Three-dimensional Confinement Research Articles

Application of Geocell Track Substructure Support System to Correct Surface Degradation Problems Under High-Speed Passenger Railroad Operations

Ballast fouling and associated degradation of track geometry is a serious problem for railway systems in general and high-speed passenger rail systems in particular. This paper presents the results of a field test on Amtrak’s Northeast Corridor where a long-term problem area existed near Oakington Road, Havre de Grace, Maryland, near MP 63.7 between Philadelphia and Washington DC. This test looked at the application of a new generation of three-dimensional cellular confinement systems (geocells) in reducing the rate of track geometry degradation, particularly in poor subgrade and ballast locations which require frequent, expensive, track surface maintenance. The field test compared two distinct sets of rebuilt track conditions, to include zones with and without a layer of geocell material. Both zones were rebuilt with improved drainage and a good, well-defined track structure and substructure (to include a well-defined depth of clean ballast). The test measurements included pre-maintenance and post-maintenance track geometry measurements together with comparative subgrade pressure measurements inside and outside the geocell cell zones. The pressure cell measurements, which looked at subgrade pressure under left and right rails in both the geocell zone and the control (non-geocell) zones, included measurements under both Acela high-speed trains and lower speed regional trains. In all cases, the subgrade pressures in the geocell zone were approximately half of those for the cells in the control zone (no geocell). Track geometry measurements were made using Amtrak’s track geometry vehicle which measures key track geometry parameters at 1-ft intervals along the track. There were several well-defined locations in the overall test zone that experienced significant track geometry degradation; these were all corrected during reconstruction. In the zones with no geocell material, these geometry variations reappeared within 6 to 7 months with the same if not greater amplitudes. By contract, in the geocell zone, the “after” geometry variations were significantly smaller than the pre-reconstruction geometry variations. Furthermore, the rate of geometry degradation was signficantly less for the geocell zones compared to the pre-geocell time periods for the exact same track. This indicated the effectiveness of the geocell material in reducing the rate of track geometry degradation and extending the surfacing maintenance cycles. Analysis of the rate of degradation showed that the effect of installing the geocell material was to significantly reduce the rate of degradation (and thus increase the surfacing cycle) by a factor of 6.7 times the pre-geocell installation surfacing cycle.

A High-Power Broadband Terahertz Source Enabled by Three-Dimensional Light Confinement in a Plasmonic Nanocavity

The scope and potential uses of time-domain terahertz imaging and spectroscopy are mainly limited by the low optical-to-terahertz conversion efficiency of photoconductive terahertz sources. State-of-the-art photoconductive sources utilize short-carrier-lifetime semiconductors to recombine carriers that cannot contribute to efficient terahertz generation and cause additional thermal dissipation. Here, we present a novel photoconductive terahertz source that offers a significantly higher efficiency compared with terahertz sources fabricated on short-carrier-lifetime substrates. The key innovative feature of this source is the tight three-dimensional confinement of the optical pump beam around the terahertz nanoantennas that are used as radiating elements. This is achieved by means of a nanocavity formed by plasmonic structures and a distributed Bragg reflector. Consequently, almost all of the photo-generated carriers can be routed to the terahertz nanoantennas within a sub-picosecond time-scale. This results in a very strong, ultrafast current that drives the nanoantennas to produce broadband terahertz radiation. We experimentally demonstrate that this terahertz source can generate 4 mW pulsed terahertz radiation under an optical pump power of 720 mW over the 0.1–4 THz frequency range. This is the highest reported power level for terahertz radiation from a photoconductive terahertz source, representing more than an order of magnitude of enhancement in the optical-to-terahertz conversion efficiency compared with state-of-the-art photoconductive terahertz sources fabricated on short-carrier-lifetime substrates.

