Semiconductor nanomembranes: a platform for new properties via strain engineering
© Cavallo and Lagally; licensee Springer. 2012
Received: 17 October 2012
Accepted: 8 November 2012
Published: 15 November 2012
New phenomena arise in single-crystal semiconductors when these are fabricated in very thin sheets, with thickness at the nanometer scale. We review recent research on Si and Ge nanomembranes, including the use of elastic strain sharing, layer release, and transfer, that demonstrate new science and enable the fabrication of materials with unique properties. Strain engineering produces new strained forms of Si or Ge not possible in nature, new layered structures, defect-free SiGe sheets, and new electronic band structure and photonic properties. Through-membrane elastic interactions cause the double-sided ordering of epitaxially grown nanostressors on Si nanomembranes, resulting in a spatially and periodically varying strain field in the thin crystalline semiconductor sheet. The inherent influence of strain on the band structure creates band gap modulation, thereby creating effectively a single-element electronic superlattice. Conversely, large-enough externally applied strain can make Ge a direct-band gap semiconductor, giving promise for Group IV element light sources.
The evolution to miniaturization of electronic device structures has also increased applications through novel approaches and designs. A platform technology aiding this evolution that has recently seen rapid development is based on the use of thin crystalline semiconductor sheets of the order of 100 nm or less, called nanomembranes, as an alternative to bulk substrates[1–19]. These nanomembranes can be completely freestanding or tethered to a substrate, and they can be flat[4, 20] or shaped into three-dimensional (3D) structures[21–23]. Conventional top-down patterning techniques are used in the fabrication of the device structures, and conventional growth techniques are used in the creation of layered structures[1–22]. The bottom-up (self-assembly) part of the fabrication comes about via strain engineering, as we will describe.
Crystalline nanomembranes (NMs) are distinguished from bulk materials most significantly by thinness, flexibility, nearness of two surfaces or interfaces, and the essential fact that in some part of their processing, nanomembranes are free of any constraint: they are released from a rigid handling substrate via removal of a sacrificial layer. Unique structural, electronic, and optical properties have been measured for these nanomembranes, both for flat and curled films[1–19, 24–26]. NMs may be transferred to a large variety of hosts. This ability to transfer has been successfully used for the fabrication of hybrid or highly mismatched single-crystal multilayer stacks and for the development of bendable and stretchable electronics[2, 4, 18, 20].
In addition to exploiting thinness and transferability for fabricating novel devices, one can take advantage of the mechanical compliance of freestanding NMs to establish a uniform or spatially varying strain field in the thin crystalline sheet[4, 20, 27–29], in some cases producing strain distributions that are not possible in the bulk. Elastic strain sharing between a crystalline SiGe sheet sandwiched between two crystalline Si sheets completely unsupported by a solid allows the fabrication of tensilely strained SiNMs[4, 20, 28]. This method has been developed to create defect-free single crystals of SiGe, something not feasible with conventional approaches. A spatially varying strain field has been established in Si nanoribbons by growing ‘local stressors’ (e.g., Ge or InAs quantum dots (QDs)) rather than a uniform stressor layer[27, 29, 31]. Additionally, one can use applied mechanical strain, as opposed to lattice mismatch-induced strain, to create new properties. In all these cases, induced strain gives us control over the lattice constant and the symmetry of lattice expansion or contraction.
Producing strain in a material offers the possibility of tuning material properties. In particular, in semiconductors, electronic band structure and charge transport are the essential properties that control device behavior. Strain can modify band gaps and carrier mobility, both on a global and a local scale[29, 33]. For this reason, strain engineering has significant implications for the development of a crystalline nanomembrane-based technology. Examples include the fabrication of high-performance and novel electron device structures as well as nanoscale photonic and thermoelectric devices[1–19, 34–36]. In other materials, such as oxides, strain sensitively affects magnetic, ferroelectric, and pyroelectric behavior.
