Generalized Transfer Matrix Method Research Articles

High Detectivity Organic Photodetectors With Molybdenum (VI) Oxide and C60Layers

This paper proposes high-sensitive polymer/ fullerene bulk-heterojunction organic photodetectors (OPDs). A typical polymeric hole transport layer, (poly(3,4-ethylenedioxythophene):poly(styrenesulfonate), has substitutes with a molybdenum (VI) oxide (MoO3) layer. A thin C 60 hole blocking layer was also introduced to reduce the dark current performance of the OPD. Optical interference simulation also accomplished along with the generalized transfer matrix method to show the behavior of wavelengths in OPDs. As a result, the lowest dark current density of 14 pA/cm2, and 40% above EQE, has achieved in the visible range. In regards to the photodetector characteristics, a reasonable responsivity of 0.21 A/W and high detectivity of $2.4 \times 10^{12}$ cmHz $^{1/2}/\text{W}$ were also obtained.

Morphology-Controlled High-Efficiency Small Molecule Organic Solar Cells without Additive Solvent Treatment.

This paper focuses on nano-morphology-controlled small-molecule organic solar cells without solvent treatment for high power-conversion efficiencies (PCEs). The maximum high PCE reaches up to 7.22% with a bulk-heterojunction (BHJ) thickness of 320 nm. This high efficiency was obtained by eliminating solvent additives such as 1,8-diiodooctane (DIO) to find an alternative way to control the domain sizes in the BHJ layer. Furthermore, the generalized transfer matrix method (GTMM) analysis has been applied to confirm the effects of applying a different thickness of BHJs for organic solar cells from 100 to 320 nm, respectively. Finally, the study showed an alternative way to achieve high PCE organic solar cells without additive solvent treatments to control the morphology of the bulk-heterojunction.

Optical modeling-assisted characterization of dye-sensitized solar cells using TiO2 nanotube arrays as photoanodes

Photovoltaic characteristics of dye-sensitized solar cells (DSSCs) using TiO2 nanotube (TNT) arrays as photoanodes were investigated. The TNT arrays were 3.3, 11.5, and 20.6 μm long with the pore diameters of 50, 78.6, and 98.7 nm, respectively. The longest TNT array of 20.6 μm in length showed enhanced photovoltaic performances of 3.87% with significantly increased photocurrent density of 8.26 mA·cm−2. This improvement is attributed to the increased amount of the adsorbed dyes and the improved electron transport property with an increase in TNT length. The initial charge generation rate was improved from 4 × 1021 s−1·cm−3 to 7 × 1021 s−1·cm−3 in DSSCs based on optical modelling analysis. The modelling analysis of optical processes inside TNT-based DSSCs using generalized transfer matrix method (GTMM) revealed that the amount of dye and TNT lengths were critical factors influencing the performance of DSSCs, which is consistent with the experimental results.