Size-tunable Lateral Confinement in Monolayer Semiconductors

Three-dimensional confinement allows semiconductor quantum dots to exhibit size-tunable electronic and optical properties that enable a wide range of opto-electronic applications from displays, solar cells and bio-medical imaging to single-electron devices. Additional modalities such as spin and valley properties in monolayer transition metal dichalcogenides provide further degrees of freedom requisite for information processing and spintronics. In nanostructures, however, spatial confinement can cause hybridization that inhibits the robustness of these emergent properties. Here, we show that laterally-confined excitons in monolayer MoS2 nanodots can be created through top-down nanopatterning with controlled size tunability. Unlike chemically-exfoliated monolayer nanoparticles, the lithographically patterned monolayer semiconductor nanodots down to a radius of 15 nm exhibit the same valley polarization as in a continuous monolayer sheet. The inherited bulk spin and valley properties, the size dependence of excitonic energies, and the ability to fabricate MoS2 nanostructures using semiconductor-compatible processing suggest that monolayer semiconductor nanodots have potential to be multimodal building blocks of integrated optoelectronics and spintronics systems.

Rainbow trapping in a chirped three-dimensional photonic crystal

Light localization and intensity enhancement in a woodpile layer-by-layer photonic crystal, whose interlayer distance along the light propagation direction is gradually varied, has been theoretically predicted and experimentally demonstrated. The phenomenon is shown to be related to the progressive slowing down and stopping of the incident wave, as a result of the gradual variation of the local dispersion. The light localization is chromatically resolved, since every frequency component is stopped and reflected back at different positions along the crystal. It has been further discussed that the peculiar relation between the stopping position and the wave vector distribution can substantially increase the enhancement factor to more than two orders of magnitude. Compared to previously reported one- and two-dimensional photonic crystal configurations, the proposed scheme has the advantage of reducing the propagation losses by providing a three-dimensional photonic bandgap confinement in all directions. The slowing down and localization of waves inside photonic media can be exploited in optics and generally in wave dynamics, in many applications that require enhanced interaction of light and matter.

Three-dimensional photonic confinement in imprinted liquid crystalline pillar microcavities

We demonstrate the feasibility of a thermal imprint technology capable of structuring organic thin films with liquid crystalline properties forming feature sizes on a several micrometer scale. The imprint technique can directly be applied onto a variety of substrates including dielectric mirrors. The so fabricated three-dimensional microcavities have lateral extensions up to 20 μm and heights between 1 and 5 μm. Exemplarily, pillar microcavities were produced wherein three-dimensional photonic confinement is observed by the formation of 0D cavity mode patterns. The imprint technique further favors the formation of hemispherical pillar geometries rather than cylindrical pillars, resulting in equidistant mode spacings of transversal cavity modes.

Two-dimensional versus three-dimensional constraints in hetero-epitaxy/orientation relationships

Molecular dynamics simulations have been performed to compare the orientation relationships (ORs) that develop between Ag films/particles equilibrated with Ni, depending on whether the Ag is subjected to three-dimensional (3-D) confinement by being embedded in Ni, or to 2-D confinement by equilibration with a Ni substrate. Previous results of both simulations and experiments have shown that Ag films equilibrated with planar Ni substrates display a large number of different ORs; in particular, Ag equilibrated on Ni{100} displays an OR of Ag{111} // Ni{100} , often referred to as an oct-cube OR. Here it is shown that a Ag particle embedded in Ni displays an OR of Ag{111} // Ni{111} , i.e., a cube-on-cube OR. It has also been shown that as the confinement of a Ag particle is gradually increased from 2-D to 3-D, by equilibrating a Ag particle on Ni(100) substrates with progressively deeper dimples, a transition in OR occurs from oct-cube to cube-on-cube. This result contradicts the conventional notion which supposes that the ORs displayed in the presence of 3-D confinement (e.g., during phase transformations) will also tend to be displayed in epitaxy on a substrate.

