Escape Probability Of Photons Research Articles

The Escape Probability of Photons Emitted in a Spherical Homogeneous Shell

We present a general expression for calculating the escape probability of photons from a dusty homogeneous spherical shell.

Light Extraction Efficiency Enhancement of White Organic Light-Emitting Diodes (OLEDs) by Micro/Nano-Patterning the Substrate Layer

We demonstrate the enhancement of light extraction efficiency of surface-emitting white Organic Light Emitting Diodes (OLEDs) by incorporating micro/nano-metric structures on the outer surface of the 3-layer substrate (SiO2-Si3N4-SiO2). To enhance light extraction efficiency of the OLEDs, various light scattering structures including plano-convex & plano-concave micro-lens array, flat-top & round-top nano-pillars array, and wavy structures were engraved on the outer surface of the substrate layer. For optimization, we varied the thickness of the internal layers of the OLEDs, and height, width, period, and radius of the micro/nano-scale structures. The performance of the micro/nano-structured OLEDs was simulated and analyzed using Lumerical FDTD and GPVDM simulators. We examined the far field light intensity, transmitted power, angular distribution of light, photon escape probability, photon density, internal & external quantum efficiency, and current-voltage curve of the designed OLEDs. We investigated the results in different locations, especially after the substrate layer: Far Field-1 (0 μm), and Far Field-2 (2.5 μm). Compared to conventional OLEDs, the micro/nano-structured OLEDs showed higher external quantum efficiency. The highest external quantum efficiency of 67.304% (Far Field-1) was detected in the round-top nano-pillars array engraved white OLED having structure period of 1.2 μm. We strongly believe that, the proposed micro/nano-structured white OLEDs are suitable for lighting applications.

Optimization of the efficiency of a nanowire solar cell by nanowire tapering

Thermodynamics shows that the open-circuit voltage (Voc) of a solar cell is dependent on the external radiative efficiency at Voc. In planar solar cells with low photon recycling probability, this efficiency is limited to 2% due to total internal reflection of the emitted light, providing a penalty of 101 mV to the Voc. Tapered nanowire solar cells allow for an adiabatic expansion of the guided optical mode into air, allowing to reduce this loss. For this purpose, we first perform simulations of the photon escape probability in tapered nanowires with both finite difference time domain simulations as well as with rigorous coupled-wave analysis, showing photon escape probabilities up to 47.2% for normally tapered nanowires and up to 92% for inversely tapered nanowires. We subsequently show that by fine tuning the recipe for reactive ion etching of the tapered InP nanowires, we can decrease the nanowire tapering angle from 4.5° down to 1.8°, allowing to significantly increase the measured external radiative efficiency. We finally observe an open-circuit voltage of 0.746 V at a tapering angle of 2.46°.

Enhanced Light Extraction of Infrared AlGaAs-Based LEDs With Micron Array

In order to improve the light extraction efficiency (LEE) of a plane AlGaAs-based LED (Device A), three different surface periodic micron-scale arrays, micron pillar (Device B), micron truncated cone (Device C) and micron cone (Device D), are prepared by the conventional ultra-violet (UV) lithography. The morphology of the three devices B–D is characterized by a scanning electron microscopy (SEM). The periodic array structures improve the photon escape probabilities. In comparison to the Device A, the light output powers (LOPs) of the Devices B–D increase 54.0%, 145.5% and 157.2% at an injection current of 500 mA, respectively. Moreover, we use the Monte Carlo ray-tracing method to simulate the LEE of the four devices. The energy distribution of the Devices B-D is more concentrated in the middle region in contrast with the Device A.

