基于自适应并行计算的新型纳米结构半导体器件计算机模拟研究
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摘要
本论文结合自适应技术和并行计算技术,针对新型纳米结构半导体器件建立了扩展模型,提出了一套完整一致的自适应并行计算方法,对这些器件进行计算机模拟和特性分析。该方法在器件模拟时,可以自动估计追踪物理量与电特性的变化,自动进行网格加密,达到器件特性分析上自动计算和模拟。基于自适应网格划分技术,有限体积方法,单调迭代方法,误差估计方法和并行计算方法开发出的模拟工具,已经成功的应用到模拟硅基器件,有机发光器件和纳米结构MOS器件。实验结果表明提出的方法在器件特性分析上达到了很高的精度。所提出的理论与算法已开发出一套计算机模拟程序,可以用于不同尺寸,不同结构的新型纳米结构半导体器件的特性分析;理论分析和实际测试的结果都显示了其具有良好的收敛性、高效性,可以实现对新型纳米结构半导体器件快速、精确的计算机模拟。
With the development of computer technology, continuously improvement of the processor speed, maturity of network communication technology, and the improvement of software tools, provides parallel processing technology into the rapid development. It has been recognized that parallel processing technology is the road to achieve high-performance computing. Adaptive technology is a future-oriented technology, it can get the economic, security and comfort, as well as to reduce and avoid distortion and noise. It describes a new class of "smart components / intelligence structure," These smart components change in the working conditions of the time and have a goal of the initiative to optimize the mechanical properties of regulation. Both mainstream technologies have laid an important foundation for large-scale complex computing. This paper is using the two mainstream technologies to simulate the new nanostructure semiconductor devices and to solve the high degree of coupling complex nonlinear systems.
At present, the main problems of semiconductor device simulation include: device model increasingly complex, so need to complement and develop the classic drift diffusion model; coupled partial differential equations system will inevitably lead to the difficulty of the discrete increase in the numerical solution of the stability and reliability; with the invention of the new structure and the new materials devices, device physics model and parameters are growing complexity, thus increasing the difficulty of analyze devices character; increasing in the number of equations and taking into account characteristics of multi-dimensional and transient, there are very large systems of nonlinear equations to be solved, thus must rely on advanced technology and parallel iterative method to be effective in solving the problems.
This paper proposes a new adapive parallel computation algorithm used for new nanostructure semiconductor devices. With the method used for device simulation, it can automatically track and estimated physical and electrical characteristics of the device, refine automatically mesh, calculate and simulate automatically. Experimental results show that the method provide a high level of accuracy for analysis of the device character. The methods can hold parallel distributed computing on personal computer or workstation, and achieve high accuracy, high performance, fast computer-aided design simulation requirements.
In this thesis, we present two parallel algorithms. The first one is a PDD approach and the second is a PIVPS. With the applied adaptive computing methodology, the novel parallel algorithms have been developed and successfully implemented on a Linux cluster with MPI library. Compared with the measured data, numerical results on various devices have been presented to show the accuracy and efficiency of the method. It gives the speedup, efficiency, and maximum difference to show the performance of the parallel algorithms. The parallel and adaptive computing methods proposed in this paper show that cluster parallel computing is a feasible alternative that can be used to provide fast characterization of semiconductor devices.
Then we proposed the adaptive computing procedure that contains, such as Gummel decoupled algorithm, finite volume method, monotone iteration, error estimation and 1-irregular mesh refinement methodologies in device simulation. Then use the adaptive technology to simulate organic light emitting devices. First simulate a two dimension dual layer organic light emitting device. For the difference of material parameters, different materials thickness and length of the OLED device structure, the simulation has get the intrinsic and terminal voltage and current characteristics. Through comparison with the experimental results, it shows that this two-dimensional simulation technology for OLED device gets the accuracy and numerical robustness. Further simulate the optical properties and electrical characteristics of multilayer organic light emitting device, given Ag/LiF/Alq3/EML/TPD/Ag device structure, as the EML thickness changes, get the details of simulation results including the combination of carrier rates, the exciton luminescence rate and the current-voltage characteristics.
At last this article proposed the matrix eigenvalue problem parallelization method for nanostructure semiconductor devices. As semiconductor device dimensions shrink to lead to quantum effect of devices, this paper introduced the Schrodinger -Poisson model which include all the quantum mechanisms. However, the solution of Schrodinger-Poisson model needs to spend a lot of time, the model can not be widely used in engineering applications. This new simulation technique provides a fast, efficient, and accurate approach to extract device parameters in which quantum confinement effects are significant. The results are also found to compare quite well with experimental data. The speedup and efficiency are also presented to show the computational performance.
This dissertation has proposed integrity and uniform method for computer simulation semiconductor devices and nano-structure devices. The presented algorithms have been developed a computer simulation program that can be used for kinds of different sizes and different structure of nano-semiconductor devices analyzing character. From the theoretical and practical test results have demonstrated their good convergence, accuracy, efficiency and the effectiveness of high-speed computing characteristics.
With the development of computer technology, continuously improvement of the processor speed, maturity of network communication technology, and the improvement of software tools, provides parallel processing technology into the rapid development. It has been recognized that parallel processing technology is the road to achieve high-performance computing. Adaptive technology is a future-oriented technology, it can get the economic, security and comfort, as well as to reduce and avoid distortion and noise. It describes a new class of "smart components / intelligence structure," These smart components change in the working conditions of the time and have a goal of the initiative to optimize the mechanical properties of regulation. Both mainstream technologies have laid an important foundation for large-scale complex computing. This paper is using the two mainstream technologies to simulate the new nanostructure semiconductor devices and to solve the high degree of coupling complex nonlinear systems.
At present, the main problems of semiconductor device simulation include: device model increasingly complex, so need to complement and develop the classic drift diffusion model; coupled partial differential equations system will inevitably lead to the difficulty of the discrete increase in the numerical solution of the stability and reliability; with the invention of the new structure and the new materials devices, device physics model and parameters are growing complexity, thus increasing the difficulty of analyze devices character; increasing in the number of equations and taking into account characteristics of multi-dimensional and transient, there are very large systems of nonlinear equations to be solved, thus must rely on advanced technology and parallel iterative method to be effective in solving the problems.
This paper proposes a new adapive parallel computation algorithm used for new nanostructure semiconductor devices. With the method used for device simulation, it can automatically track and estimated physical and electrical characteristics of the device, refine automatically mesh, calculate and simulate automatically. Experimental results show that the method provide a high level of accuracy for analysis of the device character. The methods can hold parallel distributed computing on personal computer or workstation, and achieve high accuracy, high performance, fast computer-aided design simulation requirements.
In this thesis, we present two parallel algorithms. The first one is a PDD approach and the second is a PIVPS. With the applied adaptive computing methodology, the novel parallel algorithms have been developed and successfully implemented on a Linux cluster with MPI library. Compared with the measured data, numerical results on various devices have been presented to show the accuracy and efficiency of the method. It gives the speedup, efficiency, and maximum difference to show the performance of the parallel algorithms. The parallel and adaptive computing methods proposed in this paper show that cluster parallel computing is a feasible alternative that can be used to provide fast characterization of semiconductor devices.
