Macrosteps dynamics and the growth of crystals and epitaxial layers

Step pattern stability of the vicinal surfaces during growth was analyzed using various surface kinetics models. It was shown that standard analysis of the vicinal surfaces provides no indication on the possible step coalescence and therefore could not be used to elucidate macrostep creation during growth. A scenario of the instability, leading go macrostep creation, was based on the dynamics of the step train, i.e. the step structure consisting of the high (train) and low (inter-train) density of the steps. The critical is step motion at the rear of the train which potentially leads to the step coalescence i.e. creation of the double and multiple step. The result of the analysis shows that the decisive factor for the step coalescence is the step density ratio in and out of the train. The ratio lower than 2 prevents double step formation irrespective of the kinetics. For higher ratio the coalesce depends on step kinetics: fast incorporation from lower terrace stabilizes the single steps, fast incorporation from upper leads to step coalescence. The double step is slower than the single steps, so the single steps behind catch up creating multistep and finally macrostep structure. The final surface structure consists of the macrosteps and superterraces, i.e. relatively flat vicinal segments. The macrostep alimentation from lower superterrace leads to emission of the single steps which move forward. Thus the single step motion is dominant crystal growth mode in the presence of the macrosteps. These steps finally are absorbed by the next macrostep. The absorption and emission of single steps sustain the macrostep existence, i.e. the macrostep fate is determined the single step dynamics. The condition for single step emission was derived. In addition, the macrosteps are prone to creation of the overhangs which results from surface dynamics coupling to impingement from the mother phase. The angular preferential access of the bulk material to the macrostep edge, leads to the overhang instability and creation of inclusions and dislocations.     

Distinct Growth Phenomena Observed on Zinc Cadmium Thiocyanate Crystals by Atomic Force Microscopy

Atomic force microscopy is used to investigate the surface morphology of the prismatic (100) face of ZCTC crystal grown at 30°C at a supersaturation of 0.16. This surface is distinctly formed by periodic “macrosteps” that advance along different directions and join with each other leading to the interlaced growth layers with an inclination of about 137°. These two “macrostep” trains well correspond to the pyramidal faces of (0 ) and (01 ) in orientation, therefore they probably propagate from the edges of these faces. The “macrosteps” are practically formed by highly dense steps at the front with regular elementary steps in between. The alternation of “macrosteps” and elementary steps vividly reflects Chernov's “kinematic waves of steps” theory (Chernov , (1984)) on a nanometer scale. Wide indentations and long clefts are generated at the “macrosteps”. The former is generated by twodimensional nucleation growth at a relatively faster growth rate than that of the underlying layer. The latter is probably caused by step trains generated by individual growth sources that have not merged.     

Step bunching behaviour on the {0 0 0 1} surface of hexagonal SiC

Surface topography of the {0 0 0 1} facet plane of as-grown 6H- and 4H-SiC crystals was studied ex situ by Nomarski optical microscopy (NOM) and atomic force microscopy (AFM). The surface polarity and the polytype of grown crystals largely affect the growth surface morphology of SiC{0 0 0 1} via differences in several thermodynamic and kinetic parameters. NOM observations revealed giant steps of a few micrometers in height on the {0 0 0 1} growth facet, and it was found that a morphological transition of the growth facet occurred when the growth conditions were changed. AFM imaging of the stepped structure of SiC{0 0 0 1} detected steps of height equal to the unit c-lattice parameter (c=1.512 nm for 6H-SiC and 1.005 nm for 4H-SiC). They are fairly straight and very regularly arranged, giving rise to equidistant step trains. Upon nitrogen doping, these regular step trains on the 6H-SiC(0 0 0  )C and 4H-SiC(0 0 0  )C surfaces became unstable: the equidistant step trains were transformed into meandering macrosteps of height greater than 10 nm. In this paper, we discuss the mechanism of macrostep formation (step bunching) on the SiC{0 0 0 1} surfaces through the consideration of the interplay between step energetics (repulsive step interaction) and kinetics (asymmetric step kinetics) on the growing crystal surface and elucidate how they affect the growth surface morphology of the SiC{0 0 0 1} facet.     

