Broken Bond Model Research Articles

Germanium negative-U center in GaAs.

The DX center related to the Ge impurity in GaAs is investigated by ab initio pseudopotential calculations within the local-density aproximation. Our results indicate that the behavior of the ${\mathrm{Ge}}_{\mathrm{Ga}}$ defect is qualitatively different from the broken-bond model usually associated to ${\mathrm{Si}}_{\mathrm{Ga}}$, even if the electronic structure behaves in a very similar way. Indeed, for the Ge impurity our calculations show that already for breathing-mode relaxations of the Ge neighbors, in ${\mathit{T}}_{\mathit{d}}$ symmetry, a negative-U behavior is found, and many details of the experimental data can be explained. \textcopyright{} 1996 The American Physical Society.

On the surface segregation of silicon in Cu 3Si

Silicon segregates to a large extent to the surface of a Cu 3Si alloy stabilized at 700 K. The top layer contains as much as 70 at% Si, the second and third layers are also significantly enriched in silicon. Such a phenomenon could largely account for the renewal of the surface layers of the silicide as the silicon is consumed during the direct synthesis (of methylchlorosilane by reaction with methyl chloride). As demonstrated by calculations of the segragation free enthalpy based on the broken-bond model, the difference in surface tension between Cu and Si is the main driving force involved in the observed segregation.

MICROSCOPIC ORIGIN OF THE DX CENTER IN GaAs AND AlxGa1−xAs

The DX center in n-type Al x Ga 1−x As has been studied over the past two decades because of technological importance and physical interest. We review from the theoretical side the development of studies on the microscopic origin of the DX center. Recent studies based on the state-of-the-art technique calculations especially focus on the neutral onsite and negatively charged broken-bond models among many models proposed so far. It has not been confirmed from total energy calculations which model is energetically stable. Many theoretical efforts, however, reveal that the broken-bond model reproduces a variety of experimental results for the DX center and is hence the best candidate.

Energetics and local vibrations of the DX center in GaAs.

The negatively charged broken-bond geometry is a strong candidate for the microscopic origin of the DX center in GaAs but the validity of the broken-bond model is still controversial. We thus examine the model for the Si-related DX center, performing large-scale supercell calculations within the local-density approximation. The highly efficient conjugate-gradient minimization technique is combined with the norm-conserving-pseudopotential method in order to include both short-range and medium-range lattice relaxations. First, we compare the total energy of the broken-bond geometry with that of the negatively charged on-site geometry, which is also a candidate for the DX center. It is found that the broken-bond geometry has a lower total energy, supporting the broken-bond model for the DX center. Second, the barrier height for the broken-bond geometry is found to be comparable to observed emission barriers for the DX center. Third, the broken-bond model is shown to be consistent with results of a Fourier-transform infrared-absorption measurement for the local vibrational frequency of Si in pressurized GaAs, although the neutral on-site model also reproduces the experimental results within the calculational accuracy. Most of the results in this work indicate that the broken-bond model is consistent with experiments. Finally, we find that the broken-bond model with the neutral charge state is unstable and thus expect that the Si atom moves to the substitutional site after the DX center is photoexcited.

Surface segregation study of a dilute Pd 1Fe 99 alloy by LEIS and XPS

Pd segregates to a large extent to the surface of a Pd 1Fe 99 alloy stabilized at 870 K. The outer layer composition contains as much as 55 ± 5 at% Pd as deduced from LEIS data. Complementary XPS measurements performed at various exit angles with respect to the surface indicated that the Pd enrichment extends to more than one layer below the very surface. A calculation of the segregation free enthalpy based on the broken bond model using macroscopic thermodynamic data, allows us to describe the concentration equilibrium between the first and second layers well.

Surface segregation study of a diluted Pd 1Fe 99 alloy by LEIS and XPS

Abstract Pd segregates to a large extent to the surface of a Pd1Fe99 alloy stabilized at 870 K. The outer layer composition contains as much as 55 ± 5 at% Pd as deduced from LEIS data. Complementary XPS measurements performed at various exit angles with respect to the surface indicated that the Pd enrichment extends to more than one layer below the very surface. A calculation of the segregation free enthalpy based on the broken bond model using macroscopic thermodynamic data, allows us to describe the concentration equilibrium between the first and second layers well.

