The size dependence of equilibrium elastic strain in finite epitaxial islands

The equilibrium elastic strain in epitaxial islands of small size is shown to have a sawtooth dependence on island width by minimizing the systems energy as calculated from a periodic interaction potential between substrate and overgrowth. Such a sawtooth variation is consistent with Vincent's observations and idea that a given misfit between island and substrate may not be entirely accommodated by an integral number of identical misfit dislocations, and hence, the remaining misfit, which depends in part on island width, will be accommodated by residual elastic strain. The present calculations of mechanical equilibrium support these ideas and further reveal that in some cases misfit dislocations may over compensate for the misfit, thereby introducing an elastic strain of opposite sign to that normally expected. Other results of the calculations are in agreement with earlier theoretical and experimental observations.     

Prediction of dislocation formation in epitaxial multilayers subject to in-plane loading

A theoretical model is described to predict equilibrium distributions of misfit dislocations in one or more anisotropic epitaxial layers of a multilayered system deposited on a thick substrate. Each layer is regarded as having differing elastic and lattice constants, and the system is subject to biaxial in-plane mechanical loading. A stress transfer methodology is developed enabling both the stress and displacement distributions in the system to be estimated for cases where the interacting dislocations are of a pure edge configuration. Energy methods are used to determine equilibrium distributions of the dislocations for given external applied stress states. It is shown that the new model accurately reproduces known exact analytical solutions for the special case of just one isotropic epitaxial layer applied to an isotropic semi-infinite substrate having the elastic constants of the substrate but differing lattice constants. The model is used to consider equilibrium dislocation distributions in capped epitaxial systems with misfit dislocations. It is shown that the simplifying assumptions often made in the literature, regarding the uniformity of elastic properties and the neglect of anisotropy, can lead to critical thicknesses being underestimated by 15–18%. The application of uniaxial tensile stresses increases the value of critical thicknesses. The model can be used to analyse dislocations in various non-neighbouring layers provided the dislocation density has the same value in all layers in which dislocations have formed. This type of analysis enables the prediction of the deformation of metallic multilayers subject to mechanical and thermal loading.     

The role of surface steps in the asymmetric surface dislocation nucleation in vicinal heterostructures with compressive and tensile stresses

The surface nucleation of misfit dislocations in vicinal (001)-oriented heterostructures is discussed. It is shown that beside the asymmetrical stressing of opposite dislocation slip planes due to the vicinal substrate, the surface steps have a similar effect. The effect of the steps has the same-sign asymmetry for a compressive stressed epilayer, but is opposite in the tensile case. The effect on dislocation nucleation energy is calculated. For miscut angles used normally, the step energy contribution exceeds that due to the vicinal substrate. The effect on epilayer tilting is also discussed.     

Energetics of growing epilayer-substrate combinations of comparable bond strength and in Kurdjumov-Sachs orientation

In this paper we address the problems related to critical misfit and thickness in epilayer-substrate combinations of comparable bond strengths; specifically the case in which a pseudomorphic monolayer (ML) is stable and the critical thickness is about three MLs or less. Of particular interest are the average energies related to misfit strain f _KS and misfit dislocations (MDs)—in the latter case the individual contributions of the oscillatory strains V and the epilayer-substrate disregistry V_MD. The individual energies are of interest because they may play different roles in the realization of specific growth modes. The analytical approach involves the following assumptions: (a) a rigid substrate as source of a periodic epilayer atom-substrate interaction potential which we model in terms of a low order truncated Fourier series; and (b) an epilayer which (i) deforms harmonically with zero strain gradient normal to the film plane, (ii) grows in Kurdjumov-Sachs (KS) orientation due to small misfit. f _KS and in the layer-by-layer growth mode.Arguments are presented claiming that this interfacial situation may be approximated by a one-dimensional problem in which epilayer stiffness constants and equilibrium structure, as well as epilayer-substrate interaction depend on epilayer thickness; which poses a complex problem. An approximate solution could be obtained by assuming these quantities to be independent of thickness and proximities of the vacuum and the substrate. The most prominent conclusions are that the equilibrium density of MDs and hence the transition from misfit accommodation by MS to one containing MDs is a catastrophic process and that sustained minimum energy may require the overcoming of an energy barrier. While elementary implementation of the results to equilibrium growth mode theory suggests—independently of the catastrophic nature—that energetically favored misfit strain relief by misfit dislocations may, or may not, effect a transition to Stranski-Krastanov growth, a crude numerical calculation favors the transition. A proper implementation of the results require extensive numerical calculations and is planned for the near future.     

