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HVPE反应器的环形分隔进口数对生长均匀性的影响赖晓慧;左然;师珺草;刘鹏;童玉珍;张国义【摘要】利用FLUENT软件对3种环形分隔进口(4环、8环、12环)的氢化物气相外延(HVPE)反应器的生长均匀性进行了二维数值模拟研究.分别考虑输运模型和输运-生长模型,模拟过程保持相同的GaCl、NH3及N2气体进口流量.结果显示:在只考虑输运的模型中,反应室流动均匀性随着进口环数的增多而改善.8环进口时,衬底上方温度分布最均匀；4环进口时,衬底上方的GaC1浓度较高,但均匀性最差,V/Ⅲ比也较低；8环及12环进口可得到均匀的GaCl浓度分布及较高的V/Ⅲ比.在包括输运和GaN生长的模型中,尽管8环进口反应器衬底上方的GaCl浓度低于12环进口反应器,却因其较薄的边界层厚度而导致较高的生长速率,并且生长均匀性较高.因此,8环进口反应室更有利于GaN的HVPE生长.%Two-dimensional numerical simulation was performed by FLUENT for the HVPE reactor with different segmented annular inlets,considering the transport model and transport-growth model,with the flow rates of GaCl,NH3 and N2 kept constant.When only considering the gas transport,the results show that the flow uniformity is improved by increasing the number of annular inlets and the 8 annular inlets reactor can give the most uniform temperature distribution on the substrate.The GaC1 concentration on the substrate of 4 annular inlets is high,but the uniformity is poor,and the V/Ⅲratio is also low.The 8 and 12 annular inlets can give uniform GaCl concentration distribution on the substrate,and high V/Ⅲ ratio.When the GaN growth rate is also considered,the results show that the growth rate for 8 inlets is higher than that of the 12 inlets because of the thinner boundary layer ofthe GaCl concentration,although the GaCl concentration for 8 annular inlets is lower than that of the 12 annular inlets on the substrate.Thus,the 8 annular inlets is more advantageous to the GaN HVPE growth.【期刊名称】《发光学报》【年(卷),期】2013(034)006【总页数】6页(P797-802)【关键词】HVPE;GaN;环形进口;反应器设计;数值模拟【作者】赖晓慧;左然;师珺草;刘鹏;童玉珍;张国义【作者单位】江苏大学能源与动力工程学院,江苏镇江212013;江苏大学能源与动力工程学院,江苏镇江212013;江苏大学能源与动力工程学院,江苏镇江212013;北京大学物理学院宽禁带半导体研究中心,北京100871;北京大学物理学院宽禁带半导体研究中心,北京100871;北京大学物理学院宽禁带半导体研究中心,北京100871【正文语种】中文【中图分类】O471 引言GaN作为第三代半导体材料，广泛应用于蓝光LED、半导体激光器和大功率电子器件HEMT的制备。
有限体积法定价带随机波动率的欧式期权甘小艇;关南星;张坤【摘要】考虑求解带随机波动率的欧式期权定价问题的有限体积方法，先将相应的Black-Scholes 方程简化为与之等价的守恒形式，再基于重心对偶剖分和线性有限元空间，构造向后 Euler 和 Crank-Nicolson 有限体积格式。
数值实验表明，所构造的有限体积格式有效。
%We considered a finite volume method for pricing European options with stochastic volatility.We first simplified the corresponding Black-Scholes equation to the equivalent conservation form.Then,we constructed backward Euler and Crank-Nicolson finite volume schemes based on barycenter dual partition and a linear finite element space.Numerical experiments show that the proposed finite volume schemes are effective.【期刊名称】《吉林大学学报（理学版）》【年(卷),期】2016(054)006【总页数】7页(P1307-1313)【关键词】欧式期权定价;有限体积法;数值实验【作者】甘小艇;关南星;张坤【作者单位】楚雄师范学院数学与统计学院，云南楚雄 675000; 同济大学数学系，上海 200092;楚雄师范学院数学与统计学院，云南楚雄 675000;楚雄师范学院数学与统计学院，云南楚雄 675000【正文语种】中文【中图分类】O241.82期权定价问题目前流行的数值求解方法主要有两类: 随机方法和确定性方法. 随机方法主要借助计算机采用Monte-Carlo模拟方法对期权进行定价,但该方法存在设计复杂、计算时间长、计算精度不理想等缺陷,且对求解美式期权问题不是特别有效. 因而,人们更倾向于研究确定性方法的求解[1-2]. 有限体积法[3]和有限差分法、有限元法相同,是求解偏微分方程数值解的重要方法之一. 该方法格式构造简单、网格剖分灵活、数值精度高,且易于处理复杂的边界条件,尤其可以保持某些物理量局部守恒性,使得其在计算流体力学等领域应用广泛.目前,关于有限体积法在期权定价中的应用已有很多结果[4-6]. 文献[7-12]采用拟合有限体积法(fitted finite volume method)的数值离散方法对不同期权模型进行了定价. 拟合有限体积法本质上是应用局部拟合技术对传统有限体积法的改进,其主要思想是通过求解定义在每个离散区间上的两点边值问题近似区间上的精确解. 但由于该方法不基于有限元空间的求解,通常不利于高次元的构造,特别是针对二维偏微分方程定解问题时,仅限于矩形网格的网格剖分,因此对于复杂边界条件的处理具有明显的局限性. 本文考虑经典有限体积法[13-15]定价二维带随机波动率的欧式期权模型. 基于三角剖分和重心对偶剖分,构造了带随机波动率的欧式期权模型的向后Euler和Crank-Nicolson两种稳定的有限体积格式,并给出相应的离散过程. 数值实验以3个不同收益函数为例,验证了所构造有限体积格式的有效性和稳健性.设u(x,y,t)表示期权价格,则带随机波动率的欧式期权满足如下偏微分方程[10]:其中: x和y分别表示原生资产价格和方差; ρ表示x和y的相关系数; ξ和μ表示方差为y的随机过程中产生的常数参数; r为无风险利率. 设求解区域为:(x,y,t)∈(0,X)×(ζ,Y)×(0,T),并记Ω=[0,X]×[ζ,Y].为方便,本文在方程(1)中令τ=T-t,并利用待定系数法将方程(1)简化为如下标准形式(仍记时间变量为t):式(2)中的系数矩阵分别为对方程(1)施加的初值条件(即收益函数)分别为:1) 标准期权: u(x,y,0)=g(x),其中g(x)=max(0,x-E),式中E为期权的敲定价格.2) 现金或零报酬期权: u(x,y,0)=g(x),其中g(x)=BH(0,x-E),式中: B>0为常数; H为Heaviside函数.3) 蝶式套利期权: u(x,y,0)=g(x),其中上述初值条件相应的边界条件为特别地,边界条件y=ζ和y=Y需求解相应退化后的一维问题[6]. 本文主要考虑欧式看涨期权的有限体积离散,看跌期权的处理方法类似.对Ω做三角剖分Th={k},节点集用NP表示. 设剖分族是正则拟一致的,即存在常数δ0,γ与h无关,使得hk/ρk≤δ0,h/hk≤γ,其中:(s): 圆s⊂k}.做Th的对偶剖分如下: 对于每个单元k∈Th,任取一点,用直线连接Q与k的三边中点,这些直线将三角形k分成3个子区域. 对于每个节点P∈NP,所有包含P的上述子区域的并,构成了围绕P的体积 (box或control volume),记作bP. 于是可得Th的对偶剖分={bP,P∈NP}. 显然有bP. 本文取Q为三角形k的重心,即对偶剖分为重心对偶剖分,如图1所示.定义1 与三角剖分Th相应的线性有限元空间定义为∀k∈Th}.定义2 与对偶剖分相应的分片常数空间定义为常数,∀}.定义3 与三角剖分Th相应的分片常数空间定义为常数,∀k∈Th}.定义4 有界线性算子: )→Vh和分别定义为其中: Qk为单元k的重心; x=(x,y).任取,由高斯散度定理知,抛物型方程(2)可转化为如下积分形式: 求u∈H1(Ω),使得其中n为边界∂bP的单位外法向量.将方程(6)中的未知函数u限制在有限元空间Uh上,得到经典的有限体积格式: 求uh: (0,T]→Uh,使得类似文献[14-15]的方法,将方程(7)中的系数矩阵A和B分别用aij)2×2和近似替换,则可得另一高效的半离散有限体积格式: 求uh∈Uh,使得由于方程(8)中含有低阶导数项,尽管有限体积离散得到的代数系统不再对称,但针对方程中变系数的近似逼近处理却可极大节省计算量,且可较好地保持数值精度[15-16]. 下面以一个内节点为例,推导半离散格式(8)的离散方程. 由cos(n,x)ds=dy和cos(n,y)ds=-dx可知,方程(8)中右边第二项可变形为其中:同理,对低阶项有因为uh在k∈Th中为线性函数,易知有因此,结合式(9)～(12)知如下离散方程成立:其中：表示Δk的面积; Φi∈U h为相应节点Pi的基函数.此外,在边界节点上,边界条件x=0和x=X可直接由下式计算得到:考察边界条件y=ζ和y=Y,需求解退化后的一维问题,相应的计算可参见文献[6]. 经有限体积离散,半离散格式(8)的矩阵形式为其中: u为所求的未知向量; M为质量矩阵; A为刚度矩阵; b为经边界处理后所得的右端向量.下面构造方程(8)的全离散有限体积格式. 令0=t0<t1<…<tNT=T表示时间区间[0,T]的一个均匀剖分,其中τ=tl-tl-1(l=1,2,…,NT),记τ. 求解方程(2)的向后Euler 有限体积格式为: 求使得与格式(16)相对应的矩阵形式为在时间区间中点处采用Crank-Nicolson逼近,则可得相应的Crank-Nicolson有限体积格式为: 求使得类似地,与格式(18)相应的矩阵形式为代数方程组(17),(19)可采用多种数值方法求解,如Jacobi方法、 Gauss-Seidel方法、 SOR迭代、 GMRES方法和多重网格方法等,本文主要采用GMRES方法进行求解.下面以3个带随机波动率的欧式看涨期权为例,验证本文有限体积格式的有效性和稳健性. 其中,时间方向均采用Crank-Nicolson格式,离散后的代数方程组均采用GMRES方法求解.例1 取模型(1)中的参数为相应的初始条件为u(x,y,0)=max(0,x-E); 边界条件为u(0,y,t)=0,u(X,y,t)=X-E. 模型参数(20)与文献[16]取值相同. 当网格剖分取(m,n,l)=(50,50,280)时,例1在不同时间点处对应的欧式期权价格曲面如图2所示. 由图2可见,由有限体积格式计算所得的数值解是稳健的,且与文献[16]所得结论吻合.例2 取模型(1)中的参数为相应的初始条件为u(x,y,0)=BH(0,x-E); 边界条件为u(0,y,t)=0,u(X,y,t)=B. 模型参数(21)与文献[16]取值相同,所得数值解在不同时间点处的欧式期权价格曲面如图3所示,其中网格剖分为(m,n,l)=(50,50,280). 由图3可见,本文所构造的格式是稳健的,且与文献[16]所得结论吻合.例3 取模型(1)中的参数为初始条件为边界条件为模型参数(22)与文献[16]取值相同. 由于收益函数式(23)较复杂,其计算也较复杂. 当网格剖分取(m,n)=(200,200)时,所得边界y=ζ和y=Y上的数值解如图4所示. 当网格剖分取(m,n,l)=(50,50,280)时,所得不同时间点处的欧式期权价格曲面如图5所示. 由图4和图5可见,期权图形与文献[16]所得结论吻合.【相关文献】[1] 张凯. 美式期权定价: 基于罚方法的金融计算 [M]. 北京: 经济科学出版社,2012. (ZHANG Kai. Pricing American Options: Financial Computation Based on the Penalty Method [M]. Beijing: Economic Science Press,2012.)[2] 赵文雯,袁缘,朱本喜,等. 求解美式期权定价问题的预估校正方法 [J]. 