In-situ optical diagnostics of boron-doped diamond films growth

Interferometry is desirable method for in-situ measurement of thin, dielectric film growth, as it don't modify conditions of film deposition. Here we present interferometrical measurements of thickness of doped diamond films during Chemical Vapor Deposition (CVD) process. For this purpose we used semiconductor laser with 405 nm wavelength. Additional ex-situ measurement using spectral interferometry and ellipsometry have been performed. We found that doping diamond with boron does not cause degradation of interference of light inside the film. To our knowledge this is first study of optical monitoring of boron doped, polycrystalline diamond films deposition. Full Text: PDF References J. Asmussen, D. Reinhard, Diamond Films Handbook, 1st ed. (CRC Press 2002). CrossRef R. S. Sussmann, CVD diamond for electronic devices and sensors. (Chichester, U.K.: J. Wiley 2009). CrossRef E. Bakker, Y. Qin, "Electrochemical Sensors", Anal. Chem. 78, 12 (2006). CrossRef V. Prajzler et al., "Design and investigation of properties of nanocrystalline diamond optical planar waveguides", Opt. Express 21, 7 (2013) CrossRef N.J. Alberto et al., "Nanodiamond coated Bragg gratings for sensing applications", Proc. SPIE 8421 (2012). CrossRef R. Bogdanowicz et al., "Nucleation and growth of CVD diamond on fused silica optical fibres with titanium dioxide interlayer", Phys. Status Solidi (a) 210, 10 (2013). CrossRef M. Smietana et al., "Application of diamond-like carbon films in optical fibre sensors based on long-period gratings", Diamond Relat. Mater. 16, 4 (2007). CrossRef R. Bogdanowicz et al., "Amperometric sensing of chemical oxygen demand at glassy carbon and silicon electrodes modified with boron-doped diamond", Sens, Actuator B-Chem. 189 (2013) CrossRef C.E. Nebel et al., "Diamond and biology", J. R. Soc. Interface 4, 14 (2007). CrossRef R. Bogdanowicz et al., "Influence of the boron doping level on the electrochemical oxidation of the azo dyes at Si/BDD thin film electrodes", Diamond Relat. Mater. 39, (2013). CrossRef J.J. Gracio et al., "Diamond growth by chemical vapour deposition", J. Phys. D: App. Phys. 43, 37 (2010). CrossRef J. Luo, X. Ying, P. Wang, L. Chen, "Study on the growth of CVD diamond thin films by in situ reflectivity measurement", Diamond Relat. Mater. 11, 11 (2002). CrossRef A.M. Bonnot, R. Schauer, B. Weidner, "HFCVD diamond film nucleation and growth studies by in-situ optical technique and ex-situ AFM observations", Diamond Relat. Mater., 7, 2 (1998). CrossRef C.D. Zuiker, D.M. Gruen, A.R. Krauss, "In situ laser reflectance interferometry measurement of diamond film growth", J. Appl. Phys. 79, 7 (1996). CrossRef M. Bass et al., Handbook of opitcs, Volume IV: Optical Properties of Meterials, Nonlinear Optics, Quantum Optics (McGraw-Hill 2009). E.D. Palik ed., Handbook of Optical Constants of Solids (Elsevier 1998). D.I. Siapkas, C.L. Mitsas, "Generalized matrix method for analysis of coherent and incoherent reflectance and transmittance of multilayer structures with rough surfaces, interfaces, and finite substrates", Appl. Opt. 34, 10 (1995). CrossRef C. Katsidis, D.I. Siapkas, "General Transfer-Matrix Method for Optical Multilayer Systems with Coherent, Partially Coherent, and Incoherent Interference", Appl. Opt. 41, 19 (2002). CrossRef

Effect of incidence angle and polarization on the optimized layer structure of organic solar cells

We theoretically and experimentally investigate the effect of the incidence angle and polarization of sunlight on the optimized layer structure of organic solar cells (OSCs) to obtain the best absorption efficiency in a realistic deployment situation. We use the generalized transfer matrix method with respect to the incidence angle and polarization, which can calculate the spatial distribution of the optical power dissipation in both the incoherent glass substrate and the coherent multilayer without using any indirect correction factor. The angular dependence of the short-circuit current, the open-circuit voltage, and the output electric power is calculated and compared with the experimental results. Using the simulation parameters matched with the experimental results, we calculate the generation energy density per day by considering the variation of the incidence angle during daytime and determine the optimized thickness of the active region for maximum absorption efficiency. We show that the optimized active-region thickness based on the generation energy density per day is different from that determined from the variation of the short-circuit current density in only normal incidence, which is generally used for optimizing device structure of OSCs.

Effect of an Incoherent Glass Substrate on the Absorption Efficiency of Organic Solar Cells at Oblique Incidence Analyzed by the Transfer Matrix Method with a Glass Factor

We theoretically investigate the effect of the incoherent glass substrate on the absorption efficiency of organic solar cells (OSCs) at oblique incidence. The light propagation in the mixed incoherent glass substrate and coherent multilayer is calculated based on the transfer matrix method with a simple correction factor, which is derived at oblique incidence by taking multiple reflections inside the glass substrate. The validity of the proposed method is demonstrated by comparing the calculation results with those obtained by the generalized transfer matrix method. We investigate how the multiple reflections within the incoherent glass substrate affect the light absorption efficiency of thin-film OSCs, depending on the incidence angle and polarization.

