Epitaxial Substrate Research Articles

Possibility of the use of intermediate carbidsiliconoxide nanolayers on polydiamond substrates for gallium nitride layers epitaxy

The results of using carbidsiliconoxide (a-C:SiO1.5) films with a thickness of 30–60 nm, produced by the pyrolysis annealing of oligomethylsilseskvioksana (CH3–SiO1.5)n with cyclolinear (staircased) molecular structure, as intermediate films in the hydride vapor phase epitaxy of gallium nitride on polycrystalline CVD-diamond substrates are presented. In the pyrolysis annealing of (CH3–SiO1.5)n films in an atmosphere of nitrogen at a temperature of 1060°C, methyl radicals are carbonized to yield carbon atoms chemically bound to silicon. In turn, these atoms form a SiC monolayer on the surface of a-C:SiO1.5 films via covalent bonding with silicon. It is shown that GaN islands grow on such an intermediate layer on CVD-polydiamond substrates in the process of hydride vapor phase epitaxy in a vertical reactor from the GaCl–NH3–N2 gas mixture.

Monolithically Integrated InGaAs Nanowires on 3D Structured Silicon-on-Insulator as a New Platform for Full Optical Links.

Monolithically integrated III-V semiconductors on a silicon-on-insulator (SOI) platform can be used as a building block for energy-efficient on-chip optical links. Epitaxial growth of III-V semiconductors on silicon, however, has been challenged by the large mismatches in lattice constants and thermal expansion coefficients between epitaxial layers and silicon substrates. Here, we demonstrate for the first time the monolithic integration of InGaAs nanowires on the SOI platform and its feasibility for photonics and optoelectronic applications. InGaAs nanowires are grown not only on a planar SOI layer but also on a 3D structured SOI layer by catalyst-free metal-organic chemical vapor deposition. The precise positioning of nanowires on 3D structures, including waveguides and gratings, reveals the versatility and practicality of the proposed platform. Photoluminescence measurements exhibit that the composition of ternary InGaAs nanowires grown on the SOI layer has wide tunability covering all telecommunication wavelengths from 1.2 to 1.8 μm. We also show that the emission from an optically pumped single nanowire is effectively coupled and transmitted through an SOI waveguide, explicitly showing that this work lays the foundation for a new platform toward energy-efficient optical links.

Direct growth of single-crystalline III-V semiconductors on amorphous substrates.

The III–V compound semiconductors exhibit superb electronic and optoelectronic properties. Traditionally, closely lattice-matched epitaxial substrates have been required for the growth of high-quality single-crystal III–V thin films and patterned microstructures. To remove this materials constraint, here we introduce a growth mode that enables direct writing of single-crystalline III–V's on amorphous substrates, thus further expanding their utility for various applications. The process utilizes templated liquid-phase crystal growth that results in user-tunable, patterned micro and nanostructures of single-crystalline III–V's of up to tens of micrometres in lateral dimensions. InP is chosen as a model material system owing to its technological importance. The patterned InP single crystals are configured as high-performance transistors and photodetectors directly on amorphous SiO2 growth substrates, with performance matching state-of-the-art epitaxially grown devices. The work presents an important advance towards universal integration of III–V's on application-specific substrates by direct growth.

Thermal expansion behaviors of epitaxial film for wurtzite GaN studied by using temperature-dependent Raman scattering

