Model For Surface Segregation Research Articles

C‐Type Relationship between Critical Time and Evaporation Parameter for Surface Segregation in the Case of Evaporation

The relationship between the critical time and evaporation parameter is discussed in terms of the kinetic model for surface segregation in the case of evaporation. An interesting phenomenon is observed that the variation of critical time obeys a C‐type law in kinetic curves with different evaporation parameters. The C‐type law of critical time is found to be caused by that of maximum evaporation flux. The existence of C‐type law is proved by the fitted kinetics curve of the Mg surface segregation of Al–0.8 wt% Mg alloy, which confirms the model of surface segregation in the case of evaporation to be reliable.

Mechanisms of the formation of a surface phase with the matrix composition in a Ca2Nb2O7 single crystal

We have studied the local composition and nanoscale surface morphology of a calcium niobate, Сa2Nb2O7, single crystal after thermally stimulated heterosegregation with the aim of identifying the mechanisms underlying the formation of a surface phase with the matrix composition. The identity of the compositions of the surface phase and matrix is accounted for in terms of a liquid-phase model for surface segregation, which includes diffusion, melting, and crystallization processes.

Lattice resolved annular dark-field scanning transmission electron microscopy of (Al, In)GaN/GaN layers for measuring segregation with sub-monolayer precision

We have performed lattice resolved annular dark-field (Z-contrast) scanning transmission electron microscopy and combined this with energy-dispersive X-ray spectroscopy as well as simulations to measure quantitatively segregation across strained interfaces in AlGaN/GaN and GaN/InGaN multiple quantum wells of nominal thicknesses between 8 and 0.25 nm. The compositional profiles obtained were corrected for detector dark current and non-linearity of the Z-contrast imaging process before we fitted exponential functions to the profiles across the interface regions. From these, we could highly accurately determine the layer widths, interface widths, and segregation lengths. Experimental values of the segregation lengths calculated varied from 0.3 nm (for InGaN-on-GaN) to 1.4 nm (for AlGaN-on-GaN), with error bars of only ±0.05 nm. A comparison with simulations based on a simple two-state-exchange model for surface segregation shows that the segregation energy for indium atoms is about an order of magnitude smaller than both the corresponding segregation energy for aluminium/gallium atoms and the activation energies for surface segregation of cations in these nitride systems.

Oxygen incorporation in homoepitaxial N-polar GaN grown by radio frequency-plasma assisted molecular beam epitaxy: Mitigation and modeling

We have investigated the effect of gallium deposition and desorption cycles and ultrathin (15 Å) AlN layers on the oxygen impurity concentrations in homoepitaxial N-polar GaN layers. Secondary ion mass spectroscopy (SIMS) indicates that three Ga deposition and desorption cycles reduce the total oxygen by 70%–80%, while ten cycles reduces the total oxygen by more than 90%. We present a model of surface segregation and incorporation which accurately captures the distribution of oxygen in these layers. By fitting the model to the SIMS data, we are able to determine the fraction of an oxygen layer adsorbed on a GaN surface which segregates upon initiation of epitaxial GaN growth. Under the conditions investigated, we find this fraction to be 80%.

Ultra-fast grain boundary diffusion and its contribution to surface segregation on a martensitic steel. Experiments and modeling

Phosphorus surface segregation was measured by Auger Electron Spectroscopy on a 17-4 PH martensitic stainless steel at 450, 550 and 600 °C. Surface segregation was shown to be much faster than expected which was attributed to a high contribution of phosphorus diffusion along the former austenitic grain boundaries. A model of surface segregation was developed following the Darken–du Plessis approach and taking account of both bulk and grain boundary solute diffusion. The phosphorus grain boundary diffusion coefficient in 17-4 PH was estimated: D GB < = 6.2 10 4 exp(− 157 kJ mol − 1 /RT)cm 2 s − 1 . It is found to be more than three orders of magnitude higher in 17-4 PH steel than in α-iron.

Kinetic Model of Surface Segregation in Pt-Based Alloys

A new vacancy model describes the kinetic process of surface segregation on clean surfaces via atomic movement through vacancies. The detailed segregation mechanism of two impurity metals (Au and Co) in Pt(111) is examined using periodic density functional theory, carefully evaluating energy barriers for each step in the segregation process. Au shows a strong surface segregation trend to the clean Pt(111) surface, while Co segregating to the surface is neither thermodynamically nor kinetically favorable.

Model of surface segregation driving forces and their coupling

Separating the surface segregation enthalpy into three elementary contributions (cohesive, alloy, and size) has been proposed by many authors but rarely tested quantitatively. A three element separation rule has been derived from a tight-binding Hamiltonian 15 years ago. It has yielded very satisfying results for various environments (close-packed surfaces, vicinal surfaces, grain boundaries, and clusters) for the Cu-Ag system and for many other alloys. However recently this rule has stumbled over the Co-Pt system. We therefore develop an approach---the coupled three effects model (CTEM)---based on a systematic study of the properties of permutation enthalpies---both in the bulk and in the surface---as a function of the value of the mixed interaction involved in the $N$-body interatomic potentials derived from the second moment approximation of the tight-binding scheme. We show that both the disagreement previously observed for Co-Pt and the agreement mentioned above for Cu-Ag can be explained by the variation of the alloy effective pair interactions (EPIs) in the surface and by the existence of coupling coefficients between the three effects. We also show that the surface EPIs are proportional to the bulk EPIs when the difference of atomic radii of the components can be neglected, while they differ from an additive constant in the presence of a large size effect. We suggest general criteria to determine alloys where the present improvements are expected to be significant.

