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22 Dec 2003

Volume 83, Issue 25, pp. 5121-5321

Issue Cover Spotlight Figure

Appl. Phys. Lett. 83, 5310 (2003); http://dx.doi.org/10.1063/1.1635070 (3 pages)

Z. G. Chiragwandi, O. Nur, M. Willander, and N. Calander
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InN island shape and its dependence on growth condition of molecular-beam epitaxy

Y. G. Cao, M. H. Xie, Y. Liu, Y. F. Ng, H. S. Wu, and S. Y. Tong

Appl. Phys. Lett. 83, 5157 (2003); http://dx.doi.org/10.1063/1.1635077 (3 pages) | Cited 24 times

Online Publication Date: 17 December 2003

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During molecular-beam epitaxy of InN films on GaN(0001) surface, three-dimensional (3D) islands are observed following an initial wetting layer formation. Depending on deposition condition, the 3D islands take different shapes. Pyramidal islands form when excess nitrogen fluxes are used, whereas pillar-shaped islands are obtained when excess indium fluxes are employed. The pillar-shaped islands are identified to represent the equilibrium shape, whereas the pyramidal ones are limited by kinetics. As the size of islands increases, their aspect ratio shows a decreasing trend, which is attributed to a gradual relaxation of strain in the layer by defects. © 2003 American Institute of Physics.
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68.55.-a Thin film structure and morphology
81.15.Hi Molecular, atomic, ion, and chemical beam epitaxy
68.55.A- Nucleation and growth
81.05.Ea III-V semiconductors

Near-equilibrium strain relaxation and misfit dislocation interactions in PbTe on PbSe (001) heteroepitaxy

Karin Wiesauer and Gunther Springholz

Appl. Phys. Lett. 83, 5160 (2003); http://dx.doi.org/10.1063/1.1633675 (3 pages) | Cited 4 times

Online Publication Date: 17 December 2003

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Strain relaxation of PbTe layers on PbSe (001) by misfit dislocation formation is shown to take place near equilibrium without kinetic barriers. A comparison of the experimental data with different strain relaxation models shows that mutual dislocation interactions are of crucial importance for the strain relaxation process. This results in faster relaxation than predicted by the models for noninteracting dislocation arrays. © 2003 American Institute of Physics.
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68.60.Bs Mechanical and acoustical properties
62.40.+i Anelasticity, internal friction, stress relaxation, and mechanical resonances
61.72.Yx Interaction between different crystal defects; gettering effect
81.15.Hi Molecular, atomic, ion, and chemical beam epitaxy
61.72.Lk Linear defects: dislocations, disclinations
81.40.Jj Elasticity and anelasticity, stress-strain relations

Band structure and fundamental optical transitions in wurtzite AlN

J. Li, K. B. Nam, M. L. Nakarmi, J. Y. Lin, H. X. Jiang, Pierre Carrier, and Su-Huai Wei

Appl. Phys. Lett. 83, 5163 (2003); http://dx.doi.org/10.1063/1.1633965 (3 pages) | Cited 99 times

Online Publication Date: 17 December 2003

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With a recently developed unique deep ultraviolet picoseconds time-resolved photoluminescence (PL) spectroscopy system and improved growth technique, we are able to determine the detailed band structure near the Γ point of wurtzite (WZ) AlN with a direct band gap of 6.12 eV. Combined with first-principles band structure calculations we show that the fundamental optical properties of AlN differ drastically from that of GaN and other WZ semiconductors. The discrepancy in energy band gap values of AlN obtained previously by different methods is explained in terms of the optical selection rules in AlN and is confirmed by measurement of the polarization dependence of the excitonic PL spectra. © 2003 American Institute of Physics.
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71.20.Nr Semiconductor compounds
78.66.Fd III-V semiconductors
78.55.Cr III-V semiconductors
78.47.-p Spectroscopy of solid state dynamics
71.15.-m Methods of electronic structure calculations
78.20.Ci Optical constants (including refractive index, complex dielectric constant, absorption, reflection and transmission coefficients, emissivity)
71.35.Cc Intrinsic properties of excitons; optical absorption spectra

Effect of hydrogen and deuterium on the microstructure of amorphous Si solar cell material

E. Sutter and D. L. Williamson

Appl. Phys. Lett. 83, 5166 (2003); http://dx.doi.org/10.1063/1.1633968 (3 pages)