Trapping of Molecular Hydrogen in Porous Silicon and at Si/SiO2 Interfaces and a Possible Reinterpretation of the Pb Center

AbstractMany recent studies of the highlighted problem of visible-range photoluminescence of porous silicon (po-Si) indicate the presence of hydrogen in this material. However, its actual role is not clear with the discussed possibilities ranging from passivation of the surface defects to some form of active participation in the photoluminescence (PL) mechanism itself. At the same time, in several magnetic resonance studies of po-Si the so-called Pb center, originally identified with the <111>-directed silicon broken bond stabilized at Si/SiO2 interfaces, has been reported.Very recently the paramagnetic state of molecular hydrogen in bulk silicon has been identified. The spin-Hamiltonian parameters of the related Si-NL52 EPR spectrum appear to be identical to those of the Pb center. This observation casts severe doubts on the original interpretation of the Pb center while, on the other hand, offering new evidence of a prominent presence of hydrogen molecules both in po-Si and at the Si/SiO2 interface. In this paper the similarities of Si-NL52 and Pb centers are examined in detail, and it is argued that the centers are the same. It is concluded that many features of the Pb center which could not be explained within the broken-bond model can be understood with the interstitial hydrogen molecule model.

On the interaction between steps in vicinal fcc surfaces: I. Steps along 〈001〉

Atomistic computer simulations are used to study the zero-temperature interaction between steps in vicinal free fcc surfaces in order to test the continuum-elastic theory of Marchenko and Parshin (MP). Two different types of surface steps, both parallel to 〈001〉 but situated, respectively, on the (100) and (110) planes, are investigated using two qualitatively different interatomic potentials, one of the embedded-atom-method type and the other the Lennard-Jones potential. In agreement with the MP theory, for the largest step separations δ the energy due to the step-step repulsion is found to decrease as δ −2, with a strength given by the surface-stess tensor and the elastic moduli of the material. Surprisingly, for both potentials and for both types of steps the δ −2 power law appears to be obeyed even for the smallest step separations, albeit with a 2–3 times smaller interaction strength. The relationship of our simulation results with a nearest-neighbor broken-bond model is also explored.

Validity of the broken-bond model for the DX center in GaAs.

The validity of the broken-bond model for the DX center is examined by performing supercell calculations within the local-density approximation for column-IV donors in GaAs. We confirm that the broken-bond geometry is the most stable among the atomic structures accompanied with large lattice relaxation. The calculated bond length between the dopant and the As atoms as frequency of the local vibrational model (LVM) in the broken-bond geometry agree with extended-x-ray absorption-fine-structure and Fourier-transform--infrared-absorption measurements, respectively, supporting the broken-bond model for the DX center. Furthermore we predict from the present calculation that there exists another infrared light active LVM with 274 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in the broken-bond geometry. Detection of this mode would be clear evidence for the broken-bond model of the DX center.

Solid-liquid interfacial free energy

The solid-liquid interfacial free energy has been estimated by a broken-bond model modified to take the entropy loss of the liquid in contact with the crystal into account. The predictions for f.c.c., h.c.p., b.c.c., diamond and s.c. structures are compared with experimental data from supercooling and dihedral angle measurements.

A broken-bond model for grain boundaries in face-centered cubic metals

The interrelation between the number of nearest-neighbor atomic bonds broken upon formation of a grain boundary in an fcc metal and the related zero-temperature boundary energy is investigated by atomistic simulation. Using both a Lennard–Jones and an embedded-atom-method potential, the structures and energies of symmetrical and asymmetrical tilt and twist boundaries are determined. As in free surfaces, a practically linear relationship between the nearest-neighbor miscoordination per unit area of the grain boundary and the related interface energy is obtained. The so-called random-boundary model, in which the interactions across the interface are assumed to be entirely randomized, is shown to provide a basis for understanding the role of broken bonds in both high-angle grain boundaries and free surfaces, thus naturally permitting the analysis of ideal cleavage-fracture energies. A detailed study of low-angle boundaries shows that only the dislocation cores—but not their strain fields—give rise to broken bonds. The complementarity between the dislocation model of Read and Shockley for low-angle boundaries and a broken-bond model for high-angle boundaries is thus elucidated.

