic properties of Nd 3+-doped novel fluorophosphate glass

Judd–Ofelt analysis is performed for the new MgF 2–BaF 2–Al(PO 3) 3–Ba(PO 3) 2-based glass system to evaluate the spontaneous emission probability as well as quality factor and branching ratio. The variation of intensity parameters Ω 2 , Ω 4 , and Ω 6 are analyzed as a function of Nd 2O 3 concentration. It is found that the efficiency for the 4F 3/2→ 4I 9/2 transition enhances and the efficiency for the 4F 3/2→ 4I 11/2 transition diminishes as the difference between Ω 4 and Ω 6 increases with an increase in Nd 2O 3 concentration. The emission cross section for the 4F 3/2→ 4I 13/2 transition varies from 1.1×10 −20 to 1.15×10 −20 cm 2, and for the 4F 3/2→ 4I 11/2 transition it varies from 2.97×10 −20 to 2.69×10 −20 cm 2 with an increase in Nd 2O 3 concentration from 1 to 5 wt%. Analysis on non-radiative decay is performed based on multiphonon relaxation mechanisms. The above results are also compared with those of other host glass materials with the similar Nd 3+ dopant concentration, which suggests that present new glass is promising for fiber laser applications.

The Meyer-Neldel rule in the processes of thermal emission and hole capture in Ge/Si quantum dots

The hole thermal-emission rates and the cross sections for hole capture to the bound states in Ge quantum dots in Si are determined by admittance spectroscopy. The capture cross sections and the activation energies for emission rate are found to be related to each other by the Meyer-Neldel rule with a characteristic energy of 27±3 meV, which does not depend on the quantum-dot size. It is established that the capture cross section changes with temperature following the activation law. The experimental data are evidence of a unified multiphonon mechanism for the activation processes of hole transitions from the Ge quantum dots to the Si valence band and hole capture back into the quantum dots.

Crystal structure and spectroscopic study of novel two- and three-dimensional photoluminescent Eu(III)-adipate compounds.

Two new photoluminescent compounds with the formulas of [Eu(2)(adipate)(3)(H(2)O)].H(2)O (1) and [Eu(2)(adipate)(3)(4H(2)O)] (2) were synthesized by using Eu(III) chloride and adipic acid under hydrothermal reaction conditions in aqueous solution. Compound 1, a 3-D layered framework, possesses infinite Eu-O-Eu polyhedral chains and self-assembled adipate ligands between Eu-O layers. Compound 2 has dimeric Eu(2)O(16) units interconnected by adipate ligand, resulting in 2-D open frameworks with a cavity among the ligands. Crystal data 1: monoclinic space group C2/c, with a = 14.2486(12) A, b = 8.2733(7) A, c = 39.298(2) A, beta = 99.530(6) degrees, and Z = 8. 2: monoclinic space group P2(1)/c, with a = 11.661(4) A, b = 14.011(3) A, c = 9.013(4) A, beta = 110.87(3) degrees, and Z = 2. The ligand conformations of two Eu(III)-adipate (1 and 2) compounds present anti/anti/anti, gauche/anti/gauche, and intermediate forms. Both compounds 1 and 2 showed strong red luminescence upon excitation, and their luminescence decay involves the multiphonon relaxation mechanism.

The temperature dependence of radiative and nonradiative processes at Er–O centers in Si

Er-doped silicon is a promising material for silicon microphotonics light sources. Luminescence from Er–O centers in silicon exhibits an intensity quenching as the temperature is raised from 4 to 300K. We present the first unified description of the excitation and de-excitation processes over the entire temperature range. We model the phenomena in terms of exciton Auger, impurity Auger, and multiphonon transition processes. A set of rate equations that includes all of these processes is written to describe the energy transfer, and the normalized luminescence intensity versus temperature is computed and compared to experimental data. The proposed model fits the experimental photoluminescence data over the entire temperature range. Junction photocurrent spectroscopy measurements confirm the presence of a non-radiative multiphonon backtransfer mechanism. The photocurrent generated from the direct optical excitation of Er centers was found to increase with temperature in the form expected from the energy backtransfer model.

Effect of Ligand Deuteration on the Decay of Eu3+(5D0) in Tris(2,2,6,6-tetramethyl-3,5-heptanedionato)europium(III)

Contributions to the first-order rate constant for the decay of the Eu3+(5D0) state of tris(2,2,6,6-tetramethyl-3,5-heptanedionato)europium(III), Eu(thd)3, from radiative and multiphonon mechanisms are evaluated independently by measuring the luminescence decay rates in undeuterated Eu(thd)3, fully deuterated Eu(thd-d19)3, and α-deuterated Eu(thd-d1)3, which is also designated Eu(α-D,thd)3. In the latter case, deuterium substitution is at the α-carbon, between the carbonyl groups of the β-diketonate ligand. These measurements yield a multiphonon contribution of 332 s-1, of which 157 s-1 is attributed to relaxation via the Cα−H stretching vibration and 175 s-1 to relaxation via the C−H stretching modes of the tert-butyl groups. By use of the measured total Eu3+(5D0) relaxation rate constant and the multiphonon rate constants given above, the Eu3+(5D0) radiative relaxation rate constant is inferred to be 1930 s-1. It is suggested that this unusually high radiative rate constant may be due to an increased allowedness in the 5D0 → 7FJ transitions due to contributions to the predominantly 4f crystal-field wave functions from a low-lying ligand-to-metal charge-transfer state.

