Calculations of LPE layer thickness

Three basic cases of LPE growth with and without nucleation were examined. The expressions for layer thickness and growth efficiency calculations were developed. Criteria for LPE growth classification were obtained. It was shown the nucleation takes place at critical values of supersaturation of the solution. The values of critical supersaturation may be calculated from growth efficiency experimental data for LPE growth.     

The influence of natural convection on the mass transfer kinetics in LPE growth

The simplified scheme has been suggested for quantitative estimation of the effect of natural convection on the LPE layers thickness while growing from a finite solution with parallel horizontal and vertical substrates. The convective-diffusive mass transfer model is being developed on the base of boundary layer approximation. In the case of horizontal growth the layer thickness is determined by effective solution thickness which is distinguished for an upper and lower substrate and depends on convection intensity. For the vertical growth system the expression describing the variation of layer thickness along the substrate has been obtained and the vertical temperature gradient necessary for eliminating a wedge shaped growth in this case is calculated. The experimental investigations of LPE growth of GaP layers from finite solution with horizontal and vertical substrates are carried out. The thickness and shape of LPE layers obtained in both cases coincide well with results of calculation.     

Nucleation and growth kinetics for the crystallization of ice from dextrose solutions in a continuous stirred tank crystallizer with supercooled feed

The crystallization of ice in aqueous dextrose solutions is studied in an adiabatic continuous stirred tank crystallizer with a supercooled feed stream. The effective diameter of the ice crystals was determined for various values of mean crystal residence time, feed supercooling, magma density, stirring rate, and dextrose concentration. For all process conditions the supercooling was measured at 9-12 different locations in the crystallizer. These local supercoolings were averaged algebraically to yield the bulksupercooling. From the experimental results growth and nucleation rates have been calculated. By comparing the experimental growth rates to growth rates calculated by means of a mathematical model kinetics for the inbuilding of water molecules into the ice lattice have been determined. The growth rate appears to be directly proportional to the interface supercooling. The rate constant decreases exponentially with increasing weight percentage of dextrose in the solution. The nucleation rate was found to be directly proportional to total crystal surface per unit volume of suspension and proportional to the bulksupercooling to the power 2.1. Nucleation is believed to occur by breakage of dendrites from the surface of parent crystals.     

A simple numerical method for the simulation of the (GaIn)P liquid phase epitaxy process

On the basis of the solution of the diffusion equation for step-cooling and uniform cooling accomplished by RODE a numerical procedure is derived for the LPE process. The dependence of the diffusion coefficient and the slope of the liquids curves on temperature and chemical composition in the ternary system have been taken into account by an empirical approach. Effects of nucleation and evaporation of phosphorus at growth temperature are considered by dividing the diffusion space. The dependence of layer thickness on growth time and the compositional variation of the grown layers are calculated and compared with the experimental results.     

Heat and mass transfer problems in solution growth of GaP crystals by the travelling solvent method (TSM)

The influence of the natural convection on the heat and mass transfer process during growth of GaP crystals from the solution is considered. The two-dimensional quasi-stationary thermodiffusive hydrodynamic problem for the GaP growth system by travelling solvent method (TSM), as a model, has been solved. Computation is given for the temperature and concentration field distribution in the solution. The picture of vortex configuration for different lengths of the liquid zone, the shape of the growing and dissolving interfaces and also the boundary layers thickness are obtained. The experimental dependence of the growth rate on the convection intensity observed mostly confirmed the calculation results.     

Heterogeneous gas bubble formation during GaP solution growth

The gas bubble formation on seed surface, during growth of GaP crystals from the solution, is considered on the basis of the model for heterogeneous nucleation. It is shown that the bubble formation in this case could be a consequence of the interaction between gallium oxide, Ga₂O₃, and gallium generating gaseous gallium protoxide, Ga₂O₃, during heating. The size of the bubbles incorporated in the crystal depends on the kinetics of this reaction and the dissolution rate of Ga₂O₃ in liquid gallium. The values of forces that act on gaseous bubbles in the liquid zone are estimated. It is shown that the migration behaviour of these bubbles is mainly determined by Archimed and thermocapillary forces and depends on growth situations. The methods for avoiding bubble formation in GaP solution growth are suggested.     

A Method of Determining the Liquid Phase Epitaxial GaAs Growth Mechanism Based on Growth Rate Measurements

It has been proved that the dependence of the growth rate V of a LPE GaAs layer on the relative supersaturation σ of the solution at the interphase boundary can be determined on the basis of growth rate measurements of this layer in the case when crystallization is controlled by the kinetics of surface processes. The relation V = f(σ) obtained for homoepitaxial GaAs layers grown at different solution cooling rates are compared with the theoretical relations derived by BRICE making use of a single growth mechanism assumption. Based on the above and by use of the experimental data of MUSZYńSKI the growth mechanism of homoepitaxial GaAs layers on a substrate oriented in the [100] direction is determined. The results are in accordance with the crystallization model of A^IIIB^V semiconductor compounds from the liquid phase proposed by FAUST and JOHN .     

