半导体物理与器件-Neamen版
半导体物理与器件(尼曼第四版)答案
半导体物理与器件(尼曼第四版)答案第一章：半导体材料与晶体1.1 半导体材料的基本特性半导体材料是一种介于导体和绝缘体之间的材料。
它的基本特性包括：1.带隙：半导体材料的价带与导带之间存在一个禁带或带隙，是电子在能量上所能占据的禁止区域。
2.拉伸系统：半导体材料的结构是由原子或分子构成的晶格结构，其中的原子或分子以确定的方式排列。
3.载流子：在半导体中，存在两种载流子，即自由电子和空穴。
自由电子是在导带上的，在外加电场存在的情况下能够自由移动的电子。
空穴是在价带上的，当一个价带上的电子从该位置离开时，会留下一个类似电子的空位，空穴可以看作电子离开后的痕迹。
4.掺杂：为了改变半导体材料的导电性能，通常会对其进行掺杂。
掺杂是将少量元素添加到半导体材料中，以改变载流子浓度和导电性质。
1.2 半导体材料的结构与晶体缺陷半导体材料的结构包括晶体结构和非晶态结构。
晶体结构是指材料具有有序的周期性排列的结构，而非晶态结构是指无序排列的结构。
晶体结构的特点包括：1.晶体结构的基本单位是晶胞，晶胞在三维空间中重复排列。
2.晶格常数是晶胞边长的倍数，用于描述晶格的大小。
3.晶体结构可分为离子晶体、共价晶体和金属晶体等不同类型。
晶体结构中可能存在各种晶体缺陷，包括：1.点缺陷：晶体中原子位置的缺陷，主要包括实际缺陷和自间隙缺陷两种类型。
2.线缺陷：晶体中存在的晶面上或晶内的线状缺陷，主要包括位错和脆性断裂两种类型。
3.面缺陷：晶体中存在的晶面上的缺陷，主要包括晶面位错和穿孔两种类型。
1.3 半导体制备与加工半导体制备与加工是指将半导体材料制备成具有特定电性能的器件的过程。
它包括晶体生长、掺杂、薄膜制备和微电子加工等步骤。
晶体生长是将半导体材料从溶液或气相中生长出来的过程。
常用的晶体生长方法包括液相外延法、分子束外延法和气相外延法等。
掺杂是为了改变半导体材料的导电性能，通常会对其进行掺杂。
常用的掺杂方法包括扩散法、离子注入和分子束外延法等。
尼曼-半导体物理与器件@第四版@对应PPT@第十章
加小正栅压的p型 衬 底 MOS 电 容 器 的能带图
资源整合，共享知识第十章 金属-氧化物-半导体场效应晶体管基础
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半导体物理与器件 第四版对应课件 Semiconductor Physics and Devices Basic Principles by Neamen
主要内容
• 双端MOS结构 • 电容-电压特性 • MOSFET基本工作原理 • 频率限制特性 • 小结
资源整合，共享知识第十章 金属-氧化物-半导体场效应晶体管基础
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半导体物理与器件 第四版对应课件 Semiconductor Physics and Devices Basic Principles by Neamen
p型半导体在 阈值反型点 时的能带图
表面处的电子浓度等于体内的空穴浓度，该条件称为阈值反型
点，所加栅压为阈值电压。当外加栅压大于这一值之后，其变
化所引起的空间电荷区变化很小。空间电荷区最大宽度xdT为
xdT
4 s fp
eNa
12
此时es 2e fp
资源整合，共享知识第十章 金属-氧化物-半导体场效应晶体管基础
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半导体物理与器件 第四版对应课件 Semiconductor Physics and Devices Basic Principles by Neamen
对于n型衬底MOS电容器
电势fn同样是EFi和
EF之间的势垒高度：
fn
Vt
ln
Nd ni
xdT
4 s fn
eNd
12
此时同样es 2e fn
资源整合，共享知识第十章 金属-氧化物-半导体场效应晶体管基础
半导体物理与器件教学大纲
半导体物理与器件（教学大纲）Semiconductor Physics and Devices课程编码：12330540学分：课程类别：专业基础课计划学时： 48 其中讲课： 48 实验或实践： 0 上机：0适用专业：IC设计、电信推荐教材：尼曼（Donald H.Neamen）著，赵毅强，姚素英。
解晓东译，《半导体物理与器件》（第3版），电子工业出版社，2010参考书目：D. A. Neamen，《Semiconductor Physics and Devices: Basic Principles》，清华出版社，2003R. T. Pierret著，黄如等译，《半导体器件基础》，电子工业出版社，2004刘恩科、朱秉升、罗晋生等，《半导体物理学》，西安交通大学出版社，2004黄昆、谢希德，《半导体物理学》，科学出版社，1958曾谨言，《量子力学》，科学出版社，1981谢希德、方俊鑫，《固体物理学》,上海科学技术出版社，1961课程的教学目的与任务本课程是集成电路专业的重要选修课之一。
本课程较全面地论述了半导体的一些基本物理概念、现象、物理过程及其规律，并在此基础上选择目前集成电路与系统的核心组成部分，如双极型晶体管（BJT）、金属－半导体场效应晶体管（MESFET）和ＭOS场效应晶体管（MOSFET）等，作为分析讨论的主要对象来介绍半导体器件基础。
学习和掌握这些半导体物理和半导体器件的基本理论和分析方法，为学习诸如《集成电路工艺》、《集成电路设计》等后续课程打下基础，也为将来从事微电子学的研究以及现代VLSI与系统设计和制造工作打下坚实的理论基础。
课程的基本要求本课程要求学生掌握半导体物理和半导体器件的基本概念和基本规律，对于基础理论，要求应用简单的模型定性说明，并能作简单的数学处理。
学习过程中，注意提高分析和解决实际问题的能力，并重视理论与实践的结合。
本课程涉及的物理概念和基本原理较多，为了加深对它们的理解，在各章节里都给学生留有一些习题或思考题，这些题目有的还是基本内容的补充。
半导体物理与器件第四版第一章课后答案
o
3
a
8 3
r
o a 3 5.43 3 1.176 A 8 8 Center of one silicon atom to center of
Then r
nearest neighbor 2r 2.35 A
a (b) d 2 0.7071a 2 0.70715.65 d 3.995 A _______________________________________
1.6
o
3.38 10 23 cm 3 _______________________________________
(a) a 3 22.2 21.8 8 A Then a 4.62 A Density of A: 1 1.01 10 22 cm 3 8 3 4.62 10 Density of B: 1 1.01 10 22 cm 3 8 3 4.62 10 (b) Same as (a) (c) Same material _______________________________________
o
1.13
(a)
1 a2 4.619 10 8
3 For 1.12(a), A-atoms Surface density 1
a
22.2 21.8
4.619 A
o
2
4.687 1014 cm 2
For 1.12(b), B-atoms: Surface density
Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 1 By D. A. Neamen Problem Solutions ______________________________________________________________________________________
半导体物理与器件第四版课后习题答案1