III-nitride materials have attracted considerable attention in the last decade due to their wide applications in solidstate light devices with their direct wide band-gaps and higher quantum efficiencies. InGaN/GaN multiple quantum well is important active region for light-emitting diode, which can be tuned according to indium composition in the InxGa1-xN alloy system. Owing to difficulty in fabricating bulk materials, GaN thin films are heteroepitaxially grown on latticemismatched and thermal-expansion-mismatched substrates, such as sapphire (Al2O3), Si and SiC, which subsequently results in a mass of threading dislocations and higher residual strains. On the one hand, dislocations and defects existing in GaN epifilms trap the carriers as scattering centers in the radiative recombination process between electrons and holes, and play an important role in drooping the internal quantum efficiency. On the other hand, higher built-in electric field induced by residual strains existing in GaN epifilm could make the emission wavelength red-shifted.It is common knowledge that temperature is one of the important factors in the growth process of epitaxial films, as a result, further research on thermal expansion behaviors is needed. Based on the above analysis, an in-depth study of thermal expansion behavior of wurtzite GaN epitaxial film is of vital importance both in theory and in application.In this study, we investigate the thermal expansion behaviors of wurtzite GaN epitaxial films by using temperaturedependent Raman scattering in a temperature range from 83 K to 503 K. According to the physical implication, Gruneisen parameter is almost a constant (Gruneisen parameters of all phonon modes are in a range between 1 to 2 for GaN) that characterizes the relationship between the phonon shift and the volume of a solid-state material. More importantly, Gruneisen parameter is relatively insensitive to temperature and suitable for building the connection between the phonon shift and thermal expansion coefficient. Therefore, the linear relationship between the phonon shift and temperature is built and utilized to calculate the thermal expansion coefficient according to the physical implication of the Gruneisen parameter. Conclusions can be obtained as follows. (1) The thermal expansion coefficient of GaN epifilm can be calculated in a certain temperature range by measuring the phonon modes of E2 (high), A1 (TO) and E1 (TO) through using temperature-dependent Raman scattering when the corresponding Gruneisen parameters are determined. (2) The calculated thermal expansion coefficients of GaN epifilm are consistent with the theoretical values.Conclusions and methods in this paper provide an effective quantitative analysis method to characterize the thermal expansion behaviors of other III-nitride epitaxial thin films, such as AlN, InN, AlGaN, InGaN, InAlN etc., which can be of benefit to reducing the dislocation density and improving the luminescence efficiency of light emitting diode. Therefore, research on thermal expansion behaviors of epifilms using temperature-dependent Raman scattering has a direction for further studying the latter-mismatch and thermal-expansion-mismatch between the epitaxial film and substrate.

Epitaxial Growth of Thin Ferroelectric Polymer Films on Graphene Layer for Fully Transparent and Flexible Nonvolatile Memory.

Enhancing the device performance of organic memory devices while providing high optical transparency and mechanical flexibility requires an optimized combination of functional materials and smart device architecture design. However, it remains a great challenge to realize fully functional transparent and mechanically durable nonvolatile memory because of the limitations of conventional rigid, opaque metal electrodes. Here, we demonstrate ferroelectric nonvolatile memory devices that use graphene electrodes as the epitaxial growth substrate for crystalline poly(vinylidene fluoride-trifluoroethylene) (PVDF-TrFE) polymer. The strong crystallographic interaction between PVDF-TrFE and graphene results in the orientation of the crystals with distinct symmetry, which is favorable for polarization switching upon the electric field. The epitaxial growth of PVDF-TrFE on a graphene layer thus provides excellent ferroelectric performance with high remnant polarization in metal/ferroelectric polymer/metal devices. Furthermore, a fully transparent and flexible array of ferroelectric field effect transistors was successfully realized by adopting transparent poly[bis(4-phenyl)(2,4,6-trimethylphenyl)amine] semiconducting polymer.

Fabrication of quasi-superlattices at the interface between 3C-SiC epitaxial layer and substrates of hexagonal SiC polytypes by sublimation epitaxy in vacuum

Transmission electron microscopy has been used to study the structure of a transition layer between a hexagonal substrate (6H-SiC and 4H-SiC) and a cubic silicon carbide layer grown by sublimation epitaxy in vacuum. It is shown by microdiffraction analysis that the transition layer with a thickness of 210 nm is constituted by alternating layers of cubic (3C) and hexagonal (6H) silicon carbide. It is demonstrated that 6H-SiC/3C-SiC and 4H-SiC/3C-SiC quasi-superlattices can be produced by this method.

Texture and properties of epitaxial substrates for second-generation tape superconductors

Data on the degree of cube texture perfection, magnetic, and strength properties of two groups of alloys, namely, nickel- and copper-based compositions are reported. For all the alloys under study, a certain quantitative ratio of principal texture components in the alloys subjected to cold rolling to 98.6–99.0% degree of deformation was shown to be a criterion for the possibility of preparing a sharp cube texture in tapes in the course of subsequent recrystallizing annealing. Optimum compositions of nickel-based alloys, which are nonmagnetic at a working temperature of superconductor, were found; all copper-based alloys are nonmagnetic at this temperature. The strength properties of recrystallized nickel- and copper-based tapes are substantially higher than those of tapes made of pure metals.