Metastability and crystal growth kinetics on L‐arginine phosphate

Stability of saturated L‐Arginine Phosphate (LAP) solution studied as a function of supercooling rate and crystal growth kinetics investigated as a function of supersaturation are reported in this communication. Solution stability was studied by observing the metastable zone width at different cooling rates employing a polythermal method. Analysis of the experimental data yielded the kinetic constant of nucleation and the order of nucleation. Crystal growth rates studied on small seed crystals with regular morphology, under normal growth conditions and at different supersaturation levels were found to satisfy BCF surface diffusion model. Crystal growth rates were investigated normal to the (100), (010) and (00 ) faces. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Untersuchungen zur heteroepitaktischen Abscheidung von GaP auf GaAs aus der Sn-Lösung

The used liquid-phase epitaxy apparates are described and the experimental conditions of growth on GaP and Ga(AsP) onto GaAs-substrates are reported. The influence of growing conditions (temperature, cooling rate, composition of melt) on the quality of interface and on the inlusion of solvent are discussed. The consequence of varying degrees of substrat-misorientation on the surface morphology has been studied.     

AlxGa1−xAs LPE growth

Al_xGa_1−xAs LPE growth was studied within the temperature range of 930–900°C with Al concentrations in solutions from 0.04 to 2.4 at.%. AlAs concentration in layers has been shown to grow with the cooling rate increase of solution. Interface and volume nucleation parameter dependence of K_i and K_v and formation time t_f on Al concentration in Ga solution have been found. Addition of Al to Ga solution increases critical values of As supersaturation (supercooling) and, as a result, increase in thickness of Al_xGa_1−xAs layers compared with GaAs layers have been determined in spite of As concentration lowering in Ga solution.     

Numerical modeling and investigation of liquid phase epitaxy of Hg1–xCdxTe infrared detectors

Numerical investigations have been performed for modeling the global temperature field of an industrial liquid phase epitaxy (LPE) facility and to estimate the temperature fluctuations in a Te‐rich solution during the LPE growth. The numerical results agreed well with experimental data and therefore provide reliable reference points for experimenters for further improvements of the growth conditions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study of the metastable region in the growth of GaN using the Na flux method

It was revealed that the metastable region, in which liquid phase epitaxy (LPE) of GaN single crystals proceeds without the generation of polycrystals, expands with growth temperature in the Na flux method. The metastable region appears when LPE growth proceeds at temperatures above 1073 K, although generation of polycrystals inevitably occurs on a crucible at temperatures less than 1073 K. The highest growth rate of 14 μm/h in a small experimental setup was achieved at a temperature of 1163 K with a nitrogen pressure of 5.5 MPa due to complete suppression of the growth of polycrystals on a crucible, even though the supersaturation at this condition reached a fairly high level.Also, an LPE crystal with a flat surface could easily be obtained under high-temperature conditions.     

Impact of malonic acid on the segregation of glycine polymorphs – Analytical assisted molecular approach

Proton dissociation assisted negative polarity of malonic acid molecules admist glycine zwitterions leads to orgination of γ nucleation in the solution. Alteration in the nucleation behaviour and segregation of glycine polymorphs in the presence of malonic acid over a wide range of concentrations has been investigated both by experimental and analytical approaches. Complete changeover in the nucleation behaviour from 100% α to 100% γ is observed at the critical concentration of the additive. Shifting in the overall charge environment of the system towards cationic in the presence of malonic acid favours the nucleation of γ through induced charge compensation in the solution. Tuning of merohedral twinning in γ nucleation by the additive concentration has been well revealed in the present work. CNT based analytical approach employed elucidates well the experimental observations through the estimated interfacial energy, volume excess free energy, critical radius, activation energy barrier and nucleation rates of α and γ polymorphs. Structural affirmation of the nucleated polymorphs was carried out by powder x‐ray diffraction.     

Batch Precipitation of Calcium Sulphate

Results of the experiments with batch neutralisation of sulphuric acid with milk of lime have been used for calculation of the nucleation and growth rates and of the product crystal sizes of the calcium sulphate dihydrate. The procedure is based on the experimental values of calcium concentration in solution measured at various time intervals.     

In situ Observation Setup for Semiconductor Growth Interface from Solution in a Magnetic Field

A setup for in situ observation was developed which makes possible the optical visualization of a solid-liquid interface during solution growth of semiconductors in an external magnetic field. This setup consisted of an optimized monoellipsoidal mirror furnace, a near-infrared optical system, and static or rotating electromagnetic facility. The target crystals were GaP, GaAs and CdTe.     