The surface and interface nucleation of misfit dislocations as a possible source of asymmetric strain relaxation in vicinal heterostructures

The surface nucleation of misfit dislocations in vicinal (001) oriented heterostructures with compressive and tensile stresses is discussed. It is shown that beside the asymmetrical stressing of opposite dislocation slip planes due to the vicinal substrate, the surface steps have a similar effect. The effect of the steps has the same-sign asymmetry for a compressive stressed epilayer, but opposite for the tensile case. The effect on dislocation nucleation energy is calculated. For miscut angles used normally, the step energy contribution exceeds that of due to the vicinal substrate. The extension to interface nucleation is treated qualitatively.     

Effect of epitaxial strain on the atomic structure of Pd clusters on MgO(100) substrate

Morphology and atomic structure of supported Pd clusters on MgO(100) substrate are investigated theoretically using a mixed approach: a semi-empirical potential for the metal bonding within the cluster and a potential fitted to ab initio calculations for the metal-oxide interaction. We find that the clusters adopt a truncated pyramidal morphology in agreement with experimental results. The detailed study of the epitaxial relation as a function of cluster size shows the existence of a critical size around 3 nm where elastic strain due to the misfit between the substrate and the deposit is released by the introduction of interfacial dislocations.     

Occurrence of rotation domains in heteroepitaxy

Heteroepitaxy can involve materials with a misfit of crystal structure. Rotation domains in the epilayer are a fundamental consequence. We derive a general expression for their (minimum) number which is determined by the mismatch of the rotational symmetries of the substrate and epilayer. In the case of a mismatch of rotational symmetry, the number of rotation domains of material A on material B is different from that of B on A. A larger number of rotation domains can occur due to domain structure or nearly fulfilled additional symmetries of the substrate surface.     

Investigation of dislocations in 8circ off-axis 4H-SiC epilayer

This paper reports that the etching morphology of dislocations in 8^circ off-axis 4H-SiC epilayer is observed by using a scanning electronic microscope. It is found that different types of dislocations correspond with different densities and basal plane dislcation (BPD) array and threading edge dislocation (TED) pileup group lie along some certain crystal directions in the epilayer. It is concluded that the elastic energy of threading screw dislocations (TSDs) is highest and TEDs is lowest among these dislocations, so the density of TSDs is lower than TEDs. The BPDs can convert to TEDs but TSDs can only propagate into the epilyer in spite of the higher elastic energy than TEDs. The reason of the form of BPDs array in epilayer is that the big step along the basal plane caused by face defects blocked the upstream atoms, and TEDs pileup group is that the dislocations slide is blocked by dislocation groups in epilayer.     

Nano-islands on a composite substrate with misfit dislocations

Spatial arrangements of nano-islands (quantum dots) on the free surface of a composite two-layer substrate containing misfit dislocations of edge type are theoretically examined. It is shown that the elastic interaction between misfit dislocations and nano-islands is capable of causing coagulation of nano-islands. The coagulation of nano-islands is shown to be favourable when the upper-layer thickness is smaller than a critical thickness, H₀. An analytical form of H₀ is presented for the partial case with four-to-one correspondence between nano-islands and cells of the misfit dislocation network. Received: 5 December 2000 / Accepted: 29 March 2001 / Published online: 20 June 2001     

Sheared solid materials

We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. We assume that the elastic energy density is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure. With this new ingredient, solving the equations yields formation of dislocation dipoles or slips. In plastic flow high-density dislocations emerge at large strains to accumulate and grow into shear bands where the strains are localized. In addition to the elastic displacement, we also introduce the local free volumem. For very smallm the defect structures are metastable and long-lived where the dislocations are pinned by the Peierls potential barrier. However, if the shear modulus decreases with increasingm, accumulation ofm around dislocation cores eventually breaks the Peierls potential leading to slow relaxations in the stress and the free energy (aging). As another application of our scheme, we also study dislocation formation in two-phase alloys (coherency loss) under shear strains, where dislocations glide preferentially in the softer regions and are trapped at the interfaces.     