Stark effect in finite-barrier quantum wells, wires, and dots

The properties of confined carriers in low-dimensional nanostructures can be controlled by external electric fields and an important manifestation is the Stark shift of quantized energy levels. Here, a unifying analytic theory for the Stark effect in arbitrary dimensional nanostructures is presented. The crucial role of finite potential barriers is stressed, in particular, for three-dimensional confinement. Applying the theory to CdSe quantum dots, finite barriers are shown to improve significantly the agreement with experiments.

High refractive index metamaterials using corrugated metallic slots.

We report on a method for realizing high refractive index metamaterials using corrugated metallic slot structures at terahertz frequencies. The effective refractive index and peak index frequency can be controlled by varying the width of the air gap in the corrugated slot arrays. The phenomenon occurs because of the secondary resonance effect due to the fundamental inductive-capacitive resonance, which generates a red-shift of the fundamental resonance determined by twice the length of the corrugated metallic slots. In addition, multiple gaps in the corrugated slots act as plasmonic hotspots which have the properties of three-dimensional subwavelength confinement due to extremely strong enhancement of the terahertz waves. The versatile characteristics of the structures may have many potential applications in designing compact optical devices incorporating various functionalities and in developing highly sensitive spectroscopic/imaging systems.

Microphase-separated structures under spherical 3D confinement

This focus review introduces recent progress made in microphase-separated structures under three-dimensional (3D) confinement. Block copolymers spontaneously form unique structures when the polymer molecules are assembled in confined spaces. The polymers are frustrated because of the limited space for phase separation, resulting in morphologies that are more complex than those of bulk films. In addition to conventional parameters such as block ratio, molecular weight and interactions of constituent polymers, the confinement effect is a significant parameter for controlling the morphologies. Here I give an overview of experimental and theoretical results for spherical 3D confinement and discuss the prospects for this area of research.

Parametric analysis of mechanically driven compositional patterning in SiGe substrates

A recently demonstrated approach for creating structured compositional gradients in the near-surface region of SiGe substrates is studied parametrically using a multiresolution coarse-grained lattice kinetic Monte Carlo simulation method. In the “stress patterning” process, a patterned elastic stress field is generated in the SiGe substrate by pressing an array of micro-indenters into it. The stressed substrate is then thermally annealed to drive the atomic diffusion in which the larger Ge atoms are pushed away from the areas of compressive stress. By varying a subset of the parameters that characterize the high-dimensional input space of the process (e.g., indenter spacing, indenter tip shape, and indenter array symmetry) we show that technologically interesting compositional configurations may be readily generated. In particular, we show that it is theoretically possible to generate arrays of well-delineated nanoscale regions of high Ge content surrounded by essentially pure Si. Such configurations may be useful as Ge “quantum dots” that exhibit three-dimensional quantum confinement, which have otherwise been very challenging to create with high degrees of size and spatial uniformity. These simulation results will be instrumental in guiding future experimental demonstrations of stress patterning.

Mechanistic investigations of confinement effects on the self-assembly of symmetric amphiphilic copolymers in thin films.

The self-assembly of a copolymer thin film, whose molecular structure is composed of one hydrophobic branch and two hydrophilic branches, gives a cylindrical structure consisting of a hydrophobic core and a hydrophilic outer surface. The confinement-induced loss of entropy leads the copolymer to self-assemble into a hexagonal arrangement of cylindrical structures. This hexagonal arrangement is of two induced self-assembly structures under one-dimensional confinement in thin films, i.e., micellar structures with uniform density of an individual core, as well as lamellar structures with two separated hydrophobic layers and one hydrophilic layer. When the repulsive force of the confinement is greater for the hydrophobic polymeric component than for the hydrophilic polymeric component, the self-assembled density of the cores is broad. A proportional change in the individual volume suggests interactions between the walls and the hydrophobic core, which plays a vital role in the formation of the self-assembled structure. A basic understanding of the one-dimensional confinement investigated in this study serves to elucidate the more complex two- and three-dimensional confinements and provides further insights for the design of nanomaterials with novel morphologies.

