Kinetic investigations within the transition region from polyhedral to skeletal growth mode (I). Growth kinetics of the basal face of zinc single crystals under diffusion conditions

The effect of diffusion in the vapour phase on the kinetics of growth of zinc single crystals in the presence of argon has been studied. The shift of the basal face in normal direction as a function of the time has been measured at constant temperature and supersaturation and argon pressures varying within the range 5–250 Torr as well as in vacuum 1 × 10⁻⁶ Torr. It has been established that the crystal size R changes with the time t following a linear and a parabolic law in the kinetic and the diffusion regimes, respectively. The kinetic critical size R_k for the transition from a kinetic to a diffusion regime has been experimentally obtained. A relatively good agreement is found between the experimentally established and theoretically calculated values of the critical size. The problems related to the transition of the basal faces of zinc single crystals from a kinetic to a diffusion growth mode is discussed.     

2<Emphasis Type="Italic">D</Emphasis> quasi-periodic Rauzy tiling as a section of 3<Emphasis Type="Italic">D</Emphasis> periodic tiling

A method for constructing a 2D quasi-periodic Rauzy tiling Til as a section of some 3D periodic tiling Til ^3D is considered. The translation lattice of the tiling Til ^3D and its connectivity graph are constructed using the discrete modeling of packings. The calculation of the layer-by-layer growth polyhedron for the tiling Til ^3D made it possible to estimate from upper the shape of a growth polygon for the tiling Til. As a result, the growth shape in six out of eight growth sectors has been rigorously proven. A set of quasi-periodic tilings (locally indistinguishable from the Rauzy tiling Til), including seven centrosymmetric tilings, has been obtained.     

The Effect of Solid and Liquid Inclusions on Morphology of Crystallization Front

The interaction between crystallization front and solid particles was studied for substances characterized by the normal growth mechanism (continuous growth). It has been measured the critical velocity below which the particle of radius R is repulsed by moving interface and above it is captured. It has been shown that critical velocity is proportional to R⁻(1.4–1.8) what satisfactorily agrees with Chernov-Temkin's theory. Data have been received about change of interface morphology at capture of solid particles for growth from pure and impurity-contained melt. The dendrites have been found to split at interaction with particles and concentration inhomogeneities. Taking for example Al-Cu alloy, possibility has been shown to disperse the dendritic structure by formation concentration inhomogeneities in the melt.     

Growth of CaMoO4 and SrMoO4 crystals in silica gel media

Growth kinetics and characterization of calcium and strontium molybdate crystals grown in silica gel have been studied under a variety of parameters. The changes in nucleation characteristics, growth habit, quality of these crystals were carefully observed and are found directly related to pH of the medium. The profound influence of pH on spontaneous crystallization of CaMoO₄ crystals has been carefully investigated; and its crystallization range has been determined. The wide morphological change of SrMoO₄ with respect to pH variation has been studied. The quality of the crystals has been critically examined.     

Direct melt crystal growth of isotactic polybutene‐1 trigonal phase

The morphology, crystalline structure and crystal growth kinetics of melt‐crystallized thin isotactic polybutene‐1 films have been studied with transmission electron microscopy, electron diffraction and optical microscopy. It is demonstrated that a bypass of tetragonal phase crystallization and direct melt crystal growth of the trigonal phase can be achieved via self‐seeding at atmospheric pressure using solution‐grown trigonal crystals as nuclei. Electron microscopy and optical microscopy observations show that melt‐crystallized isotactic polybutene‐1 single crystals of the trigonal phase have rounded or hexagonal morphologies around 75°C. The growth rate of trigonal crystals in the melt has been obtained by in‐situ optical microscopy. The growth rate of trigonal crystals in the melt is 1/100 and 1/1000 that of tetragonal crystals in the melt around 70 and 90°C, respectively. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

PVT and CVT Growth and Characterization of SnSxSe2-x (0 ⩽ <x 2) Single Crystals

Single crystals of solid solutions of tin sulphoselenide have been grown in the same ampoule. Specific conditions for growing single crystals of SnSSe have also been identified. A study of microstructures on the growth surfaces responds to the mechanism of growth of these crystals. The dependence of electrical resistivity, Hall mobility, carrier concentration with the values of the configuration parameter x has been studied.     

Doping process control in silicon epitaxy (I). System identification

The transition behaviour of the phosphorus incorporation in silicon epitaxial layers grown in a CVD reactor has been investigated, considering the reactor as a linear control system with u = lg p⁰_PH3 (t) as the input and y = lg N(t) as the output. The response of system to both upward and downward step inputs has been studied experimentally, using SiH₄ and PH₃ sources. The dopant system of a horizontal silicon epitaxial reactor has been identified and a mathematical model relating to the transient behaviour of the system has been found. The parameters of the model have been estimated from layer growth experiments. The step response functions found can be approximated by an exponential function relating to n time constants T, all equal to each other. It was found for the system investigated that the second order model is of sufficient accuracy for the optimal control calculations described in the next part of this series.     