Ge and Si combine to make an ideal model system for strain engineering studies in thin sheets. Ge has a lattice constant that is 4% larger than that of Si. Even at submonolayer Ge coverages, strain has a significant impact on the structure of the Si (001) surface, via modified step structure and surface dislocation formation, features that have been quantified with scanning tunneling microscopy a number of years ago[38–41]. We focus here on the recent scientific developments related to Group IV semiconductor NMs that emphasize new materials and structures with new properties that cannot be fabricated or obtained in other ways.
Creating silicon sheets with unique strain symmetries
Crystalline nanomembranes offer a powerful platform for using and tuning strain to create materials that have unique properties which are not achievable in bulk materials or with conventional processes. Nanomembranes, because of their thinness, enable elastic strain sharing, a process that introduces large amounts of strain and unique strain distributions in single-crystal materials, without the formation of extended defects. The reason is that the strain energy in a material increases as its thickness increases; in contrast to the bulk, at the same stress, a thin sheet will not contain sufficient strain energy to create dislocations or does not contain sufficient strain energy to fracture. It is thus possible to make new strained materials using crystal symmetry as the driver.
The experimental demonstration is done with a trilayer Si(110)/Si(1-x)Ge x (110)/Si(110) nanomembrane, an elastically twofold symmetric system in which it is possible to transfer strain that is biaxially isotropic. Tensilely strained Si(110) has emerged as an option for complementary metal oxide semiconductor devices because of its high carrier mobility[36, 43]. Traditional methods to fabricate tensilely strained Si(001) rely on epitaxial growth of a Si layer on plastically relaxed SiGe(001) substrates. This process does produce strained Si(001), although with nonuniform strain and with roughness. It is not effective, however, for fabricating strained Si(110). For a given Ge concentration, the kinetic critical thickness for plastic relaxation is much lower in the (110) than in the (001) orientation. As a consequence, strain grading in SiGe(110) results in a threading dislocation density that is more than ten times higher in (110)- than in (001)-oriented relaxed SiGe substrates. Furthermore, other strain relief mechanisms, i.e., roughening and mosaic tilt, have been reported for strain relaxation in SiGe(110).
where εm is the mismatch strain at the interface, and ε, M, and h are the layer strain, biaxial moduli, and thicknesses of the Si and SiGe layers. Equation 1 shows that the use of high-Ge-content SiGe layers and ultrathin Si layers maximizes the strain in the two Si films. The upper limit to the thickness of the SiGe film is defined by the kinetic critical thickness for plastic relaxation of this layer during growth.
After release, all peaks are shifted to higher diffraction angle, corresponding to a uniform in-plane expansion of the lattice. The uniform peak shifts and the interface fringes confirm that the SiGe layer has elastically relaxed during the release step. Transfer of the compressive strain in the SiGe film is determined by the relative thicknesses of the Si and SiGe layers. For the (110)-oriented trilayer schematically shown in Figure3b, the in-plane biaxial tensile strain is ε|| = 0.49% in the Si layers after release. The lack of significant surface roughening and crosshatch in these trilayer structures indicates that there is no relaxation via 3D growth or misfit dislocation formation. The surface roughness must be small so that the charge mobility enhancements resulting from strain are not negated by surface roughness scattering of charge carriers. The absence of ridges in the Si capping layer excludes the presence of microtwins or mosaic tilt in the SiGe layer.
Mixed-crystal-orientation composite nanomembranes
The transfer of (110) SiNMs (even unstrained) to a (001)-oriented Si template and subsequent overgrowth can be used to fabricate mixed-crystal-orientation templates (Scott SA et al., unpublished). This architecture may allow the fabrication, in close proximity to each other, of p- and n-channel devices on Si(110) (high hole mobility) and Si(001) (high electron mobility) regions, respectively, with the benefit of reducing the current drive imbalance between p-type metal oxide semiconductor (PMOS) and n-type metal oxide semiconductor (NMOS) devices. Additionally, the ability to transfer a dislocation-free strained Si(110) nanomembrane to Si(001) promises hole mobility enhancements of up to 75% compared to the (001) universal mobility. Furthermore, rotating the strained (110) membrane relative to its (001) host during transfer offers a concrete possibility of optimizing channel direction in n- and p-type devices.
