Pub Date : 2009-05-27DOI: 10.1109/IWCE.2009.5091121
Chi-kang Li, Yuh‐Renn Wu, Jasprit Singh
InGaN/GaN LEDs offer important lighting devices for human livings. These devices have high efficiency and lifetimes at low injection power but so far show degradation under high injection conditions. Current spreading and heat dissipation are key reasons for degradation under high power operation. In this paper, we have developed a three-dimensional (3-D) finite element method (FEM) to examine the heat generation and dissipation and a two-dimensional (2D) Finite element Poisson and drift-diffusion solver for the analysis of current spreading. As we know, the junction temperature plays an important role to the performance of the LED, and it will influence the optical performance. Therefore, the discussion of different surface current density and sapphire width will be considered in this paper. We examine how current flow can be altered by careful design of the LEDs. Results for a conventional LED and an LED with ion-implantation to improve current flow are presented. Our simulations show that improved device design based on modifying current flow paths can improve the device operation.
{"title":"Modeling of Junction Temperature and Current Flow in High Power InGaN/GaN Light Emission Diodes Using Finite Element Methods","authors":"Chi-kang Li, Yuh‐Renn Wu, Jasprit Singh","doi":"10.1109/IWCE.2009.5091121","DOIUrl":"https://doi.org/10.1109/IWCE.2009.5091121","url":null,"abstract":"InGaN/GaN LEDs offer important lighting devices for human livings. These devices have high efficiency and lifetimes at low injection power but so far show degradation under high injection conditions. Current spreading and heat dissipation are key reasons for degradation under high power operation. In this paper, we have developed a three-dimensional (3-D) finite element method (FEM) to examine the heat generation and dissipation and a two-dimensional (2D) Finite element Poisson and drift-diffusion solver for the analysis of current spreading. As we know, the junction temperature plays an important role to the performance of the LED, and it will influence the optical performance. Therefore, the discussion of different surface current density and sapphire width will be considered in this paper. We examine how current flow can be altered by careful design of the LEDs. Results for a conventional LED and an LED with ion-implantation to improve current flow are presented. Our simulations show that improved device design based on modifying current flow paths can improve the device operation.","PeriodicalId":443119,"journal":{"name":"2009 13th International Workshop on Computational Electronics","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121681074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-05-27DOI: 10.1109/IWCE.2009.5091126
M. Auf der Maur, M. Povolotskyi, F. Sacconi, G. Romano, G. Penazzi, A. Pecchia, A. Di Carlo
The TIBERCAD project [1] is aimed at the implementation of a device simulator which captures the most important physical concepts encountered in present and emerging electronic and optoelectronic devices. On the one hand the down-scaling of device dimensions requires the inclusion of more advanced quantum mechanical concepts which go beyond classical transport theories. On the other hand, functionality of new emerging devices is based both on electrons/holes, and other quasi-particles such as excitons, polaritons, etc. Usually the active part of a device which needs a more elaborate and careful treatment is small compared to the overall simulation domain. The computational cost of the more accurate model however forbids its application to the whole domain, especially when using atomistic approaches. TIBERCAD implements the following physical models: (a) A structural model that allows to calculate strain and shape deformation of lattice mismatched heterostructures based on linear elasticity theory of solids, assuming pseudomorphic interfaces between different materials [2]. External mechanical forces can be included in the simulation. (b) Quantum-mechanical models to calculate eigenstates of confined particles based on the envelope function approximation including single-band and multiband k . p approach. We solve a stationary Schrodinger equation and obtain energy spectrum, particle density and probabilities of optical transitions [3]. (c) Semi-classical transport models that consider electrons, holes and excitons. Transport is treated in the drift-diffusion approximation. The electrochemical potentials are used as dependent variables such that the particle flux is equal to the gradient of a driving potential multiplied by a particle conductivity: φ
