Browsing by Issue Date, starting with "2017-06-25"

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Effects of substrate and annealing on GaN films grown by plasma-assisted molecular beam epitaxy
(2017-06-25)
Yang, Zu-Po
;
Tsou, Tsung-Han
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Lee, Chao-Yu
;
Kan, Ken-Yuan
;
Yu, Ing-Song
GaN films were deposited by plasma-assisted molecular beam epitaxy on different substrates, i.e. Si (111), Sapphire (0001) and 4H-SiC (0001) with 4 degrees of miscutting orientation. Due to the lattice mismatch between GaN films and substrates, the substrates profoundly affect the growth mechanism of GaN films on them during the epitaxy. The smooth and complete GaN films can be obtained on 4H-SiC substrates based on the analyses of reflection high energy electron diffraction, scanning electron microscopy and atomic force microscopy. Higher quality of GaN films on 4H-SiC was also confirmed by high resolution X-ray diffraction. Photoluminescence measurements show that the compress stress existed in GaN films grown on sapphire, but tensile stress was observed in the films grown on 4H-SiC and Si. Meanwhile, in-situ annealing treatment of post expitxy can remove Ga droplets on GaN films and decrease the surface roughness and defect density of GaN films; however, thermal decomposition on the surface of GaN films was observed in the characterizations of X-ray photoelectron spectroscopy. (C) 2016 Elsevier B.V. All rights reserved.
Performance of p-side-up thin-film AlGaInP light-emitting diodes with textured composite aluminum-doped zinc oxide transparent conductive layers
(2017-06-25)
Tseng, Ming-Chun
;
Wuu, Dong-Sing
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Chen, Chi-Lu
;
Lee, Hsin-Ying
;
Lin, Yu-Chang
Composite transparent conductive layers (TCLs) were deposited on the GaP window layer of p-side-up thin-film AlGaInP light-emitting diodes (LEDs) in order to enhance their light-extraction efficiency. The composite TCLs were fabricated from aluminum-doped zinc oxide (AZO) layers grown through atomic-layer deposition and pulsed-laser deposition. The results showed that wet-etching of composite AZO thin films improved the light extraction efficiency of the corresponding LED devices. The droop efficiencies of LEDs with flat AZO thin films, composite AZO thin films, and optimum textured composite AZO thin films were 29%, 30%, and 22%, respectively. LEDs with textured composite AZO layers exhibited favorable optoelectronic performance. When the injection current was increased from 20 to 1000 mA, the emission wavelengths of LEDs with flat AZO thin films, composite AZO thin films, and optimum textured composite AZO thin films shifted by 3, 5, and 3 nm, respectively. The optimum textured composite AZO thin film can not only improve LED performance but also effectively substitute flat TCLs in AlGaInP LED applications. (C) 2016 Elsevier B.V. All rights reserved.
Impact of repeated uniaxial mechanical strain on flexible a-IGZO thin film transistors with symmetric and asymmetric structures
(2017-06-26)
Liao, Po-Yung
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Chang, Ting-Chang
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Su, Wan-Ching
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Chen, Bo-Wei
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Chen, Li-Hui
This letter investigates repeated uniaxial mechanical stress-induced degradation behavior in flexible amorphous In-Ga-Zn-O thin-film transistors (TFTs) of different geometric structures. Two types of via-contact structure TFTs are investigated: symmetrical and UI structure (TFTs with Iand U-shaped asymmetric electrodes). After repeated mechanical stress, I-V curves for the symmetrical structure show a significant negative threshold voltage (VT) shift, due to mechanical stress-induced oxygen vacancy generation. However, degradation in the UI structure TFTs after stress is a negative VT shift along with the parasitic transistor characteristic in the forward-operation mode, with this hump not evident in the reverse-operation mode. This asymmetrical degradation is clarified by the mechanical strain simulation of the UI TFTs. Published by AIP Publishing.
