含石墨烯层的半导体功率器件的电—热—力特性研究
|
摘要
随着三维立体封装的发展,功率器件的功率密度随集成度的增加而不断提高,其中半导体功率器件的可靠性方面的问题越来越突出,相应地,它的电-热-力特性研究就显得非常重要。
该硕士论文主要基于混合非线性有限元方法进行含石墨烯层的半导体功率器件的电-热-力仿真分析研究。考虑到材料参数的温变特性,用直接迭代法求解电-热-力之间的非线性耦合问题。基于有限元算法,利用时间差分代替时间微分的方式,成功解决了电-热-力问题中稳态和瞬态的求解。基于典型算例,对比了商用仿真软件以及其它论文的结果,验证了该算法针对含石墨烯层的多栅指HEMT(高电子迁移率晶体管场效应管)这一模型的仿真精度。
进一步地,应用上述算法,该硕士论文深入地研究了含石墨烯层的多栅指HEMT的稳态和瞬态的电-热-力特性。研究表明,石墨烯层可以明显降低多栅指HEMT的最高温升以及温升产生的热应力。论文中分别比较了含石墨烯层的多栅指HEMT的在不同条件下对应的数值结果,对石墨烯层的合理应用提供了明确的指导。
With the development of three-dimensional packaging, power density of power devices with ever-increasing integration. The reliability problems of semiconductor power devices are becoming increasingly prominent. In this case, electro-thermo-mechanical characteristic of these devices is needed to be studied urgently.
The study on electro-thermo-mechanical characteristic of semiconductor power devices with graphene layers in this thesis is based on mixed nonlinear finite element method. Considering the temperature-dependent material parameters, the nonlinear electro-thermo-mechanical coupling is solved by the direct iteration method. Based on finite element method (FEM), time differential is replaced by time difference, solving steady-state and transient-state problems. The analysis method is compared to the commercial simulation software and the results of other papers in typical examples, to ensure that the analysis method is of accuracy for the model of multiple-gate HEMT (High Electron Mobility Transistor) with graphene layers.
Then, using the above analysis method, in-depth study for steady-state and transient-state characteristic of multiple-gate HEMT with graphene layers is done in this thesis. The results show that graphene layers can reduce the maximum temperature rise and thermal stress which is caused by temperature rise significantly. This thesis compares numerical results of multiple-gate HEMT with graphene layers under different conditions respectively. Clear guidance is given for the reasonable application of graphene layers.
该硕士论文主要基于混合非线性有限元方法进行含石墨烯层的半导体功率器件的电-热-力仿真分析研究。考虑到材料参数的温变特性,用直接迭代法求解电-热-力之间的非线性耦合问题。基于有限元算法,利用时间差分代替时间微分的方式,成功解决了电-热-力问题中稳态和瞬态的求解。基于典型算例,对比了商用仿真软件以及其它论文的结果,验证了该算法针对含石墨烯层的多栅指HEMT(高电子迁移率晶体管场效应管)这一模型的仿真精度。
进一步地,应用上述算法,该硕士论文深入地研究了含石墨烯层的多栅指HEMT的稳态和瞬态的电-热-力特性。研究表明,石墨烯层可以明显降低多栅指HEMT的最高温升以及温升产生的热应力。论文中分别比较了含石墨烯层的多栅指HEMT的在不同条件下对应的数值结果,对石墨烯层的合理应用提供了明确的指导。
With the development of three-dimensional packaging, power density of power devices with ever-increasing integration. The reliability problems of semiconductor power devices are becoming increasingly prominent. In this case, electro-thermo-mechanical characteristic of these devices is needed to be studied urgently.
The study on electro-thermo-mechanical characteristic of semiconductor power devices with graphene layers in this thesis is based on mixed nonlinear finite element method. Considering the temperature-dependent material parameters, the nonlinear electro-thermo-mechanical coupling is solved by the direct iteration method. Based on finite element method (FEM), time differential is replaced by time difference, solving steady-state and transient-state problems. The analysis method is compared to the commercial simulation software and the results of other papers in typical examples, to ensure that the analysis method is of accuracy for the model of multiple-gate HEMT (High Electron Mobility Transistor) with graphene layers.