KDP晶体中包裹体形成机制的探讨

本文介绍了包裹体对KDP晶体质量的影响,并从两个方面探讨了KDP晶体生长过程中包裹体的形成机制.通过分析KDP晶体表面原子结构研究了不同杂质的吸附情况以及杂质对生长台阶的阻碍作用,通过分析晶体生长过程中流体动力学和质量输运条件的变化研究了旋转晶体的流体切应力和表面过饱和度,结果表明吸附杂质对生长台阶的阻碍和表面过饱和度的不均匀造成了生长台阶的弯曲和宏观台阶的形成,导致生长台阶形貌的不稳定是包裹体形成的重要原因.     

In situ atomic force microscopy studies of growth mechanisms and surface morphology of zinc thiourea sulfate crystals

In situ atomic force microscopy (AFM) has been utilized in studies of the growth mechanism on the (100) face of zinc tris (thiourea) sulphate (ZTS) crystals growing from solution. The growth on the (100) face of pure ZTS crystal is mainly controlled by two dimensional (2D) nucleation mechanisms, under which the hillock is formed through layer‐by‐layer growth. It is easier to form 2D nuclei at edge dislocation and the apex of steps. The growth of 2D nucleus is in accord with nucleation‐spreading mode. The growth rate along the 〈010〉 direction is faster than that along 〈001〉 direction, both of which increase firstly and then decrease with the spread of nucleus. The kinetic coefficients of one nucleus have been roughly estimated to be 3.6 × 10⁻⁴ cm/s and 1.8 × 10⁻⁴ cm/s in two directions, while the activation energy E was calculated to be 53.7 kJ/mol and 55.4 kJ/mol, respectively. The 2D nuclei can be generated under lower supersaturation with the addition of EDTA. If there are several hillocks growing together, step bunches will form when the steps moving in the same direction meet each other, while the meeting of steps that move in the inverse direction will result in the separation of steps. The ability of nucleation of edge dislocation outcrops are different even they are close to each other on the same surface. When the nucleus was generated at the edge dislocation sites, it cannot spread speedily until finishes an “incubation period”. Moreover, the detour of microsteps was observed due to the existence of pits. If the microcrystals attached on the surface block the step advancement, or leave the surface or are covered by the macrosteps, the pits are formed. If the macrosteps advanced across the pits, the pits will be covered and the liquid inclusions may form. However, if the microcrystal forming in the pit grow up and expose on the surface, the pit will not be covered by macrosteps. The formation of solid inclusions may be caused by the microcrystals being embedded into the single steps which move layer‐by‐layer.     

Some observations of growth hillocks and growth layers on potassium hydrogen tartrate crystals

Some observations of growth hillocks and growth layers on the as-grown surfaces of potassium hydrogen tartrate (KHT) crystals obtained at 30 °C from aqueuos solutions of different supersaturations are reported and discussed. It is found that macrospirals, isolated growth hillocks, and growth layers are typical features observed on these crystals. Bunching of rectilinear growth layers originating from growth hillocks produced parallel macrosteps on the {010} faces. In certain cases, interaction of thick rounded layers of unequal height, emitted from neighbouring strong sources, gave rise to residual steps (pseudo-interlaced steps). Isolated growth hillocks produced by microbes were also observed.     

Micromorphology of as-grown surfaces of crystals

This paper describes and discusses the micromorphology of as-grown surfaces of single crystals. After a brief introduction to the methods of observation of surfaces, the mechanism of growth and development of crystals is first outlined. Here the formation of bunches and macrosteps, the relationship between the growth mechanism and the surface entropy factor, and the effect of impurities on the surface morphology are described. Common structures observed on the as-grown surfaces are then explained in relation to growth conditions of the crystals. The following growth structures are described: elementary spirals, macrospirals, hillocks of dislocation and nondislocation origin, interlacing and slip patterns, macrosteps, inclusions, block structures, growth striations and impurity striations.     