Strain Coupling of Conversion-type Fe3O4 Thin Films for Lithium Ion Batteries
(2017-06-26)
Hwang, Sooyeon
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Meng, Qingping
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Chen, Ping-Fan
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Kisslinger, Kim
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Cen, Jiajie
Lithiation/delithiation induces significant stresses and strains into the electrodes for lithium ion batteries, which can severely degrade their cycling performance. Moreover, this electrochemically induced strain can interact with the local strain existing at solid-solid interfaces. It is not clear how this interaction affects the lithiation mechanism. The effect of this coupling on the lithiation kinetics in epitaxial Fe3O4 thin film on a Nb-doped SrTiO3 substrate is investigated. In situ and ex situ transmission electron microscopy (TEM) results show that the lithiation is suppressed by the compressive interfacial strain. At the interface between the film and substrate, the existence of LixFe(3)O(4) rock-salt phase during lithiation consequently restrains the film from delamination. 2D phase-field simulation verifies the effect of strain. This work provides critical insights of understanding the solid-solid interfaces of conversion-type electrodes.
Cooperative Polar/Steric Strategy in Achieving Site-Selective Photocatalyzed C(sp(3))-H Functionalization
(2017-06-27)
Yamada, Keiichi
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Fukuyama, Takahide
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Fujii, Saki
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Ravelli, Davide
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Fagnoni, Maurizio
Synergistic control over the S(H)2 transition states of hydrogen abstraction exploiting polar and steric effects provides a promising cooperative strategy for site-selective C(sp(3))-H functionalization using decatungstate anion photocatalysis. By using this photocatalytic approach, the C-H bonds of substituted lactones and cyclic ketones were functionalized selectively. In the remarkable case of 2-isoamyl 4-tert-butyl cyclohexanone (1t) bearing five methyl, five methylene, and three methine C-H bonds, one methine C-H bond in the isoamyl tether was selectively functionalized.
Characteristics of surface plasmon coupled quantum well infrared photodetectors
(2017-06-28)
Hsu, Wei-Cheng
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Ling, Hong-Shi
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Wang, Shiang-Yu
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Lee, Chien-Ping
;
電機學院
Quantum Well Infrared Photodetectors (QWIPs) with different structures were characterized for the study of surface plasmon wave coupling. Detailed comparisons between surface plasmon coupled and etched grating coupled devices were investigated. A bias dependence for the enhancement of the responsivity of surface plasmon coupled devices was found, especially for the samples with non-uniform quantum wells. The non-uniform QWIPs with surface plasmon coupling showed an asymmetric enhancement with respect to the bias directions. Stronger enhancements were shown under the biases when a higher effective electric field region is close to the collector. The change of the photocarrier escape probability due to the narrow coupling bandwidth of the surface plasmon wave is attributed to this unexpected bias dependence. Published by AIP Publishing.
Roles of nitrogen functionalities in enhancing the excitation-independent green-color photoluminescence of graphene oxide dots
(2017-06-28)
Teng, Chiao-Yi
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Ba-Son Nguyen
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Yeh, Te-Fu
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Lee, Yuh-Lang
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Chen, Shean-Jen
Fluorescent graphene oxide dots (GODs) are environmentally friendly and biocompatible materials for photoluminescence (PL) applications. In this study, we employed annealing and hydrothermal ammonia treatments at 500 and 140 degrees C, respectively, to introduce nitrogen functionalities into GODs for enhancing their green-color PL emissions. The hydrothermal treatment preferentially produces pyridinic and amino groups, whereas the annealing treatment produces pyrrolic and amide groups. The hydrothermally treated GODs (A-GODs) present a high conjugation of the nonbonding electrons of nitrogen in pyridinic and amino groups with the aromatic pi orbital. This conjugation introduces a nitrogen nonbonding (n(N 2p)) state 0.3 eV above the oxygen nonbonding state (n(O 2p) state; the valence band maximum of the GODs). The GODs exhibit excitation-independent green-PL emissions at 530 nm with a maximum quantum yield (QY) of 12% at 470 nm excitation, whereas the A-GODs exhibit a maximum QY of 63%. The transformation of the solvent relaxation-governed pi* -> n(O 2p) transition in the GODs to the direct pi* -> n(N 2p) transition in the A-GODs possibly accounts for the substantial QY enhancement in the PL emissions. This study elucidates the role of nitrogen functionalities in the PL emissions of graphitic materials and proposes a strategy for designing the electronic structure to promote the PL performance.