Then, using the above analysis method, in-depth study for steady-state and transient-state characteristic of multiple-gate HEMT with graphene layers is done in this thesis. The results show that graphene layers can reduce the maximum temperature rise and thermal stress which is caused by temperature rise significantly. This thesis compares numerical results of multiple-gate HEMT with graphene layers under different conditions respectively. Clear guidance is given for the reasonable application of graphene layers.
引文
[1]邱碧秀,微系统封装原理与技术,电子工业出版社, 2006.
[2] R. R. Tummala, Fundamentals of Microsystems Packaging, McGraw-Hill, 2001.
[3]黄庆安和唐洁影,微系统封装基础,南京,东南大学出版社, 2004.
[4] The International Technology Roadmap for Semiconductors http://www.itrs.net/ Links/2009ITRS/Home2009.htm (Semiconductor Industry Association, 2009).
[5] A. Klumpp, R. Merkel, R. Wieland, and P. Ramm,“Chip-to-Wafer stacking technology for 3D system integration,”Proceedings of the 53rd Electronic Components and Technology Conference, pp. 1080-1083, 2003.
[6] http://www2.imec.be/imec_com/3dim-integration-program.php
[7] http://www.emc3d.org/documents/library/technical/IMEC%20Technical%20Review_3D_introduction.pdf
[8] U.K. Mishra, P. Parikh, Y.F. Wu,“AlGaN/GaN HEMTs– anoverview of device operation and applications,”Proc. IEEE ,vol.90, pp. 1022–1031, Dec. 2002.
[9] B. A. Kopp, A. J. Billups, and M. H. Luesse,“Thermal analysis and considerations for gallium nitride microwave power amplifier packaging,”Microw. J., vol. 44, pp. 72–82, Dec. 2001.
[10] S. Sinha and K. E. Goodson,“Review: multiscale thermal modeling in nanoelectronics,”International J. for Multiscale Computational Engineering, vol. 3, no. 1, pp. 107-133, 2005.
[11] E. Pop, S. Sinha, and K. E. Goodson,“Heat generation and transport in nanometer-scale transistors,”Proc. IEEE, vol. 94, no. 8, pp. 1587-1601, Aug. 2006.
[12]王春,纳米金刚石-碳纳米管-石墨烯性能的第一原理研究,吉林大学博士学位论文, 2009.
[13] A. K. Geim,“Graphene: Status and Prospects,”Science, vol. 324, pp.1530-1534, 2009.
[14] William J. Evans, Lin Hu, and Pawel Keblinski,“Thermal conductivity of graphene ribbons from equilibrium molecular dynamics: Effect of ribbon width, edge roughness, and hydrogen termination,”APPLIED PHYSICS LETTERS, vol.96, pp. 203112, 2010.
[15]刘忠良,碳化硅薄膜的外延生长-结构表征及石墨烯的制备,中国科技大学博士学位论文, 2009.
[16] Ni, Z.H., et al.,“Graphene Thickness Determination Using Reflection and Contrast Spectroscopy,”Nano Letters, vol.7, no. 9, pp. 2758-2763, 2007.
[17] Keun Soo Kim, Yue Zhao, Houk Jang, Sang Yoon Lee, et al.,“Large-scale pattern growth of graphene films for stretchable transparent electrodes,”Nature, vol. 475, pp. 07719, 2009.
[18] Y. Q. Wu, P. D. Ye, M. A. Capano, et al.,“Top-gated graphene field-effect-transistors formed by decomposition of SiC,”APPLIED PHYSICS LETTERS, vol.92, pp. 092102, 2008.
[19] Mark P. Levendorf, Carlos S. Ruiz-Vargas, Shivank Garg, et al.,“Transfer-Free Batch Fabrication of Single Layer Graphene Transistors,”Nature, vol. 9, no. 12, pp. 4479–4483, 2009.