TeO2 for enhancing structural, mechanical, optical, gamma and neutron radiation shielding performance of bismuth borosilicate glasses

The synthesized 12Bi2O3– 8BaO–12ZnO-0.5CeO2-17.5SiO2- (50-x) B2O3- xTeO2 glasses with x = 0, 10, 20, 30 and 40 mol% (coded BiTe-0 to BiTe-40) were investigated in terms of physical, structural, optical and mechanical properties to examine the influence of CeO2 and TeO2 on the heavy metal oxide (HMO) borosilicate network. Density values increased continuously with increasing TeO2 concentration with BiTe-40 glass exhibiting maximum value of 5.0875 gcm−3. This property helped in enhancement of refractive index values from 1.769 for BiTe-0 to 1.942 for BiTe-40. Fourier transform infrared (FTIR) analysis of studied glasses revealed the presence of additional small peak at 683 cm−1 in BiTe-30 and BiTe-40 which confirmed the formation of stable TeO4 units in the glass network. The deep brown colour of the glass existing due to bismuth's presence was nullified by CeO2 and TeO2 additives which improved transparency of the glass. Urbach analysis of these glasses led to optical bandgap variation between 3.27 eV and 2.73 eV for 0–40 mol% TeO2 concentration. Makishima and Mackenzie model was utilized for evaluation of elastic property of the glasses, and Poisson's ratio ranging between 1.935 and 1.953 was obtained. Vickers micro-indentation test on the current glasses revealed decreasing microhardness from 4.116 to 4.076 GPa with TeO2 variation from 0 to 40 mol% at 9.8 N load. Gamma radiation shielding parameters were determined using Phy-X/PSD software and it was found that BiTe-40 glass produce maximum MAC (mass attenuation co-efficient) values in high photon energy region 3.5–15 MeV. The present article also contains a detailed emphasis on behaviour of gamma radiation build-up factors at different incident photon energy and TeO2 concentration. The increasing trend of exposure build up factor (EBF) was seen with increasing penetration depth inside the samples at all energies, indicating that glasses of larger thickness improve the escape probability of photons. Meanwhile, fast neutron removal cross-section (FNRCS) was highest for BiTe-10 sample (0.10118 cm−1) which also surpassed the value of ordinary concrete (0.093 cm−1). Overall, the present glass system bested other conventional shields available commercially in terms of gamma and neutron radiation shielding effectiveness.

Photon emission from inside the innermost stable circular orbit

We consider a situation where a light source orbiting the innermost stable circular orbit (ISCO) of the Kerr black hole is gently falling from the marginally stable orbit due to an infinitesimal perturbation. Assuming that the light source emits photons isotropically, we show that the last radius at which more than 50\% of emitted photons can escape to infinity is approximately halfway between the ISCO radius and the event horizon radius. To evaluate them, we determine emitter orbits from the vicinity of the ISCO, which are uniquely specified for each black hole spin, and identify the conditions for a photon to escape from any point on the equatorial plane of the Kerr spacetime to infinity by specifying regions in the two-dimensional photon impact parameter space completely. We further show that the proper motion of the emitter affects the photon escape probability and blueshifts the energy of emitted photons.

Photon emission from circular equatorial Kerr orbiters

We consider monochromatic and isotropic photon emission from circular equatorial Kerr orbiters. We derive analytic expressions for the photon escape probability and the redshift-dependent total flux collected on the celestial sphere as a function of emission radius and black hole parameters. These calculations crucially involve the critical curve delineating the region of photon escape from that of photon capture in each emitter's sky. This curve generalizes to finite orbital radius the usual Kerr critical curve and displays interesting features in the limit of high spin, which we investigate by developing a perturbative expansion about extremality. Although the innermost stable circular orbit appears to approach the event horizon for very rapidly spinning black holes, we find in this regime that the photon escape probability tends to $5/12+1/(\sqrt{5}\pi)\arctan\sqrt{5/3}\approx54.65\%$. We also obtain a simple formula for the flux distribution received on the celestial sphere, which is nonzero. This confirms that the near-horizon geometry of a high-spin black hole is in principle observable. These results require us to introduce a novel type of near-horizon double-scaling limit. We explain the dip observed in the total flux at infinity as an imprint of the black hole: the black hole "bite".