A nonlinear model for surface segregation and solute trapping during planar film growth

Surface segregation and solute trapping during planar film growth is one of the important issues in molecular beam epitaxy, yet the study on surface composition has been largely restricted to experimental work. This paper introduces some mathematical models of surface composition during planar film growth. Analytical solutions are obtained for the surface composition during growth.

Unified kinetic model of dopant segregation during vapor-phase growth

We develop a unified kinetic model for surface segregation during vapor phase growth that concisely and quantitatively describes the observed behavior in silicon-based systems. A simple analytic function for the segregation length is derived by treating terrace-mediated and step-edge-mediated mechanisms in parallel. The predicted behavior of this parameter is examined through its temperature, flux, and terrace length dependence. Six distinct temperature regimes are predicted for the segregation length that depend on the relative segregation energies and activation barriers of the two mechanisms. The model is compared to reported behavior of Sb and P in Si(001) and excellent agreement is obtained using realistic energies and preexponential factors. The model accounts for the experimentally observed anomalous low-temperature segregation of Sb as a consequence of the competition between step-edge-mediated segregation, dominant at low temperatures, and terrace-mediated segregation, dominant at higher temperatures. The generalized treatment of segregation mechanisms in the model makes it applicable to other segregating systems, including metals and III-V semiconductors.

Thermodynamic Modeling of Surface Segregation in Au-Ti Nanoparticles

The surface composition of nanoparticles is generally different from the average or bulk composition; this phenomenon is commonly referred to as surface segregation. In the present work, the surface segregation in Au-Ti nanoparticles has been analyzed based on a thermodynamic model that incorporates the size effect into the quasichemical model. The calculated surface compositions of Au-Ti nanoparticles are compared with that of the bulk Au-Ti alloys.

Effect of fluorine doping on the properties of tin oxide based powders prepared via Pechini’s method

Surface modification of ceramic powders is an important method to change and control the properties of the material. Grain size, surface charge density and consequently the powder–surroundings interfacial properties can be modified by the use of additives. The surface properties of SnO2-based powders doped with F, prepared via an organic chemical route derived from Pechini’s method, was studied using infrared spectroscopy (FT-IR), surface area determination, X-ray diffraction (XRD), dynamic electrophoretic mobility and thermogravimetric analysis. The results showed that there is an F saturation concentration (5mol%), above which, the surface characteristics of the powder became constant. Compared to the pure SnO2, addition of F to the oxide results in a powder that has a greater surface area. Water suspensions of the powder presents an interface that is acidic (isoelectric point=3.31) and more hydrophobic. Furthermore, F-doped SnO2 presents different types of adsorption sites for water adsorption. All the results constitute strong arguments supporting the additives surface segregation model, detrimental to the theory of solid solution formation.

Arsenic incorporation and its influence on microstructure of wurtzite GaN grown by molecular-beam epitaxy

We present a comprehensive study on the incorporation of As in a local area and its influence on the microstructures of wurtzite GaN grown by rf-plasma-assisted molecular-beam epitaxy. Using transmission electron microscopy (TEM) and secondary ion mass spectrometry (SIMS), we found that the incorporation of As in GaN is correlated with the formation of intrinsic basal plane stacking faults. The stacking fault, analyzed by high-resolution TEM, can be regarded as a stacking sequence of cubic GaAs or Ga(N,As) inserted into hexagonal GaN. Indeed, it may be energetically favorable for the As incorporation to form a thin cubic layer in hexagonal GaN, resembling the thermodynamically stable cubic phase for GaAs. We found experimental evidence of As surface segregation and analyzed it by fitting the As SIMS profiles with a one-dimensional empirical surface segregation model. This result declares a significantly large tendency of As surface segregation with the surface segregation coefficient R∼0.99, which indicates the difficulties to incorporate As into GaN, and thus to grow the ternary GaNAs alloys.

Surface segregation of Ge during Si growth on Ge/Si( [formula omitted]) at low temperature observed by high-resolution RBS

The Si/Ge/Si(0 0 1) multilayer with about 1 ML Ge layer is fabricated by evaporating Si overlayer on a Ge/Si(0 0 1) surface at 20–300 °C. The depth profile of the Ge atoms is observed by high-resolution Rutherford backscattering spectroscopy to investigate the possibility of Ge delta doping in Si. The observed profile of the Ge atoms spreads over several atomic layers even at 20 °C and a significant amount of Ge is located in the surface layer at higher temperatures. The results at 20–150 °C are well explained with two-layer model for surface segregation of the Ge atoms and the segregation rates are estimated. The activation energy for surface segregation of Ge atoms in amorphous Si is evaluated to be 0.035 eV, which is much smaller than the value reported for Si deposition at 500 °C. The small activation energy suggests that local heating during the Si deposition is dominant at low temperature.