Online Publication Date: 17 December 2003

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We investigate hydrogenated and deuterated amorphous Si (a-Si:H and a-Si:D) solar cell material, prepared under conditions of high hydrogen and deuterium dilution, respectively. Using cross-sectional transmission electron microscopy, we provide direct observation of the microstructure of these materials. We observe that the high hydrogen dilution results in homogeneous a-Si:H material with no evidence of microvoids. In contrast, the replacement of hydrogen with deuterium produces a heterogeneous mixture of amorphous and microcrystalline material. The amorphous phase contains significant numbers of microvoids or low-density deuterium-rich domains. The observed heterogeneity is related to the effect of the substitution of hydrogen with deuterium on the microstructure of the Si film. © 2003 American Institute of Physics.
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68.55.-a Thin film structure and morphology
61.43.Dq Amorphous semiconductors, metals, and alloys

Large optical nonlinearities in BiMnO3 thin films

Alok Sharan, Ilsin An, Chi Chen, Robert W. Collins, James Lettieri, Yunfa Jia, Darrell G. Schlom, and Venkatraman Gopalan

Appl. Phys. Lett. 83, 5169 (2003); http://dx.doi.org/10.1063/1.1632544 (3 pages) | Cited 17 times

Online Publication Date: 17 December 2003

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Large third-order optical nonlinearities were observed in epitaxial thin films of BiMnO3 grown on SrTiO3 substrates. Using 140 fs laser pulses at 900 nm, a negative nonlinear refractive index (nI ∼ −0.53 cm2/GW) and a nonlinear absorption coefficient (αI ∼ −0.08 cm/kW) for BiMnO3 are measured at room temperature. Large electric-field-induced enhancement of three to four orders of magnitude in the second-harmonic response at 450 nm is observed with effective nonlinear coefficients of deff ∼ 40(115) pm/V at 300 (473) K under applied fields of ∼707 (177) V/mm, respectively, from a 110 nm multivariant thin film. © 2003 American Institute of Physics.
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42.70.Mp Nonlinear optical crystals
42.65.Ky Frequency conversion; harmonic generation, including higher-order harmonic generation
78.20.Ci Optical constants (including refractive index, complex dielectric constant, absorption, reflection and transmission coefficients, emissivity)
78.66.Nk Insulators
78.20.Jq Electro-optical effects

Three-dimensional dielectric network structures with large photonic band gaps

Martin Maldovan, W. Craig Carter, and Edwin L. Thomas

Appl. Phys. Lett. 83, 5172 (2003); http://dx.doi.org/10.1063/1.1635664 (3 pages) | Cited 4 times

Online Publication Date: 17 December 2003

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Several three-dimensional dielectric network structures possessing large photonic band gaps are presented. Two of these photonic crystals show gaps as large as 26% of the midgap frequency for a refractive index contrast 3.6:1. Four of the proposed structures consist of three-connected networks and a fifth structure has a mixture of three- and four-connected nodes. The realization of these structures using block polymer self-assembly, interference lithography and layer-by-layer lithography is briefly discussed. © 2003 American Institute of Physics.
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42.70.Qs Photonic bandgap materials

Limit of the Rayleigh scattering loss in silica fiber

K. Saito, M. Yamaguchi, H. Kakiuchida, A. J. Ikushima, K. Ohsono, and Y. Kurosawa

Appl. Phys. Lett. 83, 5175 (2003); http://dx.doi.org/10.1063/1.1635072 (3 pages) | Cited 10 times

Online Publication Date: 17 December 2003

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The limit of the Rayleigh scattering and total losses in silica fiber was determined from the results of the Rayleigh scattering and structural relaxation measurements. Annealing condition during fiber drawing was optimized, and much potential to reduce the Rayleigh scattering loss has been verified. Total loss can be reduced below 0.15 dB/km at 1.55 μm, for example, even when annealing time is 0.1 s. Total loss below 0.14 dB/km can be realized by increasing the annealing time. © 2003 American Institute of Physics.
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42.81.Dp Propagation, scattering, and losses; solitons
81.40.Tv Optical and dielectric properties related to treatment conditions
81.40.Gh Other heat and thermomechanical treatments
78.35.+c Brillouin and Rayleigh scattering; other light scattering
81.05.Kf Glasses (including metallic glasses)