吉林大学学报(理学版),2015,53(6): 1156-1160. (ZHAO Wenwen,YUAN Yuan,ZHU Benxi,et al. Prediction-Correction Method for Pricing American Options [J]. Journal of Jilin University (Science Edition),2015,53(6): 1156-1160.)[3] LI Ronghua,CHEN Zhongying,WU Wei. Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods [M]. New York: Marcel Dekker,2000.[4] Zvan R,Forsyth P A,Vetzal K R. Penalty Methods for American Options with Stochastic Volatility [J]. Journal of Computational and Applied Mathematics,1998,91(2): 199-218. [5] 甘小艇,殷俊锋. 二次有限体积法定价美式期权 [J]. 计算数学,2015,37(1): 67-82. (GAN Xiaoting,YIN Junfeng. Quadratic Finite Volume Method for Pricing American Options [J]. Mathematic Numerica Sinica,2015,37(1): 67-82.)[6] 甘小艇,殷俊锋. 有限体积法定价美式期权 [J]. 应用数学与计算数学学报,2014,28(3): 253-265. (GAN Xiaoting,YIN Junfeng. Finite Volume Method for Pricing American Options [J]. Communication on Applied Mathematics and Computation,2014,28(3): 253-265.)[7] WANG Song. A Novel Fitted Finite Volume Method for the Black-Scholes Equation Governing Option Pricing [J]. IMA Journal of Numerical Analysis,2004,24(4): 699-720. [8] ZHANG Kai,WANG Song. Pricing Options under Jump Diffusion Processes with Fitted Finite Volume Method [J]. Applied Mathematics and Computation,2008,201(1/2): 398-413.[9] ZHANG Kai,WANG Song. A Computational Scheme for Uncertain Volatility Model in Option Pricing [J]. Applied Numerical Mathematics,2009,59(8): 1754-1767.[10] Huang C S,Hung C H. On Convergence of a Fitted Finite-Volume Method for the Valuation of Options on Assets with Stochastic Volatilities [J]. IMA Journal of Numerical Analysis,2010,30(4): 1101-1120.[11] ZHANG Kai,WANG Song. Pricing American Bond Options Using a Penalty Method [J]. Automatica,2012,48(3): 472-479.[12] ZHANG Kai,WANG Song. A Robust Numerical Scheme for Pricing American Options under Regime Switching Based on Penalty Method [J]. ComputationalEconomics,2014,43(4): 463-483.[13] LIN Yanping,LIU Jianguo,YANG Min. Finite Volume Element Methods: An Overview on Recent Developments [J]. International Journal of Numerical Analysis and Modeling (Series B),2013,4(1): 14-34.[14] GAN Xiaoting,YIN Junfeng. Symmetric Finite Volume Method for Second Order Variable Coefficient Hyperbolic Equations [J]. Applied Mathematics and Computation,2015,258(19): 1015-1028.[15] GAN Xiaoting,YIN Junfeng. Symmetric Finite Volume Element Approximations of Second Order Linear Hyperbolic Integro-Differential Equations [J]. Computers and Mathematics with Applications,2015,70(10): 2589-2600.[16] Huang C S,Hung C H,WANG Song. A Fitted Finite Volume Method for the Valuation of Options on Assets with Stochastic Volatilities [J]. Computing,2006,77(3): 297-320.。
三维S形进气道沿程结冰参数分析方法李静;刘振侠;胡剑平【摘要】提出了一种三维进气道沿程结冰参数分析方法.采用欧拉-拉格朗日法计算气液两相流场,得到进气道结冰表面的水滴撞击特性以及水滴运动轨迹.利用用户自定义函数(UDF)对FLUENT进行二次开发,编写了三维进气道结冰参数数值模拟程序.通过对三维S形进气道的数值计算,得到了唇口及沿程管道的水收集率以及水滴分布情况,分析了水滴的质量浓度分布在进气道沿程中的变化情况,发现管道曲率的变化、横截面半径的变化、水滴的撞击是影响水滴浓度在管道中变化的主要因素.三维进气道沿程结冰参数分析方法可以改善目前把大气结冰参数直接用于发动机进口部件结冰数值计算的误差.【期刊名称】《科学技术与工程》【年(卷),期】2018(018)021【总页数】5页(P141-145)【关键词】三维S形进气道;两相流;结冰参数;户自定义函数;数值模拟【作者】李静;刘振侠;胡剑平【作者单位】西北工业大学动力与能源学院,西安710072;西北工业大学动力与能源学院,西安710072;西北工业大学动力与能源学院,西安710072【正文语种】中文【中图分类】V231.1飞机飞行中，与大气中过冷水滴发生碰撞的部件，如机翼、发动机旋转帽罩、进气道等部件均会发生结冰现象。
发动机进气道作为发动机进口部件重要的组成部分之一，空气通过进气道进入发动机以保证发动机的正常工作。
结冰会导致进气道的气动外形发生改变，造成发动机气动性能恶化；不断堆积的结冰还会减小进气道气流的流通面积，造成通过的气流不断减少，使得发动机推力不断下降；当气流夹带着进气道脱落的结冰进入到发动机内部后，很可能打坏整台发动机。
因此，进气道结冰会给飞行的安全性带来难以估量的危害。
目前国内外大部分的结冰数值模拟计算研究都是将大气结冰参数直接用于发动机结冰部件[1-3]，忽略了气流在通过进气道时，结冰参数也会随之改变的事实，造成最终结冰数值计算的不准确[4-7]。
INTRODUCTIONAs one of the Air Independent Propulsion (AIP) and the mature technology of diesel engine, Closed Cycle Diesel Engine (CCD) system has the advantages of mature technology and low cost. The characteristics of intake mixture gas is one of factors which have great influence on the operation conditions of diesel engine, the studying of this parameters’ effects on performance is important for improving the performance of CCD.This paper used the 4102BG diesel engine as power unit of CCD, and the works toward it have been carried out as follows:1. The principles of simulation of all the subsystems were described. According to the structure drawings and test data of the diesel engine, the simulation model was established in GT-Power. Its validation is conformed through the results comparison of simulation and test data.2. Based on the simulation model, the effects of characteristic parameters such as mixture components, specific heat ratio and system pressure on performance of CCD are analyzed.3. In order to realize the goal of this study, some improvements have been made. Based on the original test bench, the measure and control systems are improved, and the absorber of carbon dioxide and ancillary measure and control equipments are added to the test bench.4. Reference to the simulation results, experimental studies are done. In the semi-closed condition, qualitative study of argon on performance of CCD is done. In the closed condition, the effects of argon, water flow of the absorber on the performance are studied qualitatively, as well as the load characteristics.The simulation and experimental results suggest that, in the intake mixture gas, the low specific heat ratio of carbon dioxide makes the combusting condition worse, which results in a worse performance. The argon inserted in the intake gas can compensate the effect of carbon dioxide and improve the performance of CCD. Simulation results suggestted that the effect of oxygen on the performance of CCD is not so obviously. The specific heat ratio of mixture can affect the performance of CCD obviously. In a certain extent, increasing the system pressure can improve the performance of CCD.Based on the previous study, the closed cycle diesel engine test bench achieves close operation though adding absorber of carbon dioxide. In our nation, this is first CCD test-bed based onmulti-cylinder diesel engine and can operate in close. And it