Then we proposed the adaptive computing procedure that contains, such as Gummel decoupled algorithm, finite volume method, monotone iteration, error estimation and 1-irregular mesh refinement methodologies in device simulation. Then use the adaptive technology to simulate organic light emitting devices. First simulate a two dimension dual layer organic light emitting device. For the difference of material parameters, different materials thickness and length of the OLED device structure, the simulation has get the intrinsic and terminal voltage and current characteristics. Through comparison with the experimental results, it shows that this two-dimensional simulation technology for OLED device gets the accuracy and numerical robustness. Further simulate the optical properties and electrical characteristics of multilayer organic light emitting device, given Ag/LiF/Alq3/EML/TPD/Ag device structure, as the EML thickness changes, get the details of simulation results including the combination of carrier rates, the exciton luminescence rate and the current-voltage characteristics.
At last this article proposed the matrix eigenvalue problem parallelization method for nanostructure semiconductor devices. As semiconductor device dimensions shrink to lead to quantum effect of devices, this paper introduced the Schrodinger -Poisson model which include all the quantum mechanisms. However, the solution of Schrodinger-Poisson model needs to spend a lot of time, the model can not be widely used in engineering applications. This new simulation technique provides a fast, efficient, and accurate approach to extract device parameters in which quantum confinement effects are significant. The results are also found to compare quite well with experimental data. The speedup and efficiency are also presented to show the computational performance.
This dissertation has proposed integrity and uniform method for computer simulation semiconductor devices and nano-structure devices. The presented algorithms have been developed a computer simulation program that can be used for kinds of different sizes and different structure of nano-semiconductor devices analyzing character. From the theoretical and practical test results have demonstrated their good convergence, accuracy, efficiency and the effectiveness of high-speed computing characteristics.
引文
[1] 王可定,徐福培,计算机模拟及其应用,东南大学出版,1997.
[2] 傅廷亮,计算机模拟技术,中国科技大学出版社,2001.
[3] H.K.Gummel, A self-consistent iterative scheme for one-dimension steady state transistor calculation, IEEE Transactions on electron devices,ED-11.October 1964,pp.455–465.
[4] 阮 刚,集成电路工艺和器件的计算机模拟—IC TCAD 技术概论,复旦大学出版社,2007.
[5] R. W. Dutton, A. J. Strojwas, Perspectives on Technology and Technology Driven CAD., IEEE Trans. CAD, Vol. 19, No. 2, pp. 1544-1 560,2000.
[6] Lundstrom M,Datta S,Physical device simulation in a shrinking world. IEEE Circuits and devices,1990;6(1):32
[7] Hess K,Lugli P,Computational electrics:semiconductor transport and device simulation. Netherlands: Kluwer Academic Publishers,1991:3~263
[8] C. Moglestue, Monte Carlo simulation of semiconductor devices, Chapman &Hall, London, 1993.
[9] W. van Roosbroeck, Theory of flow of electrons and holes in germanium and other semiconductors, Bell Syst. Tech. J., Vol. 29, pp. 560-562, 1950.
[10] M. Ieong and T.-W. Tang, Influence of Hydrodynamic Models on the Prediction of Submicrometer Device Characteristics, IEEE Trans. Eelc. Dev., Vol.44, pp.2242-225 1, 1997.
[11] K. Blstekjaer, Transport Equations for Electrons in Two-Valley Semiconductors, IEEE Trans. Elec. Dev., Vol. 17, pp. 38-47, 1970.
[12] 赵鸿麟,半导体器件计算机模拟,天津大学出版社,1989
[13] S. Selberherr, Analysis and Simulation of Semiconductor Devices, Springer-Verlag, Wein-New York, 1984.
[14]Selberherr S,Analysis and simulation of semiconductor devices[M],Springer-verlag Press,1984:16-22
[15]Chen D T,Kan E C,Ravaioli U,An Analytical Formation of the Length Coefficient for the Augmented Drift-diffusion Model including Velocity Overshoot. IEEE Trans Electron Devices,1991,38(6): 1484-1489
[16]Blakey P A, Burdick S A, Sandborn P A, On the Use of Chornber Augmented Drift-diffusion Equation for Modeling GaAs Device, IEEE Trans Electron Devices,1988,35(11): 1991-1994
[17]Chen D T, Kan E C, Hess K, Field-induced Anisotropic Distribution Functions and Semiconductor Transport Equations with tensor Form Coefficients .IEEE Trans Computer Aided Design,1991,10(10) : 87-95
[18]Stwart R A, Kan E C, A Fully Nonparabolic Hydrodynamic Model for Describing Hot Electron Transport in GaAs, Solid-state Electronics,1990. 33(7):819-823
[19] M. Lundstorm, Fundamentals of Carrier Transport, Modular Series on Solid State Devices, V. X, Addison-Wesley Publishing Company Inc., Reading, MA,1990.
[20] M. G. Ancona, Simulation of Quantum Confinement Effects in Ultra-Thin-Oxide MOS Structures, IEEE J. TCAD, pp. 1-17, 1998.
[21] S.-H. Lo, D.A Buchanan, and Y. Taur, Modeling and Characherization of Quantization, Polysilicon Depletion, and Direct Tunneling Effects in MOSFETs with Ultrathin Oxides, IBM J. Res. Dev. pp. 327-337, 1999.
[22] M. J. van Dort, et al., A Simple Model for Quantization Effects in Heavily-doped Silicon MOSFET at Inversion Conditions, Solid-State Elec., Vol. 37, No. 3, pp. 411-414, 1994.
[23] M. G. Ancona, Quantum Correction to the Equation of State of an Electron Gas in a Semcionductor, Phys. Rev. B, Vol 39, No. 13, pp. 9536-9540, 1989.
[24] G. Paasch and H. Ubensee, A Modified Local Density Approximation, Phys. Stat. Sol., (b) 113, pp. 165-178, 1982.
[25] W. Hansch, et al., "Carrier Transport Near the Si/Si02 Interface of a MOSFET," Solid-State Elec., Vol. 32, No. 10, pp. 839-849, 1989.
[26] M. Ieong, et al., Efficient Quantum Correction Model for Multi-dimensional CMOS Simulations, IEEE SISPAD 1998, pp. 129-1 32, 1998.
[27] K. Kramer, et al., Semiconductor Devices: a simulation approach, Prentice Hall, 1997.
[28] R.E. Bank, et al., Mathematical modelling and simulation of electrical circuits and semiconductor devices, Birkhauser Verlag, 1994.
[29] R. W. Dutton and Zhiping Yu, Technology CAD: computer simulation of IC processes and devices, Kluwer Academic, 1993.
[30] R. S. Varga, Matrix Iterative Analysis, Springer, New York, 2000.
[31] C.V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992.
[32] D. S. Watkins, QR-Like Algorithms for Eigenvalue Problems, J. Comp. App. Math., Vol. 123, pp. 67-83, 2000.