(Invited) Border Trap Density in Al2O3/InGaAs MOS: Dependence on Hydrogen Passivation and Bias Temperature Stress

We report on the role of hydrogen (forming gas) post-metal annealing to passivate border traps in Al2O3/In0.53Ga0.47As (100) gate stacks and of bias temperature stress treatments to generate/depassivate such traps. Experiments are carried out with Pd metal gates that efficiently dissociate molecular hydrogen during forming gas annealing, and they make use of InGaAs epitaxial layer substrates that are capped with arsenic after completion of their growth, to avoid unintentional oxide formation and disorder at the channel surface prior to atomic layer deposition of the Al2O3 gate dielectric. We find that forming gas anneal (FGA) greatly reduces both the interface trap density and border trap density measured in the gate stacks, but that the effectiveness of FGA for border trap passivation saturates for anneals with thermal budgets greater than 450°C/30 min. Both negative and positive bias temperature stress treatments are found to have no effect on the extracted border trap densities compared to non-treated capacitors.

Injection-dependent Minority Carrier Lifetime in Epitaxial Silicon Layers by Time-resolved Photoluminescence

Time-resolved photoluminescence (TRPL) is used to evaluate the injection-dependent effective minority carrier lifetime of high resistivity epitaxial silicon layers grown on highly doped CZ-Si substrates. Effective lifetimes ranging from 10μs to 200μs are estimated for excess carrier densities between 1x1017 cm-3 and 2x1016 cm-3. Standard models are used to separate the contribution from the different recombination mechanisms. The influence of the epitaxial layer and substrate parameters on the minority carrier effective lifetime measurement is discussed.

Effect of sulfur passivation of InSb (0 0 1) substrates on molecular-beam homoepitaxy

The aqueous sodium sulfide solution has been used for pre-epitaxial preparation of epi-ready InSb (001) substrates for molecular beam epitaxy (MBE) of InSb layers. X-ray photoemission spectroscopy study shows that the S-treated surface of InSb (001) substrate generally does not contain a native oxide layer and is covered with a sulfide protecting overlayer. Atomic-force microscopy and transmission electron microscopy have been applied to compare surface topography and structural properties of InSb layers grown by MBE on S-treated and untreated epi-ready InSb (001) substrates. The MBE growth of InSb layers with very smooth surface possessing the root-mean-square roughness as low as 0.1nm and good structural quality has been demonstrated on the S-treated substrates.

Preferential orientation relationships in Ca2MnO4 Ruddlesden-Popper thin films

A high-throughput investigation of local epitaxy (called combinatorial substrate epitaxy) was carried out on Ca2MnO4 Ruddlesden-Popper thin films of six thicknesses (from 20 to 400 nm), all deposited on isostructural polycrystalline Sr2TiO4 substrates. Electron backscatter diffraction revealed grain-over-grain local epitaxial growth for all films, resulting in a single orientation relationship (OR) for each substrate-film grain pair. Two preferred epitaxial ORs accounted for more than 90% of all ORs on 300 different microcrystals, based on analyzing 50 grain pairs for each thickness. The unit cell over unit cell OR ([100][001]film ∥ [100][001]substrate, or OR1) accounted for approximately 30% of each film. The OR that accounted for 60% of each film ([100][001]film ∥ [100][010]substrate, or OR2) corresponds to a rotation from OR1 by 90° about the a-axis. OR2 is strongly favored for substrate orientations in the center of the stereographic triangle, and OR1 is observed for orientations very close to (001) or to those near the edge connecting (100) and (110). While OR1 should be lower in energy, the majority observation of OR2 implies kinetic hindrances decrease the frequency of OR1. Persistent grain over grain growth and the absence of variations of the OR frequencies with thickness implies that the growth competition is finished within the first few nm, and local epitaxy persists thereafter during growth.