Revealing the internal luminescence quantum efficiency of perovskite films via accurate quantification of photon recycling

The internal luminescence quantum efficiency ($Q_\mathrm{i}^\mathrm{lum}$) provides an excellent assessment of the optoelectronic quality of semiconductors. To determine $Q_\mathrm{i}^\mathrm{lum}$ of perovskite films from the experimentally accessible external luminescence quantum efficiency ($Q_\mathrm{e}^\mathrm{lum}$) it is essential to account for photon recycling, and this requires knowledge of the photon escape probability ($p_\mathrm{e}$). Here, we establish an analysis procedure based on a curve fitting model that accurately determines $p_\mathrm{e}$ of perovskite films from photoluminescence (PL) spectra measured with a confocal microscope and an integrating sphere setup. We show that scattering-induced outcoupling of initially-trapped PL explains commonly observed red-shifted and broadened PL spectral shapes and leads to $p_\mathrm{e}$ being more than 10% higher in absolute terms compared to earlier assumptions. Applying our model to CH$_3$NH$_3$PbI$_3$ films with exceptionally high $Q_\mathrm{e}^\mathrm{lum}$ up to 47.4% sets a real benchmark for $Q_\mathrm{i}^\mathrm{lum}$ at $78.0 \pm 0.5\%$, revealing there is beyond a factor of two more scope for reducing non-radiative recombination than previously thought.

Nanowire Solar Cell Above the Radiative Limit

AbstractA lossless solar cell operating at the Shockley–Queisser limit generates an open circuit voltage (Voc) equal to the radiative limit. At Voc, the highly directional beam of photons from the sun is absorbed and subsequently externally re‐emitted into a 4π solid angle, providing a large photon entropy loss. A solar cell can beat the Shockley–Queisser limit and approach the 46.7% ultimate limit by decreasing the output solid angle of the light emission at open circuit conditions. Here, a design for an indium phosphide single nanowire solar cell capable to operate 159 mV above the radiative limit is presented. The spontaneous emission factor is first optimized into a guided mode of the nanowire toward 68%. The authors subsequently launch a guided mode at the bottom straight part of the tapered nanowire yielding a photon escape probability of 81% for a tapering angle of θ = 1.2° and a top facet with a radius of 83 nm. When assuming homogeneous light emission along the nanowire, an outcoupling efficiency of 42% of the emitted light is obtained. The final optimization is the reduction of the emission cone toward 11 × 10−3 sr by focusing the guided mode with an external lens.

Escape probability of a photon emitted near the black hole horizon

We investigate the escape of photons from the vicinity of the horizon to infinity in the Kerr-Newmann black hole spacetime. We assume that a light source is at rest in a locally nonrotating frame and photons are emitted isotropically. Then, we evaluate the escape probability of the emitted photons. The main result of this paper is the following. If the black hole is extremal with the nondimensional spin parameter $a_*> 1/2$, however close to the horizon the light source would be, the escape probability remains nonzero. The near-horizon limit value of the escape probability is a monotonically increasing function of $a_*$ and takes a maximum $\sim$29.1\% at $a_*=1$, i.e., for the extremal Kerr case. On the other hand, if the black hole is extremal with $0\leq a_*\leq 1/2$ or if the black hole is subextremal, the near-horizon limit value is zero.

Deformation of the emission line profile of optically dense spherical plasma caused by rotation of substance

The transfer of resonance radiation in optically dense spherical plasma, rotating around the axis of symmetry, is studied numerically. Frequency shifts in the red and blue wings of the spectrum, frequency broadening of the emission line profile and the absorption line profile, caused by the rotational broadening effect (RBE), are investigated for calcium plasma at the resonant transition with the wavelength of 397 nm. The RBE of absorption and emission lines is explained by broadening of the elementary ion absorption profiles which demonstrate the Doppler dependence on frequency. Location of the frequency of absorption maximum in broadband radiation transmitted through the plasma, as well as location of the frequencies of intensity maximum of the unreabsorbed emission line and intensity minimum of the reabsorbed emission line, unambiguously determine ray velocity of ions in the plasma. The RBE effect of the emission line leads to an increase in probability of photon escape from the medium. This circumstance is indirect evidence for the fact that Holstein’s effective deexcitation time for rotating plasma should decrease. Full width at half maximum (FWHM) of the emission spectrum for rotating plasma increases linearly with the growth of optical thickness of the medium. Measurement of the FWHM value can be a diagnostic method for determining concentration of ions in the plasma.

