Specific features of plastic relaxation of a metastable Ge x Si1 − x layer buried between a silicon substrate and a relaxed germanium layer

Heterostructures Ge/Ge _x Si_{1 ? x} /Si(001) grown by molecular beam epitaxy have been investigated using atomic scale high-resolution electron microscopy. A germanium film (with a thickness of 0.5–1.0 μm) grown at a temperature of 500°C is completely relaxed. An intermediate Ge_0.5Si_0.5 layer remains in a strained metastable state, even though its thickness is 2–4 times larger than the critical value for the introduction of 60° misfit dislocations. It is assumed that the Ge/GeSi interface is a barrier for the penetration of dislocations from a relaxed Ge layer into the GeSi layer. This barrier is overcome during annealing of the heterostructures for 30 min at a temperature of 700°C, after which dislocation networks having different degrees of ordering and consisting predominantly of edge misfit dislocations are observed in the Ge/GeSi and GeSi/Si(001) heteroboundaries.     

Edge misfit dislocations in GexSi1 ? x/Si(001) (x ～ 1) heterostructures: role of buffer GeySi1 ? y (y < x) interlayer in their formation

The structure of dislocations in Ge _x Si_{1 − x} (x ∼ 0.4–0.8) films grown by molecular beam epitaxy on Si(001) substrates tilted by 6° toward the nearest (111) plane has been studied. The epitaxy of GeSi films on substrates deviating from the exact (001) orientation has allowed us to establish the main mechanism of formation of edge misfit dislocations (MDs), which most effectively (for heterostructures of the given composition) relieve stresses caused by the mismatch between lattice parameters of the film and substrate. Despite the edge MDs being defined as immobile (sessile) dislocations, their formation proceeds according to the gliding mechanism proposed by Kvam et al. [J. Mater. Res. 5, 1900 (1990)]. A comparative estimation of the propagation velocities of the primary and induced 60° dislocations, as well as the resulting 90° MDs, has been performed. It has been established that the condition providing for the most effective edge MD formation by the induced nucleation mechanism is the appearance of 60° MDs in a stressed film immediately after it reached a critical thickness. A source of these dislocations can be provided by a preliminarily grown buffer GeSi layer that occurs in a metastable state at the initial stage of plastic relaxation.     

Low-density dislocation arrays at heteroepitaxial Ge/GaAs-interfaces investigated by high voltage electron microscopy

High-voltage electron microscopy in combination with a large-area thinning technique has been applied to thin epitaxial Ge layers on GaAs substrates. These layers exhibit 60° misfit dislocations along the 〈110〉 directions parallel to the interface. Various dislocation reactions are evaluated from the electron micrographs, e.g. the formation of non-glissile 90° dislocations from two nearly parallel 60° dislocations and the annihilation reaction of two crossing 60° dislocations with identical Burgers vectors. The latter reaction occasionally leads to a dislocation multiplication. The misfit dislocations in very thin layers (～0.5 μm thickness and a linear dislocation density of less than 100 dislocation lines/cm) tend to be arranged in groups rather than being equidistant. Consequences for the interpretation of x-ray topograms are discussed.     

Interface dislocation structures at the onset of coherency loss in nanoscale Ni–Cu bilayer films

We have performed a transmission electron microscopy study, using weak beam imaging, of the interface dislocation arrays that form initially at the (001) Ni–Cu interface during coherency loss. Interface dislocations were absent in the 2.5?nm Ni/100?nm Cu bilayers, but were present in the 3.0?nm Ni samples, indicating that the critical Ni film thickness for coherency loss is between 2.5 and 3?nm. The key features of the interface dislocation structure at the onset of coherency loss are: (i) the majority of interface dislocations are 60° dislocations, presumably formed by glide of threading dislocations in the coherently stressed Ni layer, and have Burgers vector in the {111} glide plane; (ii) the interface contained approximately 5% Lomer edge dislocations, with Burgers vector in the {001} interface plane, and an occasional Shockley partial dislocation and (iii) isolated segments of interface dislocations terminating at the surface are regularly observed. Possible mechanisms that lead to these dislocation configurations at the interface are discussed. This experimental study shows that near the critical thickness, accumulation of interface dislocations occurs in a somewhat stochastic fashion with favourable regions where coherency is first lost.     