Effect of the active-layer thickness on the short-circuit current analyzed using the generalized transfer matrix method

The effect of the active-layer thickness on the short-circuit current of organic solar cells (OSCs) was numerically investigated using a new optical modeling approach, the generalized transfer matrix method, where the optical interaction of an incoherent glass substrate with coherent layers is analyzed with simple matrix forms. The effect of the optical-spacer thickness on the spatial distribution of the electric-field intensity, time-averaged Poynting vector, and absorptivity was calculated. By incorporating the spectral absorptance with the solar irradiance, the short-circuit current was obtained at various thicknesses of the poly(3-hexylthiophene):phenyl-C61-butyric acid methyl ester (P3HT:PCBM) active layer to show how the variation of the P3HT:PCBM active-layer thickness affects the performance of the OSC.

Dynamic analyses of multilayered poroelastic media using the generalized transfer matrix method

Since the generalized transfer matrix method overcomes the intrinsic instability of the Thomson–Haskell transfer matrix method for both high frequencies and/or thick layers, it can produce stable and accurate solutions for the dynamic analysis of viscoelastic media as well as anisotropic media. This paper extends the generalized transfer matrix method to the dynamic analysis of multilayered poroelastic media. Main improvements include the presentation of the concisely explicit general solutions for the dynamic analysis of multilayered poroelastic media and the derivation of an analytical inversion of 8×8 order layer matrix corresponding to the general solutions. The explicit solutions are valid for the dynamic analysis of one-dimensional, two-dimensional and three-dimensional poroelastic medium problems. In addition, an efficient recursive scheme is proposed for accurate determination of the equivalent interface sources for multilayered poroelastic media due to excitation by a source at an arbitrary depth. For the dynamic analysis of multilayered poroelastic media, the generalized transfer matrix method recursively transfers both the interface stiffness matrix and equivalent source starting from the bottom half space to the top layer, without resort to the numerical solution of the assembled global equations as the exact stiffness matrix method does. While keeping the simplicity of the Thomson–Haskell transfer matrix method, the generalized transfer matrix method is both accurate and stable. The related numerical examples have demonstrated that the generalized transfer matrix method is an alternative approach to conducting the dynamic analysis of multilayered poroelastic media.

Optical characterization of free electron concentration in heteroepitaxial InN layers using Fourier transform infrared spectroscopy and a 2 × 2 transfer-matrix algebra

Fourier Transform Infrared (FTIR) reflectance spectroscopy has been implemented as a non-destructive, non-invasive, tool for the optical characterization of a set of c-plane InN single heteroepitaxial layers spanning a wide range of thicknesses (30–2000 nm). The c-plane (0001) InN epilayers were grown by plasma-assisted molecular beam epitaxy (PAMBE) on GaN(0001) buffer layers which had been grown on Al2O3(0001) substrates. It is shown that for arbitrary multilayers with homogeneous anisotropic layers having their principal axes coincident with the laboratory coordinates, a 2 × 2 matrix algebra based on a general transfer-matrix method (GTMM) is adequate to interpret their optical response. Analysis of optical reflectance in the far and mid infrared spectral range has been found capable to discriminate between the bulk, the surface and interface contributions of free carriers in the InN epilayers revealing the existence of electron accumulation layers with carrier concentrations in mid 1019 cm−3 at both the InN surface and the InN/GaN interface. The spectra could be fitted with a three-layer model, determining the different electron concentration and mobility values of the bulk and of the surface and the interface electron accumulation layers in the InN films. The variation of these values with increasing InN thickness could be also sensitively detected by the optical measurements. The comparison between the optically determined drift mobility and the Hall mobility of the thickest sample reveals a value of rH = 1.49 for the Hall factor of InN at a carrier concentration of 1.11 × 1019 cm−3 at 300° Κ.

Transfer Matrix Method to Vibration Analysis of Rotors with Coupler Offsets

In this paper a general transfer matrix method (TMM) for rotors containing global and local coupler offset was derived. Rotor response due to imbalances and offsets are then studied via the developed method. The studies showed both global and local offsets played as an external excitation that is a combined effect of all the elements behind the offset. Differences between global offset and local offset were compared and the results showed both types basically retain the same mode patterns but different jumps at the offset. The global offset, yet, imposed more significant dynamic effects since all the offsets accumulate thereafter. The whirling orbits in front and behind the offset were illustrated as well. The results, as expected, showed global offset appeared much larger radii especially after offset. The rotor's whirling orientation reversed, as rotation fell within a certain range and this feature was not changed by offsets. The TMM proposed by this study can be well applied to multiple global and local offsets.