could achieve long-term stable operation with enough gas, which is a valuable reference for the following study of CCD.Key words: CCD; Performance; Mixture gas; Simulation; Experimental1-作者-日期式注释ReferenceH.W.Rahn. The all-electric ship-an answer to future challenges.Naval Forces，1999,(2):38-46Gunter Sattler. Fuel cells going on-board. Journal of Power Sources，2000, (86):61-67 NN. Replacing Iceland's Fossil Fuels. Fuel Cell Technology News,1999,Vo1.1,(6):3G.Sattler. PEFCs for naval ships and submarines: many tasks one solution. J.PowerSources ,1998,Vo1.71: 144-149H.Kalai,B.Kbelifa,N.Badi.et a1.Correlation between high-pressure effects and alloying inGaP and AIR. Materials chemistry and physics，1995, (39):180-184Rick1 .Zadoks,Durga Prasad,Ral Kokatam.Three-Dimensional finite element model of a threaded puter modeling and simulation in engineering,1999 ,Vol.4,(4):201~211Wheatley,C.J.,Prince et parison between date from the thorney island gas trail and prediction of simple dispersion models. UKAEASRD.1986:355Raj,Phani K, Morris, John A.Source Charaterization and Heavy Gas Dispersion Models for Reactive Chemicals Volume 1.AD-A200: 121D.M.Webber. The physics of heavy gas cloud dispersal. SRD, 1983:243Pesquill F.Atmospheric diffusion. New York: Wiley, 1974:429Chan S.T.,Ermak D.L.,Morris L.K. .FEM3 model simulations of selected Thorney Island Phase I trials. Journal of hazardous materials,19 87,Vol.16:267-292Bricard P., Friedel L.. Two-phase jet dispersion. Journal of hazardous materials, 1998,Vol.59: 287-310Kaiser G D. A review of models for predicting the dispersion of ammonia in the atmosphere. Plant/Operations Progress, 1989,Vol.8,(1):58-64Gregory.M.N. Visualization in Scientific and Engineering Computation. Computer,1991, Vol.24,(9):105-115Holt T, Raman S.A review and comparative evaluation of multilevel boundary layer parameterizations for first-order and turbulent kinetic energy closure schemes. Review of Geophysics,1988,Vol.26,(4):761-780Paul,R.W.Interactive Scientific Visualization of Fluid Flow, Computer,1993,Vol.26,(10):721-733Gruia_C R. A Taxonomy of Program Visualization Systems.Computer,1993,Vo1.26,(12):613-628William L.H,etc. Interactive Visualization of Earth and Space Science Computations.Computer,1994,7:867-879Rigal A. Numerical analysis of three-time-level finite difference schemes for unsteady diffusion-convection problems. Int.J.numer methods eng,1990:30Abdellatif Agouzal. Discontinuous finite element method for convection-diffusionequations .Journal of computational mathematics, 2000,Vol.18,(6):639-644Xing-ye Yue, Li-shang Jiang,Tsi-min Shih. Finite element analysis of a local exponentially fitted scheme for time-dependent convection-diffusion problems.Journal of computational mathematics, 1999,Vo1.17,(3):225-232Alan B.Crocket, Gregory J.White, Sidney draggan. Toxic metal contamination in soil and marine sediment associated with refuse dumps at palmer station Antarctica.Intern .J .Environmental Studies, 1998,Vo1.55:161-174Zhao Junning. Source-type Solutions of Degenerate Parabolic Quasilinear Equations.J.Diff Equations,1991,Vol.92,(2):179-197Brezis H, Friedman A.Nonlinear Parabolic Equations Involuing Measures as Initial Conditions. J Math Pure et Applications, 1983,Vol.62:73-77M.Stynes,E.O’Riordan. An analysis of a singularly perturbed two-point boundary problem using only finite element techniques. p.,1991,Vol.56:663-675 Fernandes R I .Fairweather G An Alternating Direction Galerkin Method for a Class of Second-order Hyperboilc Equations in Two Space Variables. SLAM J Numer Anal.1991,Vol.28:1265-1281Jerkt Havens et al. Developments in Liquefied Natural Gas Dispersion Modeling, Int’L conf, Workshop on Mitigating the consequences of Accidental releases of hazardous matrials,1991 5:201-213Chong C.S,Sen A,de Souza R.ISE.An Interactive Knowledeg-Based Simulation Interface for Manufacturing. Operations Research Society of Japan,1994:287-293 Deslandres V, Pierreval H.An Expert System Prototype Assisting the Statistical Validation of Simulation Model. Simulation,1991,Vol.56,( 2):79-89Friedman L W, Friedman H H.Analyzing Simulation Output Using the Bootstrap Method .Simulation，1995, Vol.64,(2):95-100Gottfried B S .Use of Computer Graphics in Fitting Statistical Distribution Functions To Data Representing Random Events Simulation...Simulation 1993,Vol.60,(4):281-286 Merkutyeva G V, Merkuryev Y A.Knowledge Based Simulation Systems-a Review.Simulation, 1994,Vol.62,( 2):74-89Yunker J M, Tew J D.Simulation Optimization by Genetic Search.Mathematics and Computers in Simulation, 1994,Vo1.37:17-28Zhengjun Zhang,Yuncheng Feng. An Approximate Algorithm of Generation Variates and Computing Probabilities for Non-uniform Continuous Statistical Distribution.Simulation，1997,Vo1.69,(2):91-10Hayes L J. Calerkin Alternating-direction Methods for Nonrectangular Regions Using Patch Approximations. SLAM J Numer Anal,1981,Vo1.18:627-643Murata T. Petri nets proplerties, analysis and applications. Proceedings of the IEEE,1989,Vo1.77,(4):541-580Lin C et al. Logical inference of Horn clauses in Petri net models. IEEE Trans on Knowledge and Data Engineering, 1993, 5(4):416-425Biljon W R. Extending Petri nets for specifying man-machine dialogues Int .J. Man- Machine Studies, 1988, Vol.28 (4):437-455Oberquelle H, Kupka I, Maass H. A view of human-machine communication and cooperation .Int.J.Man-Machine Studies, 1983, Vol.19:309-333Tabak D, Levid A H. Petri net representation of decision models. IEEE Trans. Syst. Man, Cybm, 1985, SMC-15(6):812-818Feldbrugge F, Jensen K. Petri net tool overview 1986.NCS, 1987, Vol.255:20-61Best, Fernandez C. Notations and terminology on Petri net theory. Petri Net Newsletters, 1986, Vol.23:21-46Martinez, Silva M. A simple and fast algorithm to obtain all invariants of a generalized Petri net. Infonnatik-Fachbrichite, 1982, Vol.52:301-310Reisig W. Petri nets with individual tokens. Informatik-Fachberichte, 1983, Vol.66:220-249Jensen