Classification of Ge hut clusters in the arrays formed by molecular beam epitaxy at low temperatures on the Si(001) surface
aa r X i v : . [ c ond - m a t . m e s - h a ll ] D ec Classification of Ge hut clusters in the arraysformed by molecular beam epitaxy at lowtemperatures on the Si(001) surface
Larisa V Arapkina and Vladimir A Yuryev † A. M. Prokhorov General Physics Institute of the Russian Academy of Sciences,38 Vavilov Street, Moscow, 119991, RussiaE-mail: [email protected]
Abstract.
Morphological investigations and classification of Ge hut clusters formingthe arrays of quantum dots on the Si(001) surface at low temperatures in the processof the ultrahigh vacuum molecular beam epitaxy have been carried out using in situ scanning tunnelling microscopy. Two main species of Ge hut clusters composing thearrays—pyramidal and wedge-shaped ones—have been found to have different atomicstructures. The inference is made that shape transitions between pyramids and wedgesare impossible. The nucleation probabilities of pyramids and wedges equal 1 / ◦ C)nucleation of new clusters is observed during the array growth at all values of Gecoverage except for a particular point at which the arrays are more uniform than athigher or lower coverages. At higher temperatures (530 ◦ C) cluster nucleation has notbeen observed after the initial stage of the array formation.PACS numbers: 68.37.Ef, 81.07.Ta † lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . .
1. Introduction
The development of processes of the controllable formation of germanium quantum dot(QD) arrays on the silicon surface as well as multilayer Ge/Si epitaxial heterostructureson their basis is a subject of significant and permanently increasing efforts for a numberof years [1, 2, 3, 4] primarily due to their potential applications in prospective devices ofmicroelectronics and integrated microphotonics compatible with the monolithic siliconVLSI technology. Both high density of the germanium nanoclusters ( > cm − )and high uniformity of the cluster shapes and sizes (dispersion <
10 %) in thearrays are required for many practically important application of such structures[2, 4, 5, 6, 7, 8, 9, 10, 11].The main technique of formation of the germanium nanoclusters on the siliconsurface is the molecular beam epitaxy (MBE) [2, 3]. A high density of the self-assembled clusters can be obtained in the MBE process of the Ge/Si(001) structureformation when depositing germanium on the silicon substrate heated to a moderatetemperature ( . ◦ C). ‡ In this case the lower the temperature of the silicon substratein the process of the germanium deposition the higher the density of the clusters isat the permanent quantity of the deposited germanium [1, 12, 13]. For example thedensity of the germanium clusters in the array reached 6 × cm − at the substratetemperature during the deposition T gr = 360 ◦ C and the effective thickness of thedeposited germanium layer § h Ge = 8 ˚A whereas the cluster density of only about2 × cm − was obtained at T gr = 530 ◦ C and the same value of h Ge [1].There are also different ways to increase the cluster density in the arrays. Thus,the authors of Ref. [5] succeeded to reach the cluster density of about 9 × cm − inthe array using the pulsed irradiation of the substrate by a low-energy Ge + ion beamduring the MBE growth of the Ge/Si(001) heterostructure at T gr = 570 ◦ C.Obtaining of the arrays of the densely packed Ge QDs on the Si(001) surface is animportant task but the problem of formation of uniform arrays of the Ge clusters is evenmore challenging one. The process of Ge/Si(001) heterostructure formation with theGe QD dense arrays and predetermined electrophysical and photoelectric parameterscannot be developed until both of these tasks are solved. The uniformity of the clustersizes and shapes in the arrays determines not only the widths of the energy spectraof the charge carrier bound states in the QD arrays [5] but in a number of cases theoptical and electrical properties of both the arrays themselves and the device structuresproduced on their basis [14]. To find an approach to the improvement of the Ge QD ‡ Remark also that lowering of the array formation temperature down to the values of . ◦ C isrequired for the compatibility of the Ge/Si(001) heterostructure formation process with the CMOSdevice fabrication cycle [1]. It is another reason to decrease the temperature of all treatments startingfrom the Si surface preparation. § I.e. the Ge coverage or more accurately the thickness of the Ge film measured by the graduated inadvance film thickness monitor with the quartz sensor installed in the MBE chamber. lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . .
Figure 1.
In situ
STM micrographs of the Ge hut cluster arrays formed on theSi(001) surface in the process of molecular beam epitaxy at the substrate temperature T gr = 360 ◦ C and different effective thicknesses of the deposited Ge layer ( h Ge ), thevalues of h Ge are (a) 6 ˚A; (b) 8 ˚A; (c) 10 ˚A; (d) 14 ˚A. Diagonals of the images areparallel to the h i axes. array uniformity on the Si(001) surface it is necessary to carry out the morphologicalinvestigation of the clusters constituting the arrays and first of all classify them.At present, two genera of the self-assembled Ge clusters formed on the Si(001)surface are marked out—huts and domes. The former are smaller and faceted by { } planes while the later are much larger and have more sophisticated faceting[6, 13, 15, 16, 17, 18]. Our investigations of the densely packed Ge nanocluster arrayson the Si(001) surface [1] have shown that the composition of an ensemble of the hutclusters is by no means homogeneous—there are several species of the hut clustersdifferent by their geometrical shapes as well as their behaviour in the process of thearray formation. k Examples of the Ge cluster arrays formed on the Si(001) surface atdifferent T gr and h Ge are shown in Figs. 1 and 2 which obviously demonstrate that the k Here we do not consider defects of the arrays. Other article will be devoted to their investigation.Now the available information about the morphology, structure and density of the array defects as wellas their effect on the array parameters can be found in our reports [1] or [19]. lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . .
Figure 2.
The same as in Fig. 1 but for T gr = 530 ◦ C, h Ge : (a) 8 ˚A; (b) 10 ˚A; (c)11 ˚A. arrays grown at low temperature always consist of a set of morphologically different hutclusters. Some of them have often been discussed in the literature since the classicalletter by Mo et al. [16, 17, 20, 21, 22, 23, 24, 25, 26, 27] and some have not.This paper is devoted to the study of morphological differences of the Ge hut clustersformed in the process of molecular beam epitaxy at low substrate temperatures on theSi(001) surface and their classification derived from the revealed species differences.Writing about the classification of the hut clusters we have not got a goal to simplyintroduce a new terminology, as it might seem, although the latter is also proposed. ¶ The aim of classification is to sort out the hut clusters in accordance with their structuralpeculiarities which are much more important attributes than geometrical shapes. Thedifference of geometrical shapes does not necessarily imply the difference of atomic ¶ Since the pioneering paper by Mo et al. [16], a good few of descriptive and often confusing termshave been used in the literature to designate two known types of the hut clusters. In this paper, weintroduce a new strict stereometrical terminology to emphasize the structural difference between thecluster species and avoid muddle in the future. We shall name each species of the clusters in accordancewith the denominations of the geometrical bodies which most accurately describe the shapes of theclusters. lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . .
It is well known [28] that in equilibrium Ge layers grow on the Si(001) surface followingthe Stranski-Krastanow mode [29, 30]. It means that initially Ge grows layer by layeruntil reaches a thickness of a few monolayers, then nucleation of the three-dimentionalislands begins [2].Because of lower surface energy, Ge when growing wets the Si surface (this enablestracing an etymology of the term “wetting layer”). Despite the mismatch of Si andGe lattices, which is ∼ . ×
1) reconstructed [28]. Due to dimer buckling it comprises a mixtureof the c (4 ×
2) and p (2 ×
2) structures [31, 32] which are manifested in STM images ascharacteristic antiphased and cophased zigzags. As Ge atoms arrive onto the surface,the compression along the dimer rows is relieved by arising dimer vacancies. Furtherordering of the dimer vacancies in a nearly regular array of parallel trenches (or formationof the so called (2 × n ) reconstruction [28]), which are perpendicular to the dimer rows,goes on to reduce the surface strain energy beyond the Ge coverage of 0.8 monolayer(thickness of 1 ML ≈ . M × N ) patched structure [32, 33, 34, 35] exhausts theability of the dimer vacancies to accommodate the wetting layer to the strain increasingwith the growth of quantity of the deposited Ge. When the Ge coverage exceeds 3 ML,the three-dimentional nanoislands (or Ge nanoclusters) start to nucleate on the surface.They are free of dislocations in the Si/Ge interface (coherent with the Si substrate),faceted and have base sides alined with two orthogonal h i axes. At moderate growthtemperatures the composition of the cluster arrays is bimodal: A part of clusters haveshapes of regular square-based pyramids while others have rectangles in their bases[16, 36]. Due to the shapes resembling huts both square-based and rectangular-basedclusters are usually referred to as “hut” clusters. The hut clusters (coherent islands)were theoretically shown to be (under some conditions) more energetically stable thanthe strained films or dislocated islands [20, 37]. Their appearance was also found to bekinetically favourable compared to the nucleation of dislocations [37].The first STM observation of hut clusters was reported by Mo et al. in 1990 [16](the term “hut” was introduced in that article). That letter presented an experimentalinvestigation of a newly discovered metastable phase of Ge clusters which arose in theprocess of Stranski-Krastanow growth to relieve the increasing stress in the wetting layer lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . { } faceting on all sides.The first model of the cluster { } faces according to which these facets consist of(001) terraces composed by pairs of dimers of the Ge(001)-(2 ×
1) reconstructed surfacewas suggested in that communication (now this model is usually referred to as the PDmodel [36, 38, 39]). Huts were found to have “predominantly a prism shape (with cantedends), in some cases four-sided pyramids, with the same atomic structure on all fourfacets”. The observed length of the huts was really huge (up to 1000 ˚A) while theirwidths did not exceed 200 ˚A (the aspect ratio often reached 10). The question was putfor the first time in that article what caused the elongation and specific base orientationof huts. Unfortunately, no convincing answer to this question has been proposed thusfar. It should be noted that since the letter by Mo et al. , pyramidal and “elongated”clusters have alway been considered in the literature as structurally identical onesdifferent only by their base aspect ratio [21, 22, 23, 24, 25, 26, 27]. The only argumentfor this assumption—the identity of faceting—does not seem to us to be very solid.Stress relaxation via formation of the { } faceted structures, such as islands or pits[21], appears to be energetically favourable and the structures are more stable comparedto ones with different faceting [39]. This means that faceting itself cannot be consideredas the only sign of belonging to some specific group of morphologically identical clusters.Total atomic structure of clusters is defined by both the structure of their facets and theconfiguration of their apexes. If the latter is different, the clusters should be regardedas members of different species.The sound counterargument to the assumption about the cluster identity, whichis usually disregarded, was given, e.g., in Ref. [40]: “Elongated” clusters completelydisappeared from arrays after annealing at 550 ◦ C for 600 s whereas pyramids and domesremained. Moreover, a commonly adopted pathway of the dome cluster formation isas follows: some “prepyramid” (we have never observed such formations in our low-temperature MBE experiments) → pyramid → dome [17, 41]. “Elongated” huts havenever been met on this pathway. This led us to suggestion that “elongated” huts + differfrom pyramids not only by shapes but mainly by their atomic structure and, that ismore important, by the genesis and the role in the array development.Nevertheless, the question about the mechanism of hut elongation was asked andrequired answering. Before long, the simplest and at first glance the most probablescenario was proposed and immediately adopted by the community. According to thisscenario wedge arise by elongation of a pyramid due to the growth of one of its { } facets [21, 22, 23, 24, 25, 26, 27]. This hypothesis would explain everything unless thenecessity to explain why the symmetry of the pyramid is violated. Due to its shape thesquare-based regular pyramid seems to be stable enough, at least unless some exterioranisotropic agent affects it removing the degeneracy of its facets. Otherwise it is unclear + Hereinafter we shall, as a rule, refer to them as wedges, wedge-like or wedge-shaped clusters. lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . et al. proposed that an asymmetry of the stress field due to the presenceof { } faceted pits may result in the cluster anisotropic lateral growth because ofso-called equilibrium-driven elongation [26]. They found that in thick hydrogen rich Gewetting layer (between 7.7 and 8.3 ML), which is formed in the process of gas-source-molecular-beam-epitaxy (GS-MBE) † growth of Ge on Si(001) from GeH , the strainat 690 ◦ C is relieved by formation of { } faceted pits rather than islands [21], thatis in agreement with the earlier conclusion by Tersoff and LeGoues [37] according towhich pits always have a lower energy than islands of the same shape and equal size.(Goldfarb et al. observed also that at 620 ◦ C—and hence thinner wetting layer—onlyhut clusters arose [21].) Further, with the increase of Ge coverage, when the capabilityof pits to release the stress is exhausted hut clusters nucleate in the vicinity of pits[21, 22, 25]. Acknowledging a model by Jesson et al. , which explains instability of thehut cluster shapes (read “elongation”) by nucleation and growth on the facets [27], asmore common, the authors of Ref. [21] illustrate the elongation process by an example ofcluster coalescence. We agree with Goldfarb et al. that such event sometimes happensand will present below a picturesque evidence of it. However, this explanation of thecluster elongation phenomenon of course by no means can be accepted as universal. ‡ As mentioned above, investigations by Goldfarb with co-authors [26] eventuallygave a weighty argument in support of the so-called equilibrium-driven elongation or, inother words, elongation governed by energy minimization. They considered the cluster † GS-MBE much more resembles chemical vapour deposition (CVD) than the solid source ultrahighvacuum (UHV) MBE in which an atomic beam of Ge supplies the growing layer with Ge atoms ratherthan a flux of GeH or Ge H . ‡ Note, by the way, that Goldfarb with co-authors were first who reported the STM observation ofincomplete trapezoid facets of the wedges in Ref. [22]. Until now, incomplete triangular facets have notbeen observed, however. lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . α ) and the cluster growsisotropically up to some point ( eα ), then anisotropic elongation in one direction starts.The authors of Ref. [26] indicate the discrepancy of the estimates made on the basisof the model by Tersoff and Tromp [20] with experimental observations. The modelpredicts eα ≈
100 nm ( α ≈