Transfer Matrix Method to Vibration Analysis of Rotors with Coupler Offsets

In this paper a general transfer matrix method (TMM) for rotors containing global and local coupler offset was derived. Rotor response due to imbalances and offsets are then studied via the developed method. The studies showed both global and local offsets played as an external excitation that is a combined effect of all the elements behind the offset. Differences between global offset and local offset were compared and the results showed both types basically retain the same mode patterns but different jumps at the offset. The global offset, yet, imposed more significant dynamic effects since all the offsets accumulate thereafter. The whirling orbits in front and behind the offset were illustrated as well. The results, as expected, showed global offset appeared much larger radii especially after offset. The rotor's whirling orientation reversed, as rotation fell within a certain range and this feature was not changed by offsets. The TMM proposed by this study can be well applied to multiple global and local offsets.

Generalized transfer matrix method for propagation of surface waves in layered azimuthally anisotropic half-space

SUMMARY This paper presents a systematic and efficient method, namely the generalized transfer matrix method, for evaluating the dispersion curves and eigenfunctions of surface waves in multilayered azimuthally anisotropic half-space. Apart from avoiding the well-known numerical difficulties associated with the existing Thomson–Haskell method, the generalized transfer matrix method possesses the robust determination of independent polarization vectors by using the singular value decomposition (SVD) approach, the explicit inversion of the 6 × 6 eigencolumn matrix without any resort to numerical inversion and the efficient computation of eigenfunctions for layered azimuthally anisotropic media. By means of straightforward transformations, the generalized transfer matrix method leads to a twofold recursive algorithm: (1) for the recursive computation of phase velocities it starts from the bottom half-space to the top layer and (2) for the recursive solution of eigenfunctions it starts from the top layer to the bottom half-space. While keeping the simplicity of the Thomson–Haskell transfer matrix method, the generalized transfer matrix method is of unconditional stability and computational efficiency. The related numerical examples demonstrate that the generalized transfer matrix method is a powerful and robust tool for simulating the propagation of elastic surface waves in the layered azimuthally anisotropic half-space.

NONRECIPROCAL MULTIFERROIC SUPERLATTICES WITH BROKEN PARITY SYMMETRY

Multiferroic materials are characterized by the coexistence of ferroelectric and ferromagnetic (or antiferromagnetic) orders, the coupling to lattice vibration can be invoked either through piezoelectric or piezomagnetic effects. In this paper, the polaritonic band structures of multiferroic superlattices composed of oppositely polarized domains are investigated using the generalized transfer matrix method. For the primitive cell with broken parity symmetry, the polaritonic band structure is asymmetrical with respect to the forward and backward propagation directions (nonreciprocality). In particular, the band extreme points move away from the Brillouin zone center. This asymmetry in band-gap positions and widths can be used to design compact one-way optical isolators, while the extremely slow light velocities near the asymmetrical upper edges of lower bands includes the essential ingredients for designing slow light devices.

Optical Modeling and Analysis of Organic Solar Cells with Coherent Multilayers and Incoherent Glass Substrate Using Generalized Transfer Matrix Method

We present optical modeling and physical analysis results of thin-film organic solar cells (OSCs) based on a generalized transfer matrix method, which can calculate, with a simple matrix form, the mixed coherent and incoherent interaction of an incoherent glass substrate with other coherent layers. The spatial distribution of the electric field intensity, power density, and power dissipation are calculated in both coherent and incoherent layers with respect to the optical spacer thickness. By decomposing the power density and power dissipation into forward-propagating, backward-propagating, and their interference components, we demonstrate that the dependence of the spacer thickness on the total device reflectance plays an important role in determining the light absorption efficiency of the OSC.

Optical Modeling and Analysis of Organic Solar Cells with Coherent Multilayers and Incoherent Glass Substrate Using Generalized Transfer Matrix Method

We present optical modeling and physical analysis results of thin-film organic solar cells (OSCs) based on a generalized transfer matrix method, which can calculate, with a simple matrix form, the mixed coherent and incoherent interaction of an incoherent glass substrate with other coherent layers. The spatial distribution of the electric field intensity, power density, and power dissipation are calculated in both coherent and incoherent layers with respect to the optical spacer thickness. By decomposing the power density and power dissipation into forward-propagating, backward-propagating, and their interference components, we demonstrate that the dependence of the spacer thickness on the total device reflectance plays an important role in determining the light absorption efficiency of the OSC.