Ion implantation of the 4H SiC epitaxial layers and substrates with 2 MeV Se+ and 1 MeV Al+ ions

The implantations were performed in 4H silicon carbide homoepitaxial layers deposited on (00.1) substrates with 8° offcut, and reference 4H‐SiC substrates. The 2 MeV Se+ ions and 1 MeV Al+ ions were implanted with four fluences subsequently increased by the factor of 4–5×. The samples were studied by means of X‐ray diffraction topography, high‐resolution diffractometry, specular X‐ray reflectometry, and Rutherford backscattering spectrometry\channeling method. The dislocation density in the samples evaluated from the diffraction topographs did not exceed 5 × 103 cm−2. The representative roughness values evaluated from the reflectometric measurements was 2.3 ± 0.1 nm for the substrates and less than 1.4 ± 0.1 nm for the epitaxial layers.A significantly higher damage level in the case of 2 MeV Se+ ions in comparison with 1 MeV Al+ ion and a linear increase of the strain with the fluence was indicated, but the highest doses of selenium ions caused the amorphization of the implanted layer. It was also possible to obtain a good fitting of the theoretical and experimental diffraction curves approximating the strain profiles by the distribution of the point defects calculated with the SRIM 2008 code. It was confirmed that the maximum coming from surface damages observed in channeling spectra of the virgin substrate wafers was significantly higher than in the case of epitaxial layers. Copyright © 2015 John Wiley & Sons, Ltd.

Ultraclean and large-area monolayer hexagonal boron nitride on Cu foil using chemical vapor deposition

Atomically thin hexagonal boron nitride (h-BN) has been demonstrated to be an excellent dielectric layer as well as an ideal van der Waals epitaxial substrate for fabrication of two-dimensional (2D) atomic layers and their vertical heterostructures. Although many groups have obtained large-scale monolayer h-BN through low pressure chemical vapor deposition (LPCVD), it is still a challenge to grow clean monolayers without the reduction of domain size. Here we report the synthesis of large-area (4 × 2 cm2) high quality monolayer h-BN with an ultraclean and unbroken surface on copper foil by using LPCVD. A detailed investigation of the key factors affecting growth and transfer of the monolayer was carried out in order to eliminate the adverse effects of impurity particles. Furthermore, an optimized transfer approach allowed the nondestructive and clean transfer of the monolayer from copper foil onto an arbitrary substrate, including a flexible substrate, under mild conditions. Atomic force microscopy indicated that the root-mean-square (RMS) roughness of the monolayer h-BN on SiO2 was less than 0.269 nm for areas with fewer wrinkles. Selective area electron diffraction analysis of the h-BN revealed a pattern of hexagonal diffraction spots, which unambiguously demonstrated its highly crystalline character. Our work paves the way toward the use of ultraclean and large-area monolayer h-BN as the dielectric layer in the fabrication of high performance electronic and optoelectronic devices for novel 2D atomic layer materials.

Atom-scale covalent electrochemical modification of single-layer graphene on SiC substrates by diaryliodonium salts

Owing to its high conductivity, graphene holds promise as an electrode for energy devices such as batteries and photovoltaics. However, to this end, the work function and doping levels in graphene need to be precisely tuned. One promising route for modifying graphene’s electronic properties is via controlled covalent electrochemical grafting of molecules. We show that by employing diaryliodonium salts instead of the commonly used diazonium salts, spontaneous functionalization is avoided. This allows for precise tuning of the grafting density. By employing bis(4-nitrophenyl)iodonium(III) tetrafluoroborate (DNP) salt calibration curves, the surface functionalization density (coverage) of glassy carbon was controlled using cyclic voltammetry in varying salt concentrations. These electro-grafting conditions and calibration curves translated directly over to modifying single layer epitaxial graphene substrates (grown on insulating 6H-SiC (0001)). In addition to quantifying the functionalization densities using electrochemical methods, samples with low grafting densities were characterized by low-temperature scanning tunneling microscopy (LT-STM). We show that the use of buffer-layer free graphene substrates is required for clear observation of the nitrophenyl modifications. Atomically-resolved STM images of single site modifications were obtained, showing no preferential grafting at defect sites or SiC step edges as supposed previously in the literature. Most of the grafts exhibit threefold symmetry, but occasional extended modifications (larger than 4nm) were observed as well.

Crystallization of Si Templates of Controlled Shape, Size, and Orientation: Toward Micro- and Nanosubstrates

Fiber-textured polycrystalline silicon thin films have demonstrated their interest as seed layers for the epitaxial growth of high-quality materials on substrates such as glass or plastics. In the present work, we report a comprehensive study of the aluminum-induced crystallization (AIC) of isolated Si domains. Our study not only demonstrates the fabrication by AIC of shape- and size-controlled Si monocrystals at the nanoscale but also allows for the prediction of minimal annealing conditions for complete crystallization of such structures. These ultrathin [111]-oriented monocrystals are promising candidates as selected-area epitaxy substrates with both an easy control on the morphology of these structures and a low-temperature fabrication process.