晶体相场法模拟异质外延过程中界面形态演化与晶向倾侧

采用晶体相场模型研究了异质外延过程中失配应变与应力弛豫对外延层界面形态演化的影响, 并对由衬底倾角引起的外延层晶向倾侧进行了分析.研究结果表明: 在有一定倾角的衬底晶体上进行外延生长时,若衬底和外延层之间失配度较大 (ε>0.08),外延层中弹性畸变能会以失配位错的形式释放, 最终薄膜以稳定的流动台阶形式生长且外延层的晶向倾角与衬底倾角呈近似线性关系. 而当衬底和外延层之间失配度较小(ε<0.04)不足以形成失配位错时, 外延层中弹性畸变能会以表面能的形式释放,最终使薄膜以岛状形态生长. 在高过冷度条件下,衬底倾角和失配度较大时,衬底和外延层之间会形成由大量位错规则排列而成的小角度晶界从而显著改变外延层的生长位向.     

Secondary dislocation structures in a Ni–TiN system from the GMS and O-lattice theory

The preferred state in an interface is the key to evaluating misfit strain, especially for the interphase interfaces in secondary preferred state. The structure of good matching site (GMS) in a GMS clusters offers a guidance for the preferred state, especially for identifying the coincidence site lattice in two dimension for secondary preferred state and the Burgers vectors in a large misfit system. Here, we combine the GMS with O-lattice theory to calculate the secondary dislocation structure in the habit planes of the type II and III TiN precipitates in a Ni–TiN system. We find that under a slight elastic strain, the type III habit plane contains a single set of secondary dislocations, consistent with the experimental observation. The type II habit plane contains three sets of secondary dislocations, two of which can be relaxed to be nearly parallel and another of which may be invisible in diffraction contrast due to its short Burgers vector. The present study provides a reasonable interpretation to the observed interfacial dislocations, and also suggests Burgers vectors for the dislocations that are not determined experimentally.     

Misfit dislocations in nanocomposites with quantum dots,nanowires and their ensembles

We review theoretical concepts and experimental results on the physics of misfit dislocations in nanocomposite solids with quantum dots (QDs) and nanowires (quantum wires). Special attention is paid to thermodynamic theoretical models of formation of misfit dislocations in QDs and nanowires, including composite core–shell nanowires. The effects of misfit dislocations on the film growth mode during heteroepitaxy and phase transitions in QD systems are analysed. Experimental results and theoretical models of the ordered spatial arrangement of QDs growing on composite substrates with misfit dislocation networks are discussed. The influence of subsurface dislocations in composite substrates on the nucleation of QDs and nanowires on the substrate surface is considered. Models of misfit strain relaxation and dislocation formation in nanofilms on compliant substrates are also reviewed.     

Proximity Effects of the Vacuum and Substrate on the Behavior of Ultrathin Epilayers

The present considerations are motivated by (i) the need to grow thin films with perfection in crystallinity and thickness uniformity, both of importance for purposes of device fabrication and the study of two-dimensional systems, and (ii) by the importance to understand the roles of vacuum and substrate proximity effects during the ultrathin growth stage, as these effects may be decisive in tailoring the final product. It is accepted (a) that the need is best served by growing epitaxially—a substrate proximity phenomenon—and (b) that the quality of epilayers depends greatly on the mode of misfit accommodation at the epilayer-substrate interface and on the mode of growth. In classical theoretical analyses of epitaxy, these modes are modeled in terms of the interfacial lattice misfit, the amplitudes of lateral variation of interfacial atomic interaction, defect energies of the bicrystal and the elastic properties of the epilayer. The aim of this paper is to report on and search for perspective of attempts to quantify—using embedded-atom method potentials—the effects of vacuum and substrate proximities on these modeling parameters. The objective is to focus attention on the fact that the ultrathin film values of these parameters may be significantly different from their bulk values, which have been employed in the past for predictive purposes.     

Surface morphology of InGaAs on GaAs(100) by chemical beam epitaxy using unprecracked monoethylarsine, triethylgallium and trimethylindium

Temperature-dependent evolution of surface corrugation and the interface dislocation in In_0.15Ga_0.85As epilayer on GaAs(100) substrate grown by chemical beam epitaxy using unprecracked monoethylarsine have been investigated by atomic force microscope (AFM) and transmission electron microscopy (TEM). AFM images showed that the line direction of surface ridge changes from [011] to [0 1] with increasing temperature. However, TEM micrographs showed that dislocation networks are formed along both [011] and [0 1] directions at the interface. These results indicate that growth kinetics on the terrace and at surface steps generated by the dislocations play an important role in determining the direction of surface corrugation. We suggest that the temperature-dependent change of surface corrugation is caused by an anisotropic surface diffusion on the terrace and different sticking probability of adsorbates on the surface steps which were produced by interface misfit dislocation along the two orthogonal surface directions.     