[33] G. H. Golub and C. F. V. Loan, Matrix Computations, The Hohns Hopkins University Press, 1996.
[34] Yiming Li, S.S. Chung, J.L. Liu, A Novel Approach for the Two-Dimensional Simulation of Submicron MOSFET's Using Monotone Iterative Method, Proc. Int. Symposium on VLSI-TSA, pp. 27-30, 1999.
[35] A.L. Pardhanani, G.F. Carey, Multidimensional Semiconductor Device and 186 Micro-Scale Thermal Modeling Using the PROPHET Simulator with Dial-an-Operator Framework, Comp. Model. Eng. Sci., Vol. 1, No. 1, pp. 141-150,2000.
[36] Yiming Li, S. M. Sze, J.L. Liu, T.S. Chao, A New Parallel Adaptive Finite Volume Method for the Numerical Simulation of Semiconductor Devices," CCP2000 Adv. Prog. and Tech. Digest, p. 138, 2000.
[37] Yiming Li, T.S. Chao, C.S. Wang, S.M. Sze, Monotone Iterative Method for Parallel Numerical Solution of 3D Semiconductor Poisson Equation, to appear in WSES/IEEE Proc. 5th World Multiconf: CSCC, MCP and MCME, 2001.
[38] Y. Yuan, P. Banerjee, A Parallel Implementation of A Fast Multipole Based 3-D Capacitance Extraction Program on Distributed Memory Milticomputers, Proc. Int. Parallel Distri. Proce. Symp., pp. 323-330, 2000.
[39] A.J. Garcia-Loureiro, T.F. Pena, Parallel Domain Decomposition Applied to 3D Simulation of Gradual HBTs, J. Model. Simul. Microsys., Vol. 1, No. 2, pp.115-120, 1999.
[40] G. Antonoiu, G. Dima, M.D. Profirescu, Parallel Domain Decomposition for 3D Semiconductor Device Simulation, Proc. Int. Semicond. Con$, Vol. 2, pp. 371-374, 1998.
[41] V. Axelrad, Grid Quality and Its Influence on Accuracy and Convergence in Device Simulation, IEEE Trans. CAD., Vol. 17, No. 2, pp. 149-157, 1998. 187
[42] S. Sacco, F. Saleri, Mixed Finite Volume Methods for Semiconductor Device Simulation, Numerical Methods for Partial Differential Equations, Vol.13, pp.215-236, 1997.
[43] K. Tanaka, P. Ciampohni, A. Pierantoni, G. Baccarani, Comparison Between A Posteriori Error Indicators For Adaptive Mesh Generation In Semiconductor Device Simulation, Proc. Inte. Work. VLSI Proce. Dev. Model., pp.118-119, 1993.
[44] W. M. Coughran, Jr. M. R. Pinto, R. K. Smith, Adaptive Grid Generation for VLSI Device Simulation, IEEE Trans. CAD., Vol. 10, No. 10, pp. 1259-1275, 1991. 1451 J. F. Burgler, W. M. Coughran, W. Fichtner, An Adaptive Grid Refinement Strategy for the Drift-Difision Equations, IEEE Trans. CAD., Vol. 10, No. 10, pp. 1251-1258, 1991.
[46] P. A. Markowich, C. A. Ringhofer, Schmeiser, Semiconductor Equations, Springer, Vienna, 1990.
[47] M. Sharrna, G. F. Carey, Semiconductor Device Simulation Using Adaptive Refinement and Flux Upwinding, IEEE Trans. CAD., Vol. 8, No. 6, pp. 590-598, 1989.
[48] T. Kerkhoven, A Proof of Convergence of Gummel Algorithm for Realistic Boundary Conditions, SIAMJ. Numer. Anal., Vol. 23, pp. 1121-1137, 1988. 188
[49] J. W. Jerome, Consistency of Semiconductor Modeling: an Existence/Stability Analysis for the Stationary van Roosbroeck System, SIAM J. Appl. Math., Vol. 45, pp. 565-590, 1985.
[50] R. Bank, D. J. Rose, W. Fichtner, Numerical Methods for Semiconductor Simulation, IEEE Trans. Elec. Dev., Vol. ED-30, No. 9, pp. 103 1-104 1, 1983.
[51] D. L. Scharfetter, H. K. Gurnmel, Large-Signal Analysis of a Silicon Read Diode Oscillator, IEEE Trans. Elec. Dev., Vol. ED- 16, pp. 66-77, 1969.
[52] S. M. Sze, Physics of Semiconductor Devices, Wiley-Interscience, New York, 1981.
[53] S. M. Sze, Modern semiconductor devicephysics, John Wiley, New York, 1998.
[54] N. Mastorakis, Recent Advances in Applied and Theoretical Mathematics, World Scientific and Engineering Society Press, 2000.
[55] R. E. Bank, M. Holst, A New Paradigm for Parallel Adaptive Meshing Algorithms, SIAM J. Sci. Comp., Vol. 22, No. 4, pp. 141 1 - 1443,2000.
[56] J. D. Teresco, M. W. Beall, J. E. Flaherty, M. S. Shephard, A Hierarchical Partition Model for Adaptive Finite Element Computation, Comp. Meth. App. Mech. Eng., Vol. 184, No. 2-4, pp. 269-285,2000.
[57] X. D. Zhang, J.-Y. Trepanier, R. Camarero, A posteriori Error Estimation for Finite-Volume Solutions of Hyperbolic Conservation Laws, Comp. Meth. App. Mech. Eng., Vol. 185, No. 1, pp. 1-19, 2000.
[58] E. N. Lages, G. H. Paulino, I. F. M. Menezes, R. R. SilvaNonlinear, Finite Element Analysis Using an Object-Oriented Philosophy-Application to Beam Elements and to the Cosserat Continuum, Engineering mth Computers, Vol. 15, NO. 1, pp. 73-89, 1999.
[59] R. Ramakrishnan, Structured and Unstructured Grid Adaptation Schemes for Numerical Modeling of Field Problems, Appl. Numer: Math., Vol. 14, No. 1-3, pp. 285-3 10, 1994.
[60] J. R. Whiteman, The Mathematics of Finite Elements and Applications, John Wiley, New York, 1994.
[61] I. Babuska, W. C. Rheinboldt, Error Estimates for Adaptive Finite Element Computation, SIAMJ. Numer: Anal., Vol. 15, pp. 736-754, 1978.
[62] I. Babuska, W. C. Rheinboldt, A-Posteriori Error Estimates for the Finite Element Method, Int. J. Numer: Meth. Eng., Vol. 12, pp. 1597- 161 5, 1978.
[63] R. Li, Z. Chen, W. Wu, Generalized Difference Methods for Dzflerential Equations: Numerical Analysis of Finite Volume Methods, Marcel Dekker, New York, 2000.
[64] P. I. Crumpton, J. A. Mackenzie, K. W. Morton, Cell Vertex Algorithms for the Compressible Navier-Stokes Equations, J. Comp. Phys., Vol. 109, pp. 1-15, 1993.