______________________________________________________________________________________Chapter 1Problem Solutions1.1 (a)fcc: 8 corner atoms 18/1atom6 face atoms32/1atomsTotal of 4 atoms per unit cell (b)bcc: 8 corner atoms 18/1atom1 enclosed atom=1 atom Total of 2 atoms per unit cell(c)Diamond: 8 corner atoms 18/1atom6 faceatoms 32/1atoms4 enclosedatoms= 4 atomsTotal of 8 atoms per unit cell_______________________________________ 1.2 (a)Simple cubic lattice: r a 2Unit cell vol33382rra1 atom per cell, so atom vol 3413r ThenRatio%4.52%10083433rr(b)Face-centered cubic latticerd aa rd22224Unit cell vol 33321622rr a4 atoms per cell, so atom vol3443r ThenRatio%74%10021634433rr (c)Body-centered cubic latticeraa rd3434Unit cell vol 3334ra2 atoms per cell, so atom vol 3423r ThenRatio%68%1003434233r r (d)Diamond lattice Body diagonal raa rd3838Unit cell vol3338r a8 atoms per cell, so atom vol 3483r ThenRatio%34%1003834833rr _______________________________________1.3(a)oA a43.5; From Problem 1.2d,ra38Then oAa r176.18343.583Center of one silicon atom to center ofnearest neighboroAr 35.22______________________________________________________________________________________ (b)Number density22381051043.58cm 3(c)Mass density23221002.609.28105..AN W t At N 33.2grams/cm3_______________________________________1.4(a)4 Ga atoms per unit cell Number density381065.54Density of Ga atoms 221022.2cm34 As atoms per unit cell Density of As atoms 221022.2cm3(b)8 Ge atoms per unit cell Number density381065.58Density of Ge atoms221044.4cm3_______________________________________ 1.5From Figure 1.15 (a)aa d4330.0232oAd 447.265.54330.0(b)aa d7071.022oAd 995.365.57071.0_______________________________________1.674.5423232222sin a a 5.109_______________________________________ 1.7(a) Simple cubic: oAr a 9.32(b)fcc:oAr a515.524(c) bcc:oA r a 503.434(d) diamond:oAra007.9342_______________________________________ 1.8 (a)Br 2035.122035.12oBAr 4287.0(b)oAa 07.2035.12(c)A-atoms: # of atoms1818Density381007.21231013.1cm3B-atoms: # of atoms3216Density381007.23231038.3cm3_______________________________________ 1.9(a)oAr a 5.42# of atoms1818Number density38105.412210097.1cm3______________________________________________________________________________________Mass density AN W t At N ..23221002.65.12100974.1228.0gm/cm3(b)oAr a196.534# of atoms 21818Number density3810196.5222104257.1cm3Mass density23221002.65.12104257.1296.0gm/cm3_______________________________________ 1.10From Problem 1.2, percent volume of fcc atoms is 74%; Therefore after coffee is ground,Volume = 0.74 cm3_______________________________________1.11(b)oAa 8.20.18.1(c)Na: Density38108.22/1221028.2cm3Cl: Density221028.2cm3(d)Na: At. Wt. = 22.99 Cl: At. Wt. = 35.45 So, mass per unit cell23231085.41002.645.352199.2221Then mass density21.2108.21085.43823grams/cm3_______________________________________ 1.12(a)oAa 88.122.223Then oA a 62.4Density of A:22381001.11062.41cm3Density of B:22381001.11062.41cm3(b)Same as (a) (c)Same material_______________________________________ 1.13oAa619.438.122.22(a) For 1.12(a), A-atomsSurface density28210619.411a1410687.4cm2For 1.12(b), B-atoms: oAa 619.4Surface density14210687.41acm2For 1.12(a) and (b), Same material(b) For 1.12(a), A-atoms;oAa 619.4Surface density212a1410315.3cm2B-atoms;Surface density______________________________________________________________________________________14210315.321a cm 2For 1.12(b), A-atoms;oAa 619.4Surface density212a1410315.3cm2B-atoms;Surface density14210315.321acm2For 1.12(a) and (b), Same material_______________________________________ 1.14 (a)Vol. Density31oaSurface Density212oa(b)Same as (a)_______________________________________ 1.15 (i)(110) plane(see Figure 1.10(b))(ii) (111) plane(see Figure 1.10(c))(iii) (220) plane,1,1,21,21Same as (110) plane and [110]direction(iv) (321) plane6,3,211,21,31Intercepts of plane at6,3,2sq p [321] direction is perpendicular to(321) plane_______________________________________1.16(a)31311,31,11(b)12141,21,41_______________________________________ 1.17Intercepts: 2, 4, 331,41,21(634) plane_______________________________________ 1.18(a)oAa d 28.5(b)oAa d734.322(c)oAa d048.333_______________________________________ 1.19(a) Simple cubic(i) (100) plane:Surface density2821073.411a141047.4cm 2(ii) (110) plane:Surface density212a141016.3cm 2(iii) (111) plane: Area of planebh21where oAa b 689.62Now2222243222a a a hSooAh793.573.426______________________________________________________________________________________Area of plane881079304.51068923.62116103755.19cm 2Surface density16103755.19613141058.2cm2(b) bcc(i) (100) plane:Surface density 1421047.41acm2(ii) (110) plane: Surface density222a141032.6cm 2(iii) (111) plane:Surface density16103755.19613141058.2cm2(c) fcc(i) (100) plane:Surface density 1421094.82acm2(ii) (110) plane: Surface density222a141032.6cm 2(iii) (111) plane:Surface density16103755.19213613151003.1cm2_______________________________________ 1.20 (a)(100) plane: - similar to a fcc:Surface density281043.52141078.6cm 2(b)(110) plane:Surface density281043.524141059.9cm2(c)(111) plane: Surface density281043.5232141083.7cm2_______________________________________1.21oAr a703.6237.2424(a)#/cm338310703.64216818a2210328.1cm3(b)#/cm222124142a210703.62281410148.3cm2(c)oA a d74.422703.622(d)# of atoms2213613Area of plane: (see Problem 1.19)oAa b4786.92oAa h2099.826Area88102099.8104786.92121bh______________________________________________________________________________________15108909.3cm2#/cm215108909.32=141014.5cm2oAa d87.333703.633_______________________________________ 1.22Density of silicon atoms 22105cm3and4 valence electrons per atom, soDensity of valence electrons 23102cm3_______________________________________ 1.23Density of GaAs atoms22381044.41065.58cm3An average of 4 valence electrons peratom,SoDensity of valence electrons231077.1cm3_______________________________________ 1.24 (a)%10%10010510532217(b)%104%10010510262215_______________________________________ 1.25 (a)Fraction by weight7221610542.106.2810582.10102(b)Fraction by weight5221810208.206.2810598.3010_______________________________________ 1.26Volume density 1631021dcm3So610684.3dcmoAd 4.368We haveoo Aa 43.5Then85.6743.54.368oa d _______________________________________ 1.27Volume density 1531041dcm 3So61030.6dcmoAd630We have oo Aa 43.5Then11643.5630oa d _______________________________________。
尼曼半导体物理与器件第一章课件
广义原胞
尼曼半导体物理与器件第一章
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1.3.2 基本的晶体结构
立方晶系基本的晶体结构：
常见的三个基本的立方结构 （1）简单立方结构（sc） （2）体心立方结构（bcc） （3）面心立方结构（fcc）
尼曼半导体物理与器件第一章
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➢简立方结构 Simple Cubic
每个顶角有一个原子
z
➢ 体心立方结构 Body Centered Cubic
• 原胞：可以复制得到整个晶格的最小单元。
单晶晶格二维表示
•晶格、原胞的选取都不是唯一的。
尼曼半导体物理与器件第一章
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•晶胞和晶格的关系用矢量 a 、b 、c 表示，三个矢 量可不必互相垂直，长度可以不相等，基矢长度称 为晶格常数 。
•每个等效格点可用下述矢量表示
rpaqbsc
•其中，p、q、s为整数。
1. 离子晶体：离子键，例如NaCl晶体等； 2. 共价晶体：共价键，例如Si、Ge以及GaAs晶体等； 3. 金属晶体：金属键，例如Li、Na、K、Be、Mg以及Fe、 Cu、Au、Ag等； 4. 分子晶体：范德华键，例如惰性元素氖、氩、氪、氙等 在低温下则形成分子晶体，HF分子之间在低温下也通过范 德华键形成分子晶体。
• 第六章 半导体中的非平衡过剩载流子
半 • 第七章 pn结
导 • 第八章 pn结二极管
体 器
• 第九章 金属半导体和半导体异质结
件 • 第十章 金属-氧化物-半导体场效应晶体管基础
基 • 第十一章 金属-氧化物-半导体场效应晶体管：概念深入
础 • 第十二章 双极晶体管
• 第十三章 结型场效应晶体管 • 第十四章 光器件
1.11（a）-（c） 1.16 1.24（Si晶格常数5.43Å）
尼曼 半导体物理与器件第四章1
– 则整个价带范围内单位体积的总空穴浓度：
p0 ' gc E 1 f F E dE
Ev
Ev
第四章 平衡半导体（1）
8
高等半导体物理与器件
– 将前一章状态密度和分布函数代入上公式
n0
' Ec
4 2m
• f(Ec)、f(Ev)~T
T↑，Nc、Nv↑
Ec EF exp kT EF Ev exp kT
T↑，几率↑
第四章 平衡半导体（1）
13
高等半导体物理与器件
• EF位臵的影响
– EF→Ec，Ec-EF↓，n0↑—EF越高，电子（导带）
– 只要满足玻尔兹曼近似条件，下式即可成立
Ec EF n0 Nc exp kT EF Ev p0 N v exp kT
n0 p0 n Nc Nve
2 i
Eg kT
– 只要满足玻尔兹曼近似条件，n0p0的乘积为本征载流子浓 度（和材料性质有关，与掺杂无关）的平方。 – 热平衡半导体状态半导体的基本公式。
2 m kT Nc 2 h
n 2
第四章 平衡半导体（1）
32
11
高等半导体物理与器件
• 同理可得空穴浓度：
2 m kT EF Ev p0 2 exp h kT EF Ev N v exp kT
的填充水平（几率）越高；
– EF→Ev，EF-Ev↓，p0↑—EF越低，电子（价带）
的填充水平越低（空位几率越高）。
《半导体物理与器件》第四版答案第十章