{"title":"Multiscale-Multiphysics Simulation of Nanostructured Devices: the TiberCAD Project","authors":"M. Auf der Maur, M. Povolotskyi, F. Sacconi, G. Romano, G. Penazzi, A. Pecchia, A. Di Carlo","doi":"10.1109/IWCE.2009.5091126","DOIUrl":"https://doi.org/10.1109/IWCE.2009.5091126","url":null,"abstract":"The TIBERCAD project [1] is aimed at the implementation of a device simulator which captures the most important physical concepts encountered in present and emerging electronic and optoelectronic devices. On the one hand the down-scaling of device dimensions requires the inclusion of more advanced quantum mechanical concepts which go beyond classical transport theories. On the other hand, functionality of new emerging devices is based both on electrons/holes, and other quasi-particles such as excitons, polaritons, etc. Usually the active part of a device which needs a more elaborate and careful treatment is small compared to the overall simulation domain. The computational cost of the more accurate model however forbids its application to the whole domain, especially when using atomistic approaches. TIBERCAD implements the following physical models: (a) A structural model that allows to calculate strain and shape deformation of lattice mismatched heterostructures based on linear elasticity theory of solids, assuming pseudomorphic interfaces between different materials [2]. External mechanical forces can be included in the simulation. (b) Quantum-mechanical models to calculate eigenstates of confined particles based on the envelope function approximation including single-band and multiband k . p approach. We solve a stationary Schrodinger equation and obtain energy spectrum, particle density and probabilities of optical transitions [3]. (c) Semi-classical transport models that consider electrons, holes and excitons. Transport is treated in the drift-diffusion approximation. The electrochemical potentials are used as dependent variables such that the particle flux is equal to the gradient of a driving potential multiplied by a particle conductivity: φ","PeriodicalId":443119,"journal":{"name":"2009 13th International Workshop on Computational Electronics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125599817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-05-27DOI: 10.1109/IWCE.2009.5091107
A. Gagliardi, M. Auf der Maur, A. Pecchia, A. Di Carlo
Using solar power is one of the most important challenge of today technology. A big effort is devoted in going beyond traditional semiconductor, especially silicon based, solar cells. A well established and promising technology is represented by electrochemical dye solar cells (DSC). Their functioning is a complicated interplay of different parts deeply interconnected which requires a model able to catch the whole device and the different processes at the same time. We develop an extension to the TiberCAD code to simulate such kind of devices.
{"title":"Dye Solar Cell Simulations Using Finite Element Method","authors":"A. Gagliardi, M. Auf der Maur, A. Pecchia, A. Di Carlo","doi":"10.1109/IWCE.2009.5091107","DOIUrl":"https://doi.org/10.1109/IWCE.2009.5091107","url":null,"abstract":"Using solar power is one of the most important challenge of today technology. A big effort is devoted in going beyond traditional semiconductor, especially silicon based, solar cells. A well established and promising technology is represented by electrochemical dye solar cells (DSC). Their functioning is a complicated interplay of different parts deeply interconnected which requires a model able to catch the whole device and the different processes at the same time. We develop an extension to the TiberCAD code to simulate such kind of devices.","PeriodicalId":443119,"journal":{"name":"2009 13th International Workshop on Computational Electronics","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132173801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-05-27DOI: 10.1109/IWCE.2009.5091081
L. Zeng, Xiao Yan Liu, G. Du, J. Kang, R. Han
In this paper, we demonstrate a Monte Carlo simulator for ambipolar Schottky barrier MOSFETs which includes tunneling and thermal emission of electrons and holes and the appropriate treatment of carrier transport at nano-scale. The ambipolar characteristic of SB MOSFETs is reproduced by this simulator. The four operation modes in both n and p SB MOSFETs are revealed. Based on these simulations, it is summarized that the tunneling at source side dominates the carrier transport.
{"title":"A Monte Carlo Study of Ambipolar Schottky Barrier MOSFETs","authors":"L. Zeng, Xiao Yan Liu, G. Du, J. Kang, R. Han","doi":"10.1109/IWCE.2009.5091081","DOIUrl":"https://doi.org/10.1109/IWCE.2009.5091081","url":null,"abstract":"In this paper, we demonstrate a Monte Carlo simulator for ambipolar Schottky barrier MOSFETs which includes tunneling and thermal emission of electrons and holes and the appropriate treatment of carrier transport at nano-scale. The ambipolar characteristic of SB MOSFETs is reproduced by this simulator. The four operation modes in both n and p SB MOSFETs are revealed. Based on these simulations, it is summarized that the tunneling at source side dominates the carrier transport.","PeriodicalId":443119,"journal":{"name":"2009 13th International Workshop on Computational Electronics","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134396398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We conducted a first-principles examination to determine the most stable position of an icosahedral B 12 cluster near a Si (001) surface. We discovered that such a cluster is most stable when its center is located at the fourth layer position from the Si top surface where a Si dimer sits directly overhead. Scanning tunneling microscopy (STM) simulation revealed that Si dimers above the B 12 cluster are distinguishable from other dimers in empty-state STM images.