K. High-level Petri nets. Informatik-Fachberichte,1983,Vo1.66:166-180IEEE Standard for Distributed Interactive Simulation -Application Protocol[s] ,IEEE Std 1278.1-1995IEEE Standard for Distributed Interactive Simulation-Communication Servers and Protfiles[S], IEEE Std 1278.2-1995T. Damak, J.P. Babary, M.T. NihtilaE. Observer design and sensor location in distributed parameter bioreactors. Porc. DYCORD,1992,V o1.923:315-320Torfinn taxt, Anne H.Schistad Solberg. Information fusion in remote sensing. Vistas in Astronomy,1997,Vo1.41，(3):337-342Z.H. Qureshi，T.S. Ng，GC. Goodwin. Optimum experimental design for identification of distributed parameter systems. Int J. Control, 1980，Vol.31:21-29F.W.J.van den Berg, H.C.J. Hoefsloot, H .F.M. Boelens et al. Selection of optimal sensorposition in a tubular reactor using robust degree of observability criteria.Chemical Engineering Science, 2000,V ol.55:827-8372-数字式注释Reference1. H.W.Rahn. The all-electric ship-an answer to future challenges. Naval Forces，1999,(2):38-462. Wheatley,C.J.,Prince et parison between date from the thorney island gas trailand prediction of simple dispersion models. UKAEASRD.1986:3553. William L.H,etc. Interactive Visualization of Earth and Space Science Computations.Computer,1994,7:867-8794. Z.H. Qureshi，T.S. Ng，GC. Goodwin. Optimum experimental design for identificationof distributed parameter systems. Int J. Control, 1980，Vol.31:21-295. Holt T, Raman S.A review and comparative evaluation of multilevel boundary layerparameterizations for first-order and turbulent kinetic energy closure schemes. Review of Geophysics,1988,Vol.26,(4):761-7806. Paul,R.W.Interactive Scientific Visualization of Fluid Flow, Computer,1993,Vol.26,(10):721-7337. Gunter Sattler. Fuel cells going on-board. Journal of Power Sources，2000, (86):61-678. Raj,Phani K, Morris, John A.Source Charaterization and Heavy Gas DispersionModels for Reactive Chemicals Volume 1.AD-A200: 1219. D.M.Webber. The physics of heavy gas cloud dispersal. SRD, 1983:24310. Pesquill F.Atmospheric diffusion. New York: Wiley, 1974:42911. Chan S.T.,Ermak D.L.,Morris L.K. .FEM3 model simulations of selected ThorneyIsland Phase I trials. Journal of hazardous materials,19 87,Vol.16:267-29212. Bricard P., Friedel L.. Two-phase jet dispersion. Journal of hazardous materials,1998,Vol.59: 287-31013. Kaiser G D. A review of models for predicting the dispersion of ammonia in theatmosphere. Plant/Operations Progress, 1989,Vol.8,(1):58-6414. Gregory.M.N. Visualization in Scientific and Engineering Computation.Computer,1991, Vol.24,(9):105-11515. H.Kalai,B.Kbelifa,N.Badi.et a1.Correlation between high-pressure effects andalloying in GaP and AIR. Materials chemistry and physics，1995, (39):180-18416. Rick1 .Zadoks,Durga Prasad,Ral Kokatam.Three-Dimensional finite element model ofa threaded puter modeling and simulation in engineering,1999 ,Vol.4,(4):201~21117. Gruia_C R. A Taxonomy of Program Visualization Systems.Computer,1993,Vo1.26,(12):613-62818. Chong C.S,Sen A,de Souza R.ISE.An Interactive Knowledeg-Based SimulationInterface for Manufacturing. Operations Research Society of Japan,1994:287-293 19. Rigal A. Numerical analysis of three-time-level finite difference schemes for unsteadydiffusion-convection problems. Int.J.numer methods eng,1990:3020. Abdellatif Agouzal. Discontinuous finite element method for convection-diffusionequations .Journal of computational mathematics, 2000,Vol.18,(6):639-64421. Hayes L J. Calerkin Alternating-direction Methods for Nonrectangular Regions UsingPatch Approximations. SLAM J Numer Anal,1981,Vo1.18:627-64322. Alan B.Crocket, Gregory J.White, Sidney draggan. Toxic metal contamination in soiland marine sediment associated with refuse dumps at palmer station Antarctica.Intern .J .Environmental Studies, 1998,Vo1.55:161-17423. Zhao Junning. Source-type Solutions of Degenerate Parabolic QuasilinearEquations.J.Diff Equations,1991,Vol.92,(2):179-19724. Brezis H, Friedman A.Nonlinear Parabolic Equations Involuing Measures as InitialConditions. J Math Pure et Applications, 1983,Vol.62:73-7725. M.Stynes,E.O’Riordan. An analysis of a singularly perturbed two-point boundaryproblem using only finite element techniques. p.,1991,Vol.56:663-675 26. Fernandes R I .Fairweather G An Alternating Direction Galerkin Method for a Classof Second-order Hyperboilc Equations in Two Space Variables. SLAM J Numer Anal.1991,Vol.28:1265-128127. Jerkt Havens et al. Developments in Liquefied Natural Gas Dispersion Modeling,Int’L conf,Workshop on Mitigating the consequences of Accidental releases of hazardous matrials,1991 5:201-21328. NN. Replacing Iceland's Fossil Fuels. Fuel Cell Technology News,1999,Vo1.1,(6):329. Deslandres V, Pierreval H.An Expert System Prototype Assisting the StatisticalValidation of Simulation Model. Simulation, 1991,Vol.56,( 2):79-8930. Friedman L W, Friedman H H.Analyzing Simulation Output Using the BootstrapMethod .Simulation，1995, Vol.64,(2):95-10031. Gottfried B S .Use of Computer Graphics in Fitting Statistical Distribution FunctionsTo Data Representing Random Events Simulation...Simulation 1993,Vol.60,(4):281-28632. Merkutyeva G V, Merkuryev Y A.Knowledge Based Simulation Systems-a Review.Simulation, 1994,Vol.62,( 2):74-8933. Yunker J M, Tew J D.Simulation Optimization by Genetic Search.Mathematics andComputers in Simulation, 1994,Vo1.37:17-2834. Zhengjun Zhang,Yuncheng Feng. An Approximate Algorithm of Generation Variatesand Computing Probabilities for Non-uniform Continuous Statistical Distribution.Simulation，1997,Vo1.69,(2):91-1035. Xing-ye Yue, Li-shang Jiang,Tsi-min Shih. Finite element analysis of a localexponentially fitted scheme for time-dependent convection-diffusion problems.Journal of computational mathematics, 1999,Vo1.17,(3):225-23236. Murata T. Petri nets proplerties, analysis and applications. Proceedings of theIEEE,1989,Vo1.77,(4):541-58037. Lin C et al. Logical inference of Horn