[65] J. Wang, Monotone Method for Diffusion Equations with Nonlinear Difision Coefficients, Nonlinear Analysis, Vol. 35, pp. 1 13- 142, 1998.
[66] Y. Deng, G. Chen, W. M. Ni, J. Zhou, Boundary Element Monotone Iteration Scheme for Semilinear Elliptic Partial Differential Equations, Math. Comp., Vol. 65, pp. 943-982, 1996.
[67] C. V. Pao, Block Monotone Iterative Methods for Numerical Solutions of Nonlinear Elliptic Equations, Numer Math., Vol. 72, pp. 239-262, 1995.
[68] S. A. Heikkil, V Lakshmikantham, Monotone Iterative Techniques for Discontinuous Nonlinear Dzflerential Equations, Marcel Dekker, New York, 1994.
[69] W. Gropp, E. Lusk, R. Thakur, Using MPI-2: Advanced Features of the Message-Passing Interface, MIT Press, Cambridge, MA, 1999.
[70] H. El-Rewini, T. G. Lewis, Distributed & Parallel Computing, Manning, Greenwich, CT, 1998.
[71] K. Dowd, C. Severance, High Performance Computing, 0' Reilly, Sebastopol, 1998.
[72] P. S. Pacheco, Parallel Programming with MPI, Morgan Kaufmann, San Francisco, CA, 1997.
[73] http://www.openmp.org
[74] OpenMP Application Program Interface Version 2.5,May,2005.
[75] GA.Geist,A.Beguelin,J.Dongarra,W.Jiang,R.Manehek,V.Sunderam,PVM: Parallel Virtual Machine,A Users’ Guide and Tutorial for Networked Parallel Computing,MIT Press,Cambridge,MA,1994.
[76] Message Passing Interface Forum,MPI:A Message Passing Interface Standard,University of Tennessee,1995.
[77] IBM Parallel Environment for AIX,MPI Programming Guide,Handbook,2003.
[78] S.-T. Lim, M. H. Chun, K. W. Lee, D.-M. Shin, Organic light emitting diodes with red emission using (2,6-dimethyl-4H-pyran-4'-ylidene) malononitrile moiety, Optical Materials, 21, 217, 2002.
[79] M.Pope, H.Kallmann, P.J.Magnante, Electroluminescence in organic crystals, J.Chem.Phys. (1963) 38, 042.
[80] W.Helfrich, W.G.Schneider, Recombination rediation in anthracene crystals, Phys. Rev. Lett (1965)14,229.
[81] W. Helfrich, W. G.Schneider, transient of volume-controlled current and recombination radiation in anthracene, J.Chem.Phys.(1966)44,2902.
[82] F. Lohmann, W. Mehl, Dark injection and radiative recombination of electrons and holes in naphthalene crystals, J. Chem. Phys. (1969) 50, 500.
[83] D. F. Williams, M. Schadt, A simple electroluminescence diode, Proc. IEEE, (1970)58,476.
[84] J.Michl, V. B. Koutechy, Electronic aspects of organic photochemistry, New York: John Wiley & Sons, Inc, 1990.
[85] P. S. Vincett, W. A. Barlow, R. A. Hann, G. B. Roberts, Electrical conduction and low voltage blue electroluminescence in vacuum-deposited organic films, Thin Solid Film (1982)94, 171.
[86] C. W. Tang, S. A. Vanslyke, Organic electroluminescent diodes, Appl. Phys. Lett (1987)51, 913.
[87] J. H. Burroughes, D. D. C. Bradley, A. R. Brown, R. N. Marks, K. Mackay, R.H.Friend, P. L. Burnsan, A. B. Holmes, Light-emitting diodes based on conjugated polymers, Nature (1990) 347, 539.
[88] J. Dresdner, Double injection electroluminescence in anthracene, RCA Rev, (1969) 30, 322.
[89] Jingsong Huang, Kaixia Yang, Zhiyuan Xie, Baijun Chen, Hongjin Jiang, and Shiyong Liu, Effect of well number on organic multiple-quantum-well electroluminescent device characteristics Appl. Phys. Lett. (1998) 73, 3348.
[90] A. Dodabalapur, L. J. Rothberg, T. M. Miller, Color variation with electroluminescent organic semiconductors in multimode resonant cavities Appl. Phys. Lett. (1994) 65, 2308.
[91] A. Dodabalapur, L. J. Rothberg, T. M. Miller, E. W. Kwock, Microcavity effects in organic semiconductors Appl. Phys. Lett. (1994) 64, 2486.
[92] C. Adachi, S. Tokito, T. Tsutsui, S. Saito, Electroluminescence in organic films with a 3-layer structure,Jpn.J. Appl. Phys.(1988) 27, L269.
[93] C. Adachi, S. Tokito, T. Tsutsui, S. Saito, Organic electroluminescent devices with a 3-layer structure, Jpn. J. Appl. Phys. (1988) 27, L713.
[94] 汤顺青,“色度学”,(1990)北京理工大学出版社,152.
[95] 李亨,“颜色技术原理及其应用”,(1994)科学出版社,53.
[96] S.R. Forrest, D.D.C. Bradley, M.E. Thompson, Measuring the Efficiency of Organic Light-Emitting Devices, (2003)15, 1043.
[97] A. Ryer, Light measurement handbook, International light, Newburyport, MA 1997.
[98] W. L. Wolfe, Introduction to radiometry: Tutorial texts in opotical engineering, v.TT29, SPIE Optical Engineering Press, Bellingham, 1998.
[99] C. Adachi, M. A. Baldo, M. E. Thompson, S. R. Forrest, Nearly 100% internal phosphorescence efficiency in an organic light-emitting device J. Appl. Phys. (2001) 90,5048.
[100] Sze,S.M, Physics of semiconductor devices.Wiley-Interscience,New York(1981)
[101] Waler, A. B., Kambili A., Martin S. J.: Electrical Transport Modelling in Organic Electroluminescent Devices. J. Phys.: Condens. Matter 14 (2002) 9825-9876.
[102] Kepler R G, Beeson P M, Jacobs S J, et al, Electron and hole mobility in tris(8-hydroxyquinolindato-N108) aluminum. Appl Phys Lett, 1995, 66(26): 3618-3620.
[103] Crone,B.K.,Davids.P.S.,Campbell.I.H.,Smith,D.L.:Device Model Investigation of Bilayer Organic Light Emitting Diodes.J.Appl.Phys.87(2000)1974-1982.
[104] P. S. Davids, 1. H. Campbell and D. L. Smith, J. Appl. Phys. 82 6319 (1997).
[105] Malliaras G G and Scott J C, J. Appl. Phys. 83, 5399 (1998).
[106] M. Pope and C. E. Swenberg, Electronic Processes in Organic Crystals (Clarendon, Oxford, 1982).
[107] Lupton,J.M.,Samuel,I.D.W.:Temperature-Dependent Single Carrier Device Model for Polymeric Light Emitting Diodes.J.Phys.D:Appl.Phys.32(1999)2973-2984.