Generalized transfer matrix theory of electronic transport through a graphene waveguide

In the effective mass approximation, electronic property in graphene can be characterized by the relativistic Dirac equation. Within such a continuum model we investigate the electronic transport through graphene waveguides formed by connecting multiple segments of armchair-edged graphene nanoribbons of different widths. By using appropriate wavefunction connection conditions at the junction interfaces, we generalize the conventional transfer matrix approach to formulate the linear conductance of the graphene waveguide in terms of the structure parameters and the incident electron energy. In comparison with the tight-binding calculation, we find that the generalized transfer matrix method works well in calculating the conductance spectrum of a graphene waveguide even with a complicated structure and relatively large size. The calculated conductance spectrum indicates that the graphene waveguide exhibits a well-defined insulating band around the Dirac point, even though all the constituent ribbon segments are gapless. We attribute the occurrence of the insulating band to the antiresonance effect which is intimately associated with the edge states localized at the shoulder regions of the junctions. Furthermore, such an insulating band can be sensitively shifted by a gate voltage, which suggests a device application of the graphene waveguide as an electric nanoswitch.

Depth profiling of ion implanted materials with skewed doping distributions using Fourier transform infrared spectroscopy

The applicability of a general transfer-matrix method for optical analysis of multilayers reported earlier [Katsidis and Siapkas, Appl. Opt. 41, 3978 (2002)] is being extended so as to simulate asymmetric implantation doping profiles using distributions with four moments. The sensitivity of infrared reflectance spectra regarding the variation of the first four moments of a Pearson free carrier distribution is demonstrated. Experimental data of 1.5 MeV as well as 2.5 MeV As implantation into p-Si followed by annealing at 1100 degrees C are presented, suggesting the need to use two joined Pearson IV distribution segments in the simulation of annealed profiles. A twin peak observed in the 1.5 MeV case is confirmed by Rutherford backscattering analysis.

Modeling and design methodology for metal-insulator-metal plasmonic Bragg reflectors

In this paper, we present a modeling and design methodology based on characteristic impedance for plasmonic waveguides with Metal-Insulator-Metal (MIM) configuration. Finite-Difference Time-Domain (FDTD) simulations indicate that the impedance matching results in negligible reflection at discontinuities in MIM heterostructures. Leveraging the MIM impedance model, we present a general Transfer Matrix Method model for MIM Bragg reflectors and validate our model against FDTD simulations. We show that both periodically stacked dielectric layers of different thickness or different material can achieve the same performance in terms of propagation loss and minimum transmission at the central bandgap frequency in the case of a finite number of periods.

Ising Model on an Infinite Ladder Lattice

In this paper we propose an Ising model on an infinite ladderlattice, which is made of two infinite Ising spin chains with interactions.It is essentially a quasi-one-dimessional Ising model because the length ofthe ladder lattice is infinite, while its width is finite. We investigatethe phase transition and dynamic behavior of Ising model on thisquasi-one-dimessional system. We use the generalized transfer matrix method toinvestigate the phase transition of the system. It is found that there is nononzero temperature phase transition in this system. At the same time, weare interested in Glauber dynamics. Based on that, we obtain the timeevolution of the local spin magnetization by exactly solving a set of masterequations.

Study of the phonon–polaritons in piezomagnetic superlattices using a generalized transfermatrix method

Piezomagnetic materials are characterized by strong coupling between magnetization andacoustic vibration and the piezomagnetic coefficients change sign with respect todomain polarization. For piezomagnetic superlattices (PMSL) with periodically upand down polarized domain structures, the piezomagnetic coefficients aremodulated periodically, and the resulting phonon–polaritons form a band-likestructure. This study, using the generalized transfer matrix method, shows thata polariton-like band-gap can be realized in piezomagnetic material with the6mm point group under a certain configuration of magnetic field, lattice displacement anddomain polarization, but the mid-gap frequency is restricted to the range of a few GHz orbelow if the domain wall effect is taken into consideration.