Heteroepitaxy of GexSi1 ? x (x ～ 0.4–0.5) films on Si(001) substrates misoriented to (111): Formation of short edge misfit dislocations alone in the misorientation direction

Relaxation of mechanical misfit stresses in Ge _x Si_{1 − x} (x ∼ 0.4–0.5) epitaxial films grown by molecular epitaxy on Si substrates misoriented from the exact orientation (001) by an angle of 6° has been studied. Possible cases of induced nucleation and interaction of 60° misfit dislocations (MDs) propagating in the misorientation direction with the formation of short edge MD segments are considered. Such configurations are classified and their various forms experimentally detected by TEM are presented. It is shown that short edge MDs are formed by two different mechanisms: (A) correlated or induced nucleation of a complementary 60° dislocation half-loop followed by the formation of an edge dislocation segment; and (B) the formation of a 90° MD segment upon intersection of the already existing complementary 60° MDs gliding in oppositely inclined {111} planes. The nonequivalency of the interaction of 60° MDs propagating in opposite directions along the substrate misorientation is shown.     

Strained germanium films in Ge/InGaAs/GaAs heterostructures: Formation of edge misfit dislocations at the Ge/InGaAs interface

Heterostructures of the “strained Ge film/artificial InGaAs layer/GaAs substrate” type have been grown by molecular beam epitaxy. A specific feature of these structures is that the plastically relaxed (buffer) InGaAs layer has the density of threading dislocations on a level of 10⁵–10⁶ cm⁻². These dislocations penetrate into the strained Ge layer to become sources of both 60° and 90° (edge) misfit dislocations (MDs). Using the transmission electron microscopy, both MD types have been found at the Ge/InGaAs interface. It has been shown that the presence of threading dislocations inherited from the buffer layer in a tensile-strained Ge film favors the formation of edge dislocations at the Ge/InGaAs interface even in the case of small elastic deformations in the strained film. Possible mechanisms of the formation of edge MDs have been considered, including (i) accidental collision of complementary parallel 60° MDs propagating in the mirror-tilted {111} planes, (ii) induced nucleation of a second 60° MD and its interaction with the primary 60° MD, and (iii) interaction of two complementary MDs after a cross-slip of one of them. Calculations have demonstrated that a critical layer thickness (h _c ) for the appearance of edge MDs is considerably smaller than h _c for 60° MDs.     

Formation of misfit edge dislocations in Ge x Si1 ? x films ( x ～ 0.4–0.5) grown on tilted Si(001) → (111) substrates

The dislocation structure of Ge _x Si_{1 − x} films (x ∼ 0.4–0.5) grown by molecular epitaxy on Si(001) substrates tilted by 6° about the 〈011〉 axis was studied. It is shown that, in the tilt direction, edge misfit dislocations (MDs) arise only in the form of short segments lying on the intersections of 60° MDs. As a result, the total length of edge MDs along the substrate tilt direction is smaller than that along the tilt axis. The deviation of the substrate surface from the singular plane made it possible to detect a dislocation configuration that consists of a short segment of an edge MD and two diverging 60° MDs propagating from it in the tilt direction. The formation of the segment is assumed to begin with simultaneous nucleation of complementary dislocation half-loops that form a short edge MD on the interface and then propagate on one side as two diverging 60° MD lines. Original Russian Text ? Yu.B. Bolkhovityanov, A.K. Gutakovskii, A.S. Deryabin, L.V. Sokolov, 2008, published in Fizika Tverdogo Tela, 2008, Vol. 50, No. 10, pp. 1783–1787.     