D X centers in Si-doped AlxGa1−xAs grown by metalorganic chemical vapor deposition

Three levels corresponding to photo energies E0(=1.7 eV), E1(=1.43 eV), and E2 (=energy gap) were observed in differential photocapacitance measurements of Si-doped AlxGa1−xAs grown by metalorganic chemical vapor deposition (0.23<x<0.4). On the other hand, E1 and E2 were observed but E0 was not observed in the differential photoconductance measurements. Both photon energies E1 and E2 cause persistent photoconductance (PPC) and the electron concentration coincides with the concentration of Si atoms. Our results support the broken-bond model proposed by D. J. Chadi and K. J. Chang [Phys. Rev. B 39, 10063 (1989)].

A theoretical study of adsorption equilibria in silicon CVD

As part of a theoretical study of adsorption processes in the chemical vapour deposition of silicon, thermochemical data are derived for the adsorption of Si-H species on the Si(111) and the dimer-reconstructed Si(001)-(2 x 1) surfaces. Essential contributions to the heats of adsorption appear to be electron pairing and two- and three-body interactions. It is shown that when the bond energies are defined in this way, also a consistent description of the bonds in silicon hydrides is provided. This demonstrates that with reasonable confidence the method can be applied to the adsorption process itself. Data are derived for species which may form one, two or even four bonds with the surface. It is assumed that on the (111) surface adsorbates bind on the “dangling bonds” which are present on this surface in a broken bond model. It is demonstrated that on the dimer reconstructed Si(001)-(2 x 1) surface, adsorbates will either bind on the surface atoms with one or two bonds, without the breaking of the dimer bonds, or, if the species have the possibility to form two or four bonds with the surface atoms, may become inserted into the dimer bonds. With the aid of the derived thermochemical data for adsorption and the Langmuir isotherm or modifications thereof, the coverage of the Si(111) and the dimer reconstructed Si(001)-(2 x 1) surfaces with species from the Si-H system is calculated. It is found that the equilibrium surface coverages of the Si(111) and the Si(001)-(2 x 1) surfaces are very similar: the hydrogen coverage is high at all temperatures, while at low supersaturation the coverage with growth species is very low on both surfaces.

Structural morphology of YBa 2Cu 3O 7- x

The structural morphology of YBa 2Cu 3O 7- x (YBCO) has been investigated by application of the periodic bond chain (PBC) theory. For x=1, the F forms were found to be {001}, {011}, {013}, {112} and {114}. Attachment energies have been calculated in broken bond model and in an electrostatic point charge model. For x=1 the theoretical growth habit is tabular to platy {001} with {011} as side faces. For x=0 {010} also becomes an F form. The habit is isometric with large {001} and {011} and small {010} faces. The outermost layer of {001} contains half of the Cu + ( x=1) or Cu 3+ and O 2- ( x=0) ions in an ordered arrangement based on a c(2x2) quadratic lattice. For the outermost layer of (010) ( x=0) an ordering scheme of the copper and oxygen ions is proposed. The occurrence of {010} rather than {011} on grown crystals has to be ascribed to external factors.

Anisotropy of solid Si-liquid (Al,Si) interfacial tension in the binary and Sr-doped Al-Si eutectic alloy

The atomic structure of interfaces between solid Si and liquid Al-Si alloys with or without Sr doping is derived from measurements of the orientation dependence of the interfacial tension at 873 K. This involves analysing the shape of small liquid droplets inside silicon grains. The results are discussed on the basis of simple broken-bond models and the periodic bond chain concept.