[108] Kawabe,Y., Jabbour,G.E., Shaheen,S.E., Kippelen,B., Peyghambarian,N., A Model for the Current-Voltage Characteristics and the Quantum Efficiency of Single-Layer Organic Light Emitting Diodes.Appl.Phys.Lett.71(1997)1290-1292.
[109] C.V. Pao, Accelerated monotone iterations for numerical solutions of nonlinear elliptic boundary value problems, Computers and Mathematics with Applications 46 (2003) 1535–1544.
[110] J. Lekner, Theory of Reflection. Dordrecht, The Netherlands: Nijhoff,1987.
[111] B. Ruhstaller, S. A. Carter, S. Barth, H. Riel, W. Riess, J. C. Scott, Transient and steady-state behavior of space charges in multilayer organic light-emitting diodes, J. Appl. Phys., 89, 4575, 2001.
[112] S. J. Martin, G. L. B. Verschoor, M. A. Webster, and A. B. Walker, The internal electric field distribution in bilayer organic light emitting diodes, Organic Electron., 3, 129, 2002.
[113] Z. Liu and H. Nazare, White organic light-emitting diodes emitting from both hole and electron transport layers, Synthetic Metals, 111, 47, 2000.
[114] M. St??el, J. Staudigel, F. Steuber, J. Simmerer, and A. Winnacker, Impact of the cathode metal work function on the performance of vacuum-deposited organic light emitting-devices, Appl. Phys. A, 68, 387,1999.
[115] M. St??el, J. Staudigel, F. Steuber, J. Blassing, J. Simmerer, A. Winnacker, H. Neuner, D. Metzdorf, H.-H. Johannes, and W. Kowalsky, Electron injection and transport in 8-hydroxyquinoline aluminum, Synthetic Metals, 111, 19, 2000.
[116] S.I. Takagi, and A. Toriumi, Quantitative Understanding of Inversion-Layer Capacitance in Si MOSFET's, IEEE Trans. Elec. Dev., Vol. 42, No. 12, pp. 2125-2130, 1995.
[117] A. Pacelli, Self-Consistent Solution of the Schrodinger Equation in SemiconductorDevices by Implicit Iteration, IEEE Trans. Elec. Dev., Vol. 44, NO.7,pp. 1169-1171, 1997.
[118] Y. Omura, and Y. Nakajima, Quantum Mechanical Influence and Estimated Errors on Interface-State Density Evaluation by Quasi-Static C-V Measurement, Solid-State Elec., Vol. 44, pp. 15 11- 15 14,2000.
[119] I. Bar-On, and B.Codenotti, A Fast and Stable Parallel QR Algorithm for Symmetric Tridiagonal Matrices, Linear Algebra and its Appl., Vol. 220, pp. 63-95, 1999.
[120] M. Gu, and S.C. Eisenstat, A Divide-and-Conquer Algorithm for the Symmetric Tridiagonal Eigenproblem, SIAM J. Mat. Anal. App., pp. 172- 191, 1995.
[121] F. Tisseur, and J. Dongarra, A Parallel Divide and Conquer Algorithm for the Symmetric Engenvalue Problem on Distributed Memory Architectures, SIAM J. Sci. Comput., pp. 2223-2236, 1999.
[122] C.Ringhofer, C.Gardner, D.Vasileska. Effective Potentials and Quantum Fluid Models: A Thermodynamic Approach, High Speed Electronics and Systems,2003.
[123]C.Ringhofer.Computational Methods for Semiclassical and Quantum Transport in Semiconductor Devices,Acta Numerica,1997,3:485-521.
[124] S H.Lo,D.A.Buchanan,andY.Taur. Modeling and Characterization Quantization, Polysilicon Depletion,and Direct Tunneling Effects in MOSFETs Oxides. [J] IBM J.Res.Develop,1999,43:327-337.
[125] K.Ahmed,E.Ibok,G.C.F.Yeap,Q.Xiang,B.Ogle,J.J.Wortman,andJ.R. Hanser. Impact of Tunnel Currents and Channel Resistancecon the Characterization of Channel Inversion Layer Charge and Polysilicon Gate Depletion of Sub-20-A Gate Oxide MOSFETs. [J] IEEE Trans. Electron Devices,1999,46:1650-1655.
[126]Alessandro.S.Spinelli, Andrea Pacelli, Andrea L.Lacaita. Polysilicon quantization effects on the electrical Properties of MOS transistors. [J] IEEE Trans. Electron Devices. 2000,47:2366-71.
[2] 傅廷亮,计算机模拟技术,中国科技大学出版社,2001.
[3] H.K.Gummel, A self-consistent iterative scheme for one-dimension steady state transistor calculation, IEEE Transactions on electron devices,ED-11.October 1964,pp.455–465.
[4] 阮 刚,集成电路工艺和器件的计算机模拟—IC TCAD 技术概论,复旦大学出版社,2007.
[5] R. W. Dutton, A. J. Strojwas, Perspectives on Technology and Technology Driven CAD., IEEE Trans. CAD, Vol. 19, No. 2, pp. 1544-1 560,2000.
[6] Lundstrom M,Datta S,Physical device simulation in a shrinking world. IEEE Circuits and devices,1990;6(1):32
[7] Hess K,Lugli P,Computational electrics:semiconductor transport and device simulation. Netherlands: Kluwer Academic Publishers,1991:3~263
[8] C. Moglestue, Monte Carlo simulation of semiconductor devices, Chapman &Hall, London, 1993.
[9] W. van Roosbroeck, Theory of flow of electrons and holes in germanium and other semiconductors, Bell Syst. Tech. J., Vol. 29, pp. 560-562, 1950.
[10] M. Ieong and T.-W. Tang, Influence of Hydrodynamic Models on the Prediction of Submicrometer Device Characteristics, IEEE Trans. Eelc. Dev., Vol.44, pp.2242-225 1, 1997.
[11] K. Blstekjaer, Transport Equations for Electrons in Two-Valley Semiconductors, IEEE Trans. Elec. Dev., Vol. 17, pp. 38-47, 1970.
[12] 赵鸿麟,半导体器件计算机模拟,天津大学出版社,1989
[13] S. Selberherr, Analysis and Simulation of Semiconductor Devices, Springer-Verlag, Wein-New York, 1984.
[14]Selberherr S,Analysis and simulation of semiconductor devices[M],Springer-verlag Press,1984:16-22
[15]Chen D T,Kan E C,Ravaioli U,An Analytical Formation of the Length Coefficient for the Augmented Drift-diffusion Model including Velocity Overshoot. IEEE Trans Electron Devices,1991,38(6): 1484-1489
[16]Blakey P A, Burdick S A, Sandborn P A, On the Use of Chornber Augmented Drift-diffusion Equation for Modeling GaAs Device, IEEE Trans Electron Devices,1988,35(11): 1991-1994
[17]Chen D T, Kan E C, Hess K, Field-induced Anisotropic Distribution Functions and Semiconductor Transport Equations with tensor Form Coefficients .IEEE Trans Computer Aided Design,1991,10(10) : 87-95
[18]Stwart R A, Kan E C, A Fully Nonparabolic Hydrodynamic Model for Describing Hot Electron Transport in GaAs, Solid-state Electronics,1990. 33(7):819-823
[19] M. Lundstorm, Fundamentals of Carrier Transport, Modular Series on Solid State Devices, V. X, Addison-Wesley Publishing Company Inc., Reading, MA,1990.
