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A theoretical framework combining transfer matrix method simulation and energy transfer (ET) calculation reveals critical device design guidelines for developing efficient ultrathin Si solar cells sensitized by semiconductor nanocrystals (NCs).
We reduce the solution of the scattering problem defined on the half-line [0,∞) by a real or complex potential v(x) and a general homogeneous boundary condition at x=0 to that of the extension of v(x) to the full line that vanishes for x<0. We find an explicit expression for the reflection amplitude of the former problem in terms of the reflection and transmission amplitudes of the latter. We obtain a set of conditions on these amplitudes under which the potential in the half-line develops bound states, spectral singularities, and time-reversed spectral singularities where the potential acts as a perfect absorber. We examine the application of these results in the study of the scattering properties of a δ-function potential and a finite barrier potential defined in [0,∞), discuss optical systems modeled by these potentials, and explore the configurations in which these systems act as a laser or perfect absorber. In particular, we derive an explicit formula for the laser threshold condition for a slab laser with a single mirror and establish the surprising fact that a nearly perfect mirror gives rise to a lower threshold gain than a perfect mirror. We also offer a nonlinear extension of our approach which allows for utilizing a recently developed nonlinear transfer matrix method in the full line to deal with finite-range nonlinear scattering interactions defined in the half-line.
We investigate the effect of surface disorder on the chiral surface states of a three-dimensional quantum Hall system. Utilizing a transfer-matrix method, we find that the localization length of the surface state along the magnetic field decreases with the surface disorder strength in the weak disorder regime but increases anomalously in the strong disorder regime. In the strong disorder regime, the surface states mainly locate at the first inward layer to avoid the strong disorder in the outmost layer. The anomalous increase of the localization length can be explained by an effective model, which maps the strong disorder on the surface layer to the weak disorder on the first inward layer. Our work demonstrates that surface disorder can be an effective way to control the transport behavior of the surface states along the magnetic field. We also investigate the effect of surface disorder on the full distribution of conductances P(g) of the surface states in the quasi-one-dimensional (1D) regime for various surface disorder strengths. In particular, we find that P(g) is Gaussian in the quasi-1D metal regime and log-normal in the quasi-1D insulator regime. In the crossover regime, P(g) exhibits highly nontrivial forms, whose shapes coincide with the results obtained from the Dorokhov-Mello-Pereyra-Kumar equation of a weakly disordered quasi-1D wire in the absence of time-reversal symmetry. Our results suggest that P(g) is fully determined by the average conductance, independent of the details of the system, in agreement with the single-parameter scaling hypothesis.
We formulate and implement a spectral method for solving the Schrödinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials such as nanotubes (of arbitrary chirality), nanowires, nanoribbons, chiral nanoassemblies, nanosprings and nanocoils, in an accurate, efficient and systematic manner. Our work is motivated by the observation that one of the most successful methods for carrying out electronic structure calculations of bulk/crystalline systems — the plane-wave method — is a spectral method based on eigenfunction expansion. Our scheme avoids computationally onerous approximations involving periodic supercells often employed in conventional plane-wave calculations of quasi-one-dimensional materials, and also overcomes several limitations of other discretization strategies, e.g., those based on finite differences and atomic orbitals. The basis functions in our method — called helical waves (or twisted waves) — are eigenfunctions of the Laplacian with symmetry adapted boundary conditions, and are expressible in terms of plane waves and Bessel functions in helical coordinates. We describe the setup of fast transforms to carry out discretization of the governing equations using our basis set, and the use of matrix-free iterative diagonalization to obtain the electronic eigenstates. Miscellaneous computational details, including the choice of eigensolvers, use of a preconditioning scheme, evaluation of oscillatory radial integrals and the imposition of a kinetic energy cutoff are discussed. We have implemented these strategies into a computational package called HelicES (Helical Electronic Structure). We demonstrate the utility of our method in carrying out systematic electronic structure calculations of various quasi-one-dimensional materials through numerous examples involving nanotubes, nanoribbons and nanowires. We also explore the convergence properties of our method, and assess its accuracy and computational efficiency by comparison against reference finite difference, transfer matrix method and plane-wave results. We anticipate that our method will find applications in computational nanomechanics and multiscale modeling, for carrying out transport calculations of interest to the field of semiconductor devices, and for the discovery of novel chiral phases of matter that are of relevance to the burgeoning quantum hardware industry.
