Formation and diffusion of self-interstitial atoms in silicon crystals under hydrostatic pressure: Quantum-chemical simulation

A theoretical modeling of the formation of Frenkel pairs and the diffusion of a self-interstitial atom in silicon crystals at normal and high (hydrostatic) pressures has been performed using molecular dynamics, semiempirical quantum-chemical (NDDO-PM5, PM6), and ab initio (SIESTA) methods. It is shown that, in a silicon crystal, the most stable configuration of a self-interstitial atom in the neutral charge state (I ⁰) is the split configuration 〈110〉. The shifted tetrahedral configuration (T ₁) is stable in the singlet and triplet excited states, as well as in the charge state Z = +2. The split 〈110〉 interstitial configuration remains stable under hydrostatic pressure (P ≤ 80 kbar). The activation barriers for diffusion of self-interstitial atoms in silicon crystals are determined to be as follows: ΔE _a (Si)(〈110〉 → T ₁) = 0.59 eV, ΔE _a (Si)(T ₁ → T′₁) = 0.1 eV, and ΔE _a (Si)(T ₁ → 〈110〉) = 0.23 eV. The hydrostatic pressure (P ≤ 80 kbar) increases the activation barrier for diffusion of self-interstitial atoms in silicon crystals. The energies of the formation of a separate Frenkel pair, a self-interstitial atom, and a vacancy are determined. It is demonstrated that the hydrostatic pressure decreases the energy of the formation of Frenkel pairs.     

Electronic structure of substitutional defects and vacancies in GaSe

We have investigated the nature of defect states associated with substitutional impurities (Cd, In, Sn) and both Ga and Se vacancies in GaSe using ab initio electronic structure methods within density functional theory. These calculations were done using supercell model allowing for internal atomic relaxation. Binding energies (BEs) of defects obtained in this model are compared with effective mass approximation results. Significant central cell corrections are present for most of the defects. This is consistent with charge densities associated with the defect states that show clearly their strongly localized nature. Because of the difficulties associated with LDA/GGA in giving the correct band gap in semiconductors, we have only compared the acceptor BEs with available experiments. Our theoretical results agree well with the experiment for Cd_Ga and V_Ga. The fundamental role played by the Ga dimers in the formation of defect states is discussed.     

Electrical properties and diffusion behavior of hafnium in single crystal silicon

Electrical properties and diffusivity of Hf in single crystal Si have been studied. Several deep level defects were found for Hf in both the upper and lower half of the silicon band gap, and their parameters were measured. Energy levels, concentrations, and capture cross sections were determined for all Hf defects. The DLTS spectra depend on the cooling rate. Analysis of electrical properties yielded a dominant deep level defect at E_C -0.27 eV, which showed field enhanced emission due to Poole–Frenkel effect, confirming its donor nature. This agreed with results obtained using CV and TSCAP. In the lower half of the bandgap, a defect level at E_V +0.24 eV was found to have a capture barrier of 0.04 eV. Diffusivity of Hf was studied using two methods for Hf incorporation in Si – ion implantation and sputtering. Analysis of broadening of the Hf profile in implanted samples, which were annealed for 168 h, allowed us to estimate the diffusivity of Hf as 1.7×10^-15 cm²/s at 1250 °C: the spreading of implanted profiles at lower temperatures was too small. Analysis of Hf depth profiles in the sputtered and annealed samples reveals that Hf appears to have a fast and slow component to its diffusivity whose migration energy was determined to be 3.5±0.3 eV and 4.1±0.3 eV respectively. The fast and slow component are ascribed to interstitial and substitutional Hf with an energy level of E_C -0.27 eV and E_V +0.43 eV respectively. The mechanism for the fast component seems to indicate a direct interstitial diffusion mechanism whereas the diffusion of the substitutional Hf seems most consistent with the concerted exchange diffusion mechanism. In addition, estimates of solubility for both, interstitial and substitutional Hf, are included. PACS 61.72.Tt; 66.30.Jt; 71.55.Cn     