Quasi-Classical Description of the “Quantum Bottleneck” Effect for Thermal Relaxation of an Atom in a Resonator

We consider the escape of a photon from a single-mode optical cavity with a controlled variable intensity. The source of the photon is a relaxing two-level atom. The quantum bottleneck effect involves a counterintuitive decrease of the probability of photon escape from the cavity with the increase of its escape intensity. Numerical simulations of the process were carried out using the basic Lindblad quantum equation for the Jaynes-Cummings model with thermal relaxation. A quasi-classical description of the bottleneck mechanism is presented, similar to the Zeno effect. The counterintuitive behavior described plays an important role in the description of the exchange of single photons in nanosystems and in molecular complexes converting solar energy in bacteria.

Improvement of light extraction for AlGaN-based near UV LEDs with flip-chip bonding fabricated on grooved sapphire substrate using laser ablation

Mesh-textured flip-chip (FC) structures of AlGaN-based near ultraviolet-light-emitting diodes (NUV- LEDs) are fabricated using an Nd:YAG laser scriber. Compared with the output power of the reference FC-LEDs, those of conventional sapphire substrate (CSS) FC-LEDs and the patterned sapphire substrate FC-LEDs with laser-scribed mesh-textured backsides were improved by 28.7% and 7.2%, respectively. The CSS FC-LED is enhanced using the mesh-textured trench pattern attributable to an increase in the light-extraction efficiency resulting from an increase in the photon-escape probability due to enhanced light scattering at the trench-patterned-sapphire/air interface. Furthermore, the current–voltage curves depict that the laser scribing process does not adversely affect the electrical properties of the FC-LEDs. A Trace-Pro simulation revealed that the laser-scribed-trench CSS FC-LED is effective for light extraction.

Rigorous wave-optical treatment of photon recycling in thermodynamics of photovoltaics: Perovskite thin-film solar cells

The establishment of a rigorous theory on thermodynamics of light management in photovoltaics that accommodates various loss mechanisms as well as wave-optical effects in the absorption and reemission of light is at stake in this contribution. To this end, we propose a theoretical framework to calculate the open-circuit voltage enhancement resulting from photon recycling ($\Delta V^{\mathrm{PR}}_{\mathrm{oc}}$) with rigorous wave-optical treatment. It can be applied to both planar thin-film and nanostructured single-junction solar cells. We derive an explicit expression for $\Delta V^{\mathrm{PR}}_{\mathrm{oc}}$, which reveals its dependence on internal quantum luminescence efficiency, parasitic reabsorption, and on photon escape probabilities of reemmited photons. While the internal quantum luminescence efficiency is an intrinsic material property, both latter quantities can be determined rigorously for an arbitrary solar cell architecture by three-dimensional electrodynamic dipole emission calculations. We demonstrate the strengths and validity of our framework by determining the impact of photon recycling on the $V_{\mathrm{oc}}$ of a conventional planar organo-metal halide perovskite thin-film solar cell and compare it to established reference cases with perfect antireflection and Lambertian light scattering. Our calculations reveal $\Delta V^{\mathrm{PR}}_{\mathrm{oc}}$ values of up to 80 mV for the considered device stack in the absence of angular restriction and up to 240 mV when the escape cone above the cell is restricted to $\theta_{\mathrm{out}}=2.5^\circ$ around the cell normal. These improvements impose severe constraints on the parasitic absorption as a parasitic reabsorption probability of only 2\% reduces the $\Delta V^{\mathrm{PR}}_{\mathrm{oc}}$ to 100 mV for the same angular restriction. Our work here can be used to provide design guidelines.