Hermitian and gauge-covariant Hamiltonians for a particle in a magnetic field on cylindrical and spherical surfaces

We construct the Hermitian Schrödinger Hamiltonian of spin-less particles and the gauge-covariant Pauli Hamiltonian of spin one-half particles in a magnetic field, which are confined to cylindrical and spherical surfaces. The approach does not require the use of involved differential-geometrical methods and is intuitive and physical, relying on the general requirements of Hermicity and gauge-covariance. The surfaces are embedded in the full three-dimensional space and confinement to the surfaces is achieved by strong radial potentials. We identify the Hermitian and gauge-covariant (in the presence of a magnetic field) physical radial momentum in each case and set it to zero upon confinement to the surfaces. The resulting surface Hamiltonians are seen to be automatically Hermitian and gauge-covariant. The well-known geometrical kinetic energy also emerges naturally.

A condition for small bootstrap current in three-dimensional toroidal configurations

It is shown that, if the maximum of the magnetic field strength on a magnetic surface in a threedimensional magnetic confinement configuration with stellarator symmetry constitutes a line that is orthogonal to the field lines and crosses the symmetry line, then the bootstrap current density is smaller compared to that in quasi-axisymmetric (qa) [J. Nuhrenberg et al., in Proc. of Joint Varenna−Lausanne Int. Workshop on Theory of Fusion Plasmas, Varenna, 1994, p. 3] and quasi-helically (qh) symmetric [J. Nuhrenberg and R. Zille, Phys. Lett. A 129, 113 (1988)] configurations.

Non-monotonous polymer translocation time across corrugated channels: Comparison between Fick-Jacobs approximation and numerical simulations

We study the translocation of polymers across varying-section channels. Using systematic approximations, we derive a simplified model that reduces the problem of polymer translocation through varying-section channels to that of a point-like particle under the action of an effective potential. Such a model allows us to identify the relevant parameters controlling the polymer dynamics and, in particular, their translocation time. By comparing our analytical results with numerical simulations we show that, under suitable conditions, our model provides reliable predictions of the dynamics of both Gaussian and self-avoiding polymers, in two- and three-dimensional confinements. Moreover, both theoretical predictions, as well as Brownian dynamic results, show a non-monotonous dependence of polymer translocation velocity as a function of polymer size, a feature that can be exploited for polymer separation.

Nearly diffraction-limited conjugated polymer microlasers utilizing two-dimensional distributed Bragg resonators

We report nearly diffraction-limited lasing from the two-dimensional distributed Bragg reflector (DBR) resonator with a conjugated polymer layer as the gain medium. The resonator consists of four Bragg mirrors, which are fabricated by dot-matrix holography. The in-plane optical confinement in this cavity is achieved via two-dimensional Bragg reflections and the vertical confinement is provided through total internal reflection at the slab interface, leading to a three-dimensional confinement of the emitter. Upon optical pumping, the cavity emits nearly diffraction limited laser emission perpendicular to the surface with a threshold of 9 μJ/cm2 and a bandwidth of 0.31 nm which is quite advantageous to its one-dimensional counterpart. Facile fabrication of two-dimensional DBR polymer lasers with different parameters by dot-matrix holography was also demonstrated. It was further found that the cavity Q factor decreases by a factor of two and the laser threshold increases to 0.41 mJ/cm2 when the mirror size decreases to 20 μm. Our results indicate a step towards the application of polymer micro-lasers in the fields of displays and spectroscopic analyzing.