Mechano-electronic superlattice in a Si nanomembrane
It has been known for many years that the growth of Ge or Ge-rich SiGe on bulk Si(001) creates 3D nanocrystals (‘huts’ or ‘domes’, also called quantum dots)[51, 52] that act as local stressors. They have random positions on the surface; the positional order can only be improved with the growth of multiple layers that act to self-organize the nanostressor arrangement. On freestanding Si nanomembranes, growth also leads to the formation of nanostressors but with the distinct difference that the nanostressors self-organize already in a single layer if growth occurs on both sides of the NM. That is possible using CVD. Via through-membrane elastic interactions, the local strain created by a nanostressor provides a feedback for self-organization of the QDs, something that does not occur on bulk substrates. Strain sharing between the QDs and the compliant SiNM creates very small regions of high local strain in the membrane. As a result, the SiNM undergoes distortion, forming into a slightly wavy sheet, with alternate regions of high tensile and compressive strains.
The periodic strain field in the SiNM induces a periodic change in the Si band gap as a function of position along the ribbon. For this purpose, the local strain was modeled with a 2D finite element analysis of the elastic deformation and elastic energy resulting from two opposite-side QDs in one dimension, corresponding to the ribbon geometry with one line of dots on each side. The calculations predict that the maximum tensile strain beneath an epitaxially grown Ge QD with a height of 8 nm and a base width of 80 nm is 1.62% for a 25-nm-thick ribbon and 1.89% for a 10-nm-thick ribbon. The resulting reduction of the band gap can be up to 250 meV for the thinnest ribbons, more than 20% of the bulk value of the band gap. The shift occurs almost completely in the conduction band. The calculated band gap modulation in the SiNM due to the growth of nanostressors agrees with independently measured changes in the positions of bands for a uniformly biaxially strained SiNM.
A nanoribbon with a periodic change in the band offsets occurring essentially completely in the conduction band is equivalent to a one-dimensional (1D) periodic potential. One can therefore solve the Schrödinger equation to obtain the miniband structure in this 1D periodic potential. The results show that minibands with very small separations (i.e., minigaps) form within the potential well created by Ge nanostressors on Si but that only below 77 K would the thermal smearing be reduced sufficiently to make discrete minibands observable. A complete ‘phase diagram’ for possible band offsets and single-element electronic superlattices created by periodic strain as a function of nanostressor size, period, and NM thickness has been calculated.
Mechanical biaxial strain in Ge: making Ge a direct-band gap material
Mechanically straining freestanding NMs can transform Ge into a direct-band gap, efficient light-emitting material if sufficient strain can be induced. The work is based on the theoretical prediction that biaxial tensile strain in Ge has the effect of lowering the conduction-band edge at the direct (Γ) point relative to the L valley minima (which determine the fundamental, but indirect, gap at zero strain), while the overall band gap energy correspondingly decreases. In the presence of electrical or optical pumping, a substantial population of electrons at the Γ minimum can therefore be established in sufficiently tensilely strained Ge, thereby increasing the light emission efficiency and enabling optical gain. If the strain exceeds 1.9%, the fundamental band gap even becomes direct.
Figure9c shows room-temperature photoluminescence (PL) spectra measured from a 40-nm-thick Ge NM at different strains below its threshold for plastic deformation. The integrated luminescence is significantly enhanced with increasing strain. In Figure9d, the solid lines show the calculated band gap energies between the Γ or L conduction-band minima and the heavy-hole or light-hole valence-band maxima as a function of strain. In general, all four transitions shown in this graph can contribute to the PL spectra, although depending on the strain, some of them may be nearly degenerate (or too weak) so that the corresponding emission peaks cannot be resolved. The calculations show that Ge has become direct band gap at an equibiaxial tensile strain of approximately 1.8%, i.e., the Γ valley of the conduction band has moved in energy to below the L valley. The direct-gap energy at this crossover position is approximately 0.47 eV.
