Systematic design of antireflection coating for semi-infinite one-dimensional photonic crystals using Bloch wave expansion

Ushida, Jun; Tokushima, Masatoshi; Shirane, Masayuki; Yamada, Hirohito

doi:10.1063/1.1534936

Cited by 42 publications

(18 citation statements)

References 19 publications

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“…On the other hand, a 1D rugate profile composed of periodically located Gaussian peaks was considered in [10] as an EBG structure. The behaviour of the transmittance and reflectance of such a profile is characterized, at least in part, by the same features as that of conventional 1D PBG/EBG structures, which are associated with piecewise-homogeneous (layered) materials, as well as that of structures which consist of periodically located mismatched layers showing a graded permittivity profile within any period (see, for example, [11][12][13]). …”

Section: Introductionmentioning

confidence: 92%

Reflections from almost‐periodic graded anisotropic slabs

Serebryannikov

Schuenemann

2006

Micro & Optical Tech Letters

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finite-element simulation tools for high-frequency design, http://www.ansoft.com. ABSTRACT:Results are presented for plane-wave reflection from a 1D inhomogeneous anisotropic slab with components of the permittivity tensor obtained for a periodical arrangement of a finite number of Gaussian peaks, which results in an almost periodic profile. The interrelationship between the presence of band gaps (opaque ranges) in the transmission of left-and right-hand polarized waves and the behaviour of two orthogonal components of the transverse electric field is demonstrated. It is shown that there are several typical scenarios with regard to the behaviour of these components and the related polarization conversion, which depend on the frequency range and on the type of the host medium. A Riccati differential equation is used for the calculations. The obtained results can be used to extend the potentials of polarization control.ABSTRACT: Polypyrrole/poly (vinyl chloride) semi-interpenetrating networks of different compositions are prepared using ammonium per sulfate initiator at room temperature in pellet form and film form and their dielectric properties are studied at different microwave frequencies. An HP 8510 Vector network analyzer interfaced with a computer is used. The cavity-perturbation technique is employed for the study.

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Section: Introductionmentioning

confidence: 92%

Reflections from almost‐periodic graded anisotropic slabs

Serebryannikov

Schuenemann

2006

Micro & Optical Tech Letters

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“…2 Several studies about the electromigration of flip-chip solder joints have been reported. [3][4][5][6][7][8][9][10] Current crowding especially has a strong effect at the entrance spot of the Al trace into the solder joint, and it is thus the main factor responsible for the failure near the chip/anode side in most solder joints. 4,5 However, the Joule heating effect also occurs during accelerated electromigration tests.…”

Section: Introductionmentioning

confidence: 99%

“…4,5 However, the Joule heating effect also occurs during accelerated electromigration tests. [6][7][8][9][10] The temperature increase due to the Joule heating effect can be over 30 C when a solder bump is stressed by a 1.0 A current. [5][6][7] Therefore, the Cu column under-bump-metallization (UBM), a structure with a thick UBM, was developed in order to alleviate both the current crowding and the Joule heating effect in flip-chip solder joints under normal operating conditions.…”

Section: Introductionmentioning

confidence: 99%

Influence of Cu column under-bump-metallizations on current crowding and Joule heating effects of electromigration in flip-chip solder joints

Liang

Tsao

Chen

et al. 2012

Journal of Applied Physics

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The electromigration behavior of SnAg solder bumps with and without Cu column under-bumpmetallizations (UBMs) has been investigated under a current density of 2.16 Â 10 4 A/cm 2 at 150 C. Different failure modes were observed for the two types of samples. In those without Cu column UBMs, when SnAg solder bumps that had implemented 2 lm Ni UBMs were current stressed at 2.16 Â 10 4 A/cm 2 , open failure occurred in the bump that had an electron flow direction from the chip side to the substrate side. However, in those with Cu column UBMs, cracks formed along the interface of Cu 6 Sn 5 intermetallic compounds and the solder on the substrate side in the Sn-3.0Ag-0.5Cu solder bump that had an electron flow direction from the substrate side to the chip side. A three-dimensional simulation of the current density distribution was performed in order to obtain a better understanding of the current crowding behavior in solder bumps. The current crowding effect was found to account for the void formation on both the chip and the substrate side for the two kinds of solder bumps. One more important finding, as confirmed by infrared microscopy, is that the alleviation of current crowding by Cu column UBMs also helped decrease the Joule heating effect in solder bumps during current stressing. Therefore, the measured failure time for the solder joints with Cu column UBMs appears to be much longer than that of the ones with the 2 lm Ni UBMs. V

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“…where J is an integer, and λ is the wavelength of incident light in a vacuum [15], [16]. Hence, the wavelength of minimum reflectivity is 4n AR t when J is zero.…”