[20] M. G. Ancona, Simulation of Quantum Confinement Effects in Ultra-Thin-Oxide MOS Structures, IEEE J. TCAD, pp. 1-17, 1998.
[21] S.-H. Lo, D.A Buchanan, and Y. Taur, Modeling and Characherization of Quantization, Polysilicon Depletion, and Direct Tunneling Effects in MOSFETs with Ultrathin Oxides, IBM J. Res. Dev. pp. 327-337, 1999.
[22] M. J. van Dort, et al., A Simple Model for Quantization Effects in Heavily-doped Silicon MOSFET at Inversion Conditions, Solid-State Elec., Vol. 37, No. 3, pp. 411-414, 1994.
[23] M. G. Ancona, Quantum Correction to the Equation of State of an Electron Gas in a Semcionductor, Phys. Rev. B, Vol 39, No. 13, pp. 9536-9540, 1989.
[24] G. Paasch and H. Ubensee, A Modified Local Density Approximation, Phys. Stat. Sol., (b) 113, pp. 165-178, 1982.
[25] W. Hansch, et al., "Carrier Transport Near the Si/Si02 Interface of a MOSFET," Solid-State Elec., Vol. 32, No. 10, pp. 839-849, 1989.
[26] M. Ieong, et al., Efficient Quantum Correction Model for Multi-dimensional CMOS Simulations, IEEE SISPAD 1998, pp. 129-1 32, 1998.
[27] K. Kramer, et al., Semiconductor Devices: a simulation approach, Prentice Hall, 1997.
[28] R.E. Bank, et al., Mathematical modelling and simulation of electrical circuits and semiconductor devices, Birkhauser Verlag, 1994.
[29] R. W. Dutton and Zhiping Yu, Technology CAD: computer simulation of IC processes and devices, Kluwer Academic, 1993.
[30] R. S. Varga, Matrix Iterative Analysis, Springer, New York, 2000.
[31] C.V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992.
[32] D. S. Watkins, QR-Like Algorithms for Eigenvalue Problems, J. Comp. App. Math., Vol. 123, pp. 67-83, 2000.
[33] G. H. Golub and C. F. V. Loan, Matrix Computations, The Hohns Hopkins University Press, 1996.
[34] Yiming Li, S.S. Chung, J.L. Liu, A Novel Approach for the Two-Dimensional Simulation of Submicron MOSFET's Using Monotone Iterative Method, Proc. Int. Symposium on VLSI-TSA, pp. 27-30, 1999.
[35] A.L. Pardhanani, G.F. Carey, Multidimensional Semiconductor Device and 186 Micro-Scale Thermal Modeling Using the PROPHET Simulator with Dial-an-Operator Framework, Comp. Model. Eng. Sci., Vol. 1, No. 1, pp. 141-150,2000.
[36] Yiming Li, S. M. Sze, J.L. Liu, T.S. Chao, A New Parallel Adaptive Finite Volume Method for the Numerical Simulation of Semiconductor Devices," CCP2000 Adv. Prog. and Tech. Digest, p. 138, 2000.
[37] Yiming Li, T.S. Chao, C.S. Wang, S.M. Sze, Monotone Iterative Method for Parallel Numerical Solution of 3D Semiconductor Poisson Equation, to appear in WSES/IEEE Proc. 5th World Multiconf: CSCC, MCP and MCME, 2001.
[38] Y. Yuan, P. Banerjee, A Parallel Implementation of A Fast Multipole Based 3-D Capacitance Extraction Program on Distributed Memory Milticomputers, Proc. Int. Parallel Distri. Proce. Symp., pp. 323-330, 2000.
[39] A.J. Garcia-Loureiro, T.F. Pena, Parallel Domain Decomposition Applied to 3D Simulation of Gradual HBTs, J. Model. Simul. Microsys., Vol. 1, No. 2, pp.115-120, 1999.
[40] G. Antonoiu, G. Dima, M.D. Profirescu, Parallel Domain Decomposition for 3D Semiconductor Device Simulation, Proc. Int. Semicond. Con$, Vol. 2, pp. 371-374, 1998.
[41] V. Axelrad, Grid Quality and Its Influence on Accuracy and Convergence in Device Simulation, IEEE Trans. CAD., Vol. 17, No. 2, pp. 149-157, 1998. 187
[42] S. Sacco, F. Saleri, Mixed Finite Volume Methods for Semiconductor Device Simulation, Numerical Methods for Partial Differential Equations, Vol.13, pp.215-236, 1997.
[43] K. Tanaka, P. Ciampohni, A. Pierantoni, G. Baccarani, Comparison Between A Posteriori Error Indicators For Adaptive Mesh Generation In Semiconductor Device Simulation, Proc. Inte. Work. VLSI Proce. Dev. Model., pp.118-119, 1993.
[44] W. M. Coughran, Jr. M. R. Pinto, R. K. Smith, Adaptive Grid Generation for VLSI Device Simulation, IEEE Trans. CAD., Vol. 10, No. 10, pp. 1259-1275, 1991. 1451 J. F. Burgler, W. M. Coughran, W. Fichtner, An Adaptive Grid Refinement Strategy for the Drift-Difision Equations, IEEE Trans. CAD., Vol. 10, No. 10, pp. 1251-1258, 1991.
[46] P. A. Markowich, C. A. Ringhofer, Schmeiser, Semiconductor Equations, Springer, Vienna, 1990.
[47] M. Sharrna, G. F. Carey, Semiconductor Device Simulation Using Adaptive Refinement and Flux Upwinding, IEEE Trans. CAD., Vol. 8, No. 6, pp. 590-598, 1989.
[48] T. Kerkhoven, A Proof of Convergence of Gummel Algorithm for Realistic Boundary Conditions, SIAMJ. Numer. Anal., Vol. 23, pp. 1121-1137, 1988. 188
[49] J. W. Jerome, Consistency of Semiconductor Modeling: an Existence/Stability Analysis for the Stationary van Roosbroeck System, SIAM J. Appl. Math., Vol. 45, pp. 565-590, 1985.
[50] R. Bank, D. J. Rose, W. Fichtner, Numerical Methods for Semiconductor Simulation, IEEE Trans. Elec. Dev., Vol. ED-30, No. 9, pp. 103 1-104 1, 1983.
[51] D. L. Scharfetter, H. K. Gurnmel, Large-Signal Analysis of a Silicon Read Diode Oscillator, IEEE Trans. Elec. Dev., Vol. ED- 16, pp. 66-77, 1969.