[20] Kedzierski, J., et al.,“Epitaxial Graphene Transistors on SiC Substrates. Electron Devices,“IEEE Transactions on, vol.55, no. 8, pp. 2078-2085, 2008.
[21] Wang, X., et al.,“Room-Temperature All-Semiconducting Sub-10-nm Graphene Nanoribbon Field-Effect Transistors,”Physical Review Letters, vol.100, no. 20, pp. 206803-4, 2008.
[22] S. Ghosh,1 I. Calizo,1 D. Teweldebrhan,“Extremely high thermal conductivity of graphene: Prospects for thermal management applications in nanoelectronic circuits,”APPLIED PHYSICS LETTERS, vol.92, pp. 151911, 2008.
[23] Geunwoo Ko and Jihyun Kim,“Thermal Modeling of Graphene Layer on the Peak Channel Temperature of AlGaN/GaN High Electron Mobility Transistors,”Electrochemical and Solid-State Letters, vol.12, no. 2, pp. 29-31, Nov. 2008.
[24] Samia Subrina,Dmitri Kotchetkov and Alexander A.Balandin,“Heat removal in silicon-on-insulator integrated circuits with graphene lateral heat spreaders,”IEEE Electron Device Lett., vol.30, no. 12, pp.1281-1284 Dec. 2009 .
[25] J.P. Calame, R.E. Myers, F.N. Wood, S.C. Binari,“Simulations of direct die attached microchannel coolers for the thermal management of GaN-on-SiC microwave amplifiers,”IEEE Trans. Components and Packaging Technol. vol.28, pp. 797–809. Jan. 2005.
[26] Morag Garven and J.P. Calame,“Simulations and optimization of gate temperatures in GaN-on-SiC monolithic microwave integrated circuits,”IEEE Trans. Components and Packaging Technol. vol.32, pp. 63–72. Mar.. 2009.
[27] X. P. Wang, W. Y. Yin, and S. He,“Multiphysics characterization of transient electro-thermo-mechanical responses of through-silicon vias applied with a periodic voltage pulse,”IEEE Trans. Electron Devices, vol. 58, no.6, 2010.
[28] Y. B. Shi, W. Y. Yin, J. F. Mao, P. Liu, and Q. H. Liu,“Transient electrothermal analysis of multilevel interconnects in the presence of ESD pulses using the nonlinear time-domain finite-element method,”IEEE Trans. Electromagn. Compat., vol. 51, no. 3, pp. 774-783, Aug. 2009.
[29]孔凡志,电磁脉冲冲击下无源结构的瞬态电热力耦合一体化分析,上海交通大学硕士论文, 2009.
[30]王勖成.有限单元法(Finite Element Method),清华大学出版社, 2004.
[31] J. M. Jin. The Finite Element Method in Electromagnetics (Second Edition), John Wiley & Sons, 2002
[32] O. C. Zienkiewicz, and R. L. Taylor, The Finite Element Method, Fifth edition, Butterworth-Heinemann, 2000.
[33] A. Jain, R. E. Jones, R. Chatterjee, S. Pozder, and Z. H. Huang,“Thermal modelingand design of 3D integraed circuits,”IEEE Trans. Advanced Pack., vol. 33, no. 3, pp. 729-737, 2010.
[34] A. C. Polycarpou,“Introduction to the Finite Element Method in Electromagnetics”, Morgan&Claypool Publishers, 2006.
[35] J. L. Shi, W. Y. Yin, K. Kang, J. F. Mao, and L. W. Li,“Frequency-thermal characterization of on-chip transformers with patterned ground shields,”IEEE Trans. Microw. Theory Tech., vol.55, no.1, pp.1–12, 2007.
[36] Zhichun Ma, Elizabeth Bradley, Thomas Peacock, Jean R. Hertzberg, and Yung-Cheng Lee,“Solder-assembled large MEMS flaps for fluid mixing,”IEEE Trans. Advanced Pack., vol. 26, no. 3, pp.268-276, 2003.