Chapter 1010.1(a) p-type; inversion (b) p-type; depletion (c) p-type; accumulation (d) n-type; inversion_______________________________________ 10.2(a) (i) ⎪⎪⎭⎫⎝⎛=i a t fp n N V ln φ ()⎪⎪⎭⎫ ⎝⎛⨯⨯=1015105.1107ln 0259.0 3381.0=V 2/14⎥⎦⎤⎢⎣⎡∈=a fp s dTeN x φ()()()()()2/1151914107106.13381.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯⨯=--51054.3-⨯=cm or μ354.0=dT x m(ii) ()⎪⎪⎭⎫⎝⎛⨯⨯=1016105.1103ln 0259.0fp φ3758.0=V ()()()()()2/1161914103106.13758.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯⨯=--dTx51080.1-⨯=cmor μ180.0=dT x m(b) ()03022.03003500259.0=⎪⎭⎫⎝⎛=kT V⎪⎪⎭⎫⎝⎛-=kT E N N n g c i exp 2υ ()()319193003501004.1108.2⎪⎭⎫⎝⎛⨯⨯=⎪⎭⎫⎝⎛-⨯03022.012.1exp221071.3⨯=so 111093.1⨯=i n cm 3-(i)()⎪⎪⎭⎫⎝⎛⨯⨯=11151093.1107ln 03022.0fp φ3173.0=V()()()()()2/1151914107106.13173.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯⨯=--dT x51043.3-⨯=cm or μ343.0=dT x m(ii) ()⎪⎪⎭⎫⎝⎛⨯⨯=11161093.1103ln 03022.0fp φ3613.0=V()()()()()2/1161914103106.13613.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯⨯=--dT x51077.1-⨯=cm or μ177.0=dT x m_______________________________________ 10.3(a) ()2/14m ax ⎥⎦⎤⎢⎣⎡∈=='d fn s d dT d SDeN eN x eN Q φ()()[]2/14fns d eN φ∈=1st approximation: Let 30.0=fn φV Then()281025.1-⨯()()()()()()[]30.01085.87.114106.11419--⨯⨯=dN 141086.7⨯=⇒d N cm 3-2nd approximation:()2814.0105.11086.7ln 0259.01014=⎪⎪⎭⎫⎝⎛⨯⨯=fn φV Then ()281025.1-⨯()()()()()()[]2814.01085.87.114106.11419--⨯⨯=d N 141038.8⨯=⇒d N cm 3-(b) ()2831.0105.11038.8ln 0259.01014=⎪⎪⎭⎫⎝⎛⨯⨯=fn φV()566.02831.022===fn s φφV _______________________________________10.4 p-type silicon (a) Aluminum gate ⎥⎥⎦⎤⎢⎢⎣⎡⎪⎪⎭⎫ ⎝⎛++'-'=fp g m ms e E φχφφ2 We have ⎪⎪⎭⎫ ⎝⎛=i a t fp n N V ln φ ()334.0105.1106ln 0259.01015=⎪⎪⎭⎫ ⎝⎛⨯⨯=V Then()[]334.056.025.320.3++-=ms φ or 944.0-=ms φV (b) +n polysilicon gate ⎪⎪⎭⎫⎝⎛+-=fp g ms e E φφ2()334.056.0+-= or 894.0-=ms φV (c) +p polysilicon gate ()334.056.02-=⎪⎪⎭⎫⎝⎛-=fp g ms e E φφ or226.0+=ms φV_______________________________________ 10.5()3832.0105.1104ln 0259.01016=⎪⎪⎭⎫ ⎝⎛⨯⨯=fp φV ⎪⎪⎭⎫⎝⎛++'-'=fp g m ms e E φχφφ2 ()3832.056.025.320.3++-= 9932.0-=ms φV _______________________________________10.6 (a) 17102⨯≅d N cm 3- (b) Not possible - ms φ is always positive.(c) 15102⨯≅d N cm 3-_______________________________________10.7 From Problem 10.5, 9932.0-=ms φV ox ssms FB C Q V '-=φ (a) ()()814102001085.89.3--⨯⨯=∈=ox ox ox t C 710726.1-⨯=F/cm 2()()7191010726.1106.11059932.0--⨯⨯⨯--=FB V 040.1-=V (b) ()()81410801085.89.3--⨯⨯=ox C 710314.4-⨯=F/cm 2 ()()7191010314.4106.11059932.0--⨯⨯⨯--=FB V012.1-=V _______________________________________10.8 (a) 42.0-≅ms φV 42.0-==ms FB V φV(b) ()()781410726.1102001085.89.3---⨯=⨯⨯=ox C F/cm 2 (i)()()7191010726.1106.1104--⨯⨯⨯-='-=∆ox ss FB C Q V 0371.0-=V (ii)()()7191110726.1106.110--⨯⨯-=∆FB V 0927.0-=V(c) 42.0-==ms FB V φV ()()781410876.2101201085.89.3---⨯=⨯⨯=ox C F/cm 2 (i)()()7191010876.2106.1104--⨯⨯⨯-=∆FB V 0223.0-=V (ii)()()7191110876.2106.110--⨯⨯-=∆FB V0556.0-=V _______________________________________10.9 ⎪⎪⎭⎫ ⎝⎛++'-'=fp g mms e E φχφφ2 where()365.0105.1102ln 0259.01016=⎪⎪⎭⎫ ⎝⎛⨯⨯=fp φV Then ()365.056.025.320.3++-=ms φor975.0-=ms φVNowox ss ms FB C Q V '-=φor ()ox FB ms ss C V Q -='φ We have()()814104501085.89.3--⨯⨯=∈=ox ox ox t C or 81067.7-⨯=ox C F/cm 2 So now ()[]()81067.71975.0-⨯⋅---='ssQ 91092.1-⨯=C/cm 2or10102.1⨯='e Q ss cm 2- _______________________________________10.10 ()3653.0105.1102ln 0259.01016=⎪⎪⎭⎫ ⎝⎛⨯⨯=fp φV ()()()()()2/1161914102106.13653.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯⨯=--dT x510174.2-⨯=cm()dT a SDx eN Q ='m ax ()()()5161910174.2102106.1--⨯⨯⨯=810958.6-⨯=C/cm 2()()781410301.2101501085.89.3---⨯=⨯⨯=ox C F/cm 2()fp ms ox ss SDTN C Q Q V φφ2max ++'-'= ()()71910810301.2106.110710958.6---⨯⨯⨯-⨯= ()3653.02++ms φ ms φ+=9843.0(a) n + poly gate on p-type: 12.1-≅ms φV 136.012.19843.0-=-=TN V V(b) p + poly gate on p-type: 28.0+≅ms φV 26.128.09843.0+=+=TN V V (c) Al gate on p-type: 95.0-≅ms φV0343.095.09843.0+=-=TN V V_______________________________________10.11 ()3161.0105.1103ln 0259.01015=⎪⎪⎭⎫ ⎝⎛⨯⨯=fn φV ()()()()()2/1151914103106.13161.