{"title":"Stable Position of B12 Cluster Near Si (001) Surface and Its STM Images","authors":"S. Ito, T. Maruizumi, Y. Suwa","doi":"10.1149/1.3487557","DOIUrl":"https://doi.org/10.1149/1.3487557","url":null,"abstract":"We conducted a first-principles examination to determine the most stable position of an icosahedral B 12 cluster near a Si (001) surface. We discovered that such a cluster is most stable when its center is located at the fourth layer position from the Si top surface where a Si dimer sits directly overhead. Scanning tunneling microscopy (STM) simulation revealed that Si dimers above the B 12 cluster are distinguishable from other dimers in empty-state STM images.","PeriodicalId":443119,"journal":{"name":"2009 13th International Workshop on Computational Electronics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125187892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-05-27DOI: 10.1109/IWCE.2009.5091150
A. Pham, C. Jungemann, B. Meinerzhagen
In this work, simulations of mobility variation due to the combination of uniaxial stress and biaxial strain are presented. This study provides a better understanding of the mobility variation and predicts the mobility enhancement for higher stress levels. Transport in the non-equilibrium regime is also investigated. High-field channel drift velocity characteristics are evaluated and compared for different combinations of uniaxial stress and biaxial strain. A better overview of the transport enhancement due to stress/strain at different transport situations including near and non-equilibrium is provided.
{"title":"Simulation of Mobility Variation and Drift Velocity Enhancement Due to Uniaxial Stress Combined with Biaxial Strain in Si PMOS","authors":"A. Pham, C. Jungemann, B. Meinerzhagen","doi":"10.1109/IWCE.2009.5091150","DOIUrl":"https://doi.org/10.1109/IWCE.2009.5091150","url":null,"abstract":"In this work, simulations of mobility variation due to the combination of uniaxial stress and biaxial strain are presented. This study provides a better understanding of the mobility variation and predicts the mobility enhancement for higher stress levels. Transport in the non-equilibrium regime is also investigated. High-field channel drift velocity characteristics are evaluated and compared for different combinations of uniaxial stress and biaxial strain. A better overview of the transport enhancement due to stress/strain at different transport situations including near and non-equilibrium is provided.","PeriodicalId":443119,"journal":{"name":"2009 13th International Workshop on Computational Electronics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127049907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-05-27DOI: 10.1109/IWCE.2009.5091102
Jing Zhang, S. Patil
We present a coupled thermo-electrical-mechanical finite element based model to investigate material behaviors of wide bandgap (WBG) devices in operating conditions. The mechanisms of degradation and ultimately failure in wide bandgap devices are very complex. Under operating conditions, the devices are usually subject to high electric fields, high stress/strain fields, high current densities, high temperatures and high thermal gradients. The application of electronic devices is limited by lack of a detailed understanding of involved mechanisms. There is a long overdue of development of a comprehensive model which fully couples thermal, electrical and mechanical effects. The proposed model is capable of computing stress, temperature, and electric fields based on an innovative finite element approach for the solution of non-linear coupled thermo-electrical-mechanical problems. The developed model will address major issues of performance and lifetime of wide bandgap electronic devices.
{"title":"Development of Coupled Thermo-Electrical-Mechanical Models for Studying Degradation of AlGaN/GaN HFETs","authors":"Jing Zhang, S. Patil","doi":"10.1109/IWCE.2009.5091102","DOIUrl":"https://doi.org/10.1109/IWCE.2009.5091102","url":null,"abstract":"We present a coupled thermo-electrical-mechanical finite element based model to investigate material behaviors of wide bandgap (WBG) devices in operating conditions. The mechanisms of degradation and ultimately failure in wide bandgap devices are very complex. Under operating conditions, the devices are usually subject to high electric fields, high stress/strain fields, high current densities, high temperatures and high thermal gradients. The application of electronic devices is limited by lack of a detailed understanding of involved mechanisms. There is a long overdue of development of a comprehensive model which fully couples thermal, electrical and mechanical effects. The proposed model is capable of computing stress, temperature, and electric fields based on an innovative finite element approach for the solution of non-linear coupled thermo-electrical-mechanical problems. The developed model will address major issues of performance and lifetime of wide bandgap electronic devices.","PeriodicalId":443119,"journal":{"name":"2009 13th International Workshop on Computational Electronics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129416449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-05-27DOI: 10.1109/IWCE.2009.5091080
K. Willis, S. Hagness, I. Knezevic
We present a computational tool for the characterization of conductive media at THz frequencies. By coupling the Ensemble Monte Carlo (EMC) simulator of carrier dynamics and the finite-difference time-domain (FDTD) solver of Maxwell's equations, we develop and characterize a robust and versatile global simulator that interactively tracks field-particle dynamics. In this report the EMC-FDTD simulator is used to model the interaction of bulk doped silicon with THz frequency electromagnetic plane waves. The performance of the simulation tool is investigated in terms of several simulation parameters, including grid cell size and carrier ensemble size. The complex conductivity of doped silicon at THz frequencies obtained from the combined EMC-FDTD solver is in good agreement with available experimental results.