37 nm) whereas in opinion of the authors of Ref. [26]anisotropic elongation of huts starts at the nucleus size of ∼ s and l . Till its size is less than some criticalvalue, the total energy is minimum for s = l . For a greater island its square shapebecomes instable because of the strain: The island begins elongation in one of twodegenerate orthogonal directions until the total energy reaches minimum at some valueof arctan( s/l ) = π/ ± ∆. To explain the anisotropic elongation the authors of Ref. [42]have to introduce anisotropy of edge energies to violate the symmetry of a square.According to this model island grows along the direction of the lower edge free energyin which both strain and edge energies are minimum. The advantage of this constructis that for strong anisotropy the elongation occurs at any size of the island. Goldfarband co-authors extend this model to the case of a 3D faceted island with slowly growingheight [26]. According to them when island elongates its perimeter grows faster thanthe area of the strained base in such a way resulting in more effective relaxation.Nevertheless, an origin of anisotropy stays an issue in this model.As mentioned above an explanation was however proposed in the same letter [26]. Itwas observed that huts interact with parent pits as well as with different adjacent ones,their lengthwise growth often starts at one pit and ends at the other. Sometimes theelongation is finished when a hut grows along the pit boundary and reaches its corner.The effect of the hut and pit interaction was analyzed by finite element technique andfound to cause hut elongation. The pit dimensions used in calculations were 10 ×
10 nmand the wetting layer was as thick as 2 nm. The inference was made in the article thatthe following hut evolution scheme takes place: as soon as a stable critical nucleus isformed [25] it grows in the energetically favorable direction along its mutual boundarywith the parent pit until reaches the pit corner or attains an equilibrium s/l ratio. Thisfinishes the first phase of cluster elongation. The second phase implies that the clustercontinues the equilibrium growth in the perpendicular direction (from the pit) untileither an equilibrium s/l ratio is established or impingement to other pit happens.These observations and reasoning maybe correct for the particular case of GS-MBEwere propagated to all deposition methods. We have solid objections to it. First of all,only relatively rarefied arrays on very thick hydrogen-rich wetting layers were grown byGS-MBE and investigated in Ref. [26]. Dense arrays obtained by UHV MBE grow inabsolutely different manner (Figs. 1 and 2). Secondly, as it is seen from Figs. 1 and 2, no lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . h i direction goes on withdecreasing probability of Ge atom attachment to the trapezoid facets and hence withdecreasing rate of the in-height growth in comparison with the rate of the longitudinalone. Unfortunately this model appeared to disagree with experiments. Observationsof Goldfarb et al. [26] indicate that in case of interaction of pits and huts the two h i directions of elongation are not equally probable as it follows from the model ofkinetically driven elongation. Our elaborated observations, which are presented below,do not support this model either.Summarizing this brief historical review we would like to emphasize the following.To date, main milestones on the pathway of the Stranski-Krastanow growth of Ge film onSi(001) at moderate temperatures ( > ‰ ) from the pure silicon surface to hut clustersappearance are recognized as consecutive steps of the strain relief. They are following:(2 × → (2 × n ) → ( M × N ) → huts . However, despite the efforts made thereis no clarity in the issues of hut nucleation and further transformation. The processof hut nucleation appeals for detailed experimental investigation at different growthconditions by instruments assuring atomic resolution and using different depositionmethods. Formation and longitudinal growth of huts have not been understood thusfar. Elongation of pyramids has never been unambiguously observed in experiments .The best of the two theoretical models explaining the elongation of wedges also hasnot been chosen yet. Issues of evolution of the cluster arrays during Ge deposition hasbeen passed over by researchers too. There has been no systematic investigations of thestages of this very important and complicated process presented in literature. A finalphase of the array growth cycle—growth at high coverages and transition to the 2Dmode—has never been in focus of investigations. So, we can conclude now that despitethe widely adopted standpoint, investigations on the discussed problem are still far fromcompletion.The above analysis of the literature puts a number of new questions the mostobvious of which are as follows. Firstly, it is unclear whether the structure of pyramidsand wedges is identical and whether they belong to the same morphologically uniform lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . .
2. Experimental
The experiments were made using an integrated ultrahigh vacuum system based on theRiber EVA 32 molecular beam epitaxy chamber coupled through a transfer line withthe STM GPI-300 [45] scanning tunnelling microscope (STM). This instrument enablesthe STM study of samples with atomic resolution at any stage of Si surface cleaningand MBE growth. The samples can be consecutively moved into the STM chamberfor analysis and back into the MBE chamber for further processing never leaving theUHV ambient and their surfaces stay atomically clean over whole the experiment. Aprocedure of the sample preparation was as follows: initial substrates were 8 × squares cut from B-doped CZ Si(100) wafers ( p -type, ρ = 12 Ω cm). After washingand chemical treatment following a standard procedure described elsewhere (see e.g.Refs. [1, 46]) the silicon substrates mounted on the molybdenum STM holder andclamped with the tantalum fasteners were loaded into the airlock and transferred to thepreliminary annealing chamber where outgassed at the temperature of around 565 ◦ C andthe pressure of about 5 × − Torr for about 24 hours. After that the substrates weremoved for final treatment into the MBE chamber evacuated down to about 10 − Torr.There were two stages of annealing in the process of substrate heating in the MBEchamber — at ∼ ◦ C for ∼ ∼ ◦ C for ∼ ◦ C was carried out for nearly 2 . ◦ C ( ∼ . ◦ C. The rate of the further cooling down was around0 . ◦ C/s. The pressure in the MBE chamber enhanced to nearly 2 × − Torr duringthe process.The surfaces of the silicon substrates were completely purified of the oxide film asa result of this treatment. The high-order (8 × n ) surface reconstruction described inRef. [47] was always revealed by the STM on the deoxidized substrates whereas thereflected high energy electron diffraction (RHEED) § patterns obtained from the samepurified surfaces always corresponded to either (2 ×
1) or (4 ×
4) surface reconstruction[48]. This observation is in a good agreement with the model brought forward by § RHEED is usually applied in the MBE vessels for monitoring the surface perfection [3] e.g. duringthe deoxidizing process. lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . Figure 3.
A diagram of the final thermal treatment of the Si substrates during surfacedeoxidizing in the MBE chamber. us in Ref. [47] as well as with the generally accepted opinion based on the RHEEDmeasurements that the (2 ×
1) reconstruction is formed on the Si(001) surface due todeoxidization in an MBE chamber [5].Germanium was deposited directly on the purified silicon surface from the sourcewith the electron beam evaporation. The rate of Ge deposition was about 0 .
15 ˚A/s, h Ge was varied from 6 ˚A to 14 ˚A for different samples. The deposition rate and theeffective Ge film thickness h Ge were measured by the graduated in advance XTC filmthickness monitor with the quartz sensor installed in the MBE chamber. The substratetemperature T gr was 360 ◦ C or 530 ◦ C during the process. The pressure in the MBEchamber did not exceed 10 − Torr during Ge deposition. The rate of the sample coolingdown to the room temperature was approximately 0 . ◦ C/s after the deposition.The samples were heated by Ta radiators from the rear side in both preliminaryannealing and MBE chambers. The temperature was monitored with chromel-allimeland tungsten-rhenium thermocouples in the preliminary annealing and MBE chambers,respectively. The thermocouples were mounted in vacuum near the rear side of thesamples and in situ graduated beforehand against the IMPAC IS 12-Si pyrometer whichmeasured the sample temperature through chamber windows with an accuracy of ± (0 . T ◦ C + 1 ◦ C).The atmosphere composition in the MBE camber was monitored using theSRS RGA-200 residual gas analyzer before and during the process.After Ge deposition and cooling, the prepared samples were moved for analysis intothe STM chamber in which the pressure did not exceed 10 − Torr. The STM tip was exsitu made of the tungsten wire and cleaned by ion bombardment [49] in a special UHVchamber connected to the STM chamber. The images were obtained in the constanttunneling current mode at the room temperature. The STM tip was zero-biased whilethe sample was positively or negatively biased for empty or filled states mapping.The WSxM software [50] was used for processing of the STM images. lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . .
Figure 4.
STM micrographs of the pyramidal Ge clusters; completely shaped clusters: T gr = 530 ◦ C, h Ge = 11 ˚A (a); T gr = 360 ◦ C, h Ge = 10 ˚A (b); a cluster with unfinishedfacets (marked by an arrow): T gr = 360 ◦ C, h Ge = 14 ˚A (c); a structure of vertex, sidesand edges (d) and a structure of a nucleus of 1 monolayer high over the wetting layer(e): T gr = 360 ◦ C, h Ge = 6 ˚A (corresponding features on toppings are marked by thesame numerals). lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . .
3. Classification
As mention above an array of the self-assembled germanium hut clusters formed onthe Si(001) surface consists of a set of morphologically different clusters. All the clustershave the edges of bases oriented along the h i directions in common. Yet in spite ofthe apparent variety of the cluster forms (Figs. 1 and 2) an analysis of the STM imagesgives evidence that only two main species of the hut clusters exist—ones having squarebases and shapes of the regular pyramids and those with rectangular bases which haveshapes of the wedges. We have already cited the paper by Mo et al. [16], in whichboth species of the hut clusters were described for the first time, as well as a number ofpublications which investigated the details of their formation [20, 21, 22, 23, 24, 25, 26].Unfortunately their structure has not been yet clearly visualised and identified.(a) (b)(c) Figure 5.
STM images of the wedge-like Ge clusters; a cluster with an unfinished side: T gr = 530 ◦ C, h Ge = 11 ˚A (a); the entirely formed cluster: T gr = 360 ◦ C, h Ge = 10 ˚A (b);a structure of the ridges (two closely neighbouring clusters), the shifted features aremarked by the arrows: T gr = 360 ◦ C, h Ge = 8 ˚A (c). Let us dwell on the description of each species of the clusters in more detail. lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . the pyramidal clusters in the arrays withdifferent growth parameters are shown in Fig. 4. A regular shape of the clusters isclearly seen in the pictures (a) and (b) presenting the arrays obtained at T gr = 530 ◦ C, h Ge = 11 ˚A and T gr = 360 ◦ C, h Ge = 10 ˚A, a fine structure of the faces is resolved aswell as the ( M × N ) patched structure of the wetting layer [32, 33, 34, 35]. Lines ofthe solidifying steps are revealed for the first time on the cluster incomplete faces in theimage (c) of the array obtained at T gr = 360 ◦ C, h Ge = 14 ˚A (one of them is markedby arrow in the image). Fig. 4(d) shows a vertical view of the small pyramid grown at T gr = 360 ◦ C, h Ge = 6 ˚A and having only 5 monolayers height over the wetting layer.A fine structure of the pyramid vertex and edges as well as the stepped structure of its { } facets are resolved in detail in the image (d). And at last, the same structure asthat seen in Fig. 4(d) on the pyramid vertex is clearly resolved in the image (e) of thepyramid nucleus (1 monolater high over the wetting layer) situated on the block of theGe ( M × N ) surface. k Fig. 5 demonstrates STM images of the wedge-like clusters . Being the hut clustersthey are bounded by { } planes, i.e. their heights are to the base widths as 1:10.A distinctive feature of this species of the clusters is that their base lengths are notconnected with cluster heights and are rather random. To some extent, the base lengthsof the wedge-like cluster depends on its nearest neighbours. Nevertheless, it is impossibleto confidently point out the factors which affect the lengths of the Ge wedges based uponthe available data. Reasoning from the results of the STM image analysis it may onlybe asserted that their base length-to-width ratio is distributed randomly and ratheruniformly in the interval from a little greater than 1 to more than 10. X , nm Z , n m Figure 6.
Profiles of the neighbouring wedge (the left one, taken along the short sideof base) and pyramid (the right one) shown in Fig. 4(a). k Note also that similar configuration of the pyramid apex can be discerned by an attentive observerin Fig. 4(b) which presents an image of a “ripe” pyramid in the well developed array. lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . in situ studies of the Si surface on the atomic scale immediately before the Ge deposition aswell as the investigations of its influence on the deposited Ge layer should be consideredas a task of high importance.Fig. 5(c) demonstrates the fine structure of ridges of two close wedge-like clusters( T gr = 360 ◦ C, h Ge = 8 ˚A). It is interesting that one can descry the same configurationof the ridge in the first published image of the hut cluster (see Fig. 2 in Ref. [16]).The STM images of fine structure of the vertexes and the ridges, similar to thoseshown in Figs. 4(d, e) and 5(c), helped us propose structural diagrams of both species ofthe clusters [43, 51]. It is clearly seen from the images that the fine structures of apexesof the clusters are different . The features in the uppermost parallel rows on the ridgesof the wedge-like clusters are shifted with respect to one another. (They are markedby the rows of the shifted arrows in the STM image.) We interpret these features asGe dimer pairs in accordance with the simple structural model of the hut cluster facets(PD model) proposed by Mo et al. [16]. Similar features in the images of vertexes of thepyramids are gathered in the straight rows. The difference of symmetry of the pyramidvertex from the symmetry of the elementary unit of the wedge ridge is distinctly evidentwhen compared Figs. 4(e) and 5(c).As we have already mentioned above, the difference of the atomic structure causesa ban of shape transitions between the pyramidal and wedge-shaped hut clusters whichwere intensively discussed in the literature [24, 25, 26]. In addition, particular nucleishould be sought for pyramidal and wedge-shaped clusters. The question appears aswell, why two structurally different species of hut clusters arise on the wetting layer.Fig. 6 shows the cross section profiles of the adjacent wedge-like and pyramidalclusters presented in Fig. 4(a). Both clusters are seen to have equal ratio of the basewidth to the cluster height close to 10. The base sides of the pyramidal cluster andthe base length of the wedge-like one are nearly equal whereas the base width of thewedge-like cluster is by about 1.6 times less than the sides of the pyramid base. It isa common rule which is not affected by the length of a particular wedge-like cluster:The pyramidal clusters are usually higher than the wedge-like ones if h Ge is high enough lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . h Ge greater than some valueand not to occur for the pyramids. We do observed such limitation for the wedge-shapedclusters (see below) and did not succeed to fix the height limitation of the pyramidalones. ¶ h Ge , Å D e n s i t y , c m - (a) h Ge , Å F r a c t i o n , % (b) Figure 7.