clauses in Petri net models. IEEE Trans onKnowledge and Data Engineering, 1993, 5(4):416-42538. Biljon W R. Extending Petri nets for specifying man-machine dialogues Int .J. Man-Machine Studies, 1988, Vol.28 (4):437-45539. Oberquelle H, Kupka I, Maass H. A view of human-machine communication andcooperation .Int.J.Man-Machine Studies, 1983, Vol. 19:309-33340. Tabak D, Levid A H. Petri net representation of decision models. IEEE Trans. Syst.Man, Cybm, 1985, SMC-15(6):812-81841. Feldbrugge F, Jensen K. Petri net tool overview 1986.NCS, 1987, Vol.255:20-6142. Torfinn taxt, Anne H.Schistad Solberg. Information fusion in remote sensing. Vistas inAstronomy,1997,Vo1.41，(3):337-34243. Martinez, Silva M. A simple and fast algorithm to obtain all invariants of ageneralized Petri net. Infonnatik-Fachbrichite, 1982, Vol.52:301-31044. Reisig W. Petri nets with individual tokens. Informatik-Fachberichte, 1983,Vol.66:220-24945. Jensen K. High-level Petri nets. Informatik-Fachberichte,1983,Vo1.66:166-18046. IEEE Standard for Distributed Interactive Simulation -Application Protocol[s] ,IEEEStd 1278.1-199547. IEEE Standard for Distributed Interactive Simulation-Communication Servers andProtfiles[S], IEEE Std 1278.2-199548. T. Damak, J.P. Babary, M.T. NihtilaE. Observer design and sensor location indistributed parameter bioreactors. Porc. DYCORD,1992,V o1.923:315-32049. Best, Fernandez C. Notations and terminology on Petri net theory. Petri NetNewsletters, 1986, Vol.23:21-4650. G.Sattler. PEFCs for naval ships and submarines: many tasks one solution. J.PowerSources ,1998,Vo1.71: 144-149。
涡流室直径对涡流管性能的影响胡卓焕;杨欣【摘要】In this paper,the pressured air is used as the working fluid,and the numerical simulation was carried out for the energy separation effect of the vortex tube with different vortex chambers. The cooling,heating effects and the isen-tropic efficiency curves of the vortex tube with different structures were obtained. The research shows that:with the in-crease of the ratio of the cold flow,the cooling temperature difference and the entropy efficiency decrease gradually,while the thermal temperature difference increases gradually. When the cold flow ratio is about 0.28,the vortex tube has the max-imum unit cooling capacity. And the vortex tube with larger vortex chamber usually has better energy separation effects.%以高压气体为工质,对配有不同涡流室内径的涡流管冷热分离效应进行数值模拟研究,并获得了不同结构的涡流管随冷流比变化的制冷制热结果,以及等熵效率曲线.研究表明,随着冷流比的增加,涡流管制冷温差逐渐减小,制热温差逐渐增大,而等熵效率逐渐减小.当冷流比为0.28左右时,涡流管能获得最大的单位制冷量.通常装有较大涡流室的涡流管能获得更好能量分离效果.【期刊名称】《真空与低温》【年(卷),期】2017(023)001【总页数】6页(P52-57)【关键词】涡流室;数值仿真;能量分离;湍流强度【作者】胡卓焕;杨欣【作者单位】上海理工大学能源与动力工程学院,上海 200093;上海理工大学能源与动力工程学院,上海 200093【正文语种】中文【中图分类】TB61+9.1涡流管是一种精巧的能量分离装置，其技术起源于法国冶金师Ranque在1933年发现的“涡流管效应”[1]。
非奇异H-矩阵判定的迭代准则王峰【摘要】Nonsingular H - matrices play a very important role in numerical analysis, matrix theory, mathematical economics,etc. But it is difficult to determine a nonsingular H - matrix in practice. In this paper, we gave several new sufficient conditions for nonsingular H - matrices, improved and generalized some relate results. Advantage of the results obtained was illustrated by some numerical examples.%非奇异H-矩阵是在计算数学、矩阵理论、经济数学等许多领域中有着广泛应用的重要矩阵类,但在实用中要判别非奇异H-矩阵是十分困难的.研究了非奇异H-矩阵的判定问题,给出了几个新迭代准则,推广了相关文献的主要结果,并给出相应数值例子说明论文结果的有效性.【期刊名称】《安徽大学学报（自然科学版）》【年(卷),期】2012(036)006【总页数】5页(P16-20)【关键词】非奇异H-矩阵;对角占优性;不可约;非零元素链【作者】王峰【作者单位】菏泽学院数学系,山东菏泽274015;云南大学数学与统计学院,云南昆明650091【正文语种】中文【中图分类】O151.21非奇异H－矩阵在理论上和应用上都十分重要，它的研究已广泛引起人们的注意.近年来，很多专家和学者都对其进行了广泛探讨，并给出了一些很好的充分条件和必要条件.论文在文［1－8］的基础上，讨论了非奇异h－矩阵的判定准则，得到了一些新的判定范围更广的条件，从而改进和推广了相应文献的一些结果.记Cn×n表示n阶全体复方阵的集合.设A=(aij)∈Cn×n，记Ri(A)=2，…，n}.若|aii|＞Ri(A)，则称A为严格对角占优矩阵;若存在正对角阵X，使得AX为严格对角占优矩阵，则称A为非奇异H－矩阵.若A为非奇异H－矩阵总有aii≠0，∀i∈N和文［1］中的引理1，总假定A满足:aii≠0，∀i∈N及Ri(A)＞0.文中引进下述记号【相关文献】［1］干泰彬，黄廷祝.非奇异H－矩阵的实用性充分条件［J］.计算数学，2004，20(1):109－116. ［2］王峰.非奇异H－矩阵的简捷判定.高等学校计算数学学报，2009，31(4):343－348.［3］Gan T B，Huang T Z.Simple criteria for nonsingular H－matrix［J］.Linear Algebra Appl，2003，374:317－326.［4］Gan T B，Huang T Z，Evans D J，et al.Sufficient conditions for H－matrices［J］.Inter J Comp Math，2005，82(2): 247－258.［5］庹清.非奇异H－矩阵判定的新条件［J］.工程数学学报，2008，25(4):749－752.［6］韩涛，陆全，徐仲，等.一组非奇异H－矩阵判定的新判据［J］.工程数学学报，2011，28(4):498－504.［7］Neumann M.A note generalizations of strict diagonal dominance for real matrice ［J］.Linear Algebra Appl，1979，26: 3－14.［8］Varga R S.On recurring theorems on diagonal dominance［J］.Linear Algebra Appl，1976，13:1－9.［9］庹清，谢清明，刘建州.非奇异H－矩阵的实用新判定［J］.应用数学学报，2008，31(1):143－151.［10］李继成，黄廷祝，雷光耀.H－矩阵的实用判定［J］.应用数学学报，2003，26(3):413－419.［11］郭希娟，高益明.广义对角占优矩阵和M－矩阵的判定［J］.数学研究与评论，1999，19(4):733－737.［12］Gao Y M，Wang X H.Criteria for generalized diagonally dominant matrices and M-matrices［J］.Linear Algebra Appl，1992，169:257－268.［13］宋乾坤.广义严格对角占优矩阵与M－阵的充分判据［J］.高等学校计算数学学报，2004，26(4):298－305.［14］Tian S X.Criteria condition for generalized diagonally dominant matrices［J］.Chin Quart J of Math，2001，75:271－282.。
Numerical Analysis of Forward-Current/V oltage Characteristics of Vertical GaN Schottky-Barrier Diodes and p-n Diodes on Free-StandingGaN SubstratesKazuhiro Mochizuki,Senior Member,IEEE,Tomoyoshi Mishima,Senior Member,IEEE,Akihisa Terano, Naoki Kaneda,Takashi Ishigaki,Member,IEEE,and Tomonobu TsuchiyaAbstract—Forward-current-density J F/forward-voltage V Fcharacteristics of vertical gallium-nitride(GaN)Schottky-barrierdiodes(SBDs)and p-n diodes on free-standing GaN substrateswere computationally,as well as experimentally,investigated.Based on the thermionic emission model,electron-drift mobility µn was used as a parameter tofit the J F–V F characteristics of both reported and fabricated GaN SBDs.At300K,µn wasfittedto be600cm2/V·s when electron concentration n was1×1016cm−3and750cm2/V·s when n was5×1015cm−3.Ac-cordingly,the theoreticalµn−n curve for a carrier compensation ratio of0.90was applied in the case of n-GaN layers on GaN sub-strates.With respect to GaN p-n diodes,the reported J F–V F characteristics were successfullyfitted with dislocation-mediated