Due to a lower InN bandgap energy Eg~0.7 eV, InxGa1−xN/Sapphire epifilms are considered valuable in the development of low-dimensional heterostructure-based photonic devices. Adjusting the composition x and thickness d in epitaxially grown films has offered many possibilities of light emission across a wide spectral range, from ultraviolet through visible into near-infrared regions. Optical properties have played important roles in making semiconductor materials useful in electro-optic applications. Despite the efforts to grow InxGa1−xN/Sapphire samples, no x- and d-dependent optical studies exist for ultrathin films. Many researchers have used computationally intensive methods to study the electronic band structures Ejk→, and subsequently derive optical properties. By including inter-band transitions at critical points from Ejk→, we have developed a semiempirical approach to comprehend the optical characteristics of InN, GaN and InxGa1−xN. Refractive indices of InxGa1−xN and sapphire substrate are meticulously integrated into a transfer matrix method to simulate d- and x-dependent reflectivity RE and transmission TE spectra of nanostructured InxGa1−xN/Sapphire epifilms. Analyses of RE and TE have offered accurate x-dependent shifts of energy gaps for InxGa1−xN (x = 0.5, 0.7) in excellent agreement with the experimental data.
Creating artificial matter with controllable chirality in a simple and scalable manner brings new opportunities to diverse areas. Here we show two such methods based on controlled vacuum filtration - twist stacking and mechanical rotation - for fabricating wafer-scale chiral architectures of ordered carbon nanotubes (CNTs) with tunable and large circular dichroism (CD). By controlling the stacking angle and handedness in the twist-stacking approach, we maximize the CD response and achieve a high deep-ultraviolet ellipticity of 40 ± 1 mdeg nm -1 . Our theoretical simulations using the transfer matrix method reproduce the experimentally observed CD spectra and further predict that an optimized film of twist-stacked CNTs can exhibit an ellipticity as high as 150 mdeg nm -1 , corresponding to a g factor of 0.22. Furthermore, the mechanical rotation method not only accelerates the fabrication of twisted structures but also produces both chiralities simultaneously in a single sample, in a single run, and in a controllable manner. The created wafer-scale objects represent an alternative type of synthetic chiral matter consisting of ordered quantum wires whose macroscopic properties are governed by nanoscopic electronic signatures and can be used to explore chiral phenomena and develop chiral photonic and optoelectronic devices.
The near-field radiative heat transfer (NFRHT) between two semi-infinite α-MoO3 biaxial crystals is investigated numerically based on the fluctuation–dissipation theorem combined with the modified 4 × 4 transfer matrix method in this paper. In the calculations, the near-field radiative heat flux (NFRHF) along each of the crystalline directions of α-MoO3 is obtained by controlling the orientation of the biaxial crystals. The results show that much larger heat flux than that between two semi-infinite hexagonal boron nitride can be achieved in the near-field regime, and the maximum heat flux is along the [001] crystalline direction. The mechanisms for the large radiative heat flux are explained as due to existence of hyperbolic phonon polaritons (HPPs) inside α-MoO3 and excitation of hyperbolic surface phonon polaritons (HSPhPs) at the vacuum/α-MoO3 interfaces. The effect of relative rotation between the emitter and the receiver on the heat flux is also investigated. It is found that the heat flux varies significantly with the relative rotation angle. The modulation contrast can be as large as two when the heat flux is along the [010] direction. We attribute the large modulation contrast mainly to the misalignment of HSPhPs and HPPs between the emitter and the receiver. Hence, the results obtained in this work may provide a promising way for manipulating near-field radiative heat transfer between anisotropic materials.
While an organically modified chalcogenide (ORMOCHALC) can be used to fabricate a polymeric mid-wavelength infrared (MWIR) polarizer with competitive extinction ratio compared to the commercial wire-grid polarizers, which are composed of fragile inorganic materials, there is still a knowledge gap regarding the systematic design process to obtain high transmission efficiency and extinction ratio. As such, a computational parameter study for design optimization is conducted with the geometric parameters of the bilayer grating ORMOCHALC polarizer. The computational study shows that the Fabry–Pérot cavity is the primary mechanism that determines the transmission behaviors and the extinction ratio. A bilayer grating design, guided by the parameter study, is realized through the thermal nanoimprint and metal deposition processes. The extinction ratios measured with the Fourier-transform infrared are 245, 304, and 351 at the wavelength of 3, 4, and 5 μm, respectively. Compared to the state-of-the-art of the polymeric MWIR linear polarizers, the extinction ratio is improved by 1.4 times, and the transmission efficiency is increased by 2.5 times. Theoretical analysis with the multiple-layer model based on the transfer matrix method predicts a matched transmission behavior with the experiment and a full-wave electromagnetic simulation.