The density of the Ge clusters in the arrays (a) formed at T gr = 530 ◦ C(designations: (cid:3) marks the pyramids, △ corresponds to the wedges, means thetotal value) and T gr = 360 ◦ C ( (cid:4) designates the pyramids, N means the wedges, is the total density). The fraction of the pyramidal and wedge-like Ge clustersin the arrays (b), T gr = 530 ◦ C ( (cid:3) marks the pyramids, △ designates the wedges), T gr = 360 ◦ C ( (cid:4) corresponds to the pyramids, N designates the wedges). Both graphsare plotted vs h Ge . It was observed that the wedge-like and pyramidal clusters are different not onlyin their atomic structure and geometrical shapes. The wedge-like clusters dominate inthe arrays formed at low temperatures, and their fraction grows with the growth of h Ge (Fig. 7).Fig. 7(a) plots the dependence of the cluster density on h Ge for different clustersin the arrays grown at 360 ◦ C and 530 ◦ C. It is seen that for T gr = 360 ◦ C the densityof wedges rises starting from D w ≈ , × cm − at the beginning of the three-dimensional growth of Ge (the estimate is obtained by data extrapolation to h Ge = 5 ˚A)and reaches the maximum of ∼ × cm − at h Ge ∼ D Σ ∼ × cm − is also maximum. Then both D w and D Σ slowly go down until the two-dimensional growth of Ge starts at h Ge ∼
14 ˚A and ¶ Perhaps, there is no height limitation for pyramids and namely they give rise to large clusters affectingthe properties of the Ge/Si(001) heterostructures and classified by us as one of the types of defects ofarrays (see report [1] or an article on defects of arrays [19]). lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . D Σ ≈ D w ∼ × cm − (the contribution of pyramids D p to D Σ becomes negligible— ∼ × cm − —at this value of h Ge ). The pyramid density exponentially drops for T gr = 360 ◦ C as the value of h Ge grows ( D p ≈ × exp {− . × h Ge } , h Ge ismeasured in centimeters). The maximum value of D p ≈ . × cm − obtained fromextrapolation to h Ge = 5 ˚A coincides with the estimated initial value of D w .For T gr = 530 ◦ C, the total density of clusters exhibits the same trend as D p for T gr = 360 ◦ C, D Σ ≈ × exp {− . × h Ge [cm] } . The maximum (initial) value of D Σ is estimated as 8 × cm − by extrapolation to h Ge = 5 ˚A.The graphs of cluster fractions in the arrays versus h Ge are presented in Fig. 7(b).For T gr = 360 ◦ C, portions of pyramids and wedges initially very close ( ∼
50% at h Ge ∼ h Ge rises. The content of pyramids monotonicallyfalls. The fraction of the wedge-like clusters is approximately 57% at the early stage ofthe array growth ( h Ge = 6 ˚A) and becomes 82% at h Ge = 8 ˚A. At further growth ofthe array, the content of the wedges reaches the saturation at the level of approximately88% at h Ge = 10 ˚A.At moderate values of h Ge , the proportion of pyramids to wedges for T gr = 530 ◦ Cwas found to be nearly the same as for T gr = 360 ◦ C. The content of the pyramidalclusters in the array is about 20% at h Ge = 8 and 10 ˚A.The inference may be made from this observation that contrary to the intuitivelyexpected from the consideration of symmetry, the wedge-like shape of the clusters isenergetically more advantageous than the pyramidal one, and the more advantageous themore Ge atoms (and the more the number of atomic layers) constitute the cluster. Theprobability of nucleation appears to be close to 1/2 for both wedges-like and pyramidalclusters at the initial stage of the array formation and low growth temperatures. Then, asthe array grows, the formation of pyramids becomes hardly probable and most of them,which have already been formed, vanish whereas the nucleation and further growth ofwedges continues (Fig. 1). The Ge pyramides on the Si(001) surface appear to be lessstable species than the wedges and in accordance with the “bourgeois principle” (“thesurvival of the fittest”) they loose their substance in favour of the wedge-like clusters.At higher temperatures, no nucleation of new clusters was observed in the processof the array growth (Fig. 2). The “bourgeois principle” decreases the cluster density inthe arrays and increases their sizes despite the species they belong to.It should be noted that the above analysis demonstrates that pyramidal and wedge-like clusters are really different objects which belong to different cluster species ratherthan the varieties of the same structurally uniform species as it is usually postulated inthe literature [16, 23, 24, 25, 26].Remark also that at T gr = 360 ◦ C and the flux of Ge atoms d h Ge / d t = 0 .
15 ˚A/s,the point h Ge = 10 ˚A is particular. Not only the fraction of pyramids saturates at thispoint but the array in whole has the most uniform sizes of the clusters composing it(Fig. 1). This is concluded by us not only on the basis of analysis of the STM images ofthe Ge/Si(001) arrays but also from the data of the Raman light scattering by the Ge/Siheterostructures with different low-temperature arrays of Ge quantum dots [52, 53]. We lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . T gr . At small h Ge , Geclusters are small enough and the distances between them are large enough comparedto the Ge atom (or dimer) diffusion (migration) length on the surface for nucleation ofnew clusters on the Ge wetting layer in the space between the clusters (Fig. 1(a, b)).At h Ge = 10 ˚A and the above d h Ge / d t value, the equilibrium of parameters (clustersizes and distances between them, diffusion length at given temperature, Ge depositionrate, etc.) sets in, the rate of new cluster nucleation is decreased and the abundant Geatoms are mainly spent to the growth of the available clusters (Fig. 1(c)). After theclusters reach their height limit and in spite of it, Ge atoms continue to form up theirfacets. As soon as most of the clusters reach the height limit, nucleation of new clustersbecomes energetically advantageous again and the nucleation rate rises. A second phaseof clusters appears on the wetting layer and fills whole its free surface as h Ge is increased(Fig. 1(d)). Further increase of h Ge results in two-dimensional growth mode. It is clearnow why the array is the most homogeneous (optimal) at T gr = 360 ◦ C and h Ge = 10 ˚Awhereas the dispersion of the cluster sizes is increased at higher and lower values of h Ge because of the small clusters included in the array. It is clear also that the optimal arraywill appear at different value of h Ge when T gr or d h Ge / d t are different.(a) (b) Figure 8.
STM micrographs of the Ge wedges with two ridges (obelisks), a generalview of the cluster (a) and a top view of the ridges (b); T gr = 360 ◦ C, h Ge = 14 ˚A. In addition, some threshold value of T gr must exist beyond which the cluster growthprocess always dominates and the nucleation of clusters happened once will never berepeated. An example of such arrays formed at T gr = 530 ◦ exceeding the threshold valueis given in Fig. 2. lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . Figure 9.
Profiles of the Ge obelisk presented in Fig. 8(a) measured across the ridgesalong the base width (the solid line) and over the left ridge along the base length (thedashed line). Here, as distinct from Fig. 8, X and Y mean respectively axes directedalong the cluster base width or along its length. Height is as usually counted from thewetting layer level ( Z = 0). Except for the described above main species of Ge hut clusters, different clustersare also formed on the Si(001) surface which cannot be classified as independent speciesbecause they originate from the wedge-like clusters but have specific shapes, particularformation mechanisms, maybe peculiar properties and hence should be marked out ina separate but derivative species. Fig. 8 shows clusters related to one of the speciesof derivative clusters—truncated wedge-like clusters with two ridges or obelisk-shapedclusters ( T gr = 360 ◦ C, h Ge = 14 ˚A).Profiles of the Ge obelisk shown in Fig. 8(a) taken along the short and long basesides are presented in Fig. 9. Although these clusters are the huts and have a slope ofthe facets ∼ . ◦ the ratio of the cluster height to its base width is ∼ . T gr . If the limit is reachedthe further growth of the cluster always goes on by building its trapezoid facets andincreasing its width.This species of clusters dominates in the arrays at high values of h Ge which dependon the value of T gr (see Figs. 1 and 2).A unique illustration of the process of the trapezoid facet growth is shown in lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . Figure 10.