[37] F. Z. Kong, W. Y. Yin, J. F. Mao, and Q. H. Liu,“Electro-Thermo-Mechanical Characterizations of Various Wire Bonding Interconnects Illuminated by an Electromagnetic Pulse,”IEEE Trans. Advanced Pack., vol. 33, no. 3, pp. 729-737, 2010.
[38] R. R. Reeber and K. Wang,“High temperature elastic constant prediction of some group III-nitrides,”MRS Internet J. Nitride Semicond Res., vol. 6, no.3, pp.1-5, 2001.
[39] R. R. Reeber and K. Wang,“Lattice parameters and thermal expansion of GaN,”J. Mater. Res., vol. 15, pp.40-44, 2000.
[40] J. Zou, D. Kotchetkov, A. A. Balandin, D. I. Florescu, and F. H. Pollak,“Thermal conductivity of GaN films: effects of impurities and dislocations,”J Appl Phys, vol. 92, no. 5, pp. 2534-2539, 2002.
[41] E. A. Burgemeister, V. W. Muench, and E. Pettenpaul“Thermal conductivity and electrical properties of 6H silicon carbide,”J Appl Phys, vol. 50, no. 9, pp. 5790-5794, 1979.
[42] G. R. Liu and S. S. Quek,“The Finite Element Method: A Practical Course”, Butterworth-Heinemann, 2003.
[43] K. Raleva, D. Vasileska, S. M. Goodnick, and M. Nedjalkov,“Modeling thermal effects in nanodevices,”IEEE Trans. Electron Devices, vol. 55, no. 6, pp. 1306-1316, Jun. 2008.
[44] A. C. Polycarpou,“Introduction to the Finite Element Method in Electromagnetics”, Morgan&Claypool Publishers, 2006.
[45] M. Lundstrom and Z. B. Ren,“Essential physics of carrier transport in nanoscale MOSFETs,”IEEE Trans. Electron Devices, vol. 49, no. 1, pp. 133-141, Jan. 2002.
[46] S. Sinha, E. Pop, R. W. Dutton and K. E. Goodson,“Non-equilibrium phonon distributions in sub-100 nm silicon transistors,”ASME J. Heat Transfer, vol. 128, pp. 638-647, Jul. 2006.
[47] K. K. Mei, R. Pous, and Z. chen,“The measured equation of invariance: a new concept in field computation,”IEEE Trans. Antenna and Propagation, vol. 43, no. 3, pp. 320–327, 1994.
[48] M. Falconer, and V. Tripathi,“FDTD simulation of power/ground bounce and crosstalk in IC packages,”IEEE 5th Topical Meeting on Electrical Performance of Electronin Packaging, pp. 166–168, 1996.
[49] G. T. Nobauer and H. Moser,“Analytical approach to temperature evaluation in bonding wires and calculation of allowable current,”IEEE Trans. Advanced Pack., vol. 23, no. 3, pp. 426-435, 2000.
[50] http://en.wikipedia.org/wiki/Ludwig_von_Mises
[51] Z. Ren, W. Y. Yin, Y. B. Shi and Q. H. Liu,“Thermal accumulation effects on the transient temperature response in LDMOSFETs under the impact of a periodic electromagnetic pulse,”IEEE Trans. Electron Devices, vol. 57, no. 1, pp. 345-352, Jan. 2010.
[52] C. Mao, and H. Zhou,“Noval parameter estimation of double exponential pulse (EMP, UWB) by statistical means,”IEEE Trans. Electromagn. Compat., vol. 50, no.1,pp.97-100, 2008.
[53] A. M. Darwish, A. J. Bayba, and H. A. Hung,“Thermal Resistance Calculation of AlGaN–GaN Devices,”IEEE Trans. Microwave Theory Tech., vol. 52, no.11, pp. 2611-2620, 2004.
[54] A. M. Darwish, A. J. Bayba, and H. A. Hung,“Accurate determinaion of thermal resistance of FETs,”IEEE Trans. Microwave Theory Tech., vol. 53, no.1, pp. 306-313, 2005.