Section: Optical Properties Of Tso Filmsmentioning

confidence: 99%

“…To investigate the AR characteristics of TSO films, TSO (1, 2), (1, 1), (2, 1), and (3, 1) films were each deposited on an Si substrate. Figure 3(b) shows the reflection spectra of TSO/Si samples, where the minimum reflectivity is nearly zero for all samples.When an AR coating layer with thickness t and index of refraction n AR is placed on a substrate with an index of refraction n sub , the reflectivity would be zero for normal incident light when the following conditions are satisfied:where J is an integer, and λ is the wavelength of incident light in a vacuum [15], [16]. Hence, the wavelength of minimum reflectivity is 4n AR t when J is zero.…”

mentioning

confidence: 99%

Optical and Electrical Properties of Ti&lt;SUB&gt;x&lt;/SUB&gt;Si&lt;SUB&gt;1-x&lt;/SUB&gt;O&lt;SUB&gt;y&lt;/SUB&gt; Films

Lim¹,

Yun²,

Kim³

2009

ETRI J

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Manuscript received May 19, 2009; revised Sept. 29, 2009; accepted Oct. 9, 2009 I. IntroductionTiO 2 has attracted attention due to its high dielectric constant (κ) and high refractive index (n). However, TiO 2 has disadvantages of a high leakage current and a low crystallization temperature below 400°C [1]. One way of overcoming these problems is fabricating a mixture of TiO 2 and a low κ material, such as SiO 2 and Al 2 O 3 [2]. It is expected that a mixed material like Ti x Si 1-x O y (TSO) film will show improved leakage current and breakdown voltage. If the compositions of the mixture are controlled accurately, the dielectric constant and refractive index can be tailored, which will be useful in fabricating optical and electronic devices. Plasma-enhanced atomic layer deposition (PEALD) is a powerful method to deposit thin films with precise controls of the mixed material composition and film thickness [2], [3]. Tailoring the refractive index and film thickness provides many advantages, particularly in the fabrication of antireflection (AR) coating films used as solar cells. In the field of thin film solar cells, AR coating with the designed optical thickness (a product of refractive index and film thickness) is required to enhance solar cell efficiency [4], [5]. High κ materials such as TiO 2 and ZnO have been used as AR coated films in Si thin film solar cells [6]-[8]. However, ZnO shows a photo induced variation of electrical properties under visible illumination [9].Multilayer AR coating with refractive index variation effectively enhances the solar cell efficiency [10], [11]. Precise control of the optical thickness of TSO films grown using PEALD will be useful for the light-capturing structure of thin film solar cells.To secure a wide refractive index range, a low n material (such as SiO 2 and Al 2 O 3 ) and a high n material (such as TiO 2 ) should be selected to fabricate an AR coating for a thin film solar cell. In this study, 4 ], respectively. The formation of one cycle for SiO 2 is TEOS/source purge (SP)/O 2 gas (plasma)/reactant gas purge (RP), and that for TiO 2 is TTIP/SP/O 2 gas (plasma)/RP. The plasma power density was about 0.4 W/cm 2 , and the plasma was turned on only during the supply of O 2 reactant gas. The purging gas was Ar, and the reactant gases were O 2 +Ar. The formation of one cycle for the TSO film is N Ti subcycles of TiO 2 , and N Si subcycles of SiO 2 , which designates the cycle coordinates (N Ti , N Si ).For example, TSO (1, 2) designates one cycle of TiO 2 and two cycles of SiO 2 [13]. TSOs of (1, 2), (1, 1), (2, 1), and (3, 1) were fabricated; thus, the Ti content varied with the cycle coordinates. To obtain reflection spectra curves, TSO films were deposited on a p-type Si (100) wafer as shown in Fig. 1(a), and for I-V measurement, a metal/TSO/ITO/glass structure was fabricated as shown in Fig. 1(b). The I-V measurement was performed with a voltage mode, which means that voltages were supplied and then currents were measured. In addition, the I-V curves were measured ...

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Systematic design of antireflection coating for semi-infinite one-dimensional photonic crystals using Bloch wave expansion

Cited by 42 publications

References 19 publications

Reflections from almost‐periodic graded anisotropic slabs

Reflections from almost‐periodic graded anisotropic slabs

Influence of Cu column under-bump-metallizations on current crowding and Joule heating effects of electromigration in flip-chip solder joints

Optical and Electrical Properties of Ti&lt;SUB&gt;x&lt;/SUB&gt;Si&lt;SUB&gt;1-x&lt;/SUB&gt;O&lt;SUB&gt;y&lt;/SUB&gt; Films

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Systematic design of antireflection coating for semi-infinite one-dimensional photonic crystals using Bloch wave expansion

Cited by 42 publications

References 19 publications

Reflections from almost‐periodic graded anisotropic slabs

Reflections from almost‐periodic graded anisotropic slabs

Influence of Cu column under-bump-metallizations on current crowding and Joule heating effects of electromigration in flip-chip solder joints

Optical and Electrical Properties of Ti&amp;lt;SUB&amp;gt;x&amp;lt;/SUB&amp;gt;Si&amp;lt;SUB&amp;gt;1-x&amp;lt;/SUB&amp;gt;O&amp;lt;SUB&amp;gt;y&amp;lt;/SUB&amp;gt; Films

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Optical and Electrical Properties of Ti<SUB>x</SUB>Si<SUB>1-x</SUB>O<SUB>y</SUB> Films