STM images of the Ge obelisks illustrating the mechanism of theirformation; T gr = 360 ◦ C, h Ge = 14 ˚A (a, b, c); T gr = 530 ◦ C, h Ge = 8 ˚A (d) and10 ˚A (e, f). Fig. 10(c). Several (from four to six) incomplete (001) terraces are seen near the bottomsof the clusters (the dimer pairs are distinctly resolved, the arrows show these new growingfacets in the STM image). These incomplete faces are seen to repeat the shapes of theformer faces on which they grow and which are also incomplete. The highest terraces lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . et al. which draw a different picture of the facet growth [23].First of all, they consider a triangular face as a preferential site of a new facet nucleationexplaining in such a way elongation of clusters. Then, according to their model, thefacets nucleate in the corners rather than somewhere else, etc.We would like to remark that we have not succeeded to observe the growth of thetriangular faces at the temperatures as low as 360 ◦ C. Nevertheless we observed thisprocess at T gr = 530 ◦ C. Figs. 10(d–f) demonstrate this phenomenon. The peculiaritiesof the process are as follows: A new facet formation takes place when the cluster hasalready reached its limit height and its additional trapezoid facets are well developed.The growing triangular facets are clearly observed on only one side of the clusters. Thetriangular faces can nucleate both far from the bottom corner (Figs. 10(d)) and closeto the corner (Figs. 10(e, f)). The growing (incomplete) faces replicate the shape ofinitial facet even if the latter is complex (composed by intersecting triangles due tothe developed additional trapezoid faces, see Figs. 10(e, f) in which the growing faceson the short sides of the truncated wedges are shaped by two combined triangles).It can be deduced from these observations that the described process of formation ofnew triangular facets is different from that resulting in the discussed above significantelongation of the wedge-shaped clusters at earlier stages of the cluster growth.Now we would like to attract the reader’s attention to the observed in Figs. 10(c, e, f)formation of the so called “square based clusters” from the wedge-like ones which iscaused by the extensive growth on the trapezoid facets and the cluster widening. InFig. 10(c), the nearly “square based clusters” are seen to be formed because of thewidening of the wedges with two ridges. They resemble truncated pyramids but actuallypreserve the structure of the wedge. The nearly “square based clusters” are also seen inthe upper left corner of Fig. 10(e) and upper right corner of Fig. 10(f). These clusters areformed of the formerly wedge-like ones by successive addition of new incomplete facets.Their faces are complex and their shapes are far from the shape of an ideal regularpyramid. Certainly, their structure stays that of the wedge. The genuine pyramidalcluster revealed in the upper right corner of Fig. 10(d) grows nearly uniformly on allfour its triangular faces (compare also with Fig. 4(c)). We would like also to indicate theformation of serial incomplete faces resolved on the sides of both pyramidal and wedge-shaped clusters presented in Fig. 10(d) (even the dimer pairs on the “parallel steps” areseen). This process do transform the shape of the clusters and may create nearly “squarebased clusters” from the wedges as well as so called “rectangular based clusters” fromthe pyramids (the latter process may be fancied, e.g., if a pyramid is closely surroundedby its neighbours from all sides except for one and have some room for elongation onlyin one direction). Of course, such transformed clusters are always “truncated”, have lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . .
22a complex “stepped” structure of successive incomplete facets and atomic structure ofapexes characteristic for their precursors, as it is seen in the presented STM images.
In Fig. 11, the STM images of accreted together wedge-like Ge clusters are shown—accreted clusters which formed ones with two ridges ( T gr = 360 ◦ C, h Ge = 8 ˚A), accretedclusters which gave rise a Γ-like one ( T gr = 360 ◦ C, h Ge = 10 ˚A), clusters accretedapproximately at half width formed an extended one with zigzag on the ridge and thefacets ( T gr = 360 ◦ C, h Ge = 10 ˚A) are depicted.(a) (b)(c) Figure 11.
STM images of the accreted together Ge wedges; the accreted clustersborne the clusters with two ridges, T gr = 360 ◦ C, h Ge = 8 ˚A (a); the accreted clustersgiven rise to the Γ-shaped cluster, T gr = 360 ◦ C, h Ge = 10 ˚A (b); the merged at abouthalf-length wedges formed an extended wedge-like cluster with zigzag on the ridge andthe sides, T gr = 360 ◦ C, h Ge = 10 ˚A (c). Like the obelisks the accreted clusters cannot be classified as independent speciesbecause they also originate from the wedge-like clusters. However, they also havespecific shapes and probably peculiar properties and consequently like obelisks shouldbe separated in a special but derivative species. It was found from the analysis of theSTM images obtained at different stages of the array formation that the nuclei of such lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . >
32 ˚A from one another at the initial stage ofthe array formation in the applied array growth conditions.From physical viewpoint, these clusters are obviously single and integral objects,the properties of which may be different from the properties of the usual wedge-likeclusters. Their influence upon the properties of the arrays in whole is in prospect offurther investigations.The coalescence of clusters is also seen in Fig. 4(c). The truncated wedges aremerged or even completely absorbed by the growing pyramid (the pyramids are alwaysgreater than the wedges). Such process usually takes place at high values of h Ge justbefore the beginning of the two-dimensional growth.
4. Conclusion
Summarising the above we would like to emphasise the central ideas of the paper.Morphological investigations and classification of Ge hut clusters forming the arraysof quantum dots on the Si(001) surface at low temperatures in the process of theultrahigh vacuum molecular beam epitaxy have been carried out using in situ scanningtunnelling microscopy. The study reported in the paper was made in view of thenecessity to controllably produce highly uniform and very dense arrays of Ge quantumdots at low temperatures in the process compatible with the CMOS one. Although thistask is still far from the solution an important step is made in understanding the objectproperties to be controlled.The Ge / Si(001) system appeared to be much more sophisticated than it seemed tomost of the researchers, and the knowledge about it which is present in the literaturenow seems to be very deficient and sometimes incorrect. This seems to be the maincause of failure for the last two decades to develop electronic or photonic devices on thebasis of ensembles of Ge quantum dots on the Si(001) surface.Analysis of the high quality STM images which can be obtained only using anintegrated high resolution UHV STM–MBE instrument allowed us to introduce anew classification of germanium hut clusters formed on the Si(001) surface. Thehut clusters were found to be subdivided into four species, two of which are basicand structurally different—the wedge-like and pyramidal clusters—and the rest arederivative—the obelisk-shaped and accreted wedge-shaped clusters. The conclusionwas made that shape transitions between pyramids and wedges are prohibited. Thenucleation likelihoods of pyramids and wedges appeared to equal 1 / lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . ◦ C) nucleation of new clusters is observed duringthe array growth at all values of Ge coverage except for a particular point at whichthe arrays are more uniform than at higher or lower coverages. At higher temperatures(530 ◦ C) cluster nucleation has not been observed after the initial stage of the arrayformation.The growing trapezoid and triangular cluster facets were visualised. Thepeculiarities of the facet completion were described. It was shown that the growthof incomplete facets results in a complex structure of the growing hut clusters.It was shown also that the uniformity of arrays is governed by the lengths of thewedge-like clusters. This parameter is hardly controllable as distinct to the clusterwidth which is bound to the cluster height and hence is much more predictable. Thecluster lengths are now absolutely unpredictable. Moreover the origin which determinestheir values is unknown at present. This difficulty requires extensive investigationsand intensive efforts to be overcome. But it worth while doing because both stochastic(disordered) and the most promising artificially ordered or self-arranging dense arrays ofself-assembled Ge clusters on the Si(001) surface [54] are equally required to be uniformand equally subjected to effect of the Ge wedge length unpredictability.