In surface segregation in M-plane (In,Ga)N/GaN multiple quantum well structures

Yue Jun Sun, Oliver Brandt, Bernd Jenichen, and Klaus H. Ploog

Appl. Phys. Lett. 83, 5178 (2003); http://dx.doi.org/10.1063/1.1635661 (3 pages) | Cited 7 times

Online Publication Date: 17 December 2003

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We investigate the composition profile of M-plane (In,Ga)N/GaN(1math00) multiple quantum well structures by both high-resolution x-ray diffractometry and secondary ion mass spectrometry. The results reveal significant In surface segregation, resulting in a reduced In content and much wider wells than intended. The resulting In content of ∼ 7% is lower than that obtained ( ∼ 15%) for corresponding C-plane structures grown under identical conditions, suggesting a lower In incorporation efficiency on the (1math00) plane compared to the (0001) plane. Finally, the dependence of the transition energies on the well thickness of these M-plane quantum wells evidences the absence of internal electrostatic fields along the growth direction. © 2003 American Institute of Physics.
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68.35.Dv Composition, segregation; defects and impurities
68.65.Fg Quantum wells

Robust self-assembled monolayer as diffusion barrier for copper metallization

Noboru Mikami, Nobuhiro Hata, Takamaro Kikkawa, and Hideaki Machida

Appl. Phys. Lett. 83, 5181 (2003); http://dx.doi.org/10.1063/1.1635665 (3 pages) | Cited 12 times

Online Publication Date: 17 December 2003

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Excellent results on copper (Cu) diffusion barrier characteristics of a self-assembled monolayer (SAM) of 2-(diphenylphosphino)ethyltriethoxy-silane are reported. The thickness and roughness of the SAM were determined by grazing incidence x-ray reflectometry as 1.7 and 0.3 nm, respectively. To evaluate Cu diffusion barrier performance of the SAM, Cu/SiO2/Si and Cu/SAM/SiO2/Si metal-oxide-semiconductor capacitors were prepared to measure their lifetimes under the 2 MV/cm electric bias at 498–548 K. The mean times to failure obtained from the Weibull plots of time to failures were 33.6, 9.24, 4.57, and 2.03 h at 498, 523, 533 and 548 K, respectively. These values show that the barrier characteristic of the SAM of 1.7 nm in thickness is comparable to that of physical-vapor-deposited Ta film of 20 nm in thickness. The estimated lifetime of the SAM barrier at the device operation temperature of 392 K is longer than 10 yr. © 2003 American Institute of Physics.
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68.47.Pe Langmuir-Blodgett films on solids; polymers on surfaces; biological molecules on surfaces
77.84.Jd Polymers; organic compounds
77.55.-g Dielectric thin films
85.40.Qx Microcircuit quality, noise, performance, and failure analysis
84.32.Tt Capacitors
85.40.Ls Metallization, contacts, interconnects; device isolation
66.30.-h Diffusion in solids
68.35.Fx Diffusion; interface formation

Rapid growth of evanescent wave by a silver superlens

Zhaowei Liu, Nicholas Fang, Ta-Jen Yen, and Xiang Zhang

Appl. Phys. Lett. 83, 5184 (2003); http://dx.doi.org/10.1063/1.1636250 (3 pages) | Cited 70 times

Online Publication Date: 17 December 2003

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Recent theoretical work suggested the possibility of constructing a super-resolution diffraction-free lens by using a negative refractive index medium (NRIM). The key proposition is that evanescent waves can be greatly enhanced by increasing the thickness of the NRIM. We report here experimental evidence that confirms that the transmission of evanescent waves rapidly grows with the film thickness up to about 50 nm, after which it decays as loss becomes significant. These findings represent the first step toward the understanding and realization of a diffraction-free lens. © 2003 American Institute of Physics.
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42.79.Bh Lenses, prisms and mirrors
81.05.Bx Metals, semimetals, and alloys
42.79.Wc Optical coatings
78.66.Bz Metals and metallic alloys
42.25.Bs Wave propagation, transmission and absorption
78.20.Ci Optical constants (including refractive index, complex dielectric constant, absorption, reflection and transmission coefficients, emissivity)

Slip systems and misfit dislocations in InGaN epilayers

S. Srinivasan, L. Geng, R. Liu, F. A. Ponce, Y. Narukawa, and S. Tanaka

Appl. Phys. Lett. 83, 5187 (2003); http://dx.doi.org/10.1063/1.1633029 (3 pages) | Cited 53 times