Spectroscopic studies and crystal-field analysis of U3+ ions in RbY2Cl7 single crystals

Single crystals of U3+ diluted into a matrix of RbY2Cl7 have been grown by the Bridgman–Stockbarger method. There are two different intrinsic U3+ sites in this crystalline host, each with an approximate C2v site symmetry. A third minor U3+ site was also found. Absorption, fluorescence, and excitation spectra of these crystals were obtained at 300 and 4.2 K. Transitions belonging to each U3+ site were distinguished by time-gated site-selective spectroscopy. The energy levels of the two intrinsic sites were assigned and fitted to a semiempirical Hamiltonian representing the combined atomic and crystal-field interactions for a 5f3 ion at a C2v symmetry site. Quite different 4F9/2 fluorescence lifetimes were measured for the three sites, due to a multiphonon decay mechanism which is affected by differences in their respective crystal-field strengths. These results are analyzed quantitatively using the theory for the electron–phonon interaction.

Capture Process by Shallow Donors in Silicon at Low Temperatures

Thermal capture by shallow attractive impurities has been studied by the Monte Carlo method at low temperatures. In order to model this process, the perturbation produced by the highest excited impurity states associated to the ideal Coulombic potential and the multiphonon mechanism were combined in the same simulation procedure. These excited states are considered to produce an energy quasicontinuum or impurity band where the carrier can move assisted by lattice phonons. To characterize the ground-state capture, the transition rates of multiphonon transitions from the impurity band and from the conduction band have been included. Electron capture cross sections have been calculated as a function of the temperature and compared compared with experimental data from the P + , As + and Sb + shallow donors in Si, achieving a good fitting with the Huang-Rhys factor, S, as the only free parameter.

Monte Carlo simulation of multiphonon capture mechanism by deep neutral impurities in Si in the presence of an electric field

The multiphonon emission capture mechanism by neutral centers, in the presence of an electric field below 1 MV/cm, has been numerically simulated by the Monte Carlo method. Based on common models for the initial and final states, a simple expression of the process probability has been calculated considering both nonpolar and polar electron–phonon coupling. The validity range of this expression is assumed for a carrier energy Ek<ET, where ET is the impurity level depth. In order to check the probability rate, this mechanism was included in the framework of a previous numerical procedure as one more mechanism for calculating the capture cross section as an electric-field function. This theoretical framework is given for both polar and nonpolar semiconductors. The Pt and Au acceptor levels in Si have been analyzed with the probability expression, particularized for the case of nonpolar coupling, by fitting the available experimental data of capture cross sections with the numerical results. In both cases, the values of the Huang–Rhys parameter have been confirmed with the experimental measurements and previous theoretical calculation without the applied field. According our calculations, the experimentally observed decrease of the cross sections at high fields is attributed to carrier heating. In the range of temperatures from 77 to 300 K, the dependence of the numerical capture cross sections appears as E−3/2 with a field between 5×104 V/cm and 1 MV/cm. The temperature dependence change of the numerical cross section at high electric field is also caused by electron heating.

Non-radiative relaxation processes of the Pr3+ ion

The3P0→1D2 non-radiative decay rates ANR of Pr3+ and the transition probabilities AVIB for the vibronic3H4→3P0 excitation transitions of Pr3+ were measured at 4.2 K in several host lattices. Besides the well-known dependence on the number of phonons involved in the radiationless transition, the multiphonon relaxation rates are observed to be greatly enhanced by increasing covalency and/or decreasing Pr-ligand distances. The enhanced multiphonon relaxation is ascribed to a stronger electron-phonon coupling. The increase in the electron-phonon coupling strength is confirmed by the increase of the vibronic transition probabilities AVIB in the same sequence as the ANR rates. The observed host lattice dependence of ANR can be qualitatively accounted for by a non-linear multiphonon relaxation mechanism. Under certain conditions (viz. low-lying 4f5d states, and a force constant stronger in the 4f5d than in the 4f2 states) fast3P0→1D2 non-radiative relaxation via intersystem crossing through the 4f5d state becomes the dominant relaxation mechanism, even at 4.2 K.