Reaction of H plus HONO in solid para-hydrogen: infrared spectrum of (ONH)-O-center dot(OH)
(2017-06-28)
Haupa, Karolina Anna
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Tielens, Alexander Godfried Gerardus Maria
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Lee, Yuan-Pern
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應用化學系
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應用化學系分子科學碩博班
Hydrogenation reactions in the N/O chemical network are important for an understanding of the mechanism of formation of organic molecules in dark interstellar clouds, but many reactions remain unknown. We present the results of the reaction H + HONO in solid para-hydrogen (p-H-2) at 3.3 K investigated with infrared spectra. Two methods that produced hydrogen atoms were the irradiation of HONO molecules in p-H-2 at 365 nm to produce OH radicals that reacted readily with nearby H-2 to produce mobile H atoms, and irradiation of Cl-2 molecules (co-deposited with HONO) in p-H-2 at 405 nm to produce Cl atoms that reacted, upon IR irradiation of the p-H2 matrix, readily with nearby H-2 to produce mobile H atoms. In both experiments, we assigned IR lines at 3549.6 (v(1)), 1465.0 (v(3)), 1372.2 (v(4)), 898.5/895.6 (v(6)), and 630.9 (v(7)) cm(-1) to hydroxy(oxido)-lambda(5)-azanyl radical [(ONH)-O-center dot(OH)], the primary product of HONO hydrogenation. Two weak lines at 3603.4 and 991.0 cm(-1) are tentatively assigned to the dihydroxy-lambda(5)-azanyl radical, N-center dot(OH)(2). The assignments were derived according to the consideration of possible reactions and comparison of observed vibrational wavenumbers and their IR intensities with values predicted quantum-chemically with the B3LYP/aug-cc-pVTZ method. The agreement between observed and calculated D/H- and N-15/N-14-isotopic ratios further supports these assignments. The role of this reaction in the N/O chemical network in dark interstellar clouds is discussed.
The dominant effect of non-centrosymmetric displacement on the crystal-field energy splitting in the strained a-plane ZnO epi-films on r-plane sapphires
(2017-06-28)
Wu, Yung-Chi
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Liu, Wei-Rein
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Chen, Hou-Ren
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Hsu, Chia-Hung
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Hsieh, Wen-Feng
The polarization-dependent photoluminescence (PL) of the a-plane ZnO (a-ZnO) films grown on r-plane sapphire substrates shows that the crystal-field energy splitting (Delta(CF)) becomes larger with increasing film thickness from 24 nm to 291 nm. In the use of the nonlinear fitting of the stress-strain tensor to the X-ray diffraction data, we found crystal symmetry breaking from wurtzite to monoclinic in these films and determined the corresponding lattice constants and the relaxed lattice constants. With the available lattice variables, we further used the tight-binding method to calculate the band energies and compared with the PL spectra. The results confirm that the crystal deformation and the non-centrosymmetric displacement had opposite effects on the Delta(CF) at the Gamma point and the displacement induced by the strain is the dominant effect on Delta(CF).
Unveiling the hidden nematicity and spin subsystem in FeSe
(2017-06-28)
Luo, Chih-Wei
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Cheng, Po Chung
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Wang, Shun-Hung
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Chiang, Jen-Che
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Lin, Jiunn-Yuan
The nematic order (nematicity) is considered as one of the essential ingredients to understand the mechanism of Fe-based superconductivity. In most Fe-based superconductors (pnictides), nematic order is reasonably close to the antiferromagnetic order. In FeSe, in contrast, a nematic order emerges below the structure phase transition at T-s = 90 K with no magnetic order. The case of FeSe is of paramount importance to a universal picture of Fe-based superconductors. The polarized ultrafast spectroscopy provides a tool to probe simultaneously the electronic structure and the magnetic interactions through quasiparticle dynamics. Here we show that this approach reveals both the electronic and magnetic nematicity below and, surprisingly, its fluctuations far above Ts to at least 200 K. The quantitative pump-probe data clearly identify a correlation between the topology of the Fermi surface and the magnetism in all temperature regimes, thus providing profound insight into the driving factors of nematicity in FeSe and the origin of its uniqueness.