Kinetic Modeling Of Dopant And Impurity Surface Segregation During Vapor Phase Growth: Multiple Mechanism Approach

ABSTRACTWe propose a new kinetic model for surface segregation during vapor phase growth that accounts for multiple segregation mechanisms, including mechanisms for terrace mediated exchange and step edge mediated exchange. The major result of the model is an analytic expression for the experimentally measured segregation length and profile broadening that can be readily calculated without the need for numerical simulations. We compare the model to experimental measurements for the temperature dependence of segregation of Sb in Si(001). The model is able to accurately describe both the anomalous segregation at low temperature and the transition between equilibrium and kinetically limited segregation at high temperature. An excellent agreement is obtained using realistic energies and pre-exponential factors for the kinetic rate constants. The model can be applied to other segregating systems in planar geometries, including metallic and III-V semiconducting thin films.

Segregation effects and bandgap engineering in InGaN quantum-well heterostructures

ABSTRACTThe analysis of In surface segregation and its impact on the composition profile and light emission spectra of the InGaN single quantum well heterostructures grown by Metalorganic Vapor Phase Epitaxy (MOVPE) is carried out by coupled solution of the Poisson and Schrödinger equations. Effective methods of controlling the composition profile, indium predeposition and temperature ramping during the cap layer growth are considered in terms of surface segregation model. General trends in spectra transformation upon the forward bias variation and their correlations with the quantum well electronic structure are discussed.

Surface Segregation in Group-III Nitride MBE

The rate-equation model of surface segregation [Mater. Res. Soc. Symp. Proc. 618, 185 (2000)] is applied to InGaN and InGaAlN plasma-enhanced MBE, aiming at the analysis of factors affecting the composition profiles in nitride heterostructures. Delayed In incorporation into a crystal and In “tailing” in a cap layer are found to be affected primarily by the growth temperature and elastic strain due to the lattice mismatch with the underlying layer. The ways to improve the abruptness of the epilayer interfaces – In pre-deposition, growth interruption, and temperature rise – are examined for typical InGaN/GaN quantum wells.

Surface energy, adsorption, and wetting transitions in ternary liquid alloys

Surface energy measurements have been performed on liquid Ga-Sn binary and on Ga-Pb-Sn as well as Ga-Pb-Tl ternary alloys, by the sessile drop technique under ultrahigh vacuum conditions. The purpose of these measurements was to investigate the change in adsorption behavior of Pb in Garich alloys as a consequence of ternary additions. In order to aid in the interpretation of the results, a multilayer model of surface segregation was formulated in the regular solution approximation. The results show evidence of site competition effects between the two solutes, which reduce the surface concentration of Pb in relation to binary Ga-Pb alloys. The effects of Sn on previously studied wetting-related adsorption transitions in Ga-Pb were also investigated. It was concluded that Sn additions are likely to raise the wetting temperature of the Ga-Pb alloy.

Model for Dopant and Impurity Segregation During Vapor Phase Growth

AbstractWe propose a new kinetic model for surface segregation during vapor phase growth that takes into account multiple mechanisms for segregation, including mechanisms for inter-layer exchange and surface diffusion. The resulting behavior of the segregation length shows temperature and velocity dependence, both of which have been observed in experiments. We compare our analytic model to experimental measurements for segregation of Phosphorus in Si(001), and we find an excellent agreement using realistic energies and pre-exponential factors for kinetic rate constants.

A Quantitative Model of Surface Segregation in III-V Ternary Compounds

ABSTRACTA quantitative model of surface segregation free from adjustable parameters is suggested for the growth of ternary III-V compounds. In contrast to previous approaches, the model considers the dynamics of surface population by the three elements producing the ternary alloy. The underlying assumption is that the atoms in the adsorption layer are in equilibrium with the crystal bulk. Elastic strain arising in the epitaxial layer due to the lattice constant mismatch with the substrate is found to be one of the key factors affecting segregation. Along with growth temperature, it controls the segregation efficiency and the composition profile evolution in a growing heterostructure. The effect of the V/III ratio, growth rate and other parameters is accounted for. Here, we apply the model to analyze the InGaAs growth by molecular beam epitaxy owing to the vast experimental data available for the model verification. The theoretical predictions show a good agreement with the experimental observations

A mathematical model for surface segregation in aluminum direct chill casting

A two-dimensional mathematical model for the development of macrosegregation at and close to the ingot surface during direct chill (DC) casting of aluminum rolling sheet ingots is presented. The model accounts for macrosegregation caused by exudation of interdendritic melt and macrosegregation associated with solidification shrinkage. Equations for the conservation of energy, solute, momentum, and mass during the stationary phase of the process are solved numerically by a finite-element method. The solution domain corresponds to a vertical cross section at the middle of the longest side of the slab. The main simplifications in the modeling concept are to assume that the solid in the mushy zone moves with the casting speed, and that the alloy is binary and solidifies according to the lever rule. The thickness and solute concentration of the surface layer and the macrosegregation close to the surface are calculated, and modeling results are compared to measurements on full-scale castings.