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     

外延生长薄膜中失配位错形成条件的分子动力学模拟研究

运用分子动力学方法对负失配条件下的外延铝簿膜中失配位错的形成进行了模拟研究.所采 用的原子间相互作用势为嵌入原子法(EAM)多体势.模拟结果显示：在500K下长时间静态弛豫 ，表面和内部结构完整的外延膜在9—80原子层厚度范围内(约为其热力学临界厚度的3—40 倍)均不形成失配位错，而在薄膜表面预置一个单原子层厚、三个原子直径大小的凸台或凹 坑时，失配位错则能够在15个原子层厚的外延膜上迅速形成：在动态沉积生长条件下，表面 自然形成凹凸，初始厚度为9个原子层厚的外延膜在沉积生长中迅速形成失配位错.在三种条 件下，所形成的位错均为伯格斯矢量与失配方向平行的全刃位错.分析发现：在压应力作用 下，表面微凸台诱发了其侧薄膜内部原子的挤出，造成位错形核；而表面微凹坑则直接因压 应力作用形成了一个表面半位错环核. 关键词： 外延薄膜 失配位错 分子动力学 铝     

Misfit dislocation loops in composite core-shell nanoparticles

The critical conditions have been calculated for the generation of circular prismatic loops of misfit dislocations at the interfaces in spherically symmetric composite core-shell nanoparticles. It has been shown that the formation of these loops becomes energetically favorable if the misfit parameter exceeds a critical value, which is determined by the geometry of the system. The most preferred position of the dislocation loop is in the equatorial plane of the nanoparticle. For a given radius of the nanoparticle, there is a minimum value of the critical misfit parameter below which the generation of a misfit dislocation is energetically unfavorable for any ratio of the core and shell radii. For a misfit parameter exceeding the minimum critical value, there are two critical values of the reduced radius of the particle core in the interval between which the generation of a dislocation loop is energetically favorable. This interval increases with increasing misfit parameter for a fixed particle size and decreases with decreasing particle size for a fixed misfit parameter.     

Edge misfit dislocation formation at the interface of a nanopore and infinite substrate with surface/interface effects

The model of an edge misfit dislocation at the interface of the hollow nanopore and the infinite substrate with surface/interface stress is investigated. Using the complex variable method, analytical solutions for complex potentials of a film due to an edge misfit dislocation located in the film with surface/interface effect are derived, and the stress fields of the film and the edge misfit dislocation formation energy can be obtained. The critical conditions for edge misfit dislocation formation are given at which the generation of an edge misfit dislocation is energetically favourable. The influence of the ratio of the shear modulus between the film and the infinite substrate, the misfit strain, the radius of the nanopore and the surface/interface stress on the critical thickness of the film is discussed.     

Equilibrium critical thickness for a wurtzite InGaN/GaN heterostructure

We present a finite element model to simulate a combined strained In_xGa_1−xN/GaN heterostructure and an edge misfit dislocation on the basal {0001} slip plane, taking the anisotropic elasticity into account. The introduction of a misfit dislocation partially relaxes the misfit strain. The model directly gives the residual strain, which is the exact strain field stored in the system after relaxation. The critical thickness is then determined based on an overall energy minimization approach including the dislocation core contribution. Compared with the results from other methods and available experimental data, our approach is appropriate for describing the critical thickness of the wurtzite InGaN/GaN material system.     