Polymer side-chain substituents elucidate thermochromism of benzodithiophene-dithiophenylacrylonitrile copolymers - polymer solubility correlation of thermochromism and photovoltaic performance
(2017-06-28)
Chen, Hung-Yang
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Lin, Chiao-Wen
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Chen, Chin-Ti
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Chen, Chao-Tsen
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Golder, Jan
Nine pBCNx polymers based on a donor-p-acceptor benzo[1,2-b:4,5-b']dithiophene-(E)-2,3-di(thiophen-2-yl) acrylonitrile main-chain structure and n-octyl/2-ethylhexyl as the side-chain substituents have been designed and synthesized. The thermochromism of the pBCNx polymers has been carefully examined in both solution and the thin-film state. With additional evidences from Raman spectroscopy and AFM microscopy, we have deciphered the varied colours of nine pBCNx polymers in solution and the pronounced thin-film thermochromism only observed for certain pBCNx polymers, i.e., pBCN4, pBCN5, pBCN6, and pBCN8. The alkyl side-chain, and hence the solubility or aggregation of pBCNx polymers, is a main factor of the varied colour in solution and the varied thermochromism in the thin film. We have identified that a stronger main-chain and main-chain interaction are present on the (E)-2,3-di(thiophen-2-yl) acrylonitrile moiety, whereas the poor to moderate solubility pBCN3, pBCN5', and pBCN7 exhibit pronounced thermochromism in solution, and pBCN4, pBCN5, pBCN6, and pBCN8 are four polymers which have good solubility in solution and show thermochromism in the thin-film state. We took navy blue pBCN3 (poor solubility), magenta pBCN4 (good solubility), and reddish purple pBCN5' (moderate solubility) for the fabrication of bulk heterojunction organic photovoltaics (OPVs). With a solvent annealing treatment, the power conversion efficiency of the OPVs has been improved significantly from 4.7% to 6.2% for the good solubility pBCN4, but there is little and no improvement for the moderate solubility pBCN5' and poor solubility pBCN3, respectively. Our study verifies that the good OPV performance of the pBCNx polymers can be correlated to the pronounced thin-film thermochromism. A good solubility of the polymer is a common characteristic of a material with significant thin-film thermochromism and good OPV performance.
Prenatal diagnosis of fetal aneuploidy and de novo copy number variation by isolating extravillus trophoblasts and nucleated fetal red blood cells from maternal circulation a proof of principle study using the automated Cell RevealTM platform based on nanostructure and microfluidics
(2017-06-29)
Chen, Ming
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Huang, Chung-Er
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Chang, Frank Mau-Chung
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國際半導體學院
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International College of Semiconductor Technology
Oxygen-selective adsorption in RPM3-Zn metal organic framework
(2017-06-29)
Wang, Cheng-Yu
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Wang, Linxi
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Belnick, Andrew
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Wang, Hao
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Li, Jing
Development of an oxygen selective adsorbent is anticipated to reduce the material and energy requirements for adsorptive separations of air by a factor of four, due to the relative concentrations of N-2 and O-2 in air, thereby decreasing the parasitic energy losses, carbon dioxide emissions, and cost of oxygen purification via pressure-swing adsorption. Here, we report that RPM3-Zn (a. k. a. Zn-2(bpdc)(2)(bpee); bpdc = 4,4'-biphenyldicarboxylate; bpee = 1,2-bipyridylethene) is oxygen selective over nitrogen at temperatures from 77 K to 273 K, although the oxygen capacity of the sorbent decreased markedly at increasing temperatures. Due to an oxygen diffusivity that is similar to 1000-fold greater than nitrogen, the effective oxygen selectivity increases to near infinity at low temperature at equal contact times due to N2 mass transfer limitations for gate-opening. The kinetic limitation for N-2 to open the structure has a sharp temperature dependence, suggesting this effective kinetic selectivity may be "tuned in" for other flexible metalorganic- frameworks. Although the low temperature oxygen selectivity is not practical to displace cryogenic distillation, the results suggest a new mechanism for tailoring materials for kinetic selectivity, namely, capitalizing upon the delayed opening process for a particular gas relative to another. Published by Elsevier Ltd.
STREAMING SERVICE SYSTEM, STREAMING SERVICE METHOD AND CONTROLLER THEREOF
(2017-06-29)
Ming-Hung Hsu
;
Chien-Chao Tseng
;
Min-Cheng Chan
;
Hsing-Liang Ku
;
Ming-Hao Chou
The disclosure provides a streaming service system, a streaming service method and a controller thereof The streaming service system includes a plurality of switch nodes, a plurality of surrogate servers, a content management apparatus and a controller. The switch nodes are connected, and the surrogate servers are respectively connected to one of the switch nodes. The controller is connected to the switch nodes and communicates with the content management apparatus. The content management apparatus provides server information of the surrogate servers to the controller. When a first client apparatus is joined to a streaming group, the content management apparatus informs the controller. Further, the controller selects a first surrogate server from the surrogate servers, and sets at least a portion of the switch nodes to adjust a multicast tree. The first surrogate server transmits streaming packets to the first client through a first transmission route of the multicast tree.
