Mechanism of macrostep formation in solution growth of compound semiconductor and the evidence given by space experiment

The behavior of macrostep and its formation mechanism are discussed taking solution growth of compound semiconductor as an example. The macrosteps are created by the bunching of atomic steps on a misoriented substrate and they coalesce to form larger macrosteps. At a steady state, the vertical growth of the macrostep terrace is carried out by the atomic steps supplied from a screw dislocation. Space experiments conducted by the group of Professor K. W. Benz showed that the macrostep disappears under a temperature gradient when the growth rate is decreased below a certain value. It is concluded that the non‐uniform bulk diffusion of the solute is the driving force to create the macrostep.     

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.     

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.     

Sapphire evolution of the vicinal (0001) sapphire surface upon annealing in air

The evolution of a terrace-step nanostructure (TSN) on the sapphire (0001) surface misoriented by an angle of 0.1° with respect to the (\(10\bar 10\)) plane was observed by atomic force microscopy (AFM) at temperatures from 1273 to 1673 K. It was established that, with an increase in the annealing temperature to 1373 K, the step height attains 0.44 nm at a distance of 220 nm between steps; i.e., heating by 100 K doubles these parameters. In this case, the relief periodicity is retained. Rapid cooling of the substrate to 973 K leads to partial freezing of the surface structure, which makes it possible to observe the transition from one TSN to another. It was established that two steps coalescence upon annealing to 1373 K toward the (\(10\bar 10\)) plane, which has the lowest rigidity and, consequently, the lowest atomic density. The coalescence of two steps at a specified temperature is completed at a sufficiently large distance between the steps, at which their interaction energy is negligible. Upon further annealing of the samples above 1373 K, the steps overgrow to 1 nm; however, their periodicity is broken in this case.     

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.     

Multiatomic step formation on GaAs(001) vicinal surfaces during thermal treatment

We observed the surface morphology of vicinal GaAs(001) after thermal treatment in AsH₃/H₂ atmosphere by atomic force microscopy (AFM). Clear multiatomic steps were formed under the high temperature thermal treatment. Next, we investigated the mechanism of step bunching during thermal treatment by two experiments from the view point of Ga atom evaporation. One is the selective thermal treatment using a partially masked GaAs wafer, and the evaporation amount of Ga atoms was estimated by AFM. The other is the investigation of photoluminescence (PL) peak energy shifts for AlGaAs/GaAs single quantum wells with a thermal treatment process at the top of the GaAs quantum well layer, compared to those without thermal treatment. These results indicate that the evaporation hardly occurs during the thermal treatment process. Therefore, step bunching phenomena on GaAs(001) vicinal surfaces during thermal treatment are probably caused by migration of the atoms detached from upside steps and their re-incorporation to downside steps.     

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.     

Nonlinear dynamics of layer growth and consequences for protein crystal perfection

In situ high-resolution optical interferometry of lysozyme crystal growth reveals that under steady external conditions, the local growth rate R, vicinal slope p and step velocity are not steady but fluctuate by several times their average values. The variations in p, which is proportional to the local step density, indicate that these fluctuations occur through the dynamic formation of step bunches. Our previous work with unstirred solutions has shown that the fluctuation amplitude of R increases with supersaturation and crystal size (Vekilov et al., Phys. Rev. E 54 (1996) 6650). Based on scaling arguments and numerical simulations, we have argued that the fluctuations are the response of the coupled bulk transport and nonlinear interface kinetics to finite amplitude perturbations provided by the intrinsically unsteady step generation. In this paper, we emphasize the recently discovered spatio-temporal correlation between the sequence of moving step bunches and striations (compositional variations) in the crystal, visualized by polarized-light microscopy. Hence, these unsteady kinetics have detrimental effects on the perfection of the crystals, and means to reduce and eliminate them should be sought. To this end, based on the above conclusion as to the mechanism of the kinetic unsteadiness, we accelerated the bulk transport towards the interface by forced solution flow. We found that this results in lower fluctuation amplitudes. This observation confirms that the system-dependent kinetic Peclet number, Pe_k, i.e., the relative weight of bulk transport and interface kinetics in the control of the growth process, governs the step bunching dynamics. Since Pe_k can be modified by either forced solution flow or suppression of buoyancy-driven convection under reduced gravity, this model provides a rationale for the choice of specific transport conditions to minimize the formation of compositional inhomogeneities. Interestingly, on further increase of the solution flow velocities >500 μm/s, the fluctuation amplitudes in R increased again, while the average growth rate decreased. At low supersaturations, this leads to growth cessation. The growth instability, deceleration and cessation were immediately reversible upon reduction of the flow velocity. When solutions, intentionally contaminated with ∼1% of covalent lysozyme dimer were used, these undesirable phenomena occurred at about half the flow rates required in pure solutions. Thus, we conclude that enhanced convective supply of impurities to the interface causes an increase in step-bunching related defects, growth deceleration and, in some cases, cessation. Finally, we correlate the “slow protein crystal growth” to step bunch formation. We show that in the absence of significant step density variations, the kinetic coefficient for step propagation is as high as 4×10⁻³ cm/s, which is 1–2 orders of magnitude higher than the previously determined, apparent values for any protein.     