carrier lifetimes in the high-injection region and with Shockley–Read–Hall lifetimes in the generation–recombination current region.Index Terms—Gallium compounds,power semiconductordevices,simulation.I.I NTRODUCTIONG ALLIUM NITRIDE(GaN)is an attractive material foroptical and electronic devices,as well as sensors[1]. Its high breakdown electricfield of3.27MV/cm[2],which is about10%higher than that of silicon carbide(SiC)and about ten times that of silicon,makes it ideal for power devices.GaN-based power devices are usually fabricated on substrates such as sapphire,SiC,and silicon.These substrates cause dislocations in heteroepitaxially grown GaN at high density(108–1010cm−2).Free-standing GaN substrates[3]–[6] are thus expected to open the way to explore the intrinsic per-formance of GaN and its related alloys.Schottky-barrier diodes (SBDs)[7]–[12]and p-n diodes[2],[13],[14]have so far been fabricated on GaN substrates.To further improve the perfor-mance of these diodes,electrical characteristics of these devicesManuscript received March2,2011;revised April10,2011;accepted April12,2011.The review of this paper was arranged by Editor A.Haque. K.Mochizuki, A.Terano,T.Ishigaki,and T.Tsuchiya are with the Central Research Laboratory,Hitachi Ltd.,Kokubunji185-8601,Japan (e-mail:kazuhiro.mochizuki.fb@).T.Mishima and N.Kaneda are with the Research and Development Labo-ratory,Corporate Advanced Technology Group,Hitachi Cable Ltd.,Tsuchiura 300-0026,Japan.Color versions of one or more of thefigures in this paper are available online at .Digital Object Identifier10.1109/TED.2011.2145380should be numerically investigated.Although Shelton et al.[15] and Baharin et al.[16]simulated current–voltage character-istics of GaN SBDs and p-n diodes,the substrates that they assumed were sapphire.In contrast to previous studies on heteroepitaxially grown GaN devices[15],[16],this paper on homoepitaxially grown GaN devices distinguishes itself in that the two parameters are carefully evaluated:drift mobility(μn andμp)and minority-carrier lifetime(τn andτp),where subscripts n and p represent electrons and holes,respectively.These parameters directly affect forward-current-density J F/forward-voltage V F charac-teristics of SBDs and p-n diodes.Among them,μn is known to strongly depend on carrier compensation[17],which was observed in n-type GaN on GaN substrates when net doping concentration N netDwas below5×1016cm−3[10].In the previous simulation[15],however,these parameters were ten-tatively chosen asμn=350cm2/V·s(electron concentration n:5×1016cm−3),μp=12cm2/V·s(hole concentration p: 2×1017cm−3),andτn=τp=1ns.In this paper,the J F–V F characteristics of GaN SBDs and p-n diodes on GaN substrates were numerically simulated in the cylindrical coordinate system.Moreover,to determine the compensation ratio for n-GaN on GaN substrates,GaN SBDs were fabricated.The procedure for simulation and fabrication of GaN SBDs on GaN substrates is explained in Section II.Reported[10]and measured J F–V F characteristics of GaN SBDs are compared with calculated J F–V F characteristics in Section III.The re-ported J F–V F characteristics of GaN p-n diodes[2],[14]under high-and low-injection conditions are separately investigated in Section IV.The results of this study are summarized in Section V.II.S IMULATION AND F ABRICATION OF SBDsGaN SBDs on GaN substrates were simulated in the cylin-drical coordinate system by using the thermionic emission model in a commercial device simulator,i.e.,ATLAS[18].A schematic of the GaN SBD reported in[10]is shown as an example in Fig.1.The epitaxial layers consist of7-μm-thick GaN(Si:1×1016cm−3)and2-μm-thick n+-GaN buffer.For the GaN substrate,thickness of500μm,n of5×1018cm−3,0018-9383/$26.00©2011IEEEFig.1.Schematic of the GaN SBD on GaN substrates reported in[10].TABLE IM ATERIAL AND E LECTRICAL P ROPERTIESOF GaN U SED IN THE S IMULATIONFig.2.(Open circles)Measured(as reported in[10])and calculated forward-current-density/forward-voltage characteristics of the Au/n-GaN(7µm)SBDon GaN substrates on the assumption that(a)an electron mobility is600cm2/V·s and(b)a barrier height is1.58eV.an interfacial insulator;for example,0.16–0.23-eV increase inqΦB was reported for Pt–Au/n-GaN SBDs with a1–2-nm-thickoxide layer remained at the metal–semiconductor interface[1].The apparent qΦB in linear J F–V F plots should be increasedfurther by the increase in the ideality factor n as follows[21]:n=1+{(d/εi)[(εs/W)+qD sb]/[1+(d/εi)qD sa]}(1)where d is the thickness,εi is the permittivity of the insulatinglayer,εs is the permittivity of n-GaN,W is the width of thedepletion region in n-GaN,q is the elementary charge,and D saand D sb are the densities of interface states(in cm−2eV−1)inequilibrium with Au and with n-GaN,respectively.Since it is not easy to numerically simulate metal–insulator–semiconductor tunnel diodes[21],we decided to keep usingthe thermionic emission model,regarding qΦB as afittingparameter.In Fig.2(b),qΦB of1.58eV was thus assumed,andthe three curves were calculated,withμn as a parameter.Themeasured characteristics[10],denoted by open circles,are bestfitted whenμn is600cm2/V·s.Fig.3shows the simulated isocurrent-density contours ofthe Au/n-GaN SBD forward biased at1.6V.The current-conducting area is laterally spread in the GaN substrate.Thisfinding supports the aforementioned assumption that cathodecontact resistance can be neglected.Note that an error inμn due to inaccuracy in determiningqΦB remains because the reported J F–V F characteristics ofthe Au/GaN SBD are not shown in semilog plots[10].WeMOCHIZUKI et al.:ANALYSIS OF CHARACTERISTICS OF GaN SBDs AND p-n DIODES3Fig.3.Simulated isocurrent-density contours in the Au/n-GaN SBD forwardbiased at1.6V.4IEEE TRANSACTIONS ON ELECTRON DEVICESMOCHIZUKI et al.:ANALYSIS OF CHARACTERISTICS OF GaN SBDs AND p-n DIODES5Fig.7.Calculated contours of(a)isocurrent density,(b)isoelectron con-centration,and(c)isohole