Ionization of iridium ions in the Dresden EBIT studied by X-ray spectroscopy of direct excitation and radiative recombination processes

Ir^q+ ( 41≤q≤64) ions with open-shell configurations have been produced in the electron beam of the room-temperature Dresden Electron Beam Ion Trap (Dresden EBIT) at electron excitation energies from 2 keV to 13 keV. X-ray emission from direct excitation processes and radiative capture in krypton-like to aluminium-like iridium ions is measured with an energy dispersive Si(Li) detector. The detected X-ray lines are analyzed and compared with results from multiconfigurational Dirac-Fock (MCDF) atomic structure calculations. This allows to determine dominant produced ion charge states at different electron energies. The analysis shows that at the realized working gas pressure of 5×10^-9mbar for higher charged ions the maximum ion charge state is not preferently determined by the chosen electron beam energy needed for ionization of certain atomic substates, but by the balance between ionization and charge state reducing processes as charge exchange and radiative recombination. This behaviour is also discussed on the basis of model calculations for the resulting ion charge state distribution. Received 12 July 2001 and Received in final form 10 September 2001     

Molecular picture of excited states and fragmentation paths of the Na 5 F 4 cluster

The stability against fragmentation and possible relaxation of the lowest excited states of the Na₅F₄ cluster (representative of cubic non stoechiometric clusters with an excess sodium atom, also called sodium-tail) is investigated by means of one-electron pseudopotential calculations with particular reference to photoabsorption processes from the ground state. Whereas the equilibrium configuration of the ground state has C_3v symmetry, the doubly degenerate 1²E excited state is affected by a conical intersection and a Jahn-Teller effect associated with the rotation of the sodium tail around the C₃-axis. This yields a “Mexican hat" topology for the lowest sheet with three equivalent C_s minima. Alternatively the 2²A₁ state has a minimum retaining the C_3v symmetry. The dissociation paths of the cluster along the C₃-axis into respectively Na₄F_{4 +} Na and Na₄F_{3 +} NaF are also investigated. Among the former paths, the excited states are found adiabatically stable with respect to the products. However in the A₁ symmetry, fragmentation into NaF exhibits an interesting avoided crossing between configurations correlated respectively with Na₄F₃ ^{+ +} NaF^- and Na₄F_{3 +} NaF. Such interaction, similar to the well-known charge exchange processes in elementary molecules might induce non adiabatic predissociation of the 2²A₁ state. This mechanism is invoked to explain the differences between R2PI and depletion spectra, correlated with the dissociation or relaxation of the excited states. Received 24 March 2000 and Received in final form 11 July 2000     

Impacts of fluorine on GaN high electron mobility transistors: Theoretical study

We investigate the role of fluorine (F) in GaN‐based high electron mobility transistors (HEMTs) with first principle calculations. Formation energy calculations of F in GaN and AlN reveal that energetically favored interstitial F (F_i) and substitutional F at N sites (F_N) could play important roles in the performance of HEMTs. F_i is responsible for positive threshold voltage (V_th) shift by forming F^– anion and depleting 2DEG carriers. The degradation of device performance at high temperature is ascribed to the defect energy state near conduction band edge of F_N. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Diffusion of interstitial Mn in the dilute magnetic semiconductor (Ga,Mn)As: the effect of a charge state

Migration barriers for diffusion of interstitial Mn in the dilute magnetic semiconductor (Ga,Mn)As are studied using first-principles calculations. The diffusion pathway goes through two types of interstitial sites: As coordinated and Ga coordinated. The energy profile along the path is found to depend on the ratio of concentrations between substitutional and interstitial Mn in GaAs. Two regions of distinctly different behavior, corresponding to n-type and p-type (Ga,Mn)As, are identified. The difference in mobility is a reflection of the change in the charge state of Mn interstitials (double donors) that occurs in the presence of substitutional Mn impurities (acceptors). In addition, substitutional Mn impurities are shown to act as traps for interstitial Mn. The effective migration barrier for the positively doubly charged Mn interstitials in p-type (Ga,Mn)As is estimated to vary from 0.55 to about 0.95 eV.     