Growth and Dissolution Rates on GaP(111)B Facet Surface during Solution Growth under a Transverse Static Magnetic Field

Growth and dissolution rates on GaP(111)B facet surface during solution growth have been measured using near-infrared (NIR) microscopic interferometry under a transverse static magnetic field. We show that the possibility of solutal convection in the liquid causes the difference between the growth and dissolution rates.     

The role of fuzzy interfaces in the nucleation, growth and agglomeration of aluminum hydroxide in concentrated caustic solutions

Fundamental crystal growth theory relies on classical concepts of monomeric addition at step sites on crystal surfaces. The nucleation and growth of crystalline aluminium hydroxide from concentrated caustic solutions does not follow classical crystal growth mechanistic pathways. Numerous techniques including static and dynamic light scattering, small angle X-ray and neutron scattering, cryovitirification transmission electron microscopy, rheology and atomic force microscopy have been employed in the study of aluminium hydroxide crystallisation from concentrated caustic solutions. The observations from these techniques have been interpreted on the basis polymer crystal growth theory, thermodynamic phase inversions analysis and entropically driven insolubility.

The experimental observations can be interpreted on the basis that aluminium hydroxide nuclei and crystals are surrounded by a diffuse interface which grades in density from the crystalline aluminium hydroxide particle core to the surrounding solution. A mechanism for the nucleation and growth mechanisms of aluminium hydroxide has been proposed: initial solution formation of a loose polymeric network; clustering of this network followed by gradual densification to form amorphous nuclei; further densification of the core of the nuclei to form crystallites and gradual densification but not crystallisation of the still amorphous diffuse interface.

The presence of this diffuse interface enables the slow agglomeration behaviour of aluminium hydroxides particles in concentrated caustic liquors to be explained. In liquors of very high ionic strength (in this case up to 6 M NaOH) particulate agglomeration would be expected to be rapid due to the small double layer thickness as predicted by DLVO theory. During rapid growth the diffuse interface inhibits the sufficiently close approach of the dense part of the particles to the point where attractive inter-particulate van der Waals forces would dominate and agglomeration would take place. As supersaturation is depleted and the growth rate of the diffuse interface decreases but densification is still occurring the particles can approach more closely and agglomeration will occur. Thus it is probable that the observed agglomeration behaviour is supersaturation and growth rate related.     

Analysis of ambient gas influence on silicon layers crystallized by means of LPE

Epitaxial growth of thin layers from the liquid phase can occur with the use of solutions saturated under different ambient gases. Most often this process takes place in a vacuum or gaseous atmosphere of hydrogen or argon. As the experimental data show, the morphology of crystallized layers is determined by the ambient type in which the process occurs.The cohesion energy responsible for epitaxial lateral deposition processes on the substrate surface depends on the surface free energy which is a measure of attraction of the solution atoms by substrate atoms. In the case of crystallization of an epitaxial lateral layer of Si on a substrate partially masked with dielectric, the chemical potentials of atoms in the neighboring phases (determining the interface evolution) are not without influence on the relaxation velocity of the saturated liquid phase, and on the horizontal and vertical growth rate.The aim of the investigation was to analyze experimentally the influence of the ambient gases used during the LPE growth on the cohesion of the Sn–Si solution with substrates applied for the lateral epitaxial growth of Si layers. This work presents comparative temperature analysis of the wetting angle of such surfaces as Si, SiO₂ and SiN_x by the Sn–Si solution.     

Simulation of mass transfer in a kinetic experiment based on migration of flat layers of a solution in a melt in a temperature gradient field

Mass transfer upon migration of flat liquid layers of a solution in a melt under conditions of slow change in the average temperature at a constant rate has been analyzed for the dislocation and nucleation mechanisms of interface processes. It is shown that the experimental data on the dependence of the migration rate of flat layers on their thickness can be adequately described within the theory developed for strictly steady thermal conditions. A technique is proposed for determining the overall limitations on the mass transfer at interfaces and the migration rate in the diffusion mode from the experimental results obtained in a mixed migration mode.

     

Effective Nucleation Rate in Size Dependent Growth Systems

Using of MSMPR technique for simultaneous obtaining crystal growth and nucleation data poses a problem in the case of size dependent growth systems. Namely, the necessary extrapolation of experimental population density plot down to zero size is dubious because of its very steep and varying slope. Thus only some effective nucleation rate can be determined accurately. The proposed method of calculating it comprises cutting population plot at some effective size L_e chosen as a fraction of dominant size of mass weighted CSD of product from MSMPR crystallizer. Such a point of reference enables to compare nucleation rates even of different systems. Correlations of experimental data for aluminium ammonium alum are presented.