{"title":"A Global EMC-FDTD Simulation Tool for High-Frequency Carrier Transport in Semiconductors","authors":"K. Willis, S. Hagness, I. Knezevic","doi":"10.1109/IWCE.2009.5091080","DOIUrl":"https://doi.org/10.1109/IWCE.2009.5091080","url":null,"abstract":"We present a computational tool for the characterization of conductive media at THz frequencies. By coupling the Ensemble Monte Carlo (EMC) simulator of carrier dynamics and the finite-difference time-domain (FDTD) solver of Maxwell's equations, we develop and characterize a robust and versatile global simulator that interactively tracks field-particle dynamics. In this report the EMC-FDTD simulator is used to model the interaction of bulk doped silicon with THz frequency electromagnetic plane waves. The performance of the simulation tool is investigated in terms of several simulation parameters, including grid cell size and carrier ensemble size. The complex conductivity of doped silicon at THz frequencies obtained from the combined EMC-FDTD solver is in good agreement with available experimental results.","PeriodicalId":443119,"journal":{"name":"2009 13th International Workshop on Computational Electronics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128126110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-05-27DOI: 10.1109/IWCE.2009.5091122
T. Windbacher, V. Sverdlov, S. Selberherr
The experimental data of a suspend gate field-effect transistor (SGFET) have been analyzed with three different models. A SGFET is a MOSFET with an elevated gate and an empty space below it. The exposed gate-oxide layer is biofunc- tionalized with single stranded DNA, which is able to hybridize with a complementary strand. Due to the intrinsic charge of the phosphate groups (minus one elementary charge per group) of the DNA, large shifts in the transfer characteristics are induced. Thus label-free, time-resolved, and in-situ detection of DNA is possible. It can be shown that for buffer concentrations below mmol/l the Poisson-Boltzmann description it is not valid any- more. Because of the low number of counter ions at small buffer concentrations, the screening of the oligo-deoxynucleotides/DNA is more appropriately described with the Debye-H ¨ uckel model. Additionally we propose an extended Poisson-Boltzmann model which takes the closest possible ion distance to the oxide surface into account, and we compare the analytical soultion of this model with the Poisson-Boltzmann and the Debye-H ¨ uckel model.
{"title":"Modeling of Low Concentrated Buffer DNA Detection with Suspend Gate Field-Effect Transistors (SGFET)","authors":"T. Windbacher, V. Sverdlov, S. Selberherr","doi":"10.1109/IWCE.2009.5091122","DOIUrl":"https://doi.org/10.1109/IWCE.2009.5091122","url":null,"abstract":"The experimental data of a suspend gate field-effect transistor (SGFET) have been analyzed with three different models. A SGFET is a MOSFET with an elevated gate and an empty space below it. The exposed gate-oxide layer is biofunc- tionalized with single stranded DNA, which is able to hybridize with a complementary strand. Due to the intrinsic charge of the phosphate groups (minus one elementary charge per group) of the DNA, large shifts in the transfer characteristics are induced. Thus label-free, time-resolved, and in-situ detection of DNA is possible. It can be shown that for buffer concentrations below mmol/l the Poisson-Boltzmann description it is not valid any- more. Because of the low number of counter ions at small buffer concentrations, the screening of the oligo-deoxynucleotides/DNA is more appropriately described with the Debye-H ¨ uckel model. Additionally we propose an extended Poisson-Boltzmann model which takes the closest possible ion distance to the oxide surface into account, and we compare the analytical soultion of this model with the Poisson-Boltzmann and the Debye-H ¨ uckel model.","PeriodicalId":443119,"journal":{"name":"2009 13th International Workshop on Computational Electronics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123694143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-05-27DOI: 10.1109/IWCE.2009.5091161
Huu-Nha Nguyen, D. Querlioz, S. Galdin-Retailleau, A. Bournel, P. Dollfus
This paper examines the quantum transport effects in carbon nanotube field-effect transistors (CNTFETs) within the Wigner's function formalism, using a particle Monte Carlo technique. The comparison with semi-classical simulation shows that significant differences observed at the microscopic level are not necessarily strongly reflected at the macroscopic level in terms of drain current. The dependence of quantum effects on gate length is also investigated.
{"title":"Wigner Monte Carlo Simulation of CNTFET: Comparison Between Semi-Classical and Quantum Transport","authors":"Huu-Nha Nguyen, D. Querlioz, S. Galdin-Retailleau, A. Bournel, P. Dollfus","doi":"10.1109/IWCE.2009.5091161","DOIUrl":"https://doi.org/10.1109/IWCE.2009.5091161","url":null,"abstract":"This paper examines the quantum transport effects in carbon nanotube field-effect transistors (CNTFETs) within the Wigner's function formalism, using a particle Monte Carlo technique. The comparison with semi-classical simulation shows that significant differences observed at the microscopic level are not necessarily strongly reflected at the macroscopic level in terms of drain current. The dependence of quantum effects on gate length is also investigated.","PeriodicalId":443119,"journal":{"name":"2009 13th International Workshop on Computational Electronics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114328511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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