[52] S. M. Sze, Physics of Semiconductor Devices, Wiley-Interscience, New York, 1981.
[53] S. M. Sze, Modern semiconductor devicephysics, John Wiley, New York, 1998.
[54] N. Mastorakis, Recent Advances in Applied and Theoretical Mathematics, World Scientific and Engineering Society Press, 2000.
[55] R. E. Bank, M. Holst, A New Paradigm for Parallel Adaptive Meshing Algorithms, SIAM J. Sci. Comp., Vol. 22, No. 4, pp. 141 1 - 1443,2000.
[56] J. D. Teresco, M. W. Beall, J. E. Flaherty, M. S. Shephard, A Hierarchical Partition Model for Adaptive Finite Element Computation, Comp. Meth. App. Mech. Eng., Vol. 184, No. 2-4, pp. 269-285,2000.
[57] X. D. Zhang, J.-Y. Trepanier, R. Camarero, A posteriori Error Estimation for Finite-Volume Solutions of Hyperbolic Conservation Laws, Comp. Meth. App. Mech. Eng., Vol. 185, No. 1, pp. 1-19, 2000.
[58] E. N. Lages, G. H. Paulino, I. F. M. Menezes, R. R. SilvaNonlinear, Finite Element Analysis Using an Object-Oriented Philosophy-Application to Beam Elements and to the Cosserat Continuum, Engineering mth Computers, Vol. 15, NO. 1, pp. 73-89, 1999.
[59] R. Ramakrishnan, Structured and Unstructured Grid Adaptation Schemes for Numerical Modeling of Field Problems, Appl. Numer: Math., Vol. 14, No. 1-3, pp. 285-3 10, 1994.
[60] J. R. Whiteman, The Mathematics of Finite Elements and Applications, John Wiley, New York, 1994.
[61] I. Babuska, W. C. Rheinboldt, Error Estimates for Adaptive Finite Element Computation, SIAMJ. Numer: Anal., Vol. 15, pp. 736-754, 1978.
[62] I. Babuska, W. C. Rheinboldt, A-Posteriori Error Estimates for the Finite Element Method, Int. J. Numer: Meth. Eng., Vol. 12, pp. 1597- 161 5, 1978.
[63] R. Li, Z. Chen, W. Wu, Generalized Difference Methods for Dzflerential Equations: Numerical Analysis of Finite Volume Methods, Marcel Dekker, New York, 2000.
[64] P. I. Crumpton, J. A. Mackenzie, K. W. Morton, Cell Vertex Algorithms for the Compressible Navier-Stokes Equations, J. Comp. Phys., Vol. 109, pp. 1-15, 1993.
[65] J. Wang, Monotone Method for Diffusion Equations with Nonlinear Difision Coefficients, Nonlinear Analysis, Vol. 35, pp. 1 13- 142, 1998.
[66] Y. Deng, G. Chen, W. M. Ni, J. Zhou, Boundary Element Monotone Iteration Scheme for Semilinear Elliptic Partial Differential Equations, Math. Comp., Vol. 65, pp. 943-982, 1996.
[67] C. V. Pao, Block Monotone Iterative Methods for Numerical Solutions of Nonlinear Elliptic Equations, Numer Math., Vol. 72, pp. 239-262, 1995.
[68] S. A. Heikkil, V Lakshmikantham, Monotone Iterative Techniques for Discontinuous Nonlinear Dzflerential Equations, Marcel Dekker, New York, 1994.
[69] W. Gropp, E. Lusk, R. Thakur, Using MPI-2: Advanced Features of the Message-Passing Interface, MIT Press, Cambridge, MA, 1999.
[70] H. El-Rewini, T. G. Lewis, Distributed & Parallel Computing, Manning, Greenwich, CT, 1998.
[71] K. Dowd, C. Severance, High Performance Computing, 0' Reilly, Sebastopol, 1998.
[72] P. S. Pacheco, Parallel Programming with MPI, Morgan Kaufmann, San Francisco, CA, 1997.
[73] http://www.openmp.org
[74] OpenMP Application Program Interface Version 2.5,May,2005.
[75] GA.Geist,A.Beguelin,J.Dongarra,W.Jiang,R.Manehek,V.Sunderam,PVM: Parallel Virtual Machine,A Users’ Guide and Tutorial for Networked Parallel Computing,MIT Press,Cambridge,MA,1994.
[76] Message Passing Interface Forum,MPI:A Message Passing Interface Standard,University of Tennessee,1995.
[77] IBM Parallel Environment for AIX,MPI Programming Guide,Handbook,2003.
[78] S.-T. Lim, M. H. Chun, K. W. Lee, D.-M. Shin, Organic light emitting diodes with red emission using (2,6-dimethyl-4H-pyran-4'-ylidene) malononitrile moiety, Optical Materials, 21, 217, 2002.
[79] M.Pope, H.Kallmann, P.J.Magnante, Electroluminescence in organic crystals, J.Chem.Phys. (1963) 38, 042.
[80] W.Helfrich, W.G.Schneider, Recombination rediation in anthracene crystals, Phys. Rev. Lett (1965)14,229.
[81] W. Helfrich, W. G.Schneider, transient of volume-controlled current and recombination radiation in anthracene, J.Chem.Phys.(1966)44,2902.
[82] F. Lohmann, W. Mehl, Dark injection and radiative recombination of electrons and holes in naphthalene crystals, J. Chem. Phys. (1969) 50, 500.
[83] D. F. Williams, M. Schadt, A simple electroluminescence diode, Proc. IEEE, (1970)58,476.
[84] J.Michl, V. B. Koutechy, Electronic aspects of organic photochemistry, New York: John Wiley & Sons, Inc, 1990.
[85] P. S. Vincett, W. A. Barlow, R. A. Hann, G. B. Roberts, Electrical conduction and low voltage blue electroluminescence in vacuum-deposited organic films, Thin Solid Film (1982)94, 171.
[86] C. W. Tang, S. A. Vanslyke, Organic electroluminescent diodes, Appl. Phys. Lett (1987)51, 913.
[87] J. H. Burroughes, D. D. C. Bradley, A. R. Brown, R. N. Marks, K. Mackay, R.H.Friend, P. L. Burnsan, A. B. Holmes, Light-emitting diodes based on conjugated polymers, Nature (1990) 347, 539.
[88] J. Dresdner, Double injection electroluminescence in anthracene, RCA Rev, (1969) 30, 322.
[89] Jingsong Huang, Kaixia Yang, Zhiyuan Xie, Baijun Chen, Hongjin Jiang, and Shiyong Liu, Effect of well number on organic multiple-quantum-well electroluminescent device characteristics Appl. Phys. Lett. (1998) 73, 3348.
[90] A. Dodabalapur, L. J. Rothberg, T. M. Miller, Color variation with electroluminescent organic semiconductors in multimode resonant cavities Appl. Phys. Lett. (1994) 65, 2308.
[91] A. Dodabalapur, L. J. Rothberg, T. M. Miller, E. W. Kwock, Microcavity effects in organic semiconductors Appl. Phys. Lett. (1994) 64, 2486.