Online Publication Date: 17 December 2003

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We have studied the microstructure of InGaN layers grown on two different GaN substrates: a standard GaN film on sapphire and an epitaxial lateral overgrown GaN (ELOG) structure. These two materials exhibit two distinct mechanisms of strain relaxation. InGaN epilayers on GaN are typically pseudomorphic and undergo elastic relaxation by the opening of threading dislocations into pyramidal pits. A different behavior occurs in the case of epitaxy on ELOG where, in the absence of threading dislocations, slip occurs with the formation of periodic arrays of misfit dislocations. Potential slip systems responsible for this behavior have been analyzed using the Matthews-Blakeslee model and taking into account the Peierls forces. This letter presents a comprehensive analysis of slip systems in the wurtzite structure and considers the role of threading dislocations in strain relaxation in InGaN alloys. © 2003 American Institute of Physics.
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61.72.Hh Indirect evidence of dislocations and other defects (resistivity, slip, creep, strains, internal friction, EPR, NMR, etc.)
68.55.Ln Defects and impurities: doping, implantation, distribution, concentration, etc.
61.72.Ff Direct observation of dislocations and other defects (etch pits, decoration, electron microscopy, x-ray topography, etc.)
61.72.Lk Linear defects: dislocations, disclinations

Generation of ultrahigh pressure using single-crystal chemical-vapor-deposition diamond anvils

Wendy L. Mao, Ho-kwang Mao, Chih-shiue Yan, Jinfu Shu, Jingzhu Hu, and Russell J. Hemley

Appl. Phys. Lett. 83, 5190 (2003); http://dx.doi.org/10.1063/1.1636270 (3 pages) | Cited 5 times

Online Publication Date: 17 December 2003

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Two experiments were conducted compressing Ta, Re, Pt, and an Fe-Si alloy to ultrahigh pressures using single-crystal chemical vapor deposition (CVD) and natural diamonds. In situ energy-dispersive and angle-dispersive x-ray diffraction were used to determine pressure from known equations of state. We demonstrate that CVD diamonds can be used in diamond anvil cells to reach pressures of nearly 200 GPa. © 2003 American Institute of Physics.
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07.35.+k High-pressure apparatus; shock tubes; diamond anvil cells
81.05.U- Carbon/carbon-based materials
68.55.-a Thin film structure and morphology
81.15.Gh Chemical vapor deposition (including plasma-enhanced CVD, MOCVD, ALD, etc.)
62.50.-p High-pressure effects in solids and liquids

Two types of structures for the GaAs(001)-c(4×4) surface

Akihiro Ohtake and Nobuyuki Koguchi

Appl. Phys. Lett. 83, 5193 (2003); http://dx.doi.org/10.1063/1.1635078 (3 pages) | Cited 22 times

Online Publication Date: 17 December 2003

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Scanning tunneling microscopy, reflectance difference spectroscopy, and x-ray photoelectron spectroscopy have been used to study the atomic structures of the As-stabilized GaAs(001)-c(4×4) surface. We found that the c(4×4) surfaces are classified into two phases of α (Ga–As dimer structure) and β (As–As dimer structure). While the α phase is obtained by heating the β phase under As fluxes, we found that the structural change from β to α is kinetically-limited. © 2003 American Institute of Physics.
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68.35.B- Structure of clean surfaces (and surface reconstruction)
68.35.Rh Phase transitions and critical phenomena
68.37.Ef Scanning tunneling microscopy (including chemistry induced with STM)
79.60.Bm Clean metal, semiconductor, and insulator surfaces

Intersubband spectroscopy of doped and undoped GaN/AlN quantum wells grown by molecular-beam epitaxy

A. Helman, M. Tchernycheva, A. Lusson, E. Warde, F. H. Julien, Kh. Moumanis, G. Fishman, E. Monroy, B. Daudin, D. Le Si Dang, E. Bellet-Amalric, and D. Jalabert

Appl. Phys. Lett. 83, 5196 (2003); http://dx.doi.org/10.1063/1.1635985 (3 pages) | Cited 46 times