We demonstrate GaAs thermophotovoltaic (TPV) devices with a patterned dielectric back contact (PDBC) architecture, featuring a dielectric spacer between the semiconductor and back metal contact over most of the back surface for high reflectance, and metal point contacts over a smaller area for electrical conduction. In the TPV application, high sub-bandgap reflectance is needed to reflect unused sub-bandgap photons to the thermal emitter to minimize energy losses in this portion of the thermal spectrum. We explore different PDBC fabrication processes with SU-8 and SiO2 dielectric spacer layers to maximize sub-bandgap reflectance while minimizing series resistance to increase TPV conversion efficiency. We successfully demonstrate GaAs SU-8 PDBC TPV devices with 2200 degrees C blackbody-weighted sub-bandgap reflectance of 94.9% and 96.5% with and without a front metal grid, respectively. This is 0.7% and 2.3% (absolute) higher than the mean sub-bandgap reflectance of 94.2% for GaAs baseline TPV devices with 100% Au back contact with front metal grid. Lower sub-bandgap reflectance in TPV devices with front grids indicates the front grid induces light scattering leading to additional parasitic absorption in the TPV device. We also show that for higher contact coverage fractions, the PDBC reflectance cannot in general be treated by a linear interpolation using simple 1D transfer matrix method modeling and should be treated instead as a diffraction grating by solving Maxwell's equations in 3D.
High-efficiency, four-terminal tandem solar cells composed of thin GaAs films mechanically stacked onto interdigitated back contact silicon solar cells with a glass interlayer are demonstrated. The optimal thickness of the absorber layer of a rear heterojunction GaAs subcell for use in four terminal tandem solar cells was studied. GaAs top cells with absorber layer thicknesses of 1.5, 1.9, 2.3, 2.8, and 3.5 µm were fabricated on glass and mechanically stacked onto interdigitated back-contact Si bottom cells. All tandem cells were found to have efficiencies above 30% under the AM1.5 G spectrum demonstrating a relatively weak sensitivity to thickness in the four-terminal configuration. We found the 2.8 µm absorber layer cell to have the highest top cell and tandem cell efficiency at 26.38% and 32.57%, respectively. Optical modeling with transfer matrix method for the planar top cell and Lambertian light trapping in the textured Si subcell, along with drift-diffusion Hovel equations, were used to show photon recycling enhancement to the effective diffusion length and VOC of the top cell as a result of the low-index glass interlayer.
Fabry-Perot microcavities can strongly enhance interactions between light and molecules, leading to the formation of hybrid light-matter states known as polaritons. Polaritons possess much smaller effective masses and much larger group velocities when the molecules are resonant with cavity modes that have finite (nonzero) in-plane wave vectors, giving rise to the possibilities of long-range and ultrafast ballistic transport. In this paper, we present the results of numerical simulations of the ultrafast ballistic transport phenomenon in real space and time during and after initialization with a short, spatially localized pulse. Here, we address this problem with two approaches: the standard transfer-matrix method (TMM) for planar structures and a second simulation based on the numerical solution of the Maxwell-Bloch equations that can be used for general configurations (complex metasurfaces, for instance) and excitation modes. The agreement between the TMM and the full numerical calculation with the Maxwell-Bloch equations when applied to multilayer planar configurations provides proof of the validity of both approaches for the present analyses. Overall, we find that the transport of the molecular excitons inside the cavity synchronize with the evolution of the enhanced electromagnetic field inside the cavity. Moreover, the synchronized transport rate is in good agreement with the group velocities predicted from a calculated dispersion relation across a wide range of frequencies. Finally, we relate the group velocity to the Hopfield coefficient obtained from quantum modeling and suggest that the dependence of light-matter coupling on the in-plane wave vector can be an important but overlooked factor for understanding the transport behavior of polaritons. These simulations provide an intuitive tool for understanding the collective motion of light and excitons and helps us to better understand how experimental observations of polaritons should be interpreted.
PVwindow simulates photovoltaic window properties by allowing the user build stacks of thin film materials that compose the window layers. The only needed inputs are the complex refractive indices and thicknesses of the materials. The software will simulate the optical transmission, front reflection, and back reflection of the stack using the transfer matrix method. Properties specific to PV window optics such as visible transmittance and color are also calculated. The optics code extracts the number of absorbed photons in the PV absorber layer and solves the single diode equation to yield theoretical photovoltaic metrics such as power conversion efficiency, fill factor, open circuit voltage, and short circuit current of the PV window when illuminated at an arbitrary angle or from either side of the stack. The software tool ultimately allows researchers to design photovoltaic windows and simulate their properties. The software also exports files that can be read into LBL Window software or into the EnergyPlus and Open Studio building energy modeling software to determine larger scale energy impacts of PV window integration.