Acknowledgments
The authors appreciate the Science and Innovations Agency of the Russian Federationfor funding this research under the State Contract No. 02.513.11.3130.
References [1] V. A. Yuryev, L. V. Arapkina, V. A. Chapnin, V. P. Kalinushkin, N. V. Kiryanova, O. V. Uvarov,K. V. Chizh, L. A. Krylova, R. O. Stepanov, and O. O. Zaytsev. Development of physical andtechnological basis of the controllable formation of densely packed Ge nanocluster arrays onthe silicon (100) surface by means of ultrahigh vacuum molecular beam epitaxy. Report onResearch Project 2007-3-1.3-25-01-303 of the Science and Innovations Agency of the RussianFederation, A. M. Prokhorov General Physics Institute of the Russian Academy of Sciences,Moscow, Russia, 2007. VNITC No. 0220.0 802501.[2] O. P. Pchelyakov, Yu. B. Bolkhovitjanov, A. V. Dvurechenski˘i, L. V. Sokolov, A. I. Nikiforov, A. I.Yakimov, and B. Voigtl¨ander. Silicon-germanium nanostructures with quantum dots: Formationmechanisms and electrical properties.
Semicond. , 34:1229, 2000.[3] K. Brunner. Si/Ge nanostructures.
Rep. Prog. Phys. , 65:27, 2002.[4] K. L. Wang, S. Tong, and H. J. Kim. Properties and applications of SiGe nanodots.
MaterialsScience in Semiconductor Processing , 8:389, 2005.[5] J. V. Smagina, V. A. Zinovyev, A. V. Nenashev, A. V. Dvurechenski˘i, V. A. Armbrister, and S. A.Teys. Self-assembly of germanium islands under pulsed irradiation by a low-energy ion beamduring heteroepitaxy of Ge/Si(100) structures.
JETP , 106:517, 2008.[6] K. L. Wang, D. Cha, J. Liu, and C. Chen. Ge/Si self-assembled quantum dots and theiroptoelectronic device applications.
Proc. of the IEEE , 95(9):1866, 2007.[7] F. Liu, S. Tong, J. Liu, and K. L. Wang. Normal incident mid-infrared Ge quantum dotphotodetector.
J. Electron. Mater. , 33(8):846, 2004. lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . [8] S. Tong, J.-Y. Lee, H.-J. Kim, F. Liu, and K. L. Wang. Ge dot mid-infrared photodetectors. Optical Materials , 27:1097, 2005.[9] M. Elkurdi, P. Boucaud, S. Sauvage, O. Kermarrec, Y. Campidelli, D. Bensahel, G. Saint-Girons,and I. Sagnes. Near-infrared waveguide photodetector with Ge/Si self-assembled quantum dots.
Appl. Phys. Lett. , 80(3):509, 2002.[10] S. David, M. E. Kurdi, P. Boucaud, C. Kammerer, L. Xiang, S. Sauvage, V. Le Thanh, I. Sagnes,D. Bouchier, and J.-M. Lourtioz. Ge/Si self-assembled islands integrated in 2D photonic crystalmicrocavities for realisation of silicon-based light-emitting devices.
Proc. SPIE , 5450:369, 2004.[11] A. I. Yakimov, A. V. Dvurechenskii, V. V. Kirienko, and A. I. Nikiforov. Ge/Si quantum-dotmetal-oxide-semiconductor field-effect transistor.
Appl. Phys. Lett. , 80(25):4783, 2002.[12] A. I. Yakimov, V. A. Markov, A. V. Dvurechenskii, and O. P. Pchelyakov. Coulomb staircase inSi/Ge structure.
Phil. Mag. B , 65:701, 1992.[13] G. Jin, J. L. Liu, and K. L. Wang. Temperature effect on the formation of uniform self-assembledGe dots.
Appl. Phys. Lett. , 83(14):2847, 2003.[14] L. Vescan, T. Stoica, O. Chretien, M. Goryll, E. Mateeva, and A. Muck. Size distribution andelectroluminescence of self-assembled Ge dots.
J. Appl. Phys. , 87(10):7275, 2000.[15] G. Medeiros-Ribeiro, A. M. Bratkovski, T. I. Kamins, D. A. A. Ohlberg, and R. S. Williams.Shape transition of germanium nanocrystals on a silicon (001) surface from pyramids to domes.
Science , 275:353, 1998.[16] Y.-W. Mo, D. E. Savage, B. S. Swartzentruber, and M. G. Lagally. Kinetic pathway in Stranski-Krastanov growth of Ge on Si(001).
Phys. Rev. Lett. , 65:1020, 1990.[17] A. Vailionis, B. Cho, G. Glass, P. Desjardins, David G. Cahill, and J. E. Greene. Pathway to thestrain-driven two-dimensional to three-dimensional transitions during growth of Ge on Si(001).
Phys. Rev. Lett. , 85:3672, 2000.[18] F. M. Ross, R. M. Tromp, and M. C. Reuter. Transition states between pyramids and domesduring Ge/Si island growth.
Science , 286:1931, 1999.[19] V. A. Yuryev and L. V. Arapkina. Defects of Ge quantum dot arrays on the Si(001) surface.
Physica B , 404:4719, 2009. See also arXiv:0908.0841 .[20] J. Tersoff and R. M. Tromp. Shape transitions in growth of strained islands: Spontaneousformation of quantum wires.
Phys. Rev. Lett. , 70(18):2782, 1993.[21] I. Goldfarb, P. T. Hayden, J. H. G. Owen, and G. A. D. Briggs. Nucleation of “hut” pits andclusters during gas-source molecular-beam epitaxy of Ge/Si(001) in in situ scanning tunnellingmicroscopy.
Phys. Rev. Lett. , 78(20):3959, 1997.[22] I. Goldfarb, J. H. G. Owen, D. R. Bowler, C. M. Goringe, P. T. Hayden, K. Miki, D. G. Pettifor,and G. A. D. Briggs.
In situ observation of gas-source molecular beam epitaxy of silicon andgermanium on Si(001).
J. Vac. Sci. Technol. A , 16(3):1938, 1998.[23] D. E. Jesson, G. Chen, K. M. Chen, and S. J. Pennycook. Self-limiting growth of strained facetedislands.
Phys. Rev. Lett. , 80(23):5156, 1998.[24] M. K¨astner and B. Voigtl¨ander. Kinetically self-limiting growth of Ge islands on Si(001).
Phys.Rev. Lett. , 82(13):2745, 1999.[25] I. Goldfarb. Effect of strain on the appearance of subcritical nuclei of Ge nanohuts on Si(001).
Phys. Rev. Lett. , 95:025501, 2005.[26] I. Goldfarb, L. Banks-Sills, and R. Eliasi. Is the elongation of Ge huts in the low-temperatureregime governed by kinetics?
Phys. Rev. Lett. , 97:206101, 2006.[27] D. E. Jesson, K. M. Chen, and S. J. Pennycook. Kinetic pathways to strain relaxation in theSi-Ge system.
MRS Bulletin , 21(4):31, 1996.[28] F. Liu, F. Wu, and M. G. Lagally. Effect of strain on structure and morphology of ultrathin Gefilms on Si(001).