Online Publication Date: 17 December 2003

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We report experimental and theoretical results on interband and intersubband transitions in GaN quantum wells with strained AlN barriers. All of the samples are grown by molecular-beam epitaxy on sapphire (0001) substrates. The results show that even at room temperature, strong electron localization occurs in the plane of the quantum wells due to the combined effect of monolayer thickness fluctuations and the high internal field in the GaN layers. We also demonstrate that the intersubband absorption is systematically blueshifted in n-doped quantum wells with respect to nominally undoped samples as a result of strong many-body effects, namely the exchange interaction. The results for both undoped and doped quantum wells are in good agreement with simulations. © 2003 American Institute of Physics.
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78.67.De Quantum wells
78.30.Fs III-V and II-VI semiconductors
78.55.Cr III-V semiconductors
71.70.Gm Exchange interactions

Monocrystalline YBa2Cu3O7−x thin films on vicinal SrTiO3 (001) substrates

J. Matthijn Dekkers, Guus Rijnders, Sybolt Harkema, Henk Jan H. Smilde, Hans Hilgenkamp, Horst Rogalla, and Dave H. A. Blank

Appl. Phys. Lett. 83, 5199 (2003); http://dx.doi.org/10.1063/1.1633010 (3 pages) | Cited 16 times

Online Publication Date: 17 December 2003

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The correlation between the vicinal properties of SrTiO3 (001) substrates and the twinning in YBa2Cu3O7−x thin films grown by pulsed-laser deposition is studied using x-ray diffraction with reciprocal space mapping. The vicinal properties, i.e., angle and in-plane orientation, play a significant role in the anisotropic strain starting at the interface between substrate surface and film, and affect the twin behavior of YBa2Cu3O7−x. On substrates having an [110] in-plane orientation of the step edges, a completely preferred twin pair is observed if the vicinal angle is increased to 0.60°. Whereas on substrates having their step edges oriented along one of the crystallographic axis, the films exhibit a detwinning as the vicinal angle increases. For α = 1.10° a maximum detwinned, i.e., monocrystalline film is obtained. At this angle, the diffusion length of YBa2Cu3O7−x during the growth matches the terrace length of SrTiO3. Up to this specific angle, the films are grown perpendicular to the optical instead of the crystallographic surface. © 2003 American Institute of Physics.
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68.55.Ln Defects and impurities: doping, implantation, distribution, concentration, etc.
74.72.-h Cuprate superconductors
68.60.Bs Mechanical and acoustical properties
81.15.Fg Pulsed laser ablation deposition
61.72.Mm Grain and twin boundaries
74.78.-w Superconducting films and low-dimensional structures
68.35.Gy Mechanical properties; surface strains

Nucleation and growth in bulk metallic glass under high pressure investigated using in situ x-ray diffraction

W. H. Wang, P. Wen, D. Q. Zhao, M. X. Pan, T. Okada, and W. Utsumi

Appl. Phys. Lett. 83, 5202 (2003); http://dx.doi.org/10.1063/1.1636517 (3 pages) | Cited 7 times

Online Publication Date: 17 December 2003

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The effects of pressure up to 8.3 GPa on nucleation and growth in a Zr57Nb5Cu15.5Ni12.5Al10 bulk glass-forming alloy during heating, isothermal annealing, and cooling processes are investigated using in situ x-ray diffraction with synchrotron radiation. The metallic glass shows markedly different crystallization behaviors for different heat treatments under high pressure. Heating under high pressure can stabilize the supercooled liquid state. Isothermal high pressure annealing leads to nanocrystallization. The glass forming ability of the alloy can be enhanced by high pressure during cooling process. The effects of pressure on the nucleation and growth are discussed based on the nucleation theory. © 2003 American Institute of Physics.
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61.43.Fs Glasses
62.50.-p High-pressure effects in solids and liquids
81.40.Gh Other heat and thermomechanical treatments

Growth of quantum fortress structures in Si1−xGex/Si via combinatorial deposition

Thomas E. Vandervelde, Piyush Kumar, Takeshi Kobayashi, Jennifer L. Gray, Tim Pernell, Jerrold A. Floro, Robert Hull, and John C. Bean

Appl. Phys. Lett. 83, 5205 (2003); http://dx.doi.org/10.1063/1.1636268 (3 pages) | Cited 19 times

