Contains an introduction and a list of publications.Joint Services Electronics Program Grant DAAH04-95-1-0038National Science Foundation Grant DMR 94-2364

Mochrie, Simon G. J.

Song, Seugheon

Tsui, Ophelia

Yoon, Mirang

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Chapter 3. Step StructuresChapter 3. Step Structures and Epitaxy on SemiconductorSurfacesAcademic and Research StaffProfessor Simon G.J. Mochrie, Dr. Ophelia TsuiGraduate StudentsSeugheon Song, Mirang Yoon3.1 IntroductionSponsorsJoint Services Electronics ProgramGrant DAAH04-95-1-0038National Science FoundationGrant DMR 94-23641There is at present considerable effort directedtowards the fabrication of nanoscale semiconductorobjects. This is, in part, to allow for the investi-gation of the behavior of electrons within structuresof sufficiently small dimensions to produce quantumconfinement. Such so-called quantum dots andquantum wires typically have dimensions of a fewhundred Angstroms. In addition, quantum dots andwires have been proposed as a route to many newdevice applications.Recently, it has emerged that nanoscale structureson certain semiconductor surfaces may spontan-eously self-assemble into more-or-less ordered pat-terns. Over the last year, we have been pursuinginvestigations of two examples of this phenomenon.Our goal is to achieve a microscopic and predictiveunderstanding of the factors that determine thenanostructure and how it may be controlled andexploited in the creation of new nanoscale surfacestructures, for example, by decoration schemes tocreate chemically heterogeneous surfaces. Specif-ically, we have completed a comprehensive studyof the self-assembly of nanoscale grooves onstepped silicon surfaces. In addition, we have con-tinued studies of Ge quantum dots on Si.Self-assembly of nanoscale grooves on steppedSi(113) faceting is a remarkable phenomenon inwhich a crystal surface increases its area in orderto decrease its free energy. This is accomplishedvia the rearrangement of surface steps into regionsof low and high step density. Stepped Si(113) sur-faces realize a new paradigm for the thermo-dynamics and kinetics of faceting and the wayelasticity determines surface morphology.The phase diagram of silicon surfaces miscut fromthe [113] direction towards [001] is shown infigure 1 versus temperature and miscut angle. The(113) orientation-at zero misorientation angle-is astable phase for all temperatures studied. Above1223 K and at non-zero misorientation angles, thereoccurs a one-phase region of the phase diagram, inwhich the surface is uniformly stepped. In thisregion, we find strongly temperature-dependent,near-specular diffuse scattering, which is criticalscattering, and is the result of an increase in stepfluctuations with decreasing temperature. The stepcritical scattering anticipates a faceting transforma-tion at which the surface transforms from a homo-geneous phase of uniform orientation intocoexisting phases with different orientations.Between 1223 and 1130 K, there is a two-phaseregion. The point at T, = 1223 K and zero misori-entation (open square in figure 1) angle is actuallya special type of critical point called a tricriticalpoint. Below a triple point temperature ofT 3 = 1130 ± 10 K (dashed line in figure 1), coexist-ence between the (113) facet and the (114) facet,which lies 5.7 degrees from the [1131 direction,replaces coexistence between the [113] facet andthe stepped phase. This work inspired two inde-pendent theoretical investigations aimed at under-standing our observations which recently appearedin Physical Review Letters' and which relate thestep tricritical behavior to a two-dimensional"wetting" transition, occurring in the presence oflong-ranged repulsions and short-ranged attractionsbetween steps.In fact, upon faceting, the stepped Si(113) surfacesdescribed above spontaneously form a striking1 M. Lassig, Phys. Rev. Lett. 77: 526 (1996); S. Bhattacharjee, Phys. Rev. Lett. 76: 4568 (1996)177Chapter 3. Step StructuresFigure 1. Orientational phase diagram of steppedSi(113) surfaces misoriented towards L0011. Solid linesindicate phase boundaries; solid circles and squares rep-resent mesoscopic surface orientations measured forsamples with macroscopic misorientations of 2.1 degreesand 3.7 degrees, respectively.mesoscopically grooved morphology.2 Figure 2shows an ex-situ atomic force microscope (AFM)image of one such surface. Here, one side of eachgroove is a step-free (113) facet and the other sideis a step bunch. Individual grooves are a fewhundred Angstroms across and exceed one micronin length. Evidently, the grooves self-assemble toform the nearly periodic nanoscale grating that maybe seen in the figure. Practical interest derivesfrom the fact that it is very difficult to make suchsmall structures using lithography. Indeed, consid-erable