concentration in a p-n diode(see Fig.6)forwardbiased at5V.The minority-carrier lifetime is known to depend on in-jection level[29].If the minority-carrier lifetime under high-and low-injection conditions is denoted byτH andτL,respectivelyτH τL(4)should be satisfied[29].Under a low-injection condition,theinfluence of carrier recombination within the depletion regionextending around the p-n junction is large(i.e.,nonradiativerecombination lifetimeτNR≈τL).Under a high-injection con-dition,on the other hand,the influence of carrier recombinationwithin the minimized depletion region becomes small(i.e.,τNR≈τH).This supposition explains why the different carrierlifetimes were needed tofit the measured characteristics inFigs.6and8.It isfinally noted that the surface-recombination velocityassumed in the simulation previously described was zero(seeTable I).The quantitative agreement between the measuredand calculated forward electrical characteristics in Figs.6and8indicates that surface recombination can be negligiblysmall in p-n diodes,even with a reactive-ion-etched mesastructure[2],[14].6IEEE TRANSACTIONS ON ELECTRON DEVICES[4]K.Motoki,T.Okahisa,N.Matsumoto,M.Matsushima,H.Kimura,H.Kasai,K.Takemoto,K.Uematsu,T.Hirano,M.Nakayama,S.Nakahata,M.Ueno,D.Hara,Y.Kumagai,A.Koukitsu,and H.Seki,“Preparation of large freestanding GaN substrates by hydride vapor phase epitaxy using GaAs as a starting substrate,”Jpn.J.Appl.Phys.,vol.40, no.2B,pp.L140–L143,Feb.2001.[5]T.Paskova,D.A.Hanser,and K.R.Evans,“GaN substrates for III-nitridedevices,”Proc.IEEE,vol.98,no.7,pp.1324–1338,Jul.2010.[6]T.Yoshida,Y.Oshima,T.Eri,K.Ikeda,S.Yamamoto,K.Watanabe,M.Shibata,and T.Mishima,“Fabrication of3-in GaN substrates by hydride vapor phase epitaxy using void-assisted separation method,”J.Cryst.Growth,vol.310,no.1,pp.5–7,Jan.2008.[7]Z.Z.Bandic,P.M.Bridger,E.C.Piqette,T.C.McGill,R.P.Vaudo,V.M.Phanse,and J.M.Redwing,“High voltage(450V)GaN Schottky rectifiers,”Appl.Phys.Lett.,vol.74,no.9,pp.1266–1268,Mar.1999. [8]A.P.Zhang,J.W.Johnson,B.Luo,F.Ren,S.J.Pearton,S.S.Park,Y.J.Park,and J.-I.Chyi,“Vertical and lateral GaN rectifiers on free-standing GaN substrates,”Appl.Phys.Lett.,vol.79,no.10,pp.1555–1557,Sep.2001.[9]J.W.Johnson,A.P.Zhang,W.-B.Luo,F.Ren,S.J.Pearton,S.S.Park,Y.J.Park,and J.-I.Chyi,“Breakdown voltage and reverse recovery char-acteristics of free-standing GaN Schottky rectifiers,”IEEE Trans.Electron Devices,vol.49,no.1,pp.32–36,Jan.2002.[10]S.Hashimoto,Y.Yoshizumi,T.Tanabe,and M.Kiyama,“High-purityGaN epitaxial layers for power devices on low-dislocation-density GaN substrates,”J.Cryst.Growth,vol.298,pp.871–874,Jan.2007.[11]J.Suda,K.Yamaji,Y.Hatashi,T.Kimoto,K.Shimoyama,H.Namita,andS.Nagao,“Nearly ideal current-voltage characteristics of Schottky barrier diodes formed on hydride-vapor-phase-epitaxy-grown GaN free-standing substrates,”Appl.Phys.Express,vol.3,no.10,p.101003,Oct.2010. [12]K.Mochizuki,A.Terano,N.Kaneda,T.Mishima,T.Ishigaki,andT.Tsuchiya,“Analysis of leakage current at Pd/AlGaN Schottky barriers formed on GaN free-standing substrates,”Appl.Phys.Express,vol.4, no.2,p.024104,Feb.2011.[13]J.B.Lim,D.Yoo,J.-H.Ryou,W.Lee,S.-C.Shen,and R.D.Dupui,“Highperformance GaN pin rectifiers grown on free-standing GaN substrates,”Electron.Lett.,vol.42,no.22,pp.1313–1314,Oct.2006.[14]K.Nomoto,Y.Hatakeyama,H.Katayose,N.Kaneda,T.Mishima,andT.Nakamura,“Over1.0kV GaN p-n junction diodes on free-standing GaN substrates,”in Proc.Int.Workshop Nitride Semicond.,Tampa,FL, Sep.2010,to be published.[15]B.S.Shelton,T.G.Zhu,mbert,and R.D.Dupui,“Simulationof the electrical characteristics of high-voltage mesa and planar GaN Schottky and p-i-n rectifiers,”IEEE Trans.Electron Devices,vol.48, no.8,pp.1498–1520,Aug.2001.[16]A.Baharin,M.Kocan,G.A.Umana-Membreno,U.K.Mishra,G.Parish,and B.D.Nener,“Experimental and numerical investigation of the elec-trical characteristics of vertical n-p junction diodes created by Si implan-tation into p-GaN,”in Proc.Conf.Optoelectron.Microelectron.Mater.Devices,2008,pp.12–15.[17]V.W.Chin,T.L.Tansley,and T.Osotchan,“Electron mobilities in gal-lium,indium,and aluminum nitrides,”J.Appl.Phys.,vol.75,no.11, pp.7365–7372,Jun.1994.[18][Online].Available:/products/device_simulation/atlas.html[19]J.Neugebauer and C.G.Van de Walle,“Role of hydrogen in doping ofGaN,”Appl.Phys.Lett.,vol.68,no.13,pp.1829–1831,Mar.1996.[20]A.C.Schmitz,A.T.Ping,M.Asif Khan,Q.Chen,J.W.Yang,andI.Adesida,“Schottky barrier properties of various metals on n-type GaN,”Semicond.Sci.Technol.,vol.11,no.10,pp.1464–1467,Oct.1996. [21]H.C.Card,“Tunneling MIS structures,”Inst.Phys.Conf.Ser.,vol.50,pp.140–165,1980.[22]M.Ilegems and H.C.Montgomery,“Electrical properties of n-type vapor-grown gallium nitride,”J.Phys.Chem.Solids,vol.34,no.5,pp.885–895, May1973.[23]M.A.Khan,J.N.Kuznia,J.M.Van Hove,and D.T.Olson,“Growthof high optical and electrical quality GaN layers using low-pressure metalorganic chemical vapor deposition,”Appl.Phys.Lett.,vol.58,no.5, pp.526–527,Feb.1991.[24]I.Akasaki,H.Amano,Y.Koide,K.Hiramatsu,and N.Sawaki,“Effectsof AlN buffer layer on crystallographic structure and on electrical and optical properties of GaN and Ga1−x Al x N(0<x≤0.4)films grown on sapphire substrate by MOVPE,”J.Cryst.Growth,vol.98,no.1/2, pp.209–219,Nov.1989.[25]S.Nakamura,T.Mukai,and M.Senoh,“In situ monitoring and Hallmeasurements of GaN grown with GaN buffer layers,”J.Appl.Phys., vol.71,no.11,pp.5543–5549,Jun.1992.[26]S.Y.Karpov and Y.N.Makarov,“Dislocation effect on light emissionefficiency in gallium nitride,”Appl.Phys.Lett.,vol.81,no.25,pp.4721–4723,Dec.2002.[27][Online].Available:http://www.ioffe.ru/SV A/NSM/Semicond/GaN/index.html[28]S.M.Sze and K.K.Ng,Physics of Semiconductor Devices,3rd ed.Hoboken,NJ:Wiley,2007,p.46.