Sample size determination for a specific region in multiregional clinical trials with multiple co-primary endpoints
(2017-06-30)
Huang, Wong-Shian
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Hung, Hui-Nien
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Hamasaki, Toshimitsu
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Hsiao, Chin-Fu
;
統計學研究所
Recently, multi-regional clinical trials (MRCTs), which incorporate subjects from many countries/ regions around the world under the same protocol, have been widely conducted by many global pharmaceutical companies. The objective of such trials is to accelerate the development process for a drug and shorten the drug's approval time in key markets. Several statistical methods have been purposed for the design and evaluation of MRCTs, as well as for assessing the consistency of treatment effects across all regions with one primary endpoint. However, in some therapeutic areas (e.g., Alzheimer's disease), the clinical efficacy of a new treatment may be characterized by a set of possibly correlated endpoints, known as multiple co-primary endpoints. In this paper, we focus on a specific region and establish three statistical criteria for evaluating consistency between the specific region and overall results in MRCTs with multiple co-primary endpoints. More specifically, two of those criteria are used to assess whether the treatment effect in the region of interest is as large as that of the other regions or of the regions overall, while the other criterion is used to assess the consistency of the treatment effect of the specific region achieving a pre-specified threshold. The sample size required for the region of interest can also be evaluated based on these three criteria.
An enhanced application of Lotka-Volterra model to forecast the sales of two competing retail formats
(2017-07-01)
Hung, Hui-Chih
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Chiu, Yu-Chih
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Huang, Huang-Chen
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Wu, Muh-Cherng
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工業工程與管理學系
This research develops a sales forecasting model that can analyze the interaction effects of two retail competing formats (convenience-oriented vs. budget-oriented formats). A traditional approach to making such a forecast is based on the Lotka-Volterra equations (also called the LV-model). The LV-model assumes that the population of each species is affected by its self-growth, internal interaction within the species, and external interaction with other species. Most prior studies in business applications directly use sales data as input to the LV-model. The prior approach may result in misleading conclusions when sales data are embedded with seasonal variation, because this variation is not addressed in the original development of the LV-model. Therefore, this study proposes a forecasting framework (an enhanced application of the LV-model). The sales data of each retail format is considered as a compound data, which is decomposed into three individual components: (1) aggregate, (2) competition, and (3) seasonal components. The LV-model is used to forecast the competition component; the other two components are forecasted by typical time series methods; and the data of three components are finally combined into one. Empirical study indicates that the proposed method substantially outperforms the prior approach in terms of forecasting errors (4.4% vs. 16.7% for convenience-oriented and 5.8% vs. 16.2% for budget oriented). In addition, the proposed method reveals a more convincing predator-prey relationship between the two retail formats, which concludes that the convenience-oriented is the predator. To the opposite, the prior approach, concluding that the budget-oriented is the predator, is quite doubtful because the convenience-oriented shall be preferred while the GDP grows over time. This research makes a contribution in how to appropriately apply the LV-model in forecasting revenue and analyzing the interaction effects of two competing business species. (C) 2017 Elsevier Ltd. All rights reserved.
A Wi-Fi Union Mechanism for Internet Advertising Reciprocal Platform in Microenterprises
(2017-07-01)
Thi Thanh An Nguyen
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Chang, Che-Pin
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Yuan, Shyan-Ming
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資訊工程學系
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電機學院碩士在職專班
With the evolution of the Internet and smartphone devices, Internet advertising has become one of the most important methods for delivering promotional marketing messages to customers. However, the efficiency of Internet advertising for microenterprise is not very high, since Wi-Fi advertisingwhich is limited by a small router coverage areais mainly used. Moreover, because of the lack of money, microenterprises have been using low-cost methods to promote their products. Thus, enhancing the effectiveness of Wi-Fi advertising, and solving the problem of cost and the range of the views are now an essential investigation in this study. In this paper, we propose a reciprocal model with Wi-Fi union mechanism for Internet advertising based on fog computing architecture to enhance the efficiency of advertisement, reduce the cost, and increase the range of the views for microenterprise by using the Internet. In particular, the system was built in advertisers', publishers', and consumers' sides. In our system, we use contribution point (CP) as an exchange value among the participants. Advertisers and publishers can get CP by helping the others in the system to promote their advertisements, increasing their CP by one unit. Similarly, advertisers and publishers can use their CP to ask for assistance from the others, decreasing their CP by one unit. The result shows that the system in a Wi-Fi union is easy to use, and advertisements can be seen by all customers who are using free Wi-Fi from the stores of the union. This method can solve the problem of cost and fixed consumer groups.