Atomic force microscopy studies on liquid inclusions and induced defects of cadmium mercury thiocyanate crystal

Liquid inclusions and various defects accordingly induced on a nonlinear optical material of CMTC crystal were investigated by atomic force microscopy. Liquid inclusions are chiefly caused by formation of macrosteps, which result from impurity‐induced inhibiting of step growth and meeting of step trains advancing along different directions. Liquid inclusions induce generation of dislocations and even cracks within the crystal by three‐dimensional nucleation growth. Liquid inclusions also provide screw dislocation growth sources, leading to formation of spiral hillock trains with ridged tails. Etching experiments reveal circular hollow cores, indicative of screw dislocation growth, and negative crystals resulting from further crystallization in the liquid inclusions. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth of InGaAs/GaAs on Offcut Substrates by MOVPE: Influence on Macrosteps and Dislocations Formation

A study of the relationship between the macrosteps caused by the substrate misorientation and dislocation nucleation in MOVPE-grown InGaAs/GaAs is presented. The macrosteps could favour strain relaxation and the decrease of the critical thickness, also by generation of misfit dislocations in the 1/2〈110〉{011} glide system, as they can provide sites for stress accumulation above the average value far from the macrosteps. This adds up to the enhanced homogeneous dislocation nucleation associated with the offcut angle. The use of offcut substrates thus produces both compositional inhomogeneities and an increase of the overall dislocation density.     

AFM investigation of step kinetics and hillock morphology of the {1 0 0} face of KDP

Step velocities and hillock slopes on the {1 0 0} face of KDP were measured over a supersaturation range of 0<σ<0.15, where σ is the supersaturation. The formation of macrosteps and their evolution with distance from the hillock top were also observed. Hillock slope depended linearly on supersaturation and hillock geometry. The two non-equivalent sectors exhibited different slopes and step velocities. AFM shows an elementary step height of 3.7 Å, or half the unit cell height, whereas previous interferometric experiments assumed the elementary step was a unit cell. Values of the step edge energy (), the kinetic coefficients for the slow and fast directions (β_S and β_F), and the activation energies for slow and fast step motion (E_a,S and E_a,F) were calculated to be 24.0 erg/cm², 0.071 cm/s, 0.206 cm/s, 0.26 eV/molecule, and 0.21 eV/molecule, respectively. Analysis of macrostep evolution including the dependence of step height on time and terrace width on distance were performed and compared to predictions of published models. The results do not allow us to distinguish between a shock wave model and a continuous step-doubling model. Analysis within the latter model leads to a characteristic adsorption time for impurities (λ⁻¹) of 0.0716 s.     

Effect of zinc doping on pentaerythritol tetranitrate single crystals

In this study, the effect of zinc impurity on the organic high explosive pentaerythritol tetranitrate (PETN) single crystal has been investigated with optical microscopy and ex situ atomic force microscopy (AFM). The optical images show that the crystal shape has a transition with a predictable trend from long crystal to compact one as the zinc concentration is increased. Also, the 2‐dimentional (2‐D) growth hillocks are observed clearly on (110) face with contact AFM. The crystal growth occurs on monomolecular steps generated by 2‐D nucleation and followed by layer‐by‐layer expansion, and the macro‐steps formed onto the surface before spreading laterally as step bunches. The zinc ions are incorporated in growth steps as the zinc concentration is increased. The mechanism of inorganic impurity on molecular crystallization growth is still unclear. However, the incorporation of impurities may significantly affect growth kinetics of defect structure, and the bulk properties of molecular crystals. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Correlation of the structural imperfection and morphology of Bi<Subscript>4</Subscript>Ge<Subscript>3</Subscript>O<Subscript>12</Subscript> crystals grown by the low-gradient Czochralski method

This paper reports on the results of investigations into the morphological structure of the facets of Bi₄Ge₃O₁₂ crystals grown by the Czochralski method under the conditions of low temperature gradient (0.1–1 K/cm). A correlation between the morphological features of the facets at the crystallization front and the formation of defects in the bulk of the crystal is revealed. It is demonstrated that the {112} facets remain regular while the growing surface deviates from the (112) crystallographic plane by an angle of up to 1°. At larger deviations, there occurs a crossover from the stable facet growth to the growth of macrosteps or normal growth depending on the growth conditions.     