A discrete lattice plane analysis of the energy of coherent {0001} h.c.p. • {111} f.c.c., 〈11 [formula omitted]0〉 h.c.p.• 〈1 [formula omitted]0〉 f.c.c. interfaces

A discrete lattice plane, regular solution, broken bond model, previously used to calculate the interfacial energy of f.c.c.:f.c.c. and b.c.c.:b.c.c. interphase boundaries, is extended to the situation in which there is a change in crystal structure across the interphase boundary, specifically to an interface between an f.c.c. and h.c.p. crystal. The particular interface studied, {0001} h.c.p. • {111} f.c.c., 〈11 2 0〉 h.c.p.• 〈1 1 0〉 f.c.c. was made fully coherent by choosing the appropriate lattice parameter ratio. Both f.c.c. and h.c.p. phases are taken to be regular solutions. Minimization of the grand potential yields a set of non-linear equations in the equilibrium composition of the planes in the interface region whose solute concentration differs from that of the bulk composition in either phase. These values of the compositions are then used to compute the interfacial free energy of the boundary. The variations in the concentration profile and interfacial free energy with temperature and regular solution constants were investigated. The concentration profile was found to be diffuse and also asymmetric. The diffuseness does not vary in any simple manner with temperature. The interfacial energy decreases with increasing temperature in the various situations considered.

Structural morphology of crystals with the barite (BaSO 4) structure: A revision and extension

The structural morphology of crystals with the barite (BaSO 4) structure (sulphates, chromates, perchlorates, permanganates and tetrafluoroborates) has been determined with the use of computer programs. Uniquely defined F forms are {002}, {210}, {211}, {020} and {201}. Two different F slices were found for {101} and {200}, 33 for {011}. Attachment energies and specific surface energies have been calculated for an electrostatic point charge model as a function of the charge distribution in the anion. On this basis it is concluded that {101} behaves as an F form, {200} as an S form and {011} as a K form. The theoretical growth form shows {210}, {101} and {002} as main forms. A comparison is made with habits of natural and synthetic crystals. Experiments on KCIO 4 show that {011} appears at high supersaturations (>38;~;20%). It is shown that a broken bond model provides relative attachment energies that are higher by a factor of about three.

Phase transformations at/near the surface of ordering alloys

Abstract Theoretical calculations have been made to explain surface inherent phenomena of phase transformations at/near the surface of a Ni 4 Mo ordering alloy. In the calculations the broken bond model and the Bragg-Williams approximation are used. The calculated physical quantities are (i) surface energy, (ii) surface free energy, (iii) equilibrium degree of order and (iv) surface nucleation rate. These calculated results explain well surface inherent phenomena observed before by field-ion microscopy.

Phase transformations at/near the surface of ordering alloys

Theoretical calculations have been made to explain surface inherent phenomena of phase transformations at/near the surface of a Ni 4Mo ordering alloy. In the calculations the broken bond model and the Bragg-Williams approximation are used. The calculated physical quantities are (i) surface energy, (ii) surface free energy, (iii) equilibrium degree of order and (iv) surface nucleation rate. These calculated results explain well surface inherent phenomena observed before by field-ion microscopy.

Structural morphology of cotunnite, PbCl 2, laurionite, Pb(OH)Cl, and SbSI

The structural morphology of compounds having the PbCl 2 and the closely related SbSI structures has been determined. Based upon the nine-coordination of the Pb atoms the F forms of the PbCl 2 structure are {110}, {020}, {120}, {011}, {200}, {111} , {201}, {121} and {211}. These forms are arranged in an order of increasing attachment energies, that were calculated using a broken bond model. In the SbSI structure type the Sb atom has a seven-coordination with the consequence that {020} becomes a different surface structure and that {120} is an S face. The theoretical habit of PbCl 2 and Pb(OH)Cl is short prismatic, elongated along the c axis, with {011} as terminal form. The appearance of {211} as main form on PbCl 2 when growth takes place from pure aqueous solution is ascribed to the preferential adsorption of OH - ions on that face. The predominance of {020} and {121} on PbCl 2 from solutions containing HCl is explained by adsorption of H 3O + on these faces. The theoretical habit of the SbSI structure type is slender prismatic {110} with {011} as terminal form.