interest is emerging in employing ourgrooved silicon surfaces as a template for nanolith-ography.Figure 2. AFM image of a 10000 X 10000 A2 area of aself-assembled grating on a stepped Si(113) surface.One side of each groove is step-free, the other side isdensely-stepped.Associated with the grating of figure 2 are first-orderdiffraction peaks. The peak locations are deter-mined by the grating periodicity and the peakwidths by the degree of ordering. As illustrated infigure 3, with increasing time, these peaks grow inintensity, shift to smaller wave vectors, corre-sponding to an increase in the groove period, andbecome narrower, corresponding to an increasinglyordered structure. The peak positions and widths(HWHM) of the first-order diffraction peaks areshown on a log-log scale versus time for three rep-resentative final temperatures in figure 4. The vari-ation of the peak position versus time is consistentwith a 1/6 power-law behavior for times between afew and several hundred seconds. These resultshave lead to a theory of the growth of grooves,which reproduces the 1/6 power-law and identifiesthe rate-limiting step as the close approach ofneighboring step bunches.Mochrie, Phys. Rev. B 51: 10068 (1995).178 RLE Progress Report Number 1392 S. Song and S.G.J.Chapter 3. Step Structures2.5 - o 1200 sec(a) * 400 sec.15.0 - 120 sec.[ 40 sec.SA 12 sec.S2.0 - 4 sec.0 0 sec.10.0M 0-8 7.51.5 -x2.51.00z- -0.003 0 0.0030.50-0.02 -0.01 0 0.01 0.02a, (A-1)Figure 3. Time evolution of the first-order diffraction peaks of the structure shown in figure 2, following a temperaturequench from 1248 to 1171 K.Chapter 3. Step StructuresFigure 4. Log-log plot of thetemperatures.position and HWHM of the first-order diffraction peaks for three representative quenchA key prediction of the theory is that the character-istic length scale along the grooves-i.e., the lengthof the grooves-varies as a 1/2-power law versustime. We have recently initiated experiments to testthis important prediction. A preliminary analysisindicates agreement with theory.At longer times the groove size approaches a cons-tant value while the groove ordering continues toimprove, indicating that the surface morphology isevolving towards a periodic, ordered equilibriumstate. The variation of the limiting facet sizeversus the stepped phase misorientation angle maybe understood qualitatively on the basis ofMarchenko et al.3, where it is proposed that thelowest energy configuration of a faceted surfacecorresponds to a periodically grooved morphology.The special stability of the grooved structure origi-nates in a reduction of surface-stress-inducedelastic energy in the bulk that occurs for meso-scopic facets as compared to macroscopic facets.The period is determined by balancing the reductionin elastic energy against the cost in energy of main-taining edges between the coexisting phases. Thetheory predicts that the groove period is minimizedwhen the angles between each side of the grooveand the macroscopic surface are equal, as foundexperimentally for the two differently misorientedsamples. Thus, we have achieved an in-depthunderstanding of the mechanism responsible fornanoscale grooves on stepped Si(113) surfaces.In conclusion, we have achieved a very completeunderstanding of why and how nanoscale groovesform on stepped Si(113) surfaces. Since faceting is3 V.I. Marchenko, Zh. Eksp. Teor. Fiz. 81: 1141 (1981); Sov. Phys. JETP 54: 605 (1981); O.L. Alerhand, D. Vanderbilt, R.D. Meade,and J.D. Joannopoulos, Phys. Rev. Lett. 61: 1973 (1988).180 RLE Progress Report Number 139SPOSITION50010-29 HWHM87- 1000I< 5af 4 - 02- 5000o 1171 K (cd10 * 1193 K9 1213 K7,, ,  , , , , - 1000010 - 1  10 0  101 102  10 3  10 4  105TIME (seconds)Chapter 3. Step Structuresa widespread phenomenon, we may be confidentthat the understanding gained here will have wide-spread application to other surfaces and materials.For example, we are presently analyzing the resultsof x-ray scattering experiments on Si(112), whichspontaneously undergoes faceting to produce agrooved superstructure.3.1.1 Self-assembly of Ge Quantum Dotson Si(001)The manufacture of quantum dots and wires isexceedingly difficult. For example, it is difficult toachieve the requisite sizes with lithography.Schemes which directly build quantum-sized objectsduring growth are possible alternatives. Suchschemes include, for example, cluster formation inthe gas phase and subsequent cluster deposition,and growth on patterned substrates such asstepped surfaces.An especially promising and interesting approach isthe self-assembly of a nanostructure during strainedheteroepitaxial growth on a flat substrate. Strainedheteroepitaxial growth, involving a large lattice mis-match, generally proceeds via the formation ofislands after the initial growth of a few flat