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯⨯=--dT x 510223.5-⨯=cm ()dT d SDx eN Q ='m ax ()()()5151910223.5103106.1--⨯⨯⨯= 810507.2-⨯=C/cm 2 ()()781410301.2101501085.89.3---⨯=⨯⨯=ox C F/cm 2 ()fn ms ox ss SDTP C Q Q V φφ2m ax -+⎥⎥⎦⎤⎢⎢⎣⎡'+'-= ()()⎥⎦⎤⎢⎣⎡⨯⨯⨯+⨯-=---71019810301.2107106.110507.2 ()3161.02-+ms φ ms TP V φ+-=7898.0(a) n + poly gate on n-type: 41.0-≅ms φV 20.141.07898.0-=--=TP V V(b) p + poly gate on n-type: 0.1+≅ms φV 210.00.17898.0+=+-=TP V V (c) Al gate on n-type: 29.0-≅ms φV 08.129.07898.0-=--=TP V V _______________________________________10.12()3294.0105.1105ln 0259.01015=⎪⎪⎭⎫ ⎝⎛⨯⨯=fp φV The surface potential is ()659.03294.022===fp s φφV We have 90.0-='-=oxssms FB C Q V φV Now()FB s oxSDT V C Q V ++'=φmaxWe obtain 2/14⎥⎦⎤⎢⎣⎡∈=a fp s dTeN x φ()()()()()2/1151914105106.13294.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯⨯=-- or410413.0-⨯=dT x cm Then()()()()4151910413.0105106.1m ax --⨯⨯⨯='SDQ or()810304.3m ax -⨯='SDQ C/cm 2 We also find()()814104001085.89.3--⨯⨯=∈=ox ox ox t C or810629.8-⨯=ox C F/cm 2 Then90.0659.010629.810304.388-+⨯⨯=--T Vor142.0+=T V V_______________________________________10.13()()814102201085.89.3--⨯⨯=∈=ox ox ox t C 710569.1-⨯=F/cm 2()()1019104106.1⨯⨯='-ssQ 9104.6-⨯=C/cm 2By trial and error, let 16104⨯=a N cm 3-.Now ()⎪⎪⎭⎫⎝⎛⨯⨯=1016105.1104ln 0259.0fp φ3832.0=V()()()()()2/1161914104106.13832.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯⨯=--dT x 510575.1-⨯=cm ()m ax SDQ ' ()()()5161910575.1104106.1--⨯⨯⨯= 710008.1-⨯=C/cm 294.0-≅ms φV Then()fp ms oxss SDTN C Q Q V φφ2max ++'-'=79710569.1104.610008.1---⨯⨯-⨯=()3832.0294.0+- Then 428.0=TN V V 45.0≅V_______________________________________10.14()()814101801085.89.3--⨯⨯=∈=ox ox ox t C 7109175.1-⨯=F/cm 3- ()()1019104106.1⨯⨯='-ssQ 9104.6-⨯=C/cm 2By trial and error, let 16105⨯=d N cm 3- Now()⎪⎪⎭⎫⎝⎛⨯⨯=1016105.1105ln 0259.0fn φ3890.0=V()()()()()2/1161914105106.13890.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯⨯=--dT x510419.1-⨯=cm()m ax SDQ ' ()()()5161910419.1105106.1--⨯⨯⨯= 710135.1-⨯=C/cm 3-10.1+≅ms φV Then()()fn ms ox ss SDTP C Q Q V φφ2max -+'+'-= ()797109175.1104.610135.1---⨯⨯+⨯-= ()3890.0210.1-+Then 303.0-=TP V V, which is within thespecified value. _______________________________________ 10.15 We have 710569.1-⨯=ox C F/cm 2 9104.6-⨯='ssQ C/cm 2 By trial and error, let 14105⨯=d N cm 3-Now()⎪⎪⎭⎫⎝⎛⨯⨯=1014105.1105ln 0259.0fn φ 2697.0=V()()()()()2/1141914105106.12697.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯⨯=--dT x 410182.1-⨯=cm ()m ax SDQ ' ()()()4141910182.1105106.1--⨯⨯⨯= 910456.9-⨯=C/cm 233.0-≅ms φVThen ()()fn ms oxss SDTP C Q Q V φφ2max -+'+'-= ⎪⎪⎭⎫⎝⎛⨯⨯+⨯-=---79910569.1104.610456.9 ()2697.0233.0--970.0=V Then 970.0-=TP V V 975.0-≅ V which meets the specification._______________________________________ 10.16(a) 03.1-≅ms φV()()814101801085.89.3--⨯⨯=ox C 7109175.1-⨯=F/cm 2Now oxss ms FB C Q V '-=φ()()71019109175.1106106.103.1--⨯⨯⨯--= 08.1-=FB V V(b) ()⎪⎪⎭⎫ ⎝⎛⨯=1015105.110ln 0259.0fp φ 2877.0=V ()()()()()2/115191410106.12877.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯=--dT x 510630.8-⨯=cm()m ax SDQ ' ()()()5151910630.810106.1--⨯⨯= 810381.1-⨯=C/cm 2 Now ()fp FB oxSDTN V C Q V φ2max ++'=()2877.0208.1109175.110381.178+-⨯⨯=-- or 433.0-=TN V V_______________________________________10.17 (a) We have n-type material under the gate, so2/14⎥⎦⎤⎢⎣⎡∈==d fn s C dT eN t x φ where()288.0105.110ln 0259.01015=⎪⎪⎭⎫ ⎝⎛⨯=fn φVThen()()()()()2/115191410106.1288.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯=--dT x or 410863.0-⨯==C dT t x cm μ863.0=m (b)()()fn ms ox ox ss SD T t Q Q V φφ2max -+⎪⎪⎭⎫⎝⎛∈'+'-= For an +n polysilicon gate, ()288.056.02--=⎪⎪⎭⎫ ⎝⎛--=fn g ms e E φφ or272.0-=ms φV Now ()()()()4151910863.010106.1m ax --⨯⨯='SD Q or ()81038.1m ax -⨯='SDQ C/cm 2 We have()()91019106.110106.1--⨯=⨯='ssQ C/cm 2 We now find ()()()()81498105001085.89.3106.11038.1----⨯⨯⨯+⨯-=T V ()288.02272.0--or 07.1-=T V V _______________________________________ 10.18 (b) ⎪⎪⎭⎫⎝⎛++'-'=fp g m ms e E φχφφ2 where 20.0-='-'χφm V and()3473.0105.110ln 0259.01016=⎪⎪⎭⎫⎝⎛⨯=fp φV Then()3473.056.020.0+--=ms φ or 107.1-=ms φV (c) For 0='ss Q ()fp ms ox ox SDTN t Q V φφ2max ++⎪⎪⎭⎫⎝⎛∈'= We find()()()()()2/116191410106.13473.