Effect of Ge Core Size on Photoluminescence from Si Quantum Dots with Ge Core

The achievement of intense light emission at room temperature from group-IV materials is a crucial step toward the accomplishment of fully-Si-based optoelectronics. Recently, Ge-nanostructures on Si or embedded in Si have been also studied to realize well-defined three-dimensional hole confinement in Ge-QDs with keeping electron transport efficiency, which can enhance carrier recombination efficiency [4-7]. In our previous paper, we have reported on the formation of Si quantum dots (Si-QDs) with Ge core with an areal density as high as ~1011cm-2and their photoluminescence (PL) properties [8, 9]. We also demonstrated that, in this system, room temperature PL was promoted by hole confinement in Ge core reflecting the type II energy band discontinuity between Si clad and Ge core. In this work, we extended our research work to evaluate impact of Ge-core size on their PL characteristics. After conventional wet-chemical cleaning steps, ~2.0 nm-thick SiO2 was grown on p-Si(100) by dry O2 oxidation at 850°C. The SiO2 surface was shortly dipped into a 0.1% HF solution to etch back the SiO2 and to obtain uniform surface termination with OH bonds. Subsequently, hemispherical Si-QDs with an areal dot density of ~1011cm-2 were formed from the thermal decomposition of pure SiH4 under 67 Pa at 550˚C. After that, Ge was deposited selectively on the pre-grown Si-QDs at 370°C by using GeH4 diluted with 5% H2 where the GeH4-LPCVD time was varied in the range from 2.5 to 3 min to control core size. After the Ge core deposition, Si clad was formed in the same chamber at 530ºC by LPCVD using SiH4 under 2.7 Pa. Finally, the surface of the Si-QDs with Ge core was oxidized at room temperature by a remote VHF plasma of O2, which resulted in conformal coverage with a ~2.0 nm-thick SiO2 layer. AFM images confirm that the areal dot density (~1.0×1011cm-2) remains unchanged after the Ge deposition regardless of deposition time. This result implies Ge was deposited selectively on the pre-grown Si-QDs. From the size distribution of the dot evaluated from AFM images taken at each process steps, we confirmed that average dot heights were increased by ~2 nm and ~6 nm with GeH4-LPCVD for 2.5 min and 3 min, respectively, in comparison to the pre-grown Si-QDs. The Si-QDs with an average Ge dot size of 6nm shows PL signals peaked at ~0.69 eV at room temperature (Fig. 1). The observed PL peak is likely to be caused by radiative recombination of photogenerated electron-hole pairs through quantized states of the Ge core. It should be noted that, with a decrease in the core size down to ~2nm, PL signal was slightly shifted towered the high energy side by ~80 meV, although no significant change in the PL intensity was observed. This result can be interpreted as a result of increased quantized energy reflecting the size of the Ge core rather than the intermixing of the Si clad and Ge core. In conclusion, we demonstrated room temperature PL from the Si-QDs with different sized Ge core. The PL from the Si-QDs with Ge core is dominated by the recombination of electron-hole pairs between quantized states of Ge core, and emission wavelength can be changed by controlling the Ge core size. Acknowledgments This work was supported in part by Grant-in Aid for Scientific Research (S) 15H05762 of MEXT, Japan.

Si/SiGe Heterointerfaces in One-, Two-, and Three-Dimensional Nanostructures: Their Effect on SiGe Light Emission