Beware of poor-quality MgO substrates: A study of MgO substrate quality and its effect on thin film quality

Magnesium oxide (MgO) substrates are widely used for fundamental research of a large variety of materials. Our motivation is to make the research community aware of poor-quality MgO substrates. We acquired thirty MgO substrates from six different vendors and demonstrate that ‘single-crystal’ MgO substrates are not always single crystal, but can consist of multiple domains. These multiple-domain MgO substrates can have a significant impact on research results as demonstrated by a one-to-one correlation between the domain structure of MgO substrates and titanium nitride (TiN) thin films (i.e. poor-quality MgO substrates result in poor-quality TiN films). Poor-quality MgO substrates are shown to be a widespread problem with over 70% of the evaluated substrates exhibiting multiple domains, essentially disqualifying them as substrates for epitaxy. MgO substrate vendors and researchers are encouraged to work together to resolve the problem of inconsistent MgO substrate quality and the research community is encouraged to perform quality control of MgO substrates prior to thin film deposition. Quality control by vendors and/or researchers can be achieved by acquiring X-ray diffraction omega–phi maps in batch processes, as detailed in this paper. We also propose a simple quality grading system to differentiate MgO substrates of varying quality.

MgGa2 O4 as a new wide bandgap transparent semiconducting oxide: growth and properties of bulk single crystals

Bulk MgGa2O4 single crystals with inverse spinel structure were grown from the melt by different methods. The degree of inversion could be changed by suitable annealing, which was confirmed by differential scanning calorimetry analysis and corresponding changes of the specific heat capacity. MgGa2O4 is thermally much more stable at high temperatures than β-Ga2O3 despite of a higher melting point of about 1930 °C and could be grown under a neutral atmosphere. Melt-grown MgGa2O4 crystals were found to be either electrical insulators or n-type semiconductors depending on the presence of oxygen in the growth atmosphere and the growth method applied. Growing the crystals in the presence of oxygen resulted in electrically insulating crystals. For as-grown and intentionally undoped semiconducting crystals, the free electron concentration was in the range of 1017–1018 cm−3, but the electron mobility was relatively low, just a few cm2V−1s−1. The free electron concentration remained at a level of 1018 cm−3 after annealing in a hydrogen-containing atmosphere at 600–900 °C for 10 h. On the other hand, annealing in an oxygen-containing atmosphere above 600 °C for 10–40 h turns the crystals from the semiconducting to the insulating state. The optical bandgap at room temperature amounts to about 4.9 eV. It decreases with temperature at a rate of 1.35 meV/K. Cathodoluminescence spectra of as-grown crystals show a dominant band at 362 nm. The melt-grown crystals have sufficient size and structural quality to be used as substrates for epitaxy.

Performance-optimized gate-first 22-nm SOI technology with embedded DRAM

IBM's high-performance 22-nm silicon-on-insulator (SOI) technology is the enabling physical foundation of IBM POWER8™ processors. This paper describes, for the first time in detail, some of the unique aspects of the silicon processing, the features that enabled the industry-leading chip-level performance, and some aspects of the collaborative approach between technology and design teams that enabled both first-time-right silicon and rapid yield improvement. Most critical to the processor functional capability and power-performance achievements are the high-density on-chip memory in the form of embedded DRAM and the high-performance FET device designs based on a low-parasitic-capacitance gate-first FET architecture. Extensive on-chip analog functions are enabled by an additional comprehensive set of devices available in the technology. Fifteen levels of metal with five metal levels at an 80-nm pitch provide the interconnect and power distribution. We describe the pattern resolution enhancement strategy as well as motivation and structural aspects of the innovative features, from the low-resistance N+ epitaxy substrate under the SOI to a dual-embedded source-drain architecture and a highly scaled gate dielectric.