Atomic Force Microscopy Studies on Growth Mechanisms and Defect Formations on {110} Faces of Cadmium Mercury Thiocyanate Crystals

Growth mechanisms and defect formations on {110} faces of cadmium mercury thiocyanate crystals grown at 30°C (σ=0.24) were investigated by using atomic force microscopy (AFM). It was found that, under this condition, spiral dislocation controlled mechanism and 2D nucleation mechanism operates simultaneously and equally during growth, which is completely different from the traditional 2D nucleation and dislocation source controlled mechanisms. A number of 2D nucleus are formed at the large step terraces generated by dislocation sources, leading to the unequal growth rates of the elementary steps and thereby “step bunches” arecaused. Various defects are formed under this growth condition, which is assumed to result from the incongruence between the steps generated by different sources. A new kind of 2D defect, corresponding to one growth layer in height, was observed for the first time.     

Thermodynamic analysis of GaAs growth by molecular beam epitaxy at the surface structure transition from 3 × 1 to 4 × 2

The molecular beam epitaxy (MBE) growth of GaAs layers on a single crystal is studied in relation with the stability domain of the GaAs compound in the Ga-As binary system. The growth parameters, i.e. The Ga and As impinging atomic flows, are compared to the necessary flows as calculated by thermodynamics. In order to take into account in the real growth situation, which is not strictly at equilibrium, the flow balance at the surface of the crystal between the impinging flows and the growth and evaporated flows is written for quasi-equilibrium growth conditions, including condensation and evaporation coefficients that split the “so-called” sticking coefficient in parts related to the condensation or the evaporation phenomenon for each gaseous species. A comparison between the quasi-equilibrium simulation of the growth and the experiment is made with the assumption that the surface structure transition from gallium-stabilized to arsenic-stabilized surface corresponds to the growth of a GaAs crystal at its solidus boundary rich in gallium. The surface structure transitions are observed by reflection high energy electron diffraction (RHEED) and the impinging atomic flows are carefully calibrated and also controlled by RHEED oscillations as observed after gallium or arsenic excess as deposited on the surface. The results show that the growth is effectively performed close to equilibrium conditions as evidenced by the values of the condensations and evaporation coefficients. The evaporation coefficient of gallium is 0.4, showing that this component is the supersaturated one at the surface, and this value agrees with theoretical predictions for an evaporation process (during growth) controlled by the surface diffusion process of monoatomic species between steps.     

Growth mechanism of crystals from aqueous solutions

Microscopic processes occurring on the surface of a growing crystal or a dissolving one were observed by microcinematography. The crystals under observation were grown either in a drop of solution by evaporation or in a constant-temperature microscope stage at a chosen supersaturation. Small (approx. 0.1 mm) and large (approx. 10 mm) crystals of NaCl, Pb(NO₃)₂, NaNO₃, CdI₂, KDP and ADP were studied. It is concluded qualitatively that the layers, in general polygonal, originating in one or several active centres, are formed on the crystal face, never at the corners or edges. – The average velocity of layer motion was studied quantitatively in dependence on their thickness and supersaturation. The layer motion at constant supersaturation considerably fluctuated. – Surface patterns created by moving layers agree in most cases with predictions of the dislocation theory. Two categories of steps were found on the surface: ”︁real”︁ macrosteps and shock waves. – The velocity of layer motion for most compounds lies within (1–10) · 10⁻⁴ cm · s⁻¹.     