This brief review has summarized recent work on crystalline Group IV semiconductor nanomembranes. We have focused on work emphasizing novel science that results from using semiconductor sheets, i.e., structures in which one dimension is at the nanoscale while the other two are macroscopic. These sheets are single-crystal but extremely flexible. Because they are so thin, sheets can be highly strained. Combining growth and strain produces many new fundamental properties. Examples include the following: (1) Release of epitaxial layers of Si and SiGe from (110) SOI substrates induces elastic strain sharing among the layers, creating isotropically and biaxially strained Si(110), a strain symmetry that is not possible with bulk material. (2) The enhanced CVD growth of Si on Si(001) compared to Si(110) combined with bonding a meshed (110) membrane on top of a (001) substrate is used to create mixed-crystal-orientation surfaces consisting of uniform squares of Si(001) and Si(110). (3) 3D nanostressors that are a natural consequence of strained-layer growth produce local strain in freestanding NMs, and therefore local variations in the band gap of Si. The mechanical compliance of the NM allows the self-ordering of the nanostressors via through-membrane elastic interactions. The local strain can be made large enough to create band offsets in Si sufficiently large for miniband formation. Under some circumstances, the minigaps may be large enough to be observed at room temperature. (4) Using externally applied biaxial tensile strain, it is possible to change the band structure of Ge so that it becomes direct band gap. Thus, efficient light emission from Ge becomes possible.
These fundamental results suggest that Si and other semiconductor membranes are a disruptive technology for the development of novel device structures, allowing the integration of various functionalities (i.e., mechanical, optical, thermoelectric, and surface chemical) with high-performance electron devices.
The work described in this review that was performed at the University of Wisconsin has been supported by DOE grant number DE-FG02-03ER46028, AFOSR grant number FA9550-08-1-0337, and NSF grant number DMR-0907296.
- Rogers JA, Lagally MG, Nuzzo RG: Semiconductor nanomembranes: synthesis, assembly, and applications. Nature 2011, 477: 45.View ArticleGoogle Scholar
- Ahn JH, Kim HS, Lee KJ, Jeon S, Kang SJ, Sun Y, Nuzzo RG, Rogers JA: Heterogeneous three-dimensional electronics by use of printed semiconductor nanomaterials. Science 2006, 314: 1754.View ArticleGoogle Scholar
- Khang DY, Jiang HQ, Huang Y, Rogers JA: A stretchable form of single-crystal silicon for high-performance electronics on rubber substrates. Science 2006, 311: 208.View ArticleGoogle Scholar
- Roberts MM, Klein LJ, Savage DE, Slinker KA, Friesen M, Celler GK, Eriksson MA, Lagally MG: Elastically relaxed free-standing strained-silicon nanomembranes. Nat Mater 2006, 5: 388.View ArticleGoogle Scholar
- Yuan HC, Ma Z: Microwave thin-film transistors using Si nanomembranes on flexible polymer substrate. Appl Phys Lett 2006, 89: 212105.View ArticleGoogle Scholar
- Yuan HC, Ma Z, Roberts MM, Savage DE, Lagally MG: High-speed strained-single-crystal-silicon thin-film transistors on flexible polymers. J Appl Phys 2006, 100: 013708.View ArticleGoogle Scholar