Ordered step arrays on evaporated As (0001) vicinal surfaces

A computational procedure dealing with a one-dimensional epitaxial monolayer model was developed in part I. In this part it is extended and applied to the two-dimensional case, allowing for misfit along two perpendicular interfacial directions. The model employed differs slightly from that used by van der Merwe in that the overgrowth film is simulated by a plane of atoms linked to each other by elastic springs. This allows for an exact determination of the equilibrium boundary conditions. The results show (i) that the rectangular boundary edge is slightly deformed, lateral contractions occurring where the misfit dislocations intersect the boundary edge, (ii) that the dependence of stable structures on misfit is in good agreement with the analytical results of van der Merwe, (iii) that misfit dislocations are introduced alternately at the mutually perpendicular edges of a system having quadratic symmetry, (iv) that a segmented dependence of lowest energy on crystal size is obtained, one segment for each additional dislocation, (v) that a saw-toothed dependence of average strain on crystal size, in qualitative agreement with the experimental work of Vincent, results and (vi) that a fine structure in the energy curves results from discrete adatom peripheral growth.     

A theoretical investigation of glide dislocations in BN/AlN heterojunctions

Glide dislocations with periodic pentagon-heptagon pairs are investigated within the theory of one-dimensional misfit dislocations in the framework of an improved Peierls-Nabarro (P-N) equation in which the lattice discreteness is fully considered. We find an approximate solution to handle misfit dislocations, where the second-order derivative appears in the improved P-N equation. This result is practical for periodic glide dislocations with narrow width, and those in the BN/AlN heterojunction are studied. The structure of the misfit dislocations and adhesion work are obtained explicitly and verified by first-principles calculations. Compared with shuffle dislocations, the compression force in the tangential direction of glide dislocations has a greater impact on the normal direction, and the contributions of the normal displacement to the interfacial energy cannot simply be ignored.     

Ga1-xInxAs/InAsyP1-y/InP异质结的MOCVD生长及表征

Ga1-xInxAs(x>0.53)材料是未来长距离低损耗光纤通信的理想光源材料和探测器材料之一.我们采用水平常压MOCVD系统,在InP衬底上成功地生长了Ga1-xInxAs(x>0.53)/InAsyP1-y/Inp异质结材料.其中InAs1-yPy为组份阶梯变化的多层结构.由样品的(400)面X光衍射结果测定了各层组份.由二次离子质谱(SIMS)得到了样品剖面组份变化结果,证明InAs1-yPy层组份为阶梯状变化的.通过对光致发光结果和X光衍射结果比较,可以看到,InAsyP1-y层通过位错和弹性畸变二种方式来释放或积累Ga1-xInxAs与InP间的失配应力,从而减少了Ga1-xInxAs中的失配位错.有效地改善了Ga1-xInxAs的质量.已获得了x高达0.94表面光亮的Ga1-xInxAs/InAs1-yPy/InP异质结材料.     

A generalized Peierls–Nabarro model for kinked dislocations

We present a generalized Peierls–Nabarro model for curved dislocations incorporating directly the Peierls energies for both straight dislocations and dislocation kinks. In our model, the anisotropic elastic energy is calculated efficiently using the discrete Fourier transform on the discrete lattice sites of the slip plane, and the discreteness in both the elastic energy and the misfit energy is included. We have used our model to calculate the kink migration and nucleation energies of the 30° dislocations in silicon. The results agree well with those obtained using atomistic potentials and first principles calculations, and the experimental results.     

Au/Cu(001)异质外延岛演化的分子动力学研究

利用分子动力学弛豫方法模拟了Au/Cu(001)异质外延生长初期Au异质外延岛的形貌演化，分析了Au外延岛演化过程中的局域应力及与基体结合能随表面岛尺寸的变化. 研究结果表明：当异质外延岛小于7×7时，外延岛原子分布呈现赝Cu点阵形貌；当外延岛达到8×8后，外延岛内开始出现失配位错，失配位错数量随外延岛尺寸的增加而增加. 局域压力分析指出，外延岛上原子之间的近邻环境不同导致了所受应力的差异，而外延岛的形变则是由外延岛原子的应力分布所决定. 研究还发现，失配位错的产生导致错位原子与基体原子之间的结合强度减弱，但相对增加了非错位原子与基体原子之间的结合强度. 关键词： 异质外延 表面形貌 局域压力 分子动力学模拟