GaAs initial growth on InAs(001) vicinal surfaces observed by scanning tunneling microscopy

GaAs initial growth on InAs surfaces misoriented by 2° toward the [110] and [1 0] directions was investigated by scanning tunneling microscopy (STM). In the STM images of both InAs vicinal surfaces after GaAs deposition, white lines running in the [1 0] direction, corresponding to the grown GaAs surface, were observed. Almost all of the lines were attached only to steps running in the [110] direction (B-type steps) on both InAs surfaces; that is, the lines were seldom attached to steps running in the [1 0] direction (A-type steps). These results indicate that the B-type steps are more favorable for the sticking of deposited Ga atoms than the A-type steps during GaAs initial growth on InAs vicinal surfaces.     

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.     

Modelling the growth of nitrides in ammonia‐rich environment

Surface properties and the principal processes at the growth of gallium nitride on GaN (0001) face in ammonia‐based are modeled using DFT (density functional theory – SIESTA code) ab initio calculations and 2‐d diffusion analysis. The GaN growth methods are: ammonia‐source MBE, MOVPE, and also HVPE. The adiabatic trajectories, calculated for hydrogen‐rich and hydrogen‐free state of the GaN(0001) surface, include the adsorption of NH₃, GaCl and HCl molecules and the desorption of Ga atoms. The adsorption of ammonia and GaCl has no energy barrier. Thus, in contrast to the results concerning Plasma‐Assisted Molecular Beam Epitaxy (PA MBE), proving that the GaN(0001) surface remains in metal‐rich state, these results indicate that, in the ammonia‐rich environment, typical for HVPE and MOVP growth, the GaN(0001) surface remains in the nitrogen‐rich state. In the case of HCl adsorption, the energy barrier depends on the surface coverage, and could reach 2.0 eV. The direct desorption of single Ga atom has the energy barrier, close to 7 eV. This indicates that Ga surface diffusion (growth controlling process) length is very large, leading to strong interaction of the step kinetics and the diffusion on the terraces. This interaction leads to double–step intertwined structures both in the case of dislocation‐mediated spiral growth and in the step flow growth mode. These morphologies, proposed by the geometric arguments, are observed in the atomic force microscopy (AFM) scans of the GaN(0001) surface. Additionally we have compared the interaction energy of two hydrogen atoms obtained in the DFT SIESTA and the high precision Gaussian in coupled cluster singles, double and perturbation triples CCSD(T) approximation. Both approaches yielded virtually identical interaction energy confirming the validity of DFT analysis of ammonia‐rich growth of GaN. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Role of step orientation and step-step interaction in the in-situ creation of laterally confined semiconductor nanostructures via growth: A simulated annealing study on a parallel computing platform

We report a systematic simulated annealing study of the energetics of bi-layer height steps with edges running parallel (A type), perpendicular (B type) and at 45° (C type) to surface As dangling orbitals on As(2×4) reconstructed GaAs(001) vicinal surfaces. Employing semi-empirical interatomic potentials having two- and three-body interaction terms, we calculate the step energy and the step-step interaction energy as a function of the step separation. The step-step interaction energies are attractive for B type steps and repulsive for A and C types, in all cases decreasing in magnitude with increasing step separation. The results affirm a connection between the orientation of dangling orbitals at the step edge and the corresponding step-step elastic interaction induced nature and directionality of the surface stress. Such surface stress could be a driving force for the directional migration of atoms observed in the case of MBE growth on patterned non-planar GaAs substrates that has led to the realization of quantum wire and quantum box structures.     