Growth and Kinetic Studies of Spherulitic Gadolinium Tartrate Crystals from Silica Gel

Spherulitic growth of gadolinium tartrate dihydrate crystals by controlled diffusion in silica gel is reported. The influence of growth parameters e.g., reactant concentration, gel pH and gel ageing, on the size, quality and nucleation density of the spherulites has been studied. It is observed that under varying experimental conditions involving change in reactant concentrations, gel pH and gel ageing, the material crystallizes in the form of spherulites. The results of growth kinetics are discussed. Scanning electron microscopy confirms spherulites to be aggregates of single crystallites, with each micro-sized crystal exhibiting a cuboid morphology. Surface structures exhibited by the micro-sized crystals indicate their growth by two-dimensional nucleation mechanism.     

Axial temperature distribution in Silicon-Germanium grown by the RF-heated float zone technique

The RF-heated float zone method has been used to study the segregation behaviour of silicongermanium solid solutions in the concentration range from 0 to 25 at% germanium. Completely dislocation free crystals up to 8 at% germanium could be obtained. Since constitutional supercooling is the main reason preventing single crystalline growth, pyrometric temperature measurements have been performed to reveal the temperature slope at the interface and to determine the critical growth rate. The temperature gradient ΔT/Δz was found to increase with increasing germanium concentration.     

Crystallization of benzimidazole by solution growth method and its characterization

The potential organic NLO crystal of benzimidazole (BMZ) has been successfully grown by slow evaporation solution growth technique at room temperature. The crystalline perfection has been verified by High resolution X‐ray diffraction (HRXRD) analysis. The very low angle boundary obtained for this solution‐grown specimen may be attributed to the segregation of solvent molecules (methanol), which were entrapped within the crystal during growth. The laser damage threshold has been measured by using high intensity Q‐switched Nd:YAG laser. The observed value is greater than that of KDP and lesser than that of melt grown benzimidazole. The NLO efficiency has been determined and it is compared with the KDP crystal. The thermal behaviour has been assessed by TG/DTA analysis. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kinetic investigations within the transition region from polyhedral to skeletal growth mode (III). Growth kinetics of the basal face of zinc single crystals and its edge under diffusion conditions

The growth kinetics of the basal face and its edge of zinc single crystals grown from zinc vapours in the presence of argon at pressures 5 – 250 Torr has been investigated simultaneously. The alterations of the crystal size R and the length of the basal edge a with time t have been measured at constant temperature and supersaturation. It is shown that the R²(t) and a²(t) dependences change their initial shape into linear at one and the same moment. It is established that the transition from a kinetic to a diffusion regime can be determined both by the kinetic critical size R_k and by the kinetic critical size a_k. It is found also that in the kinetic regime the lateral growth rate of the basal edge is higher than the normal growth rate of the {0001} face. During the growth in a diffusion regime the R²(t) and a²(t) curves of a given single crystal become parallel, due to the isotropic character of the transport processes of the material. The rate determining role of the diffusion in the parent phase on the growth of the basal face and its edge is demonstrated.     

On the Presence of Faces in the Habit of Growing Crystals

Presence and size of a face in the habit are conditioned by the value of relative growth velocity R_A/R_{crit A} with respect to the critical growth velocity. It has been established that during the growth of crystals only certain values of relative growth velocities R_A/R_{crit A} occur. Faces of KBC crystals realize values of R_A/R_{crit A} between 0 and 2. Unity is the demarcation level below which appearance and above which disappearance of faces takes place. Edges and corners of crystals are places where new faces appear during changes in growth conditions.     

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 .     

Kinetic of potash alum crystallisation

Metastable zone width of potash alum in aqueous solutions has been measured as function of the cooling rate in absence as well as in presence of seed crystals. From these data, the effective nucleation rate was calculated. Growth rate of potash alum crystals has been measured in a fluidized bed. Overall growth rate coefficient, k_G, was then used for determination of the mass transfer coefficient, k_D, and the rate constant of the intergration step k_r. The dependence of k_D on hydrodynamic conditions is discussed.     

Effect of buffer layers on the dislocation structure of heteroepitaxial systems

Transmission electron microscopy (TEM) as well as X-ray topography (XRT) and X-ray diffractometry have been used for investigation of the structure of the LPE heteroepitaxial system In_0.05Ga_0.95As-In_yGa_1−yAs_1−xP_x-GaAs(111) A. A critical value of the lattice misfit has been shown to exist at the metallurgical boundary ((Δa/a)* ≈ 10⁻³) which results in the change of the film nucleation and growth mechanism as well as the change of misfit dislocations (MDs) generation mechanism. With (Δa/a)₀ > (Δa/a)* the nucleation and growth mechanism is mixed: island growth at the first stages of growth and layer-by-layer growth at large thicknesses. MDs are created in an “island film” developing a non-ordered dislocation network. The density of threading dislocations (N_d) is ∼ 10⁸ cm⁻². With (Δa/a)₀ < (Δa/a)* there is layer-by-layer mechanism of film's nucleation and growth from the very first stages of crystallization. MDs are injected into continuous layer along the inclined slip planes {111}, thus forming a regular three-dimensional grid of MDs. N_d is less than 10⁶ cm⁻² in the case. A model of dislocation structure formation in heterolayers has been proposed. Within the frame of this model the two critical values of phosphorus concentration in the quaternary melt have been quantitatively determined. These are corresponding to the change of MD generation mechanism. The expected values of N_d for (Δa/a)₀ > (Δa/a)* and (Δa/a)₀ < (Δa/a)* have been theoretically determined.     