Electronic and annealing properties of the E0.31 defect introduced during Ar plasma etching of germanium

Low energy (±80 eV) Ar plasma etching has been successfully used to etch several semiconductors, including GaAs, GaP, and InP. We have studied the only prominent defect, E_0.31, introduced in n-type Sb-doped Ge during this process by deep level transient spectroscopy (DLTS). The E_0.31 defect has an energy level at 0.31 eV below the conduction band and an apparent capture cross-section of 1.4×10⁻¹⁴ cm². The fact that no V-Sb defects and no interstitial-related defects were observed implies that the etch process did not introduce single vacancies or single interstitials. Instead it appears that higher order vacancy or interstitial clusters are introduced due to the large amount of energy deposited per unit length along the path of the Ar ions in the Ge. The E_0.31 defect may therefore be related to one of these defects. DLTS depth profiling revealed the E_0.31 concentration had a maximum (6×10¹³ cm⁻³) close to the Ge surface and then it decreased more or less exponentially into the Ge. Finally, annealing at 250 °C reduced the E_0.31 concentration to below the DLTS detection limit.     

Lattice defects of V3Si single crystals studied by positron annihilation

The sensitivity of positrons to point defects created by the irradiation of V₃Si with neutrons is demonstrated. We found no indication of thermal vacancies by thermal equilibrium measurement up to 1273 K which indicates that the monovacancy formation enthalpy for V₃Si isH _1V ^F ≧(1.84±0.14) eV. Investigations within the range of homogeneity for excess vanadium suppot the idea that substitutional defects are the dominating defect type, whereas for excess silicon a direct confirmation of existing structural vacancies as the dominating defect type is given.     

First-Principles Study of Defects in CuGaO2

Using the first-principles methods, we study the electronic structure, intrinsic and extrinsic defects doping in transparent conducting oxides CuGaO₂. Intrinsic defects, acceptor-type and donor-type extrinsic defects in their relevant charge state are considered. The calculation result show that copper vacancy and oxygen interstitial are the relevant defects in CuGaO₂. In addition, copper vacancy is the most efficient acceptor. Substituting Be for Ga is the prominent acceptor, and substituting Ca for Cu is the prominent donors in CuGaO₂. Our calculation results are expected to be a guide for preparing n-type and p-type materials in CuGaO₂.     

Fractionally charged excitations in the charge density wave state of a quarter-filled t-J chain with quantum phonons

Elementary excitations of the 4k _F charge density wave state of a quarter-filled strongly correlated electronic one-dimensional chain are investigated in the presence of dispersionless quantum optical phonons using Density Matrix Renormalization Group techniques. Such excitations are shown to be topological solitons carrying charge e/2 and spin zero. Relevance to the 4k _F charge density wave instability in (DI - DCNQI)₂ A g or recently discovered in (TMTTF)₂X ( X=PF ₆, AsF₆) is discussed. Received 30 March 2001 and Received in final form 11 May 2001     

Spin susceptibility in small Fermi energy systems: effects of nonmagnetic impurities

In small Fermi energy metals, disorder can deeply modify superconducting state properties leading to a strong suppression of the critical temperature T_c. In this paper, we show that also normal state properties can be seriously influenced by disorder when the Fermi energy E _F is sufficiently small. We calculate the normal state spin susceptibility χ for a narrow band electron-phonon coupled metal as a function of the non-magnetic impurity scattering rate . We find that as soon as is comparable to E _F, χ is strongly reduced with respect to its value in the clean limit. The effects of the electron-phonon interaction including the nonadiabatic corrections are discussed. Our results strongly suggest that the recent finding on irradiated MgB₂ samples can be naturally explained in terms of small E _F values associated with the σ-bands of the boron plane, sustaining therefore the hypothesis that MgB₂ is a nonadiabatic metal. Received 31 July 2002 / Received in final form 21 September 2002 Published online 31 December 2002     