[55] J. Park, M.W. Shin, and C. C. Lee,“Thermal modeling and measurement of GaN-based HFET devices,”IEEE Electron Device Lett., 2003, vol. 24, no. 7, pp. 424–426, 2003.
[2] R. R. Tummala, Fundamentals of Microsystems Packaging, McGraw-Hill, 2001.
[3]黄庆安和唐洁影,微系统封装基础,南京,东南大学出版社, 2004.
[4] The International Technology Roadmap for Semiconductors http://www.itrs.net/ Links/2009ITRS/Home2009.htm (Semiconductor Industry Association, 2009).
[5] A. Klumpp, R. Merkel, R. Wieland, and P. Ramm,“Chip-to-Wafer stacking technology for 3D system integration,”Proceedings of the 53rd Electronic Components and Technology Conference, pp. 1080-1083, 2003.
[6] http://www2.imec.be/imec_com/3dim-integration-program.php
[7] http://www.emc3d.org/documents/library/technical/IMEC%20Technical%20Review_3D_introduction.pdf
[8] U.K. Mishra, P. Parikh, Y.F. Wu,“AlGaN/GaN HEMTs– anoverview of device operation and applications,”Proc. IEEE ,vol.90, pp. 1022–1031, Dec. 2002.
[9] B. A. Kopp, A. J. Billups, and M. H. Luesse,“Thermal analysis and considerations for gallium nitride microwave power amplifier packaging,”Microw. J., vol. 44, pp. 72–82, Dec. 2001.
[10] S. Sinha and K. E. Goodson,“Review: multiscale thermal modeling in nanoelectronics,”International J. for Multiscale Computational Engineering, vol. 3, no. 1, pp. 107-133, 2005.
[11] E. Pop, S. Sinha, and K. E. Goodson,“Heat generation and transport in nanometer-scale transistors,”Proc. IEEE, vol. 94, no. 8, pp. 1587-1601, Aug. 2006.
[12]王春,纳米金刚石-碳纳米管-石墨烯性能的第一原理研究,吉林大学博士学位论文, 2009.
[13] A. K. Geim,“Graphene: Status and Prospects,”Science, vol. 324, pp.1530-1534, 2009.
[14] William J. Evans, Lin Hu, and Pawel Keblinski,“Thermal conductivity of graphene ribbons from equilibrium molecular dynamics: Effect of ribbon width, edge roughness, and hydrogen termination,”APPLIED PHYSICS LETTERS, vol.96, pp. 203112, 2010.
[15]刘忠良,碳化硅薄膜的外延生长-结构表征及石墨烯的制备,中国科技大学博士学位论文, 2009.
[16] Ni, Z.H., et al.,“Graphene Thickness Determination Using Reflection and Contrast Spectroscopy,”Nano Letters, vol.7, no. 9, pp. 2758-2763, 2007.
[17] Keun Soo Kim, Yue Zhao, Houk Jang, Sang Yoon Lee, et al.,“Large-scale pattern growth of graphene films for stretchable transparent electrodes,”Nature, vol. 475, pp. 07719, 2009.
[18] Y. Q. Wu, P. D. Ye, M. A. Capano, et al.,“Top-gated graphene field-effect-transistors formed by decomposition of SiC,”APPLIED PHYSICS LETTERS, vol.92, pp. 092102, 2008.
[19] Mark P. Levendorf, Carlos S. Ruiz-Vargas, Shivank Garg, et al.,“Transfer-Free Batch Fabrication of Single Layer Graphene Transistors,”Nature, vol. 9, no. 12, pp. 4479–4483, 2009.
[20] Kedzierski, J., et al.,“Epitaxial Graphene Transistors on SiC Substrates. Electron Devices,“IEEE Transactions on, vol.55, no. 8, pp. 2078-2085, 2008.