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯=--dT xor 41030.0-⨯=dT x cm μ30.0=m Now()()()()416191030.010106.1m ax --⨯⨯='SDQ or ()810797.4m ax -⨯='SDQ C/cm 2Then()()()()14881085.89.31030010797.4---⨯⨯⨯=T V()3473.02107.1+- or00455.0+=T V V 0≅V _______________________________________ 10.19Plot _______________________________________ 10.20 Plot_______________________________________ 10.21 Plot _______________________________________10.22 Plot_______________________________________10.23 (a) For 1=f Hz (low freq), ()()814101201085.89.3--⨯⨯=∈=ox ox ox t C 710876.2-⨯=F/cm 2a st s ox ox oxFB eNV t C ∈⎪⎪⎭⎫ ⎝⎛∈∈+∈=' ()()()()()()()16191481410106.11085.87.110259.07.119.3101201085.89.3----⨯⨯⎪⎭⎫ ⎝⎛+⨯⨯= 710346.1-⨯='FB C F/cm 2 dTs ox ox oxx t C ⋅⎪⎪⎭⎫ ⎝⎛∈∈+∈='minNow ()3473.0105.110ln 0259.01016=⎪⎪⎭⎫ ⎝⎛⨯=fp φV ()()()()()2/116191410106.13473.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯=--dTx51000.3-⨯=cmThen ()()()5814min 1000.37.119.3101201085.89.3---⨯⎪⎭⎫ ⎝⎛+⨯⨯='C 810083.3-⨯=F/cm 2 C '(inv)710876.2-⨯==ox C F/cm 2 (b) 1=f MHz (high freq), 710876.2-⨯=ox C F/cm 2 (unchanged) 710346.1-⨯='FBC F/cm 2 (unchanged) 8min10083.3-⨯='C F/cm 2 (unchanged) C '(inv)8min10083.3-⨯='=C F/cm 2 (c) 10.1-≅==ms FB V φV()fp FB oxSDTN V C Q V φ2max ++'=Now()dT a SDx eN Q ='m ax ()()()516191000.310106.1--⨯⨯=81080.4-⨯=C/cm 2 ()3473.0210.110876.21080.478+-⨯⨯=--TN V 2385.0-=TN V V_______________________________________10.24(a) 1=f Hz (low freq), ()()814101201085.89.3--⨯⨯=∈=ox ox oxt C 710876.2-⨯=F/cm 2a st s ox ox oxFB eNV t C ∈⎪⎪⎭⎫ ⎝⎛∈∈+∈='()()()()()()()141914814105106.11085.87.110259.07.119.3101201085.89.3⨯⨯⨯⎪⎭⎫ ⎝⎛+⨯⨯=---- 810726.4-⨯='FBC F/cm 2 dTs ox ox oxx t C ⋅⎪⎪⎭⎫⎝⎛∈∈+∈='minNow()2697.0105.1105ln 0259.01014=⎪⎪⎭⎫⎝⎛⨯⨯=fn φV()()()()()2/1141914105106.12697.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯⨯=--dT x 410182.1-⨯=cmThen()()()4814min 10182.17.119.3101201085.89.3---⨯⎪⎭⎫ ⎝⎛+⨯⨯='C 910504.8-⨯=F/cm 2C '(inv)710876.2-⨯==ox C F/cm 2(b) 1=f MHz (high freq),710876.2-⨯=ox C F/cm 2 (unchanged)810726.4-⨯='FBC F/cm 2 (unchanged) 9min10504.8-⨯='C F/cm 2 (unchanged) C '(inv)9min10504.8-⨯='=C F/cm 2 (c) 95.0≅=ms FB V φV()fn FB oxSDTP V C Q V φ2max -+'-=Now()dT d SDx eN Q ='m ax ()()()4141910182.1105106.1--⨯⨯⨯= 910456.9-⨯=C/cm 2Then()2697.0295.010876.210456.979-+⨯⨯-=--TP V378.0+=TP V V_______________________________________10.25The amount of fixed oxide charge at x is ()x x ∆ρ C/cm 2By lever action, the effect of this oxide charge on the flatband voltage is()x x t x C V ox ox FB ∆⎪⎪⎭⎫⎝⎛-=∆ρ1 If we add the effect at each point, we must integrate so that ()dx t x x C V oxt oxoxFB⎰-=∆01ρ _______________________________________10.26 (a) We have ρx Q t SS ()='∆ Then∆V C x x t dx FB ox ox ox t=-()z 10ρ ≈-'F H G I K J F H I K-z 1C t t Q t dx ox ox oxox oxSSt t t ∆∆b g =-'--=-'F H I K 1C Q t t t t Q C ox SS ox ox SSox ∆∆a for ∆V Q t FB SS ox ox=-'∈F H G I K J =-⨯⨯⨯⨯---()16108102001039885101910814...b g b g b gb gor∆V FB =-00742.V(b) We have ρx Q t SS ox()='=⨯⨯⨯--16108102001019108.b g b g =⨯=-64103.ρONow ∆V C x x t dx C t xdx FB oxox oxOox oxoxt t =-=-()zz10ρρor ∆V t FB O oxox=-∈ρ22=-⨯⨯⨯---()6410200102398851038214...bg b g b gor∆V FB =-00371.V (c) ρρx x t O ox()F H G I KJ =We find12216108102001019108t Q ox O SS O ρρ='⇒=⨯⨯⨯--.b gb g or ρO =⨯-128102. Now ∆V C t x x t dx FB ox ox O ox t ox =-⋅⋅F H G I KJ z110ρ =-⋅z122C t x dx ox O oxox t ρaf which becomes ∆V t t x t FB ox oxO oxox O oxox t =-∈⋅⋅=-∈F H G I KJ 1332302ρρaf Then∆V FB =-⨯⨯⨯---()12810200103398851028214...b g b g b gor 0494.0-=∆FB V V_______________________________________10.27 Sketch_______________________________________10.28 Sketch_______________________________________10.29 (b)⎪⎪⎭⎫⎝⎛-=-=2ln i d a t bi FB n N N V V V ()()()()⎥⎥⎦⎤⎢⎢⎣⎡⨯-=2101616105.11010ln 0259.0or695.0-=FB