Effect of wafer bonding and laser liftoff process on residual stress of GaN-based vertical light emitting diode chips

Residual stress conditions in GaN-based LEDs will have a significant influence on device performance and reliability. In this paper, GaN-based vertical LEDs under different stress conditions are fabricated by bonding with three types of submounts (Al2O3 submount, CuW submount and Si submount), changing the soak temperature (290 ℃, 320 ℃, 350 ℃ and 380 ℃) and using different laser energy densities (875, 945 and 1015 mJ·cm-2). The warpage and Raman scattering spectra of those GaN-based LEDs are measured. The experimental results show that the residual stress conditions in GaN-based vertical LEDs are a consequence of the bonded submounts and bonded metal, and the soak temperature is the primary factor that determines the degree of residual stress in LED chips. In the laser lift-off process, changing laser energy density in an appropriate range has little influence on residual strain of LED chips, and the micro-cracks in GaN layer caused by LLO process will play a role in releasing the residual stress. The warpage of epitaxial sapphire substrate becomes large after boding with Si submount, the residual stress in GaN-based vertical LEDs is tensile stress and becomes larger with the soak temperature rising. When GaN epi wafer bonds with Al2O3 submount and CuW submount, the warpages becomes small and large respectively and the residual stress in chips is compressive stress. Because of the mismatch of coefficient of thermal expansion, the compressive stress in GaN-based LED chips increases for Al2O3 submount and drops for CuW submount with the soak temperature rising.

Enhancement of Ferroelectrics: Strain-engineered Ferroelectric Thin Films

E nhancement of F erroelectrics : S train - engineered F erroelectric T hin F ilms Hongling Lu B S J In 1920, Joseph Valasek discovered that the polarization of the compound known as Rochelle Salt could be reversed by application of an external electric field. In effect, he was the first to recognize ferroelectric properties in a crystal. Ferroelectric materials are generally defined as those whose spountaneous polarization can be reversed through the application of an external electric field (Scott, 2007). (Fig. 1) Figure 1: Perovskite oxides, of general formula ABO3 with a pseudocubic structure, where A and B are two different cations, furnish many interesting ferroelectrics. The B-type cation is octahedrally coordinated with oxygen. In the example shown, BaTiO3, it is the relative symmetry breaking displacement of the Ti atoms with respect to the O atoms which is responsible for the spontaneous polarization. BaTiO3 has three ferroelectric phases: tetragonal, orthorhombic and rhombohedral. (Oxides. (n.d.). Strain engineering is a strategy employed in exploring the special behavior of ferroelectric materials where a strained layer of ferroelectric epitaxially grown with respect to the crystalline substrate layer.(Eom et al., 2008) (Fig. 2) Figure 2: Before deposition, the structure is in an (a) unstrained state. When deposited on a substrate the energetic preference of the deposited atoms to follow the underlying substrate (epitaxy) can result in the film beginning in either (b) biaxial compression or (c) biaxial tension (Schlom, Chen, Fennie, Gopalan, Muller, Pan, Uecker, 2014) This process creates a strained state. Under this strained state, the properties of the ferroelectric film differ greatly compared to the bulk ferroelectric, in a way that makes it suitable for use in applications such as memory storage on microchips. Before strain engineering, researchers used chemical alloying or doping to manipulate the properties of bulk ferroelectrics. A typical 0.1% strain--stretching of material to a length 0.1% “Strain engineering is a strategy employed in exploring the special behavior of ferroelectric materials where a strained layer of ferroelectric epitaxially grown with respect to the crystalline substrate layer.” At first, ferroelectric devices were restricted to bulk materials, but in the 1980s, thin-film, a technology utilizing extremely thin layers of material, was developed. The focus of ferroelectric study has since moved from bulk properties to its thin-film properties, especially with the promise of using ferroelectric materials in computer microchips, a type of thin- film technology. Ferroelectric materials with spontaneous polarization due to the special arrangement of atoms in a lattice structure exhibit interesting pyroelectric and piezoelectric properties and have, therefore, attracted a lot of scientific attentions. greater than the original length--will cause bulk ferroic oxides to crack. Epitaxial strain has the advantage of resulting in a more durable and ideally disorder-free film. Strain field is the electric field that results from a strained lattice structure, and in strain engineering, differences in lattice parameters between the epitaxial film and the underlying substrate are what create the strain of the overall thin-film material. Past decades have seen a rapid progress in algorithms and calculations for analyzing thin-film ferroelectrics. Some of the methods include first principles calculations(determining electronic structure by solving Schrodinger’s equation), 3 • B erkeley S cientific J ournal • S ymmetry • F all 2015 • V olume 20 • I ssue 1