Desymmetrization of the polyhedral crystal shape of tetragonal lysozyme due to face-growth rate fluctuations

We have studied the desymmetrization of the polyhedral crystalline shape of tetragonal lysozyme crystals due to the growth rate differences of the equivalent {1 0 1} planes. Using atomic force microscopy, we have observed the evolution of the multifaceted structures composed of four equivalent {1 0 1} faces during growth. In our growth condition, lateral step flow, where a large density of dislocations acts as a source of steps, is the dominant growth mechanism. The measured step flow velocities are almost independent of the separation between the neighboring steps, revealing that the local face normal growth rate is determined by the local step density. By tracing the motion of the vertex surrounded by the {1 0 1} faces, we have found that the desymmetrization of the crystalline shape is due to the large fluctuation of the local face normal growth rate, which is comparable in magnitude to the average growth rate.     

Study of the Nature and Distribution of Elementary Steps on the (100) Cleavage Faces of MgO Single Crystals by Atomic Force Microscopy

Some observations made on the nature and distribution of monolayer (elementary) steps on the (100) cleavage faces of MgO single crystals by atomic force microscopy are presented and discussed. The following types of patterns of monolayer steps are described: (1) trains of steps, (2) steps terminating on the cleaved surface at the emergence points of screw dislocations, and (3) localized pinning of advancing steps at random sites (probably at the emergence points of edge dislocations). It is shown that: (1) the origins of emergence points of monolayer steps are devoid of hollow cores due to a small Burgers vector of dislocations and (2) the minimum distance between two emerging steps due to screw dislocations and between two pinning centres due to edge dislocations depends on their sign, and is determined by the mutual interaction between neighbouring dislocations.     

Atomic force microscopy study of lysozyme crystallization

Crystallization of lysozyme from solutions has been studied by the atomic force microscopy method. The surface morphology and the growth kinetics of several faces of the orthorhombic and monoclinic modifications of lysozyme crystals are considered. The surface images are obtained at molecular resolution. For the (010) face of orthorhombic lysozyme, the phenomenon of the surface reconstruction is established—doubling of the unit-cell parameter along the a-axis. The main growth parameters of lysozyme are determined—the kink density at steps, probabilities of the attachment and detachment of building blocks, the kink and step velocities, and the dependence of the fluctuation in the step position on time.     

Direct Growth of Aggregates on {110} Faces of Cadmium Mercury Thiocyanate Crystals

New growth phenomena ‐ direct incorporation of aggregates have been observed on the {110} faces of cadmium mercury thiocyanate CdHg(SCN)₄ crystals by atomic force microscopy. These aggregates grow in two forms: some directly cover up the steps and forms new growth layers; while others are just incorporated at the step edges. These aggregates, which are mostly oriented along [111] direction, are formed by small columnar structural units. The aggregates have the similar structure of CdHg(SCN)₄ crystals and greatly vary in nature with the variation of solution supersaturation σ and growth time t. With the increase of σ the aggregates become larger, consistent with the variation of growth units dimension with the supersaturation; and with the increase of growth time the aggregates become more structurally substantial. These observations have led to a new understanding about the crystal growth.     

Nanoscale morphological features in the structural evolution of HTSC films of organometallic aerosols

The evolution of the formation of a structure in high-temperature superconducting Bi₂Sr₂CaCu₂O₈ films obtained from organometallic aerosols is investigated by atomic force microscopy and scanning electron microscopy. Nanoscale granular supramolecular structures were found for the first time in the liquid-phase and pyrolytic stages. It is shown that pyrolytic processes occur within individual nanogranules. The minimum sizes of a nanogranule are 30–50 nm in base and 5 nm in height. In the high-order crystallization stage, epitaxial recrystallization occurs, as a result of which platelike crystallites are formed. They are 15–20 nm thick, have growth steps 1–5 nm in height, and are parallel to the substrate. The nonoriented morphological forms are individual three-dimensional crystallites up to 100 nm in size.