V V(c) Apply 3-=G V V, 3≅ox V VFor 3+=G V V,sdx d ∈-=Eρ n-side: d eN =ρ1C x eN eN dx d sd s d +∈-=E ⇒∈-=E0=E at n x x -=, then snd x eN C ∈-=1 so()n s dx x eN +∈-=E for 0≤≤-x x n In the oxide, 0=ρ, so=E ⇒=E 0dxd constant. From the boundary conditions, in the oxidesn d x eN ∈-=E In the p-region,2C x eN eN dx d sa sa s+∈=E ⇒∈+=∈-=Eρ 0=E at ()p ox x t x +=, then ()[]x x teN p oxsa-+∈-=EAt ox t x =, snd sp a x eN x eN ∈-=∈-=E So that n d p a x N x N = Since d a N N =, then p n x x = The potential is ⎰E -=dx φFor zero bias, we can write bi p ox n V V V V =++where p ox n V V V ,, are the voltage drops acrossthe n-region, the oxide, and the p-region, respectively. For the oxide:soxn d ox ox t x eN t V ∈=⋅E =For the n-region:()C x x x eN x V n s d n '+⎪⎪⎭⎫ ⎝⎛⋅+∈=22Arbitrarily, set 0=n V at n x x -=, thensnd x eN C ∈='22so that()()22n sdn x x eN x V +∈=At 0=x , snd n x eN V ∈=22which is the voltagedrop across the n-region. Because ofsymmetry, p n V V =. Then for zero bias, wehavebi ox n V V V =+2 which can be written as bi sox n d s n d V t x eN x eN =∈+∈2or 02=∈-+ds bi ox n n eN V t x x Solving for n x , we obtain dbis ox ox n eN V t t x ∈+⎪⎪⎭⎫ ⎝⎛+-=222 If we apply a voltage G V , then replace bi V by G bi V V +, so ()dG bi s ox ox p n eN V V t t x x +∈+⎪⎪⎭⎫ ⎝⎛+-==222 We find2105008-⨯-==p n x x()()()()()1619142810106.1695.31085.87.11210500---⨯⨯+⎪⎪⎭⎫ ⎝⎛⨯+ which yields510646.4-⨯==p n x x cmNow soxn d ox t x eN V ∈=()()()()()()148516191085.87.111050010646.410106.1----⨯⨯⨯⨯=or359.0=ox V V We also findsnd p n x eN V V ∈==22()()()()()142516191085.87.11210646.410106.1---⨯⨯⨯=or67.1==p n V V V_______________________________________10.30(a) n-type (b) We have731210110210200---⨯=⨯⨯=ox C F/cm 2Also ()()7141011085.89.3--⨯⨯=∈=⇒∈=ox ox ox ox ox ox C t t C or 61045.3-⨯=ox t cm 5.34=nm o A 345= (c)oxssms FB C Q V '-=φ or 71050.080.0-'--=-ssQwhich yields8103-⨯='ssQ C/cm 21110875.1⨯=cm 2- (d) ⎪⎪⎭⎫ ⎝⎛∈⎪⎭⎫ ⎝⎛⎪⎪⎭⎫ ⎝⎛∈∈+∈='d s s ox ox ox FB eN e kT t C()()[][6141045.31085.89.3--⨯÷⨯= ()()()()()⎥⎥⎦⎤⨯⨯⨯⎪⎭⎫ ⎝⎛+--161914102106.11085.87.110259.07.119.3 which yields81082.7-⨯='FBC F/cm 2 or156=FB C pF_______________________________________10.31 (a) Point 1: Inversion 2: Threshold3: Depletion4: Flat-band5: Accumulation_______________________________________10.32 We have ()()[]fp ms x GS ox nV V C Q φφ2+---=' ()()max SD ssQ Q '+'- Now let DS x V V =, so ()⎩⎨⎧--='DS GS ox n V V C Q ()()⎪⎭⎪⎬⎫⎥⎥⎦⎤⎢⎢⎣⎡+-'+'+fp ms ox ss SD C Q Q φφ2m ax For a p-type substrate, ()max SDQ ' is a negative value, so we can write()⎩⎨⎧--='DS GS ox n V V C Q()⎪⎭⎪⎬⎫⎥⎥⎦⎤⎢⎢⎣⎡++'-'-fp ms ox ss SD C Q Q φφ2m ax Using the definition of threshold voltage T V ,we have()[]T DS GS ox nV V V C Q ---=' At saturation()T GS DS DS V V sat V V -== which then makes nQ 'equal to zero at the drain terminal._______________________________________10.33(a) ()[]222DS DS T GS n D V V V V L W k I --⋅'= ()()()()[]22.02.04.08.028218.0--⎪⎭⎫ ⎝⎛= 0864.0=mA (b) ()22T GS n D V V LW k I -⋅'= ()()24.08.08218.0-⎪⎭⎫ ⎝⎛= 1152.0=mA(c) Same as (b), 1152.0=D I mA(d) ()22T GS n D V V L W k I -⋅'=()()24.02.18218.0-⎪⎭⎫ ⎝⎛= 4608.0=mA _______________________________________ 10.34 (a) ()[]222SDSD T SG p D V V V V LW k I -+⋅'= ()()()()[]225.025.04.08.0215210.0--⎪⎭⎫ ⎝⎛= 103.0=D I mA(b) ()22T SG p D V V LW k I +⋅'= ()()24.08.015210.0-⎪⎭⎫ ⎝⎛= 12.0=mA(c) ()22T SG p D V V L W k I +⋅'=()()24.02.115210.0-⎪⎭⎫ ⎝⎛=48.0=mA(d) Same as (c), 48.0=D I mA_______________________________________10.35(a) ()22T GS n D V V LW k I -⋅'=()28.04.126.00.1-⎪⎭⎫ ⎝⎛⎪⎭⎫ ⎝⎛=L W26.9=⇒LW(b) ()()28.085.126.926.0-⎪⎭⎫ ⎝⎛=D I06.3=mA(c) ()[]222DSDS T GS n D V V V V L W k I --⋅'= ()()()()[]215.015.08.02.1226.926.0--⎪⎭⎫ ⎝⎛=271.0=mA_______________________________________10.36(a) Assume biased in saturation region()22T SG p D V V L W k I +⋅'=()()2020212.010.0T V +⎪⎭⎫ ⎝⎛=289.0+=⇒T V VNote: 0.1=SD V V 289.00+=+>T SG V V V So the transistor is biased in the saturation region.