Chem. Rev. , 97(4):1045, 1997.[29] Ivan N. Stranski and L. von Krastanow. Zur theorie der orientierten ausscheidung vonionenkristallen aufeinander.
Sitzungaber. Akad. Wien, Mat. Nat. K1. IIb , 146:797–810, 1937.[30] E. Bauer. Ph¨anomenologische theorie der kristallabscheidung an oberfl¨aschen, I/II.
Z. Kristallogr. , lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . Ultramicroscopy , 42–44:895, 1992.[32] F. Iwawaki, M. Tomitori, and O. Nishikawa. STM study of initial stage of Ge epitaxy on Si(001).
Ultramicroscopy , 42–44:902, 1992.[33] Fang Wu, Xun Chen, Zhenyu Zhang, and M. G. Lagally. Reversal of step roughness on Ge-coveredvicinal Si(001).
Phys. Rev. Lett. , 74:574, 1995.[34] B. Voigtl¨ander and M. K¨astner. Evolution of the strain relaxation in a Ge layer on Si(001) byreconstruction and intermixing.
Phys. Rev. B , 60:R5121, 1999.[35] D. B. Migas, P. Raiteri, L. Miglio, A. Rastelli, and H. von K¨anel. Evolution of Ge/Si(001) wettinglayer during Si overgrowth and crossover between thermodynamic and kinetic behavior.
Phys.Rev. B , 69:235318, 2004.[36] F. Iwawaki, M. Tomitori, and O. Nishikawa. STM study of epitaxial growth of Ge on Si(001).
Surf. Sci. Lett. , 253:L411, 1991.[37] J. Tersoff and F. K. LeGoues. Competing relaxation mechanisms in strained layers.
Phys. Rev.Lett. , 72(22):3570, 1994.[38] Y. Fujikawa, T. Sakurai, and M. G. Lagally. Charge transfer in the atomic structure of Ge(105).
Appl. Surf. Sci. , 252:5244, 2006.[39] P. Raiteri, D. B. Migas, Leo Miglio, A. Rastelli, and H. von K¨anel. Critical role of the surfacereconstruction in the thermodynamic stability of { } Ge pyramids on Si(001).
Phys. Rev.Lett. , 88(25):256103, 2002.[40] G. Medeiros-Ribeiro, T. I. Kamins, D. A. A. Ohlberg, and R. S. Williams. Annealing of Genanocrystals on Si(001) at 550 ◦ C: Metastability of huts and the stability of pyramids and domes.
Phys. Rev. B , 58(7):3533, 1998.[41] F. Montalenti, P. Raiteri, D. B. Migas, H. von K¨anel, A. Rastelli, C. Manzano, G. Costantini,U. Denker, O. G. Schmidt, K. Kern, and L. Miglio. Atomic-scale pathway of the pyramid-to-dome transition during Ge growth on Si(001).
Phys. Rev. Lett. , 93(21):216102, 2004.[42] A. Li, F. Liu, and M. G. Lagally. Equilibrium shape of two-dimensional islands under stress.
Phys. Rev. Lett. , 85(9):1922, 2000.[43] L. V. Arapkina, K. V. Chizh, and V. A. Yuryev. Initial stage of growth of Ge quantum dotson the Si(001) surface at low temperatures. In A. L. Aseev and A. V. Dvurechenski˘i, editors,
Russian Conference on Actual Problems of Semiconductor Photoelectronics (“Photonics-2008”) ,page 23, Novosibirsk, Russia, 19–23 August 2008. A. V. Rzhanov Institute of SemiconductorPhysics of Siberian Brunch of the Russian Academy of Sciences. See also arXiv:0907.4665 and arXiv:0908.0883 .[44] B. Voigtl¨ander. Fundamental processes in Si/Si and Ge/Si epitaxy studied by scanning tunnelingmicroscopy during growth.
Surf. Sci. Rep. , 43:127, 2001.[45] K. N. Eltsov. Ultrahigh vacuum scanning tunnelling microscope STM GPI-300.http://surface.gpi.ru/papers/gpi300e.pdf.[46] I. V. Kiryushina. Processes of liquid chemical preparation of silicon wafers in the VLSI productionwith sub-micrometer design rules. PhD thesis, JSC Mikron, Zelenograd, Moscow, Russia, 2003.In Russian.[47] L. V. Arapkina, V. M. Shevlyuga, and V. A. Yuryev. Structure and peculiarities of the (8 × n )-type Si(001) surface prepared in a molecular beam epitaxy chamber: A scanning tunnelingmicroscopy study. JETP Lett. , 87:215, 2008.[48] L. V. Arapkina, V. A. Yuryev, and V. M. Shevlyuga. STM and RHEED investigations ofthe c (8 × n ) defect structure on Si(001). In , St. Petersburg, Russia, 20–24 July 2009.[49] K. N. Eltsov, V. M. Shevlyuga, V. Yu. Yurov, A. V. Kvit, and M. S. Kogan. Sharp tungsten tipsprepared for STM study of deep nanostructures in UHV. Phys. Low-Dim. Struct. , 9/10:7, 1996.[50] I. Horcas, R. Fernandez, J. M. Gomez-Rodriguez, J. Colchero, J. Gomez-Herrero, and A. M. Baro. lassification of Ge hut clusters in the arrays formed on the Si(001) surface. . . WSxM: A software for scanning probe microscopy and a tool for nanotechnology.
Rev. Sci.Instrum. , 78:013705, 2007.[51] L. V. Arapkina, K. V. Chizh, V. M. Shevlyuga, and V. A. Yuryev. The controllable formationof densely packed arrays of Ge nanoclusters on the silicon (001) surface by means of ultrahighvacuum molecular beam epitaxy. In A. L. Aseev and A. V. Dvurechenski˘i, editors,
RussianConference on Actual Problems of Semiconductor Photoelectronics (“Photonics-2008”) , page 48,Novosibirsk, Russia, 19–23 August 2008. A. V. Rzhanov Institute of Semiconductor Physics ofSiberian Brunch of the Russian Academy of Sciences.[52] I. V. Kucherenko, V. S. Vinogradov, N. N. Mel’nik, L. V. Arapkina, V. A. Chapnin, K. V. Chizh,and V. A. Yuryev. The role of interdiffusion and spatial confinement in the formation of resonantRaman spectra of Ge/Si(100) heterostructures with quantum-dot arrays.
Phys. Solid State ,50:1970, 2008.[53] I. V. Kucherenko, V. S. Vinogradov, N. N. Melnik, L. V. Arapkina, V. A. Chapnin, K. V. Chizh,and V. A. Yuryev. Effect of interdiffusion and quantum confinement on Raman spectra ofthe Ge/Si(100) heterostructures with quantum dots. In
Proceedings of the 16th InternationalSymposium “Nanostructures: Physics and Technology” , page 199, Vladivostok, Russia, 14–18July 2008. Ioffe Physico-Technical Institute, St. Petersburg, Russia. See also arXiv:0908.1378 .[54] D. Gr¨utzmacher, T. Fromherz, C. Dais, J. Stangl, E. M¨uller, Y. Ekinci, H. H. Solak, H. Sigg,R. T. Lechner, E. Wintersberger, S. Birner, V. Holy, and G. Bauer. Three-dimensional Si/Gequantum dot crystals.