Broadband light trapping strategies for quantum-dot photovoltaic cells (>10%) and their issues with the measurement of photovoltaic characteristics

Bandgap tunability and broadband absorption make quantum-dot (QD) photovoltaic cells (PVs) a promising candidate for future solar energy conversion systems. Approaches to improving the electrical properties of the active layer increase efficiency in part. The present study focuses on optical room for enhancement in QD PVs over wide spectrum in the near-infrared (NIR) region. We find that ray-optical light trapping schemes rather than the nanophotonics approach may be the best solution for enhancing broadband QD PVs by suppressing the escape probability of internal photons without spectral dependency. Based on the theoretical study of diverse schemes for various bandgaps, we apply a V-groove structure and a V-groove textured compound parabolic trapper (VCPT) to PbS-based QD PVs along with the measurement issues for PVs with a light scattering layer. The efficiency of the best device is improved from 10.3% to 11.0% (certified to 10.8%) by a V-groove structure despite the possibility of underestimation caused by light scattering in small-area devices (aperture area: 0.0625 cm2). By minimizing such underestimation, even greater enhancements of 13.6% and 15.6% in short circuit current are demonstrated for finger-type devices (0.167 cm2 without aperture) and large-area devices (2.10 cm2 with an aperture of 0.350 cm2), respectively, using VCPT.

A mid-infrared statistical investigation of clumpy torus model predictions

We present new calculations of the CAT3D clumpy torus models, which now include a more physical dust sublimation model as well as AGN anisotropic emission. These new models allow graphite grains to persist at temperatures higher than the silicate dust sublimation temperature. This produces stronger near-infrared emission and bluer mid-infrared (MIR) spectral slopes. We make a statistical comparison of the CAT3D model MIR predictions with a compilation of sub-arcsecond resolution ground-based MIR spectroscopy of 52 nearby Seyfert galaxies (median distance of 36 Mpc) and 10 quasars. We focus on the AGN MIR spectral index $\alpha_{MIR}$ and the strength of the 9.7 $\mu$m silicate feature $S_{Sil}$. As with other clumpy torus models, the new CAT3D models do not reproduce the Seyfert galaxies with deep silicate absorption ($S_{Sil}<-1$). Excluding those, we conclude that the new CAT3D models are in better agreement with the observed $\alpha_{MIR}$ and $S_{Sil}$ of Seyfert galaxies and quasars. We find that Seyfert 2 are reproduced with models with low photon escape probabilities, while the quasars and the Seyfert 1-1.5 require generally models with higher photon escape probabilities. Quasars and Seyfert 1-1.5 tend to show steeper radial cloud distributions and fewer clouds along an equatorial line-of-sight than Seyfert 2. Introducing AGN anisotropic emission besides the more physical dust sublimation models alleviates the problem of requiring inverted radial cloud distributions (i.e., more clouds towards the outer parts of the torus) to explain the MIR spectral indices of type 2 Seyferts.

InGaN-Based Light-Emitting Diodes Grown on a Micro/Nanoscale Hybrid Patterned Sapphire Substrate.

A hybrid patterned sapphire substrate (hybrid-PSS) was prepared using an anodic aluminum oxide etching mask to transfer nanopatterns onto a conventional patterned sapphire substrate with microscale patterns (bare-PSS). The threading dislocation (TD) suppression of light-emitting diodes (LEDs) grown on a hybrid-PSS (HP-LED) exhibits a smaller reverse leakage current compared with that of LEDs grown on a bare-PSS (BP-LED). The strain-free GaN buffer layer and fully strained InGaN active layer were evidenced by cross-sectional Raman spectra and reciprocal space mapping of the X-ray diffraction intensity for both samples. The calculated piezoelectric fields for both samples are close, implying that the quantum-confined Stark effect was not a dominant mechanism influencing the electroluminescence (EL) peak wavelength under a high injection current. The bandgap shrinkage effect of the InGaN well layer was considered to explain the large red-shifted EL peak wavelength under high injection currents. The estimated LED chip temperatures rise from room temperature to 150 °C and 75 °C for BP-LED and HP-LED, respectively, at a 600-mA injection current. This smaller temperature rise of the LED chip is attributed to the increased contact area between the sapphire and the LED structural layer because of the embedded nanopattern. Although the chip generates more heat at high injection currents, the accumulated heat can be removed to outside the chip effectively. The high diffuse reflection (DR) rate of hybrid-PSS increases the escape probability of photons, resulting in an increase in the viewing angle of the LEDs from 130° to 145°. The efficiency droop was reduced from 46% to 35%, effects which can be attributed to the elimination of TDs and strain relaxation by embedded nanopatterns. In addition, the light output power of HP-LED at 360-mA injection currents exhibits a ∼ 22.3% enhancement, demonstrating that hybrid-PSSs are beneficial to apply in high-power LEDs.