The development of a light emitter compatible with Si based complementary metal-oxide- semiconductor (CMOS) circuit technology and fast optical interconnects is important for the new generations of microprocessors and computers. Self-assembled Si/Si1-xGex nanostructures (NSs) with light emission in the important optical communication wavelength range of 1.3 – 1.55 μm are compatible with conventional CMOS processes. However, the predicted and experimentally confirmed long carrier radiative lifetimes in Si and Si/Si1-xGex NSs impede the demonstration of efficient light-emitting devices and lasers. Thus, engineering of Si/Si1-xGex heterostructures with controlled composition and interface abruptness is critical in producing the desired fast and efficient photoluminescence (PL) peaked at around 0.8-0.9 eV. In this paper we assess how the nature of the interfaces between SiGe NSs and Si in heterostructures strongly affects carrier mobility and recombination for physical confinement in one dimension (corresponding to the case of quantum wells), two dimensions (quantum wires), and three dimensions (quantum dots). The interface sharpness is influenced by many factors such as growth conditions, strain, and thermal processing, which in practice can make it difficult to attain the ideal structures required. This is certainly the case for NS confinement in one dimension. However, we demonstrate that axial Si/Ge nanowire (NW) heterojunctions (HJs) with a Si/Ge NW diameter in the range 50 – 120 nm produce a clear PL signal associated with band-to-band electron-hole recombination at the NW HJ that is attributed to a specific interfacial SiGe alloy composition. For three-dimensional confinement, the experiments outlined here show that two quite different Si1-xGex NSs incorporated into a Si0.6Ge0.4 wavy structure exhibit an intense PL signal with a characteristic decay time as much as 1000 times shorter than that observed in conventional Si/SiGe NSs. The experimentally observed non-exponential PL decay in Si/SiGe NSs is explained as being due to variations of the distances separating electrons and holes at the Si/SiGe heterointerface. The results demonstrate that an abrupt Si/SiGe heterointerface reduces the carrier radiative recombination lifetime and increases the PL quantum efficiency making these SiGe NSs promising candidates for applications in CMOS compatible light-emitting devices.

Si/SiGe Heterointerfaces in One-, Two-, and Three-Dimensional Nanostructures: Their Effect on SiGe Light Emission

The nature of the interfaces between SiGe nanostructures and Si in heterostructures strongly affects carrier mobility and recombination for physical confinement in one, two, and three dimensions. The interface sharpness is influenced by many factors including growth conditions, strain, and thermal processing, which can make it difficult to attain the desired structures. This is certainly the case for nanostructure confinement in one dimension. However, axial Si/Ge nanowire heterojunctions with a Si/Ge nanowire diameter in the range 50–120 nm produce a strong photoluminescence signal associated with band-to-band electron-hole recombination at the nanowire heterojunction that is attributed to a specific interfacial SiGe alloy composition. For three-dimensional confinement, experiments show that two quite different SiGe nanostructures incorporated into a Si0.6Ge0.4 wavy structure exhibit an intense PL signal with a characteristic non-exponential decay time that is remarkably shorter (as much as 1000 times) than that found in conventional Si/SiGe nanostructures.

Si/SiGe Interfaces in Three-, Two-, and One-Dimensional Nanostructures and Their Influence on SiGe Light Emission

The nature of the interfaces between SiGe nanostructures (NSs) and Si in heterostructures strongly affects carrier mobility and recombination for physical confinement in one, two, and three dimensions. The interface sharpness is influenced by many factors including growth conditions, strain, and thermal processing, which can make it difficult to attain the desired structures. This is certainly the case for NS confinement in one dimension. However, axial Si/Ge nanowire (NW) heterojunctions (HJs) with a Si/Ge NW diameter in the range 50–120 nm produce a strong PL signal associated with band-to-band electron-hole recombination at the NW HJ that is attributed to a specific interfacial SiGe alloy composition. For three-dimensional confinement, experiments show that two quite different SiGe NSs incorporated into a Si0.6Ge0.4 wavy structure exhibit an intense PL signal with a characteristic non-exponential decay time that is remarkably shorter (as much as 1000 times) than that found in conventional Si/SiGe NSs.

Optimal search strategies of run-and-tumble walks.

The run-and-tumble walk, consisting of randomly reoriented ballistic excursions, models phenomena ranging from gas kinetics to bacteria motility. We evaluate the mean time required for this walk to find a fixed target within a two- or three-dimensional spherical confinement. We find that the mean search time admits a minimum as a function of the mean run duration for various types of boundary conditions and run duration distributions (exponential, power-law, deterministic). Our result stands in sharp contrast to the pure ballistic motion, which is predicted to be the optimal search strategy in the case of Poisson-distributed targets.