[29]B.J.Baliga,Fundamentals of Power Semiconductor Devices.New York:Springer-Verlag,2008,p.62.Kazuhiro Mochizuki(M’98–SM’99)was born inTokyo,Japan,in1963.He received the B.E.,M.E.,and Ph.D.degrees in electronic engineering fromthe University of Tokyo,Tokyo,in1986,1988,and1995,respectively.Since1988,he has been with the Central ResearchLaboratory,Hitachi Ltd.,Kokubunji,Japan.He hascontributed to advance growth,device,and modelingtechnologies for compound semiconductors.He pio-neered the vapor-phase epitaxial growth of p+GaAson highly misoriented substrates and on SiO2films, as well as the solid-phase epitaxial growth of NiTe2at Ni/p+ZnTe ohmic interfaces.These growth technologies led to drastic performance improvement in heterojunction bipolar transistors(HBTs)and optoelectronic devices.He also devised several advanced HBT’s,particularly for the operation with low-power-supply voltage and reduced power dissipation.In the areas of wide-band-gap semiconductors,he modeled leakage current of AlGaN Schottky-barrier diodes on GaN free-standing substrates,homoepitaxial growth of4H-SiC under Si-rich condition,and diffusion and segregation of B and ion implantation of Al in4H-SiC.From1999to2000,he was a Visiting Researcher with the University of California,San Diego,where he worked on GaAs tunneling-collector HBTs,GaInNAs HBTs,and GaN/W/WO3metal-base transistors. He served as the Director of Projects and Public Relations,Electronic Society, the Institute of Electronics,Information and Communication Engineers from 2005to2007and has been a Part-Time Lecturer with the University of Electro-Communications,Tokyo,since2003and with Hosei University,Tokyo,since 2010.He is the author or coauthor of87research papers in international journals and conference proceedings.He is the holder of20U.S.patents.Dr.Mochizuki is a Senior Member of the IEEE Electron DevicesSociety.Tomoyoshi Mishima(M’01–SM’02)was born inTokyo,Japan,in1955.He received the B.M.,M.S.,and Ph.D.degrees in physical electronics from TokyoInstitute of Technology,Tokyo,in1978,1980,and1983,respectively.In1983,he joined the Central Research Labo-ratory,Hitachi Ltd.,Kokubunji,Japan.From1989to1990,he was an Exchange Researcher withPhilips Central Research Laboratory,Eindhoven,The Netherlands,where he worked in the areas ofhigh-mobility2-D hole gas in Si/SiGe modulation-doped structures.He has also been a Concurrent Lecturer with Waseda Uni-versity,Tokyo,from1992to1995and from1998to1999,Tokyo Institute of Technology,Tokyo,from1996to1998and2010to2011,Nagoya Institute of Technology,Nagoya,in2002,and Hosei University,Tokyo,from2000 to present.He moved to the Research and Development Laboratory,Hitachi Cable Ltd.,Tsuchiura,Japan,in2003.He is currently responsible for research on GaN crystals and lead-free piezoelectric thinfilms as a General Manager of the Advanced Electronic Materials Research Department.He has authored or coauthored more than100research papers in international journals and conference proceedings.He has worked in the areas of compound semicon-ductor and its applications to high-frequency devices.His key emphasis was on the development of high-quality metamorphic InAlGaAs heterostructures by molecular beam epitaxy and their applications for high-frequency devices. Dr.Mishima is a member of the Japan Society of Applied Physics and the Institute of Electrical Engineers of Japan(IEE Japan).He has served as an Organizer of State-of-the-Art Program on Compound Semiconductors from 1994to1996,a Subcommittee Member of the1998International Symposium on Compound Semiconductors and the Seventh International Conference on Chemical and Biomolecular Engineering,and a Research Board of the IEE Japan from2003to2011.MOCHIZUKI et al.:ANALYSIS OF CHARACTERISTICS OF GaN SBDs AND p-n DIODES7Akihisa Terano was born in Niigata,Japan,in1967. He graduated from Department of Mechanical Engi-neering,Niigata Prefectural Technical High School, Niigata,Japan,in1985.He joined the Central Research Laboratory, Hitachi Ltd.,Kokubunji,Japan,in1985,where he has been engaged in the research and development of metal process for III–V compound semiconductordevices.Naoki Kaneda received the M.S.degree fromNagoya University,Nagoya,Japan,in1996.In1996,he joined the Advanced Research Center,Hitachi Cable,Ltd.,Tsuchiura,Japan,and startedhis work on the crystal growth of compound semi-conductor.From1998to2004,he was engagedin the development of AlGaInP epitaxial layersfor high-brightness light-emitting diodes and high-power laser diodes.He moved to metal–organicvapor-phase epitaxy technology for GaN devices.Recently,his research focuses on the development ofhigh-quality GaN epitaxial layers for power-electronics applications.Mr.Kaneda is a member of the Japan Society of AppliedPhysics.Takashi Ishigaki(M’01)received the B.E.and M.E.degrees in electrical and electronic engineering fromKobe University,Kobe,Japan,in1999and2001,respectively.He joined the Compound Semiconductor Divi-sion,NEC Corporation,Otsu,Japan,in2001,wherehe was involved in the research and development ofGaAs heterojunctionfield-effect transistors(FETs)and heterojunction bipolar transistors for microwaveapplications.Since2004,he has been with the Cen-tral Research Laboratory,Hitachi Ltd.,Kokubunji,Japan,working on the research and development of high-capacity Flash mem-ories,silicon-on-insulator complementary metal–oxide–semiconductor FETs,spin-transferred magnetic memories,and wide-band-gap semiconductor-basedpower devices.Mr.Ishigaki is a member of the IEEE Electron DevicesSociety.Tomonobu Tsuchiya was born in Gunma,Japan,in1963.He received the B.S.and M.S.degrees fromTsukuba University,Tsukuba,Japan,in1986and1988,respectively.He has been with the Central Research Laboratory,Hitachi Ltd.,Kokubunji,Japan,since1988and hasbeen working on the research and development ofcrystal growth of III–V compound semiconductorsusing metal–organic vapor-phase epitaxy.Mr.Tsuchiya is a member of the Japan Society ofApplied Physics;the Japanese Association for Crys-tal Growth;and the Institute of Electronics,Information,and CommunicationEngineering of Japan.。