[21] Wang, X., et al.,“Room-Temperature All-Semiconducting Sub-10-nm Graphene Nanoribbon Field-Effect Transistors,”Physical Review Letters, vol.100, no. 20, pp. 206803-4, 2008.
[22] S. Ghosh,1 I. Calizo,1 D. Teweldebrhan,“Extremely high thermal conductivity of graphene: Prospects for thermal management applications in nanoelectronic circuits,”APPLIED PHYSICS LETTERS, vol.92, pp. 151911, 2008.
[23] Geunwoo Ko and Jihyun Kim,“Thermal Modeling of Graphene Layer on the Peak Channel Temperature of AlGaN/GaN High Electron Mobility Transistors,”Electrochemical and Solid-State Letters, vol.12, no. 2, pp. 29-31, Nov. 2008.
[24] Samia Subrina,Dmitri Kotchetkov and Alexander A.Balandin,“Heat removal in silicon-on-insulator integrated circuits with graphene lateral heat spreaders,”IEEE Electron Device Lett., vol.30, no. 12, pp.1281-1284 Dec. 2009 .
[25] J.P. Calame, R.E. Myers, F.N. Wood, S.C. Binari,“Simulations of direct die attached microchannel coolers for the thermal management of GaN-on-SiC microwave amplifiers,”IEEE Trans. Components and Packaging Technol. vol.28, pp. 797–809. Jan. 2005.
[26] Morag Garven and J.P. Calame,“Simulations and optimization of gate temperatures in GaN-on-SiC monolithic microwave integrated circuits,”IEEE Trans. Components and Packaging Technol. vol.32, pp. 63–72. Mar.. 2009.
[27] X. P. Wang, W. Y. Yin, and S. He,“Multiphysics characterization of transient electro-thermo-mechanical responses of through-silicon vias applied with a periodic voltage pulse,”IEEE Trans. Electron Devices, vol. 58, no.6, 2010.
[28] Y. B. Shi, W. Y. Yin, J. F. Mao, P. Liu, and Q. H. Liu,“Transient electrothermal analysis of multilevel interconnects in the presence of ESD pulses using the nonlinear time-domain finite-element method,”IEEE Trans. Electromagn. Compat., vol. 51, no. 3, pp. 774-783, Aug. 2009.
[29]孔凡志,电磁脉冲冲击下无源结构的瞬态电热力耦合一体化分析,上海交通大学硕士论文, 2009.
[30]王勖成.有限单元法(Finite Element Method),清华大学出版社, 2004.
[31] J. M. Jin. The Finite Element Method in Electromagnetics (Second Edition), John Wiley & Sons, 2002
[32] O. C. Zienkiewicz, and R. L. Taylor, The Finite Element Method, Fifth edition, Butterworth-Heinemann, 2000.
[33] A. Jain, R. E. Jones, R. Chatterjee, S. Pozder, and Z. H. Huang,“Thermal modelingand design of 3D integraed circuits,”IEEE Trans. Advanced Pack., vol. 33, no. 3, pp. 729-737, 2010.
[34] A. C. Polycarpou,“Introduction to the Finite Element Method in Electromagnetics”, Morgan&Claypool Publishers, 2006.
[35] J. L. Shi, W. Y. Yin, K. Kang, J. F. Mao, and L. W. Li,“Frequency-thermal characterization of on-chip transformers with patterned ground shields,”IEEE Trans. Microw. Theory Tech., vol.55, no.1, pp.1–12, 2007.
[36] Zhichun Ma, Elizabeth Bradley, Thomas Peacock, Jean R. Hertzberg, and Yung-Cheng Lee,“Solder-assembled large MEMS flaps for fluid mixing,”IEEE Trans. Advanced Pack., vol. 26, no. 3, pp.268-276, 2003.
[37] F. Z. Kong, W. Y. Yin, J. F. Mao, and Q. H. Liu,“Electro-Thermo-Mechanical Characterizations of Various Wire Bonding Interconnects Illuminated by an Electromagnetic Pulse,”IEEE Trans. Advanced Pack., vol. 33, no. 3, pp. 729-737, 2010.