Bragg gratings are key optical elements for applications in communications, sensing, and lasers. Phase-shifted Bragg gratings are a special case where the simple periodic structure is altered to allow a narrow spectral passband within the optical bandgap. Here, we demonstrate phase-shifted silicon nitride gratings fabricated using 193 nm deep ultraviolet lithography (DUV) on the AIM Photonics 300 mm silicon photonics foundry line. We measure the grating properties and verify the results with a transfer-matrix method (TMM) model. The standard grating expressions for extracting the coupling coefficient κ and bandwidth do not apply and are updated to account for the phase shift. These results inform future designs for on-chip grating filters and distributed feedback (DFB) lasers.
Mechanical shock events experienced by electronics systems can be reproduced in the laboratory using Hopkinson bar tests. In these tests a projectile strikes an bar, creating a pulse which travels through the bar into the system. The quality of these tests depends on the closeness of the shape of the incident pulse to the shape specified for the test. This paper introduces a new way to control the shape of the incoming pulse, through the use of elastic metamaterial concepts. Two dispersion-modifying material concepts, phononic crystals, and local resonators, are examined for their wave shaping capabilities in 1D elastic waveguides. They are then evaluated using a transfer matrix method to determine the output wave shape in the time domain. The concepts are then optimized for various pulse shapes, showing that they are most effective when they are tuned to introduce dispersion near the fundamental frequency of the incident wave.
The exact solution of the A{sub 2}{sup (2)} model (or the Izergin–Korepin model) with non-diagonal boundary reflections of the type I is studied by using the off-diagonal Bethe ansatz method. The complete operator product identities of the transfer matrices are obtained with the help of fusion. Based on them and the asymptotic behaviors as well as the values at special points, the inhomogeneous T−Q relations of the system are constructed. The method and the results in this paper can be generalized to the high rank A{sub n}{sup (2)} case directly.
The Real-time Analysis for Particle-transport and In-situ Detection (RAPID) Code System, based on the Multi-stage Response-function Transport (MRT) methodology, allows for real-time simulation of nuclear systems based on 3-D continuous-energy particle transport. RAPID's steady-state (criticality) neutron transport algorithm is based on the Fission Matrix (FM) method, and has been extensively verified and validated against computational benchmarks and experiments. This paper introduces the novel 3-D time-dependent transport algorithm that has been implemented into the code, tRAPID, and its validation using the JSI TRIGA Mark-II reactor. tRAPID accurately and efficiently calculates neutron kinetics parameters (such as β{sub eff}, l{sub eff} , Λ, α{sub Rossi}) and 3-D time-dependent neutron fission source distribution and neutron importances for both prompt and delayed neutrons. tRAPID is used to simulate a rod insertion experiment performed at the JSI TRIGA Mark-II reactor, during which signals from four fission chambers at four different locations in the core were collected. The results demonstrate how tRAPID is capable of calculating detailed and accurate results with only a minimal use computational resources and time.
We study the quasiparticle current in clean ferromagnetic Josephson structures of the form $S_1/F_1/N/F_2/S_2$, where $\textit{S, F,}$ and $\textit{N}$ denote superconducting, ferromagnetic, or normal layers, respectively. Our focus is on the structure of the conductance $\textit{G}$ as a function of bias $\textit{V$, emphasizing the subgap region. We use a fully self-consistent numerical method, coupled to a transfer matrix procedure to extract $\textit{G(V)}$. We choose material parameters appropriate to experimentally realized Co Cu Nb structures. In this work, we find a resonance peak structure as a function of the intermediate layer thickness and of the misalignment angle $\phi$ between $\textit{F}$ layers. To understand this resonance structure, we develop an approximate analytic method. For experimentally relevant thicknesses, the conductance has multiple subgap peaks, which oscillate in position between low and critical bias positions. These oscillations occur in both $\phi$ and the layer thicknesses. We compare our results with those obtained for the spin valve structures ($F_1/N/F_2/S_2$) and discuss the implications of our results for the fabrication of spin Josephson devices.
This Letter introduces a method for determining the energy spectrum of lattice quantum chromodynamics by applying the Lanczos algorithm to the transfer matrix and using a bootstrap generalization of the Cullum-Willoughby method to filter out spurious eigenvalues. Proof-of-principle analyses of the simple harmonic oscillator and the lattice quantum chromodynamics proton mass demonstrate that this method provides faster ground-state convergence than the “effective mass,” which is related to the power-iteration algorithm. Lanczos provides more accurate energy estimates than multistate fits to correlation functions with small imaginary times while achieving comparable statistical precision. Two-sided error bounds are computed for Lanczos results and guarantee that excited-state effects cannot shift Lanczos results far outside their statistical uncertainties.