硅中位错运动速度

本文用化学侵蚀法显示了硅晶体印压产生的位错。测量了在不同温度、不同切应力下“花结”上刃型(或60°)位错的运动速度。设位错运动是热激活的,激活能为～2.94eV.比较了900℃下刃型(或60°)位错及螺型位错的速度,后者较小。在不同样品上进行速度的测定,说明原生位错对形变位错运动有阻碍作用。观察到原生位错和晶界位错在外加力作用下的增殖,对位错在增殖中的速度进行了测量。讨论了本工作所用的实验方法,并分析了影响速度测量值的某些因素。     

Plastic relaxation of mixed dislocation in axial nanowire heterostructures using Peach–Koehler approach

In this Letter, the plastic relaxation introduced by typical 60° mixed dislocation in zinc‐blende axial nanowire (NW) heterostructures is evaluated by numerical Peach–Koehler approach which reflects the interaction between coherent strain field and misfit dislocation. Cylindrical NW epilayers grown on NW and bulk substrate are separately modeled. We reveal that straight 60° dislocation with Burgers vector (a /2) 〈101〉 would always generate at NW center orienting [111], while aspect ratio dependent off‐center equilibrium position should be expected for NW epilayer along [001]. Moreover, the critical diameters, below which coherency is maintained, are predicted based on energy balance criterion for axial NW heterostructures along predominating growth direction [111]. The results are compared with existing theory and experimental observations. Our work provides a necessary quantitative complement to the understanding of plastic relaxation and coherency limit in axial NW heteroepitaxy. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

外延PbZr0.4Ti0.6O3薄膜厚度对其铁电性能的影响

从Landau-Devonshire唯象理论出发，考虑到晶格失配导致的NFDA3位错应力场与极化场的耦合，研究了在SrTiO₃衬底上外延生长的PbZr_0.4Ti_0.6O₃薄膜厚度对其自发极化强度、电滞回线的影响. 结果表明，产生刃位错的PbZr_0.4Ti_0.6O₃薄膜临界厚度为～1.27nm，当薄膜厚度大于临界厚度时，在所形成的位错附近，极化强度出现急剧变化，形成自发极化强度明显减弱的“死层”；随着薄膜厚度的减小，位错间距增大，“死层”厚度与薄膜总厚度之比增加. 由薄膜电滞回线的变化情况可知，其剩余极化强度随着薄膜厚度的减小而逐渐减小. 关键词： 铁电薄膜 自发极化强度 电滞回线 位错     

Dislocation and stacking fault core fields in fcc metals

Atomistic models were used to determine the properties of dislocation core fields and stacking fault fields in Al and Cu using embedded atom method (EAM) potentials. Long-range, linear elastic displacement fields due to nonlinear behaviour within dislocation cores, the core field, for relevant combinations of Shockley partial dislocations for edge, screw, and mixed (60° and 30°) geometries were obtained. Displacement fields of stacking faults were obtained separately and used to partition the core field of dissociated dislocations into core fields of partial dislocations and a stacking fault expansion field. Core field stresses were derived from which the total force, including the Volterra field plus core field, between dislocations for several dislocation configurations was determined. The Volterra field dominates when the distance between dislocations exceeds about 50b but forces due to core fields are important for smaller separation distances and were found to affect the equilibrium angle of edge dislocation dipoles and to contribute to the force between otherwise non-interacting edge and screw dislocations. Interactions among the components of a dissociated dislocation modify the equilibrium separation for Shockley partials suggesting that methods that determine stacking fault energies using measurements of separation distances should include core fields.     

Control of symmetric properties of metamorphic In_(0.27)Ga_(0.73)As layers by substrate misorientation

Asymmetry in dislocation density and strain relaxation has a significant impact on device performance since it leads to anisotropic electron transport in metamorphic materials. So it is preferred to obtain metamorphic materials with symmetric properties. In this paper, we grew metamorphic In_(0.27)Ga_(0.73) As epilayers with symmetric low threading dislocation density and symmetric strain relaxation in two (110) directions using In Al Ga As buffer layers on 7°misoriented Ga As(001)substrates. To understand the control mechanism of symmetric properties of In_(0.27)Ga_(0.73) As layers by the substrate miscut angles, In_(0.27)Ga_(0.73) As grown on 2°and 15°misoriented substrates were also characterized as reference by atomic force microscopy, transmission electron microscopy, and high resolution triple axis x-ray diffraction. The phase separation and interaction of 60°misfit dislocations were found to be the reasons for asymmetry properties of In_(0.27)Ga_90.73 As grown on 2and 15°substrates, respectively. Photoluminescence results proved that the In_(0.27)Ga_(0.73) As with symmetric properties has better optical properties than the In_(0.27)Ga_(0.73) As with asymmetric properties at room temperature. These results imply that high quality metamorphic In_(0.27)Ga_(0.73) As can be achieved with controllable isotropic electron transport property.     