Online Publication Date: 17 December 2003

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This study details the evolution of morphologies in the Si1−xGex/Si system, under kinetically controlled conditions of 550 °C growth temperature and 1 Å/s growth rate. We find that, with increasing film thickness and Ge fraction, a series of three-dimensional structures develop, starting from pits, and leading to quantum fortresses and ridges. The quantum fortress structures are of special significance because of their potential application in quantum cellular automata. We establish approximate boundaries in the parameter space of film thickness and Ge fraction, in which these structures form. We present a simple model, based on kinetics and strain, to explain the observed structures. © 2003 American Institute of Physics.
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68.65.Hb Quantum dots (patterned in quantum wells)
68.55.-a Thin film structure and morphology
68.55.A- Nucleation and growth
68.35.Ct Interface structure and roughness

4H-polytype AlN grown on 4H-SiC(11math0) substrate by polytype replication

N. Onojima, J. Suda, T. Kimoto, and H. Matsunami

Appl. Phys. Lett. 83, 5208 (2003); http://dx.doi.org/10.1063/1.1636533 (3 pages) | Cited 24 times

Online Publication Date: 17 December 2003

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4H-polytype AlN has been grown on a 4H-SiC substrate with the (11math0) face via plasma-assisted molecular-beam epitaxy. The microscopic structure of the AlN/4H-SiC interface was examined using high-resolution transmission electron microscopy, and the polytype replication of the 4H structure from the 4H-SiC(11math0) substrate was evidently confirmed. The x-ray rocking curve of (11math0) diffraction for the single crystalline 4H-AlN epilayer exhibited a very small linewidth of 90 arc sec, suggesting noticeably small tilting around the [11math0] direction. The excellent crystalline quality is probably owing to the polytype matching between the 4H-AlN epilayer and the 4H-SiC substrate, which resulted in remarkable reduction of defects at the interface. © 2003 American Institute of Physics.
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81.15.Hi Molecular, atomic, ion, and chemical beam epitaxy
81.05.Ea III-V semiconductors
68.55.A- Nucleation and growth
68.35.Ct Interface structure and roughness

Interface formation and defect structures in epitaxial La2Zr2O7 thin films on (111) Si

J. W. Seo, J. Fompeyrine, A. Guiller, G. Norga, C. Marchiori, H. Siegwart, and J.-P. Locquet

Appl. Phys. Lett. 83, 5211 (2003); http://dx.doi.org/10.1063/1.1635966 (3 pages) | Cited 33 times

Online Publication Date: 17 December 2003

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We have studied the growth of epitaxial La2Zr2O7 thin films on (111) Si. Although the interface structure can be strongly affected by the Si oxidation during the deposition process, epitaxial growth of La2Zr2O7 was obtained. A detailed study by means of transmission electron microscopy reveals two types of structures (pyrochlore and fluorite) with the same average chemical composition but strong differences in reactivity and interface formation. The structural complexity of the ordered pyrochlore structure seems to prevent excess oxygen diffusion and interfacial SiO2 formation. © 2003 American Institute of Physics.
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68.55.-a Thin film structure and morphology
68.35.Ct Interface structure and roughness
81.15.Hi Molecular, atomic, ion, and chemical beam epitaxy
68.37.Lp Transmission electron microscopy (TEM)

Peculiar surface deformation of sapphire: Numerical simulation of nanoindentation

R. Nowak, T. Manninen, K. Heiskanen, T. Sekino, A. Hikasa, K. Niihara, and T. Takagi

Appl. Phys. Lett. 83, 5214 (2003); http://dx.doi.org/10.1063/1.1635983 (3 pages) | Cited 14 times

Online Publication Date: 17 December 2003

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This report addresses the origin of peculiar anisotropic deformation of sapphire. The three-dimensional finite element simulation of the contact between spherical indenter and elastically anisotropic solid allowed us to analyze stress under the tip that penetrates in the (10math0) and (0001) planes, and consequently, to localize those regions in which particular deformation mechanisms are likely to be activated. This approach contrasts the available models of “hardness anisotropy,” which routinely apply a modified uniaxial-stress approach to this essentially three-dimensional, nonisotropic contact problem. The calculated results are in agreement with the microscopic inspection of impressions; that is, the surface features reflect the distribution of stress. The computations made it also possible to evaluate the actual radius of the tip (nominally 5 μm ball). © 2003 American Institute of Physics.
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68.35.Gy Mechanical properties; surface strains
62.20.Qp Friction, tribology, and hardness
02.70.Dh Finite-element and Galerkin methods
62.20.F- Deformation and plasticity
81.40.Lm Deformation, plasticity, and creep
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