(b) ()()2289.04.020212.0+⎪⎭⎫ ⎝⎛=D I570.0=mA(c) ()()[()15.0289.06.0220212.0+⎪⎭⎫⎝⎛=D I()]215.0-or293.0=D I mA_______________________________________10.37 ()()781410138.3101101085.89.3---⨯=⨯⨯=ox C F/cm 2 ()()()()2.122010138.342527-⨯==L W C K ox n n μ310111.1-⨯=A/V 2=1.111 mA/V 2(a) 0=GS V , 0=D I 6.0=GS V V, ()15.0=sat V DS V, ()()()245.06.0111.1-=sat I D 025.0=mA2.1=GS V V, ()75.0=sat V DS V, ()()()245.02.1111.1-=sat I D 625.0=mA8.1=GS V V, ()35.1=sat V DS V,()()()245.08.1111.1-=sat I D 025.2=mA4.2=GS V V, ()95.1=sat V DS V,()()()245.04.2111.1-=sat I D 225.4=mA (c)0=D I for 45.0≤GS V V 6.0=GS V V,()()()()[]21.01.045.06.02111.1--=D I 0222.0=mA 2.1=GS V V,()()()()[]21.01.045.02.12111.1--=D I 156.0=mA 8.1=GS V V,()()()()[]21.01.045.08.12111.1--=D I 289.0=mA 4.2=GS V V,()()()()[]21.01.045.04.22111.1--=D I 422.0=mA_______________________________________10.38()()814101101085.89.3--⨯⨯=∈=ox ox ox t C 710138.3-⨯=F/cm 2L WC K ox p p 2μ=()()()()2.123510138.32107-⨯=41061.9-⨯=A/V 2=0.961 mA/V 2(a) 0=SG V , 0=D I6.0=SG V V, ()25.0=sat V SD V()()()235.06.0961.0-=sat I D 060.0=mA2.1=SG V V, ()85.0=sat V SD V()()()235.02.1961.0-=sat I D 694.0=mA 8.1=SG V V, ()45.1=sat V SD V()()()235.08.1961.0-=sat I D02.2=mA4.2=SG V V, ()05.2=sat V SD V()()()235.04.2961.0-=sat I D04.4=mA (c)0=D I for 35.0≤SG V V6.0=SG V V()()()()[]21.01.035.06.02961.0--=D I 0384.0=mA 2.1=SG V V ()()()()[]21.01.035.02.12961.0--=D I154.0=mA8.1=SG V V ()()()()[]21.01.035.08.12961.0--=D I 269.0=mA 4.2=SG V V()()()()[]21.01.035.04.22961.0--=D I 384.0=mA_______________________________________10.39(a) From Problem 10.37,111.1=n K mA/V 2 For 8.0-=GS V V, 0=D I0=GS V , ()8.0=sat V DS V()()()28.00111.1+=sat I D 711.0=mA8.0+=GS V V, ()6.1=sat V DS V()()()28.08.0111.1+=sat I D 84.2=mA6.1=GS V V, ()4.2=sat V DS V()()()28.06.1111.1+=sat I D 40.6=mA_______________________________________10.40 Sketch _______________________________________10.41 Sketch _______________________________________ 10.42We have ()T DS T GS DS V V V V sat V -=-=so that()T DS DS V sat V V +=Since ()sat V V DS DS >, the transistor is always biased in the saturation region. Then()2T GS n D V V K I -=where, from Problem 10.37,111.1=n K mA/V 2and 45.0=T V V10.43From Problem 10.38, 961.0=p K mA/V 2()()[]22SD SD T SG p D V V V V K I -+=()T SG p V SDDd V V K V I g SD +=∂∂=→20For 35.0≤SG V V, 0=d g For 35.0>SG V V,()()35.0961.02-=SG d V g For 4.2=SG V V,()()35.04.2961.02-=d g 94.3=mA/V_______________________________________10.44(a) GS D m V I g ∂∂=()()[]{}22DS DS T GS n GSV V V V K V --∂∂=()DS n V K 2=()()05.0225.1n K =5.12=⇒n K mA/V 2(b) ()()()[()]205.005.03.08.025.12--=D I 594.0=mA(c) ()()23.08.05.12-=D I125.3=mA_______________________________________10.45We find that 2.0≅T V V Now ()()T GS oxn D V V LC W sat I -⋅=2μ where ()()814104251085.89.3--⨯⨯=∈=ox ox oxt C or81012.8-⨯=ox C F/cm 2We are given 10=L W . From the graph, for 3=GS V V, we have ()033.0≅sat I D , then ()2.032033.0-⋅=LC W oxn μ or310139.02-⨯=LC W oxn μor()()3810139.01012.81021--⨯=⨯n μwhich yields342=n μcm 2/V-s_______________________________________10.46 (a)()T GS DS V V sat V -= or8.48.04=⇒-=GS GS V V V(b) ()()()sat V K V V K sat I DS n T GS n D 22=-= so()244102n K =⨯- which yields μ5.12=n K A/V 2 (c) ()2.18.02=-=-=T GS DS V V sat V Vso ()sat V V DS DS > ()()()258.021025.1-⨯=-sat I Dor ()μ18=sat I D A(d)()sat V V DS DS <()[]22DS DS T GS n D V V V V K I --= ()()()()[]25118.0321025.1--⨯=-orμ5.42=D I A_______________________________________10.47(a) ()()814101801085.89.3--⨯⨯=ox C 7109175.1-⨯=F/cm 2(i)()()7109175.1450-⨯=='ox n nC k μ 510629.8-⨯=A/V 2 or μ29.86='nk A/V 2 (ii)()()22T GS nD V V L W k sat I -⎪⎭⎫ ⎝⎛⎪⎪⎭⎫ ⎝⎛'= ()24.02208629.08.0-⎪⎭⎫ ⎝⎛⎪⎭⎫ ⎝⎛=L W24.7=⇒L W(b) (i) ()()7109175.1210-⨯=='ox p p C k μ 510027.4-⨯=A/V 2or μ27.40='p k A/V 2(ii) ()()22T SG p D V V L W k sat I +⎪⎭⎫ ⎝⎛⎪⎪⎭⎫ ⎝⎛'= ()24.02204027.08.0-⎪⎭⎫ ⎝⎛⎪⎭⎫ ⎝⎛=L W5.15=