Triple-period partial misfit dislocations at the InN/GaN (0001) interface: A new dislocation core structure for III-N materials

The lattice-misfit InN/GaN (0001) interface supports a triangular network of α-core 90° partial misfit dislocations. These misfit dislocations provide excellent strain relief. However, in their unreconstructed form the dislocation contains numerous high-energy N dangling bonds, which must be eliminated by reconstructing the dislocation core. Existing single-period (SP) and double-period (DP) dislocation reconstruction models eliminate these dangling bonds via a like-atom dimerization, such as N-N dimers. However, we show that these N–N dimers are unstable for the III-N materials, so an entirely new reconstruction mechanism is needed. A “triple-period” (TP) structural model is developed which eliminates N dangling bonds via the formation of N vacancies instead of N-N dimers. The model contains no N–N (or III–III) bonds, fully bonds all N atoms to four group-III neighboring atoms, and satisfies the “electron counting rule” by transferring charge from In dangling bonds to Ga dangling bonds.     

初始压入位置对Ni基单晶合金纳米压痕影响研究

针对Ni基单晶合金建立初始压入γ 相的γ /γ' 模型和初始压入γ'相的γ'/γ 模型, 采用分子动力学方法模拟金刚石压头压入两种模型的纳米压痕过程, 计算两种模型[001]晶向硬度. 采用中心对称参数分析两种模型(001)相界面错配位错对纳米压痕过程的影响. 结果显示: 弛豫后, 两种模型(001)相界面错配位错形式不同, 其中γ'/γ 模型(001)相界面错配位错以面角位错形式存在; 压入深度在0.930 nm 之前, 两种模型(001)相界面错配位错变化不大, 压入载荷-压入深度及硬度-压入深度曲线较符合; 压入深度在0.930 nm之后, γ'/γ 模型(001)相界面错配位错长大很多, 导致相同压入深度时γ'/γ 模型比γ /γ'模型压入载荷和硬度计算结果小; 压入深度在2.055 nm之后, γ /γ'模型(001)相界面错配位错对γ 相中位错进入γ'相有阻碍作用, 但仍有部分位错越过(001) 相界面进入γ' 相中, γ'/γ 模型(001)相界面处面角位错对γ' 相中位错进入γ 相有更明显的阻碍作用, 几乎无位错越过(001) 相界面进入γ 相中, 面角位错的强化作用更明显, 所以γ'/γ 模型比γ /γ'模型压入载荷上升速度快.     

Inhomogeneity of misfit stresses in nickel-base superalloys: Effect on propagation of matrix dislocation loops

It is shown experimentally that, during annealing and creep under low applied stresses, matrix dislocation loops frequently cross-glide. The periodic length of the zigzag dislocations deposited in the interfaces is equal to that of the γ/γ′-microstructure. Initially, the zigzag dislocations move in the (001) interface by a combination of glide and climb but then they stop near the γ′-edges and align along ?100?. Reactions of such dislocations lead to the formation of square interfacial networks consisting of ?100? oriented edge dislocations. The complex dislocation movement is explained by the inhomogeneity of the misfit stresses between γ- and γ′-lattices. The tensile components of the stress tensor drive the dislocations through the channel, whereas the shear components near the γ′-edges cause the zigzag movement and the ?100? alignment. The total effect is the most efficient relaxation of the misfit stresses. The results are relevant, especially for single-crystal superalloys of the newest generations, which have an increased γ/γ′-misfit due to the high level of refractory elements.