Suppression of boron segregation by interface Ge atoms at SiGe/SiO2 interface

We investigate the migration pathway and barrier for B diffusion at SiGe/SiO₂ interface through first-principles density functional calculations. Similar to the diffusion mechanism reported for Si/SiO₂ interface, a substitutional B, which initially forms a B-self-interstitial complex in SiGe, diffuses to the interface and then to the oxide in form of an interstitial B. At the defect-free interface, where bridging O atoms are inserted to remove interface dangling bonds, it is energetically more favorable for the interstitial B to intervene in the Ge–O bridge bond rather than the Si–O bridge bond at the interface. As a result of the B intervention, interface Ge atoms significantly enhance the stability of B-related defects in the interface region and thereby act as traps for B dopants. At the interface with the Ge–O bridge bond, the overall migration barrier for B diffusion from SiGe to SiO₂ is estimated to be about 3.7 eV, much higher than the reported value of about 2.1 eV at Si/SiO₂ interface. Our results provide a clue to understanding the experimental observation that B segregation toward the oxide is suppressed in SiGe/SiO₂ interface.     

First‐principles study of the electronic structure and the associated magnetism of carbon‐doped TiO2

Based on first‐principles calculations, the electronic structure and the associated magnetism of carbon‐doped rutile TiO₂ have been investigated in the frame of the generalized gradient approximation (GGA). We find that the carbon substitutional oxygen ions can induce a magnetic moment of about 2.0µ_B/C, but the carbon substitutional titanium cannot provide any magnetism. Graphics of the spin density show that the magnetism is from the structure distortion around the carbon substitutional oxygen ions in the (110) plane of primitive TiO₂. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Formation of E4-Centers (E c – 0.76 eV) in Gallium Arsenide

The paper deals with the effects of the bombarding-electron energy on the velocity of E4 center (E _c – 0.76 eV) formation and the temperature dependences of the efficiency of the latter in a neutral volume and the space-charge region of n–type gallium arsenide. The specimens were Schottky diodes manufactured by depositing titanium onto epitaxial layers of n-GaAs with n = (2–4)·10¹⁵ cm³. The defect concentration was obtained by the DLTS spectroscopy method. It is shown that the number of E4 centers in the total amount of irradiation-induced defects sharply increases with increasing the bombarding-electron energy from 1.3 to 2.2 MeV. It is found out that the velocity of introducing E4 centers into the space-charge region does not depend on irradiation temperature and is by far higher than that in a neutral volume. In the latter, however, this velocity is non-linearly increasing with the irradiation temperature. It is assumed that an E4 center is a complex consisting of two unit defects generated in the adjacent sites of the Ga and As sublattices through a single collision. It is noted that its final configuration is formed as a result of interaction of these defects, which depends on the dynamics of transformation of their primary charge states.     

Interplay of local structure and magnetism in Co-doped TiO2 anatase

We report ab initio density-functional theory investigations on the local structure and magnetization of Co ions doped in TiO₂ anatase. The calculated formation energy of the pair of substitutional Co ions indicates that they have a tendency to cluster; but clustering has no noticeable effect on the low-spin state of Co. The interstitial Co, which is energetically unstable in reference to bulk cobalt, is found to be strongly attracted to a substitutional Co, and even more strongly to a substitutional Co pair. Interestingly, in a one-to-one binding, the interstitial Co enhances the magnetization of the two; whereas in a one-to-two binding, it destroys the magnetic moment of the substitutional Co pair and therefore reduces the average magnetic moment of Co ions. Our results could explain the strong sample-to-sample variability of the magnetic moment of Co measured in experiments. The magnetic interaction between substitutional and interstitial Co is discussed with bonding analysis.     