- Thurmer DJ, Deneke C, Mei Y, Schmidt OG: Process integration of microtubes for fluidic applications. Appl Phys Lett 2006, 89: 223507.View ArticleGoogle Scholar
- Songmuang R, Rastelli A, Mendach S, Schmidt OG: SiOx/Si radial superlattices and microtube optical ring resonators. Appl Phys Lett 2007, 90: 919051.View ArticleGoogle Scholar
- Mei Y, Thurmer DJ, Cavallo F, Kiravittaya S, Schmidt OG: Semiconductor sub-micro-/nanochannel networks by deterministic layer wrinkling. Adv Mater 2007, 19: 2124.View ArticleGoogle Scholar
- Ko HC, Stoykovich MP, Song J, Malyarchuk V, Choi WM, Yu C-J, Geddes JB, Xiao J, Wang S, Huang Y, Rogers JA: A hemispherical electronic eye camera based on compressible silicon optoelectronics. Nature 2008, 454: 748.View ArticleGoogle Scholar
- Cavallo F, Songmuang R, Schmidt OG: Fabrication and electrical characterization of Si-based rolled-up microtubes. Appl Phys Lett 2008, 93: 143113.View ArticleGoogle Scholar
- Yang H, Pang H, Qiang Z, Ma Z, Zhou W: Surface-normal Fano filters based on transferred silicon nanomembranes on glass substrates. Electron Lett 2008, 44: 858.View ArticleGoogle Scholar
- Yuan HC, Shin JY, Qin GX, Sun L, Bhattacharya P, Lagally MG, Celler GK, Ma ZQ: Flexible photodetectors on plastic substrates by use of printing transferred single-crystal germanium membranes. Appl Phys Lett 2009, 94: 013102.View ArticleGoogle Scholar
- Ko H, Takei K, Kapadia R, Chuang S, Fang H, Leu PW, Ganapathi K, Plis E, Kim H, Chen SY, Madsen M, Ford AC, Chueh YL, Krishna S, Salahuddin S, Javey A: Ultrathin compound semiconductor on insulator layers for high performance nanoscale transistors. Nature 2010, 468: 286.View ArticleGoogle Scholar
- Sun L, Qin G, Seo JH, Celler GK, Zhou WD, Ma ZQ: 12-GHz thin-film transistors on transferrable silicon nanomembranes for high-performance massive flexible electronics. Small 2010, 6: 2553.View ArticleGoogle Scholar
- Sun L, Qin GX, Huang H, Zhou H, Behdad N, Zhou WD, Ma ZQ: Flexible high-frequency microwave inductors and capacitors integrated on a polyethylene terephthalate substrate. Appl Phys Lett 2010, 96(1):013509.View ArticleGoogle Scholar
- Bof-Bufon CC, Cojal-Gonzalez JD, Thurmer DJ, Grimm D, Bauer M, Schmidt OG: Self-assembled ultra-compact energy storage elements based on hybrid nanomembranes. Nano Lett 2010, 10: 2506.View ArticleGoogle Scholar
- Kiefer AM, Paskiewicz DM, Clausen AM, Buchwald WR, Soref RA, Lagally MG: Si/Ge junctions formed by nanomembrane bonding. ACS Nano 2011, 5: 1179.View ArticleGoogle Scholar
- Yu M, Huang Y, Ballweg J, Shin H, Huang M, Savage DE, Lagally MG, Dent EW, Blick RH, Williams JC: Semiconductor nanomembrane tubes: three-dimensional confinement for controlled neurite outgrowth. ACS Nano 2011, 5: 2447.View ArticleGoogle Scholar
- Scott SA, Lagally MG: Elastically strain sharing nanomembranes: flexible and transferable strained silicon and silicon-germanium alloys. J Phys D: Appl Phys 2007, 40: R75.View ArticleGoogle Scholar
- Schmidt OG, Eberl K: Thin solid films roll up into nanotubes. Nature 2001, 410: 168.View ArticleGoogle Scholar
- Huang M, Boone C, Roberts MM, Savage DE, Lagally MG, Shaji N, Qin H, Blick R, Nairn JA, Liu F: Nanomechanical architecture of strained bilayer thin films: from design principles to experimental fabrication. Adv Mater 2005, 17: 2860.View ArticleGoogle Scholar
- Huang M, Cavallo F, Liu F, Lagally MG: Nanomechanical architecture of semiconductor nanomembranes. Nanoscale 2011, 3: 96.View ArticleGoogle Scholar