Comprehensive Monte Carlo simulation of the nonradiative carrier capture process by impurities in semiconductors

The main nonradiative capture mechanisms, cascade and multiphonon emission, have been numerically simulated by the Monte Carlo method. To do so, both mechanisms were included in the frame of a previous numerical procedure to which the nonacoustic-phonon contribution was also added. Different centers were studied. Capture by shallow donors (P, As, and Sb) in n-type silicon were interpreted considering only the cascade process. Capture by acceptors levels of platinum, gold, and titanium in silicon, and one level of Cr, EL2, and EL3 in gallium arsenide, were analyzed considering only multiphonon emission, and calculating the values of Huang–Rhys factor when it is not available. In the study of capture by attractive deep centers, such as single ionized donor centers of sulfur and selenium in silicon, both cascade and multiphonon mechanisms must be combined. In this case the importance of the nonacoustic phonon has been shown in the cascade process.

Multiphonon mechanism of neutron scattering in glasses

A multiphonon mechanism of neutron scattering in glasses is considered. It is due to the interaction of the neutrons with strongly fluctuating double-well potentials characteristic of glasses which may be of importance at not too low temperatures (above the liquid helium temperature). The cross section of this process is calculated and its dependence on the temperature and the neutron energy transfer is found. It is shown that, contrary to the relaxation mechanism, the multiphonon mechanism produces a cross section without a maximum in its temperature dependence. This, as well as some other features, corresponds better to the experimental observations.

Multiphonon mechanism of light scattering in glasses

The absorption of electromagnetic waves and Raman scattering in glasses are calculated. The principal scattering mechanism considered is the interaction of the electromagnetic waves with atoms tunnelling in strongly fluctuating double-well potentials which are characteristic of glasses. The temperature and frequency dependences of the absorption coefficient and the cross section of the small frequency shift Raman scattering are obtained. The results are fitted to the experimental data.

Vibrational relaxation of ammonia trapped in rare gas matrices

A theory of the vibrational energy relaxation of a symmetric top molecule trapped in a rare gas matrix is presented. The direct relaxation mechanisms of the energy on the molecular orientation and on the lattice vibrations (including the local modes) are described within the framework of the nonadiabatic coupling between the internal vibrational mode of the molecule and the low-frequency external modes. The three types of relaxation constants are analyzed. The transfer to the orientational modes of the molecule is shown to be the more efficient since the corresponding relaxation time ranges between 1 μs and 50 ns, according to the nature of the rare gas matrix and to the temperature. The multiphonon relaxation constant is calculated for two specific deexcitation channels. The phonon multimode process provides relaxation times which range between 1 ms and 10 μs. Such a process is a characteristic of the nonadiabatic treatment of the total Hamiltonian. In contrast, the multiphonon monomode process, where the vibrational energy is transferred to the vibration of the center of mass of the molecule, gives larger relaxation times around 1 ms. This process is connected to the high orders in the interaction potential anharmonicity. The third species of relaxation constant which mix the orientational and translational processes is also analyzed for various typical relaxation channels. The corresponding relaxation times are one order of magnitude longer than those obtained from the multiphonon mechanisms. The calculated relaxation times are close to the experimental measurements and exhibit the same trends with rare gas changes and temperature rises.

Tunnel modes and kinetic properties of glasses at low and high temperatures

A theoretical approach is presented intending to unify tunnel model and structural defect concepts existing in the theory of amorphous solids. Origins of double-well potentials (DWP) are discussed and two types of DWPs-soft and rigid-are emphasised. Soft DWPS are mainly responsible for low-temperature properties whereas rigid DWPs determine the properties of glasses at higher temperatures. Tunnelling in rigid DWPs is largely influenced by the barrier fluctuative preparation, the multi-phonon processes are of importance at higher temperatures. The DWP relaxation time up to room temperature is analysed. The sound attenuation due to the relaxation and multi-phonon mechanisms is calculated and their relative contributions are compared. The role of these processes in the thermal conductivity and temperature plateau formation is discussed.

Properties of iron related quenched-in levels in p-silicon

The electrical and optical properties of the thermally induced quenched-in levels in p-silicon which have heen attributed to iron are studied. The two levels, HI and H2, are located at Ev + 0.42 eV and Ev + 0.52 eV, respectively, as determined by TSCAP, DLTS, and transient photocapacitance methods. The photoionization cross sections are well described by Lucovsky's model. The hole capture by H1 is temperature dependent; a barrier of 40 meV is measured. However, multiphonon emission mechanism cannot be invoked to explain this temperature dependence due to the inferred zero lattice relaxation. The source of iron contamination is found to be the ambient conditions, in particular the quartz tube. The conflicting reports regarding the stability and the variation in the reported capture cross section values suggests that the observed Ev + 0.4 eV level must be a complex centre. The inferred near zero lattice relaxation during the electron transition implies weak coupling to the host lattice.

Time-resolved measurements of OH(v=1) vibrational relaxation on SiO2 surfaces: Isotope and temperature dependence

Picosecond infrared spectroscopy was used to measure the vibrational energy relaxation time T1 of OH(v=1) and OD(v=1) groups chemisorbed on silica surfaces over the temperature range 100≤T≤800 K. The observed T1 times and their temperature dependencies are discussed in terms of a multiphonon relaxation mechanism. Limiting low temperature lifetimes are T1=220±20 ps (1σ) for OH(v=1) and T1=149±10 ps for OD(v=1).