layers.Recently, Krishnamurthy et al., Leonard et al., andMoison et al.4 have found that it is possible toprepare near-uniformly sized and near-uniformlyspaced islands of dislocation-free Ge on Si(001),InGaAs on GaAs(001), and InAs on GaAs(001),respectively. It is this apparent self-organization ofdefect-free quantum dots that is so remarkable fromboth a technological and a scientific viewpoint.However, a fundamental understanding of quantumdot formation-whether it is kinetic or thermo-dynamic in origin-is presently lacking.In the earlier studies, it was not possible to examinein-situ island formation during the deposition andannealing processes. By contrast, we have initiatedan investigation of the in-situ self-assembly ofquantum dots of germanium on silicon as it occurs.We use both synchrotron x-ray scattering tech-niques to monitor how the surface morphologydevelops in real-time and the atomic force micro-scope to take definitive "snap shots" of the surfacemorphology by means of rapid temperaturequenches. In this way, we hope to achieve amicroscopic and predictive understanding of thefactors that determine the final morphology. As aresult, we expect to learn how to control the nano-structure.We have chosen to study, initially, the Ge-on-Sisystem, in part because of the earlier work ofKrishnamurthy et. al., and in part because of thepotential utility of Ge-Si heterostructures in deviceapplications. Figure 5 illustrates an AFM image ofa surface upon which is deposited the equivalent ofapproximately 8 monolayers of Ge at a substratetemperature of 480 K.Figure 5. AFM image of Ge quantum dots on Si(001)Three monolayers grow in a layerwise fashion, butsubsequent deposition occurs in the form of threedimensional islands-quantum dots-which may beclearly seen in the image more-or-less uniformlyspaced across the surface. This figure demon-strates that we can prepare quantum dots for study.As may be seen, some of the dots are elongatedalong two orthogonal directions, which are highsymmetry directions of the substrate. This inter-esting aspect is not understood.The development of the morphology seen in figure5 may be monitored in situ and in real time usingsynchrotron x-ray scattering. This is demonstratedin figure 6, which shows x-ray scattering results weobtained recently during Ge deposition on a Si(001)substrate, over the course of 2000 seconds at asubstrate temperature of 480 K, for coverages thatare equivalent to between approximately 1 and 8monolayers. The two peaks symmetrically located4 M. Krishnamurthy, J. Drucker, and J.A. Venables, J. Appl. Phys. 69: 6461 (1991); D. Leonard et al., J. Vac. Sci. Technol. B 12:1063 (1994); J.M. Moison et al., Appl. Phys. Lett. 64: 196 (1994).Chapter 3. Step Structuresaround the central specular peak derive from Gequantum dots as they appear on the surface. Spe-cifically, the separation from the specular peakdetermines the separation of quantum dots on thesurface.We are currently investigating the evolution of thesurface morphology versus time at different deposi-tion temperatures and for different Ge coveragesand temperatures subsequent to deposition. Ofspecial interest are the degree to which the dotsare the same size and the extent of their ordering.140012001000800 -S oo400 -2000-0.06 -0.04 -0.02 0 0.02 0.04 0.06Qo (A- 1)Figure 6. Diffraction peaks due to Ge quantum dotsduring deposition at 480 K.3.2 PublicationsBhattacharjee, S.M. "Theory of Tricriticality forMiscut Surfaces." Phys. Rev. Lett. 76(24): 4568(1996).Lassig, M. "Vicinal Surfaces and the Calogero-Sutherland Model." Phys. Rev. Lett. 77(3): 526(1996).Mochrie, S.G.J., S. Song, M. Yoon, D.L. Abernathy,and G.B. Stephenson. "Faceting of SteppedSilicon (113) Surfaces: Self Assembly of Nano-scale Gratings." Physica B 221: 105 (1996).Song, S., M. Yoon, S.G.J. Mochrie, and G.B.Stephenson. "Faceting Kinetics of SteppedSi(113) Surfaces: Dynamic Scaling and Nano-scale Grooves." Surf. Sci. Forthcoming.3.2.1 ThesisSong, S. Faceting and Tricriticality in theOrientational Phase Diagram of Stepped Si(1 13)Surfaces: Synchrotron X-ray Scattering Studies.Dept. of Phys., MIT, 19963.2.2 Invited TalksMochrie, S.G.J. "Faceting of Stepped Si(113): StepUnbinding, Dynamic Scaling, and Self-Assemblyof Nano-scale Grooves." Conference on theDynamics of Crystal Surfaces and Interfaces,Traverse City, Michigan, August 1996.Mochrie, S.G.J. "Faceting of Stepped Si(113): StepUnbinding, Dynamic Scaling, and Self-Assemblyof Nano-scale Grooves." Fall Meeting of theMaterials Research Society, Boston, Massachu-setts, December 1996.182 RLE Progress Report Number 139

Step Structures and Epitaxy on Semiconductor Surfaces

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Step Structures and Epitaxy on Semiconductor Surfaces

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