- Zhang P, Tevaarwerk E, Park B-N, Savage DE, Celler GK, Knezevic I, Evans PG, Eriksson MA, Lagally MG: Electronic transport in nanometer-scale silicon-on-insulator membranes. Nature 2006, 439: 703.View ArticleGoogle Scholar
- Chen F, Ramayya EB, Euaruksakul C, Himpsel FJ, Ding B-J, Knezevic I, Lagally MG: Quantum confinement, surface roughness, and the conduction band structure of ultrathin silicon membranes. ACS Nano 2010, 4: 2466.View ArticleGoogle Scholar
- Lee CH, Ritz CS, Huang MH, Ziwisky M, Blise R, Lagally MG: Wafer-scale integrated freestanding single-crystal silicon nanowires: conductivity and surface treatment. Nanotechnology 2011, 22: 055704.View ArticleGoogle Scholar
- Sutter P, Sutter E, Rugheimer P, Lagally MG: Nanoscale strain and band structure engineering using epitaxial stressors on ultrathin silicon-on-insulator. Surf Sci 2003, 789: 532.Google Scholar
- Paskiewicz DM, Scott SA, Savage DE, Celler GK, Lagally MG: Symmetry in strain engineering of nanomembranes: making new strained materials. ACS Nano 2011, 5: 5532.View ArticleGoogle Scholar
- Huang M, Ritz CS, Novakovic B, Yu D, Zhang Y, Flack F, Savage DE, Evans PG, Knezevic I, Liu F, Lagally MG: Mechano-electronic superlattices in silicon nanomembranes. ACS Nano 2009, 3: 721.View ArticleGoogle Scholar
- Paskiewicz DM, Tanto B, Savage DE, Lagally MG: Defect-free single-crystal SiGe: a new material from nanomembrane strain engineering. ACS Nano 2011, 5: 5814.View ArticleGoogle Scholar
- Deneke C, Malachias A, Rastelli A, Mercês Silva L, Huang M, Cavallo F, Schmidt OG, Lagally MG: Straining nanomembranes via highly mismatched heteroepitaxial growth: InAs islands on compliant Si substrates. ACS Nano 2012. web published Oct web published OctGoogle Scholar
- Sánchez-Pérez JR, Boztug C, Chen F, Sudradjat FF, Paskiewicz DM, Jacobson RB, Lagally MG, Paiella R: Direct-bandgap light-emitting germanium in tensilely strained nanomembranes. Proc Natl Acad Sci 2011, 108: 18893.View ArticleGoogle Scholar
- Euaruksakul C, Li ZW, Zheng F, Himpsel FJ, Ritz CS, Tanto B, Savage DE, Liu XS, Lagally MG: Influence of strain on the conduction band structure of strained silicon nanomembranes. Phys Rev Lett 2008, 101: 147403.View ArticleGoogle Scholar
- Chen X, Qiang Z, Zhao D, Li H, Qiu Y, Yang W, Zhou WD: Polarization-independent drop filters based on photonic crystal self-collimation ring resonators. Opt Express 2009, 17: 19808.View ArticleGoogle Scholar
- Lin YM, Dresselhaus MS: Thermoelectric properties of superlattice nanowires. Phys Rev B 2003, 68: 0753041.Google Scholar
- Sato T, Takeishi Y, Hara H: Mobility anisotropy of electrons in inversion layers on oxidized silicon surfaces. Phys Rev B 1950, 1971: 4.Google Scholar
- Ahn CH, Rabe KM, Triscone J-M: Ferroelectricity at the nanoscale: local polarization in oxide thin films and heterostructures. Science 2004, 303: 488.View ArticleGoogle Scholar
- Köhler U, Jusko O, Müller B, Horn-von Hoegen M, Pook M: Layer-by-layer growth of germanium on Si(100): strain-induced morphology and the influence of surfactants. Ultramicroscopy 1992, 42–44: 832.View ArticleGoogle Scholar
- Chen X, Zhang ZY, Lagally MG: Vacancy-vacancy interaction on Ge-covered Si(001). Phys Rev Lett 1994, 73: 850.View ArticleGoogle Scholar
- Wu F, Chen X, Zhang ZY, Lagally MG: Reversal of step roughness on Ge-covered vicinal Si(001). Phys Rev Lett 1995, 74: 574.View ArticleGoogle Scholar