[92] C. Adachi, S. Tokito, T. Tsutsui, S. Saito, Electroluminescence in organic films with a 3-layer structure,Jpn.J. Appl. Phys.(1988) 27, L269.
[93] C. Adachi, S. Tokito, T. Tsutsui, S. Saito, Organic electroluminescent devices with a 3-layer structure, Jpn. J. Appl. Phys. (1988) 27, L713.
[94] 汤顺青,“色度学”,(1990)北京理工大学出版社,152.
[95] 李亨,“颜色技术原理及其应用”,(1994)科学出版社,53.
[96] S.R. Forrest, D.D.C. Bradley, M.E. Thompson, Measuring the Efficiency of Organic Light-Emitting Devices, (2003)15, 1043.
[97] A. Ryer, Light measurement handbook, International light, Newburyport, MA 1997.
[98] W. L. Wolfe, Introduction to radiometry: Tutorial texts in opotical engineering, v.TT29, SPIE Optical Engineering Press, Bellingham, 1998.
[99] C. Adachi, M. A. Baldo, M. E. Thompson, S. R. Forrest, Nearly 100% internal phosphorescence efficiency in an organic light-emitting device J. Appl. Phys. (2001) 90,5048.
[100] Sze,S.M, Physics of semiconductor devices.Wiley-Interscience,New York(1981)
[101] Waler, A. B., Kambili A., Martin S. J.: Electrical Transport Modelling in Organic Electroluminescent Devices. J. Phys.: Condens. Matter 14 (2002) 9825-9876.
[102] Kepler R G, Beeson P M, Jacobs S J, et al, Electron and hole mobility in tris(8-hydroxyquinolindato-N108) aluminum. Appl Phys Lett, 1995, 66(26): 3618-3620.
[103] Crone,B.K.,Davids.P.S.,Campbell.I.H.,Smith,D.L.:Device Model Investigation of Bilayer Organic Light Emitting Diodes.J.Appl.Phys.87(2000)1974-1982.
[104] P. S. Davids, 1. H. Campbell and D. L. Smith, J. Appl. Phys. 82 6319 (1997).
[105] Malliaras G G and Scott J C, J. Appl. Phys. 83, 5399 (1998).
[106] M. Pope and C. E. Swenberg, Electronic Processes in Organic Crystals (Clarendon, Oxford, 1982).
[107] Lupton,J.M.,Samuel,I.D.W.:Temperature-Dependent Single Carrier Device Model for Polymeric Light Emitting Diodes.J.Phys.D:Appl.Phys.32(1999)2973-2984.
[108] Kawabe,Y., Jabbour,G.E., Shaheen,S.E., Kippelen,B., Peyghambarian,N., A Model for the Current-Voltage Characteristics and the Quantum Efficiency of Single-Layer Organic Light Emitting Diodes.Appl.Phys.Lett.71(1997)1290-1292.
[109] C.V. Pao, Accelerated monotone iterations for numerical solutions of nonlinear elliptic boundary value problems, Computers and Mathematics with Applications 46 (2003) 1535–1544.
[110] J. Lekner, Theory of Reflection. Dordrecht, The Netherlands: Nijhoff,1987.
[111] B. Ruhstaller, S. A. Carter, S. Barth, H. Riel, W. Riess, J. C. Scott, Transient and steady-state behavior of space charges in multilayer organic light-emitting diodes, J. Appl. Phys., 89, 4575, 2001.
[112] S. J. Martin, G. L. B. Verschoor, M. A. Webster, and A. B. Walker, The internal electric field distribution in bilayer organic light emitting diodes, Organic Electron., 3, 129, 2002.
[113] Z. Liu and H. Nazare, White organic light-emitting diodes emitting from both hole and electron transport layers, Synthetic Metals, 111, 47, 2000.
[114] M. St??el, J. Staudigel, F. Steuber, J. Simmerer, and A. Winnacker, Impact of the cathode metal work function on the performance of vacuum-deposited organic light emitting-devices, Appl. Phys. A, 68, 387,1999.
[115] M. St??el, J. Staudigel, F. Steuber, J. Blassing, J. Simmerer, A. Winnacker, H. Neuner, D. Metzdorf, H.-H. Johannes, and W. Kowalsky, Electron injection and transport in 8-hydroxyquinoline aluminum, Synthetic Metals, 111, 19, 2000.
[116] S.I. Takagi, and A. Toriumi, Quantitative Understanding of Inversion-Layer Capacitance in Si MOSFET's, IEEE Trans. Elec. Dev., Vol. 42, No. 12, pp. 2125-2130, 1995.
[117] A. Pacelli, Self-Consistent Solution of the Schrodinger Equation in SemiconductorDevices by Implicit Iteration, IEEE Trans. Elec. Dev., Vol. 44, NO.7,pp. 1169-1171, 1997.
[118] Y. Omura, and Y. Nakajima, Quantum Mechanical Influence and Estimated Errors on Interface-State Density Evaluation by Quasi-Static C-V Measurement, Solid-State Elec., Vol. 44, pp. 15 11- 15 14,2000.
[119] I. Bar-On, and B.Codenotti, A Fast and Stable Parallel QR Algorithm for Symmetric Tridiagonal Matrices, Linear Algebra and its Appl., Vol. 220, pp. 63-95, 1999.
[120] M. Gu, and S.C. Eisenstat, A Divide-and-Conquer Algorithm for the Symmetric Tridiagonal Eigenproblem, SIAM J. Mat. Anal. App., pp. 172- 191, 1995.
[121] F. Tisseur, and J. Dongarra, A Parallel Divide and Conquer Algorithm for the Symmetric Engenvalue Problem on Distributed Memory Architectures, SIAM J. Sci. Comput., pp. 2223-2236, 1999.
[122] C.Ringhofer, C.Gardner, D.Vasileska. Effective Potentials and Quantum Fluid Models: A Thermodynamic Approach, High Speed Electronics and Systems,2003.
[123]C.Ringhofer.Computational Methods for Semiclassical and Quantum Transport in Semiconductor Devices,Acta Numerica,1997,3:485-521.
[124] S H.Lo,D.A.Buchanan,andY.Taur. Modeling and Characterization Quantization, Polysilicon Depletion,and Direct Tunneling Effects in MOSFETs Oxides. [J] IBM J.Res.Develop,1999,43:327-337.
[125] K.Ahmed,E.Ibok,G.C.F.Yeap,Q.Xiang,B.Ogle,J.J.Wortman,andJ.R. Hanser. Impact of Tunnel Currents and Channel Resistancecon the Characterization of Channel Inversion Layer Charge and Polysilicon Gate Depletion of Sub-20-A Gate Oxide MOSFETs. [J] IEEE Trans. Electron Devices,1999,46:1650-1655.
[126]Alessandro.S.Spinelli, Andrea Pacelli, Andrea L.Lacaita. Polysilicon quantization effects on the electrical Properties of MOS transistors. [J] IEEE Trans. Electron Devices. 2000,47:2366-71.