Synthesis and nonlinear optical properties of push-pull type stilbene and pyrazoline based chromophores
(2017-07-01)
Szukalski, A.
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Parafiniuk, K.
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Haupa, K.
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Goldeman, W.
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Sahraoui, B.
In this work we present the synthesis, spectroscopic and nonlinear optical properties of push-pull type organic dyes based on 1-phenyl-2-pyrazoline or 4-(dimethylamino)phenyl chromophores as a donor part, and bridged by a double bound ortho- or meta-substituted nitrophenyl group as an acceptor. For the optical measurements we have used the poly(methyl methacrylate) based thin films doped with the dyes. Third harmonic generation measurements were performed under the picosecond laser regime with excitation wavelength at 1064 nm. The experimental results confirmed that investigated systems can be used as the efficient nonlinear optical systems for harmonic of light generation (tripled but also doubled frequency). It has also been proved the strong dependence between chemical structure (position of electron-acceptor moiety as well as the type of electron-donor unit) and nonlinear optical (NLO) response coming from series of isomers and derivatives. (C) 2017 Elsevier Ltd. All rights reserved.
Polymer solar cells based low bandgap A1-D-A2-D terpolymer based on fluorinated thiadiazoloquinoxaline and benzothiadiazole acceptors with energy loss less than 0.5 eV
(2017-07-01)
Keshtov, M. L.
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Kuklin, S. A.
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Khokhlov, A. R.
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Osipov, S. N.
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Radychev, N. A.
We synthesized an ultra low bandgap terpolymer denoted as P containing fluorinated-fluorene attached thiadiazoloquinoxaline and benzothiadiazole acceptors and thiophene as donor in its backbone and investigated its optical and electrochemical properties. This terpolymer is used for as donor along with PC71BM as electron acceptor in solution processed polymer solar cells (PSCs). The P showed a shows strong absorption band from 650 nm to 1100 nm with an optical bandgap of 1.12 eV and highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels of -5.25 eV and -3.87 eV, respectively. After the optimization of P to PC71BM weight ratio, the optimized weight ratio 1: 2 in chlorobenzene (CB) solution, the PSC showed overall power conversion efficiency of 4.10% (J(sc) of 10.96 mA/cm(2), V-oc of 0.68 V and FF of 0.55). After the solvent additive (3 v% DIO) followed by subsequent thermal annealing (SA-TA) the PCE has been increased up to 7.54% with Jsc of 16.12 mA/cm(2), Voc of 0.65 V and FF of 0.72. The increase in the PCE is related with the enhancement in the both Jsc and FF, attributed optimized nanoscale morphology of the active layer for both efficient exciton dissociation and charge transport towards the electrodes and balanced charge transport in the device, induced by the TSA treatment of the active layer. This is the highest PCE of PSCs with an energy loss about 0.47 eV with the low bandgap of 1.12 eV. (C) 2017 Elsevier B.V. All rights reserved.
Analysis of the Short-Term Response in the Drain Current of a-IGZO TFT to Light Pulses
(2017-07-01)
Liu, H. -W.
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Chan, P. -C.
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Lin, J. -H.
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Chang, C. -Y.
;
Tai, Y. -H.
In this letter, the response in the drain current (I-D) of the amorphous indium-gallium-zinc oxide thin-film transistors under positive-bias illumination stress is measured with respect to time in less than 5 s under light pulseswith altering frequencies and duty ratios. The curves of I-D under the light pulses are affected by the different defect-reacting rates under illumination and in the dark. By taking the derivative of ID, the trend of the change in the number of defects becomes clear. The total behavior of I-D in response to light pulses can be fairly predicted by the integral of the derivative terms with a correction factor of charge trapping.