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.     

Assessing the dynamics of liquid-phase solution growth via step growth models: From BCF to FEM

We examine the capability of the classical analyses of W.K. Burton, N. Cabrera and F.C. Frank (BCF) [Phil. Trans. Roy. Soc. London 243 (1951) 299–358], A.A. Chernov [Sov. Phys. Usp. 4 (1961) 116–148], G.H. Gilmer, R. Ghez and N. Cabrera [J. Cryst. Growth 8 (1971) 79–93], and R. Ghez and G.H. Gilmer [J. Cryst. Growth 21 (1974) 93–109] to model solution crystal growth and present a new formulation free of prior idealizations. Our model is based on an analysis of step motion along a vicinal crystal surface coupled with a detailed accounting of bulk and surface transport, thus representing phenomena ranging from the macro-scale to nanometers. The time-dependent governing equations of the model are solved simultaneously and self-consistently via a front-tracking Galerkin finite element method (FEM) in an arbitrary Lagrangian–Eulerian reference attached to the moving steps. Step motion and interactions are analyzed under several classical scenarios, and new results are shown to demonstrate the utility of the finite element model for studying the dynamics of growth. Such models promise to complement the rapidly advancing experimental tools applied to study solution crystal growth and provide a more rigorous underpinning of our understanding of these systems.     

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)     

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)     

In situ atomic force microscopy studies of surface morphology,growth kinetics,defect structure and dissolution in macromolecular crystallization

Surface morphologies of thaumatin, catalase, lysozyme and xylanase crystals were investigated using in situ atomic force microscopy. For thaumatin, lysozyme and xylanase crystals, growth steps having a height equal to the unit cell parameter were produced both by screw dislocations and two-dimensional nuclei. Growth of catalase crystals proceeded in alternating patterns exclusively by two-dimensional nucleation and the successive deposition of distinctive growth layers, each having a step height equal to half the unit cell parameter. The shapes of islands on successive layers were related by 2-fold rotation axes along the 〈0 0 1〉 direction. Experiments revealed that step bunching on crystalline surfaces occurred either due to two- or three-dimensional nucleation on the terraces of vicinal slopes or as a result of uneven step generation by complex dislocation sources. Growth kinetics for thaumatin and catalase crystals were investigated over wide supersaturation ranges. Strong directional kinetic anisotropy in the tangential step growth rates in different directions was seen. From the supersaturation dependencies of tangential step rates and the rates of two-dimensional nucleation, the kinetic coefficients of the steps and the surface free energy of the step edge were calculated. Adsorption of impurities which formed filaments on the surfaces of catalase and thaumatin crystals was recorded. Cessation of growth of xylanase and lysozyme crystals was also observed and appeared to be a consequence of the formation of dense impurity adsorption layers. Crystal growth resumed upon scarring of the impurity adsorption layer and clearing of the crystal surface with the AFM tip. Adsorption of three-dimensional clusters, which consequently developed into either properly aligned multilayer stacks or misaligned microcrystals was recorded. For catalase crystals, incorporation of misoriented microcrystals as large as 50×3×0.1 μm³ produced elastic deformations in growth layers of ≈0.6%, but did not result in the defect formation. Etching experiments on catalase crystals revealed high defect densities.     

Kinetic Investigations within the Transition Region from Polyhedral to Skeletal Growth Mode (V). Growth Kinetics of the Pyramidal Face of Zinc Single Crystals under Diffusion Conditions

The growth kinetics of the pyramidal face of zinc single crystals is studied in the presence of argon. The curves size vs. time provide evidence that smaller crystals grow in a kinetic regime and after reaching a certain critical size their growth continues in a diffusion regime. The growth kinetics of faces {101 } and {0001} are compared. It is established that the growth of both faces simultaneously changes from a kinetic to a diffusion growth mode. During the transition between the two regimes, however, loss of the morphological stability only of the smooth {0001} face is observed, while the {101 } face with macro steps formed on the surface acquires a skeletal shape after prolonged growth. It is shown that the appearance of morphological instability depends on the surface structure of the crystal faces.