[38] R. R. Reeber and K. Wang,“High temperature elastic constant prediction of some group III-nitrides,”MRS Internet J. Nitride Semicond Res., vol. 6, no.3, pp.1-5, 2001.
[39] R. R. Reeber and K. Wang,“Lattice parameters and thermal expansion of GaN,”J. Mater. Res., vol. 15, pp.40-44, 2000.
[40] J. Zou, D. Kotchetkov, A. A. Balandin, D. I. Florescu, and F. H. Pollak,“Thermal conductivity of GaN films: effects of impurities and dislocations,”J Appl Phys, vol. 92, no. 5, pp. 2534-2539, 2002.
[41] E. A. Burgemeister, V. W. Muench, and E. Pettenpaul“Thermal conductivity and electrical properties of 6H silicon carbide,”J Appl Phys, vol. 50, no. 9, pp. 5790-5794, 1979.
[42] G. R. Liu and S. S. Quek,“The Finite Element Method: A Practical Course”, Butterworth-Heinemann, 2003.
[43] K. Raleva, D. Vasileska, S. M. Goodnick, and M. Nedjalkov,“Modeling thermal effects in nanodevices,”IEEE Trans. Electron Devices, vol. 55, no. 6, pp. 1306-1316, Jun. 2008.
[44] A. C. Polycarpou,“Introduction to the Finite Element Method in Electromagnetics”, Morgan&Claypool Publishers, 2006.
[45] M. Lundstrom and Z. B. Ren,“Essential physics of carrier transport in nanoscale MOSFETs,”IEEE Trans. Electron Devices, vol. 49, no. 1, pp. 133-141, Jan. 2002.
[46] S. Sinha, E. Pop, R. W. Dutton and K. E. Goodson,“Non-equilibrium phonon distributions in sub-100 nm silicon transistors,”ASME J. Heat Transfer, vol. 128, pp. 638-647, Jul. 2006.
[47] K. K. Mei, R. Pous, and Z. chen,“The measured equation of invariance: a new concept in field computation,”IEEE Trans. Antenna and Propagation, vol. 43, no. 3, pp. 320–327, 1994.
[48] M. Falconer, and V. Tripathi,“FDTD simulation of power/ground bounce and crosstalk in IC packages,”IEEE 5th Topical Meeting on Electrical Performance of Electronin Packaging, pp. 166–168, 1996.
[49] G. T. Nobauer and H. Moser,“Analytical approach to temperature evaluation in bonding wires and calculation of allowable current,”IEEE Trans. Advanced Pack., vol. 23, no. 3, pp. 426-435, 2000.
[50] http://en.wikipedia.org/wiki/Ludwig_von_Mises
[51] Z. Ren, W. Y. Yin, Y. B. Shi and Q. H. Liu,“Thermal accumulation effects on the transient temperature response in LDMOSFETs under the impact of a periodic electromagnetic pulse,”IEEE Trans. Electron Devices, vol. 57, no. 1, pp. 345-352, Jan. 2010.
[52] C. Mao, and H. Zhou,“Noval parameter estimation of double exponential pulse (EMP, UWB) by statistical means,”IEEE Trans. Electromagn. Compat., vol. 50, no.1,pp.97-100, 2008.
[53] A. M. Darwish, A. J. Bayba, and H. A. Hung,“Thermal Resistance Calculation of AlGaN–GaN Devices,”IEEE Trans. Microwave Theory Tech., vol. 52, no.11, pp. 2611-2620, 2004.
[54] A. M. Darwish, A. J. Bayba, and H. A. Hung,“Accurate determinaion of thermal resistance of FETs,”IEEE Trans. Microwave Theory Tech., vol. 53, no.1, pp. 306-313, 2005.
[55] J. Park, M.W. Shin, and C. C. Lee,“Thermal modeling and measurement of GaN-based HFET devices,”IEEE Electron Device Lett., 2003, vol. 24, no. 7, pp. 424–426, 2003.