Opportunities and Limitations for Nanophotonic Structures To Exceed the Shockley-Queisser Limit.

Nanophotonic engineering holds great promise for photovoltaics, with several recently proposed approaches that have enabled efficiencies close to the Shockley-Queisser limit. Here, we theoretically demonstrate that suitably designed nanophotonic structures may be able to surpass the 1 sun Shockley-Queisser limit by utilizing tailored directivity of the scattering response of nanoparticles. We show that large absorption cross sections do not play a significant role in the efficiency enhancement, and on the contrary, directivity enhancement constitutes the nanoscale equivalent to concentration in macroscopic photovoltaic systems. Based on this principle, we discuss fundamental limits to the efficiency based on directivity bounds and a number of approaches to get close to these limits. We also highlight that, in practice, achieving efficiencies above the Shockley-Queisser limit is strongly hindered by whether high short-circuit currents can be maintained. Finally, we discuss how our results are affected by the presence of significant nonradiative recombination, in which case both directivity and photon escape probability should be increased to achieve voltage enhancement.

Ultrathin Epitaxial Silicon Solar Cells with Inverted Nanopyramid Arrays for Efficient Light Trapping.

Ultrathin c-Si solar cells have the potential to drastically reduce costs by saving raw material while maintaining good efficiencies thanks to the excellent quality of monocrystalline silicon. However, efficient light trapping strategies must be implemented to achieve high short-circuit currents. We report on the fabrication of both planar and patterned ultrathin c-Si solar cells on glass using low temperature (T < 275 °C), low-cost, and scalable techniques. Epitaxial c-Si layers are grown by PECVD at 160 °C and transferred on a glass substrate by anodic bonding and mechanical cleavage. A silver back mirror is combined with a front texturation based on an inverted nanopyramid array fabricated by nanoimprint lithography and wet etching. We demonstrate a short-circuit current density of 25.3 mA/cm(2) for an equivalent thickness of only 2.75 μm. External quantum efficiency (EQE) measurements are in very good agreement with FDTD simulations. We infer an optical path enhancement of 10 in the long wavelength range. A simple propagation model reveals that the low photon escape probability of 25% is the key factor in the light trapping mechanism. The main limitations of our current technology and the potential efficiencies achievable with contact optimization are discussed.

A NEW APPROACH TO DETERMINE OPTICALLY THICK H2COOLING AND ITS EFFECT ON PRIMORDIAL STAR FORMATION

We present a new method for estimating the H2 cooling rate in the optically thick regime in simulations of primordial star formation. Our new approach is based on the TreeCol algorithm, which projects matter distributions onto a spherical grid to create maps of column densities for each fluid element in the computational domain. We have improved this algorithm by using the relative gas velocities to weight the individual matter contributions with the relative spectral line overlaps, in order to properly account for the Doppler effect. We compare our new method to the widely used Sobolev approximation, which yields an estimate for the column density based on the local velocity gradient and the thermal velocity. This approach generally underestimates the photon escape probability because it neglects the density gradient and the actual shape of the cloud. We present a correction factor for the true line overlap in the Sobolev approximation and a new method based on local quantities, which fits the exact results reasonably well during the collapse of the cloud, with the error in the cooling rates always being less than 10%. Analytical fitting formulae fail at determining the photon escape probability after formation of the first protostar (error of ∼40%) because they are based on the assumption of spherical symmetry and therefore break down once a protostellar accretion disk has formed. Our method yields lower temperatures and hence promotes fragmentation for densities above ∼1010 cm−3 at a distance of ∼200 AU from the first protostar. Since the overall accretion rates are hardly affected by the cooling implementation, we expect Pop III stars to have lower masses in our simulations, compared to the results of previous simulations that used the Sobolev approximation.