Thermodiffusion and Morphological Stability in Convectionless Crystal Growth Systems from Melts and Melt-Solutions

Crystal growth experiments of multicomponent systems under microgravity require an exact analysis of the diffusion phenomena in the nutrient fluid phase. The contribution of the Soret effect to the transport and distribution of matter in a convectionless casting arrangement for shaped crystal growth and in THM melt-solution zones have been investigated. Some semiconductor systems were analysed from experimental (Bi_1-xSb_x mixed crystals) and theoretical (PbTe, InP, GaAs, CdTe compounds) point of view. The criterion for constitutional supercooling was correspondingly modified. It has been distinguished between associated (AIV BVI, AII BVI) and dissociated (AIII–BV) melt-solutions, containing different species of diffusion (molecules or atoms, respectively).     

Growth of ZnSe<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>S<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> solid solution crystals from vapor phase

Partially faceted ZnSe_{1 − x} S _x solid solution crystals have been grown from a vapor phase in a closed stationary horizontal system. The growth has been performed in cylindrical quartz ampoules—∼10 mm in diameter and evacuated to a residual pressure of less than ∼10⁻³ Pa-at a temperature of 1050°C and a temperature drop between the source and growth zones of 10–16°C. The crystal structure, optical absorption, and composition inhomogeneity along the ingot length have been investigated by X-ray diffractometry and optical spectroscopy in the wavelength range of 300–3000 nm. The solid-solution composition range corresponding to cubic polymorphs is determined. The concentration dependences of the lattice parameter and band gap are presented.     

Calculation of Diffusion-limited Growth of Hg1−x Cdx Te Epilayers on CdTe from Te-rich Melts by Step-Cooling LPE

Calculations of layer thicknesses and composition profiles in Hg_1−xCd_xTe layers on CdTe substrates for the growth from Te-rich melts have been carried out for liquidus temperatures of 460 °C, 480 °C, and 500 °C. This has been made on the basis of the multicomponent diffusion model of SMALL and GHEZ and the solid-liquid phase relation of BRICE . It could be shown that growth velocity increases only slightly with rising liquidus temperature. On the other hand, the interdiffusion velocity of Hg and Cd in the solid increases remarkably at a higher temperature. Therefore, to get layers with a constant x-value a higher supersaturation of the melt is necessary. The x-value decreases with rising supercooling by about 0.003 K⁻¹. To demonstrate the thermodynamically and kinetically advantageous properties of CdTe as substrate material, comparative calculations for a “hypothetical” HgTe substrate have been involved.     

MOVPE growth of spontaneously ordered (GaIn) and (AlIn)P layers lattice matched to GaAs substrates

A systematic study of the metal-organic vapour-phase epitaxial growth of (GaIn)P and (AlIn)P layers deposited on GaAs substrates with (001) and (110) orientation is presented. Special attention has been paid to the growth on (001)-oriented wafers with different misorientations to the growth direction. The influence of the growth conditions on the properties of the epitaxial layers such as lattice mismatch, alloy composition, photoluminescence (PL) wavelength, FWHMs of PL peaks and atomic ordering is discussed. Layers with mirrorlike surfaces and various degrees of order could be deposited at growth temperatures T_g ranging from 595 °C to 750 °C for (GaIn)P and 720 °C to 800 °C for (AlIn)P. In addition to the influence of T_g on the Ga incorporation during the (GaIn)P growth we found the Ga distribution coefficient k_Ga to be affected by the misorientation of the substrates. k_Ga correlates presumably with the number of kinks and steps on the substrate surface. Transmission electron diffraction (TED) and PL investigations show that the degree of order — often described by the ordering paramter η — depends strongly on T_g the ordering is more pronounced when the layers are deposited on substrates misoriented towards the (1 11) lattice plane. Strong ordering has been observed for (GaIn)P samples grown at 680 °C on substrates 2° misoriented towards the [1 10] direction and at 650 °C on substrates 6° misoriented towards the same direction. For the (AlIn)P samples striking ordering has been found when they were grown at 720 °C.     

New empirical kinetic equation of size dependent crystal growth and its use

Size dependent crystal growth kinetic can be measured indirectly in Mixed Suspension Mixed Product Removal Crystallizer by means of differential number balance of crystal product population. Some simple formula relating growth rate G and crystal size L is needed for statistical processing of scattered experimental crystal size distribution data. The new exponential formula has been proposed which provides physically realizable values of G at extreme size values. The formula is simple enough to yield analytic solution of the number balance. Methods of estimation of three formula parameters and nucleation rate and examples of experimental data fitting have been presented as well.