The role of Co impurities and oxygen vacancies in the ferromagnetism of Co-doped SnO2: GGA and GGA+U studies

The electronic structure and ferromagnetic stability of Co-doped SnO₂ are studied using the first-principle density functional method within the generalized gradient approximation (GGA) and GGA+U schemes. The addition of effective U_Co transforms the ground state of Co-doped SnO₂ to insulating from half-metallic and the coupling between the nearest neighbor Co spins to weak antimagnetic from strong ferromagnetic. GGA+U_Co calculations show that the pure substitutional Co defects in SnO₂ cannot induce the ferromagnetism. Oxygen vacancies tend to locate near Co atoms. Their presence increases the magnetic moment of Co and induces the ferromagnetic coupling between two Co spins with large Co-Co distance. The calculated density of state and spin density distribution calculated by GGA+U_Co show that the long-range ferromagnetic coupling between two Co spins is mediated by spin-split impurity band induced by oxygen vacancies. More charge transfer from impurity to Co-3d states and larger spin split of Co-3d and impurity states induced by the addition of U_Co enhance the ferromagnetic stability of the system with oxygen vacancies. By applying a Coulomb U_O on O 2 s orbital, the band gap is corrected for all calculations and the conclusions derived from GGA+U_Co calculations are not changed by the correction of band gap.     

Numerical results for ground states of spin glasses on Bethe lattices

The average ground state energy and entropy for ±J spin glasses on Bethe lattices of connectivities k + 1 = 3..., 26 at T = 0 are approximated numerically. To obtain sufficient accuracy for large system sizes (up to n = 2¹²), the Extremal Optimization heuristic is employed which provides high-quality results not only for the ground state energies per spin e_k+1 but also for their entropies s_k+1. The results indicate sizable differences between lattices of even and odd connectivities. The extrapolated ground state energies compare very well with recent one-step replica symmetry breaking calculations. These energies can be scaled for all even connectivities k + 1 to within a fraction of a percent onto a simple functional form, e _{k + 1} = E _SK - (2E _SK + )/, where E _SK = - 0.7633 is the ground state energy for the broken replica symmetry in the Sherrington-Kirkpatrick model. But this form is in conflict with perturbative calculations at large k + 1, which do not distinguish between even and odd connectivities. We also find non-zero entropies per spin s_k+1 at small connectivities. While s_k+1 seems to vanish asymptotically with 1/(k + 1) for even connectivities, it is numerically indistinguishable from zero already for odd k + 1 ≥ 9. Received 9 August 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: sboettc@emory.edu www.physics.emory.edu/faculty/boettcher     

Locations of implanted 19F* atoms in Si,Ge and diamond studied through their nuclear quadrupole interactions

The Hartree-Fock cluster procedure was used to obtain the associated electronic distributions for ¹⁹F^* (I = 5/2, E ^x = 197 KeV excited nuclear state of the ¹⁹F atom) at possible sites in crystalline Si, Ge and diamond and to calculate nuclear quadrupole coupling constants v _Q and the asymmetry parameter η of the electric field gradient at the modelled sites. Lattice relaxation effects have been incorporated by employing a geometry optimization method to obtain minimum energy configurations for the clusters modelling each site. The intrabond (IB), antibonding (AB) and substitutional (S) sites in the bulk and the atop site on the surface were studied. From a comparison with v _Q and η values observed in time differential perturbed angular distribution (TDPAD) measurements we were able to identify the high frequency component in Si and Ge with ¹⁹F^* at the intrabond site. In diamond two high frequency components are observed. These are identified with ¹⁹F^* at intrabond and substitutional sites. For the low frequency site in Si and Ge the assignment is made to ¹⁹F^* implants at dangling bonds in the bulk resulting from implantation damage. In diamond none of the sites studied could provide lower frequency nuclear quadrupole parameters close to the observed ones. This revised version was published online in August 2006 with corrections to the Cover Date.