- Wu F, Lagally MG: Ge-induced reversal of surface stress anisotropy on Si(001). Phys Rev Lett 1995, 75: 2534.View ArticleGoogle Scholar
- Freund LB, Suresh S: Thin film materials. Cambridge: Cambridge University Press; 2003.Google Scholar
- Mizuno T, Sugiyama N, Tezuka T, Moriyama Y, Nakaharai S, Takagi S: (110)-surface strained-SOI CMOS technology. IEEE Trans Electron Dev 2005, 52: 367.View ArticleGoogle Scholar
- Sugiyama N, Moriyama Y, Moriyama Y, Tezuka T, Nakaharai S, Takagi S: Kinetics of epitaxial growth of Si and SiGe films on (110) Si substrates. Appl Surf Sci 2004, 224: 188.View ArticleGoogle Scholar
- Arimoto K, Yamanaka J, Nakagawa K, Sawano K, Shiraki Y, Usami N, Nakajima K: Growth temperature dependence of lattice structures of SiGe/graded buffer structures grown on Si(1 1 0) substrates by gas-source MBE. J Crystal Growth 2007, 301: 343.View ArticleGoogle Scholar
- Yang M, Chan VWC, Chan KK, Shi L, Fried DM, Stathis JH, Chou AI, Gusev E, Ott JA, Burns LE, Fischetti MV, Ieong M: Hybrid-orientation technology (HOT): opportunities and challenges. IEEE Trans Electron Dev 2006, 53: 965.View ArticleGoogle Scholar
- Houghton DC: Strain relaxation kinetics in Si1−xGex/Si heterostructures. J Appl Phys 1991, 70: 2136.View ArticleGoogle Scholar
- Pike WT, Fathauer RW, Anderson MS: Cross-Hatched Surface Morphology in SiGe Epitaxial Layers on (100) Si. In 19th Annual Conference on the Physics and the Chemistry of Semiconductor Interfaces: Jan. 28–30 1992; Death Valley, California. New York: American Vacuum Society; 1992.Google Scholar
- Wortman JJ, Evans RA: Young's modulus, shear modulus, and Poisson's ratio in silicon and germanium. J Appl Phys 1965, 36: 153.View ArticleGoogle Scholar
- Scott SA, Paskiewicz DM, Savage DE, Lagally MG: Silicon nanomembranes incorporating mixed crystal orientations. ECS Trans 2008, 16: 215.View ArticleGoogle Scholar
- Mo YW, Savage DE, Swartzentruber BS, Lagally MG: Kinetic pathway in Stranski-Krastanov growth of Ge on Si(001). Phys Rev Lett 1990, 65: 1020.View ArticleGoogle Scholar
- Teichert C, Bean JC, Lagally MG: Self-organized nanoscale structures in Si1-x Gex/Si films. Appl Phys, A 1998, 67: 675.View ArticleGoogle Scholar
- Tersoff J, Teichert C, Lagally MG: Self-organization in growth of quantum dot superlattices. Phys Rev Lett 1996, 76: 1675.View ArticleGoogle Scholar
- Ritz CS, Kim-Lee HJ, Detert DM, Kelly MM, Flack FS, Savage DE, Cai Z, Evans PG, Turner KT, Lagally MG: Ordering of nanostressors on freestanding silicon nanomembranes and nanoribbons. New J Phys 2010, 12: 103011.View ArticleGoogle Scholar
- Kim-Lee HJ, Savage DE, Ritz CS, Lagally MG, Turner KT: Control of three-dimensional island growth with mechanically responsive single-crystal nanomembrane substrates. Phys Rev Lett 2009, 102: 225103.View ArticleGoogle Scholar
- Vastola G, Shenoy VB, Zhang Y-W: Ordering of epitaxial quantum dots on nanomembranes. ACS Nano 2012, 6: 3377.View ArticleGoogle Scholar
- Liu Z, Wu J, Duan WH, Lagally MG, Feng L: Electron phase diagram of single-element silicon “strain” superlattice. Phys Rev Lett 2010, 105: 016802.View ArticleGoogle Scholar
- Fischetti MV, Laux SE: Band structure, deformation potentials, and carrier mobility in strained Si, Ge, and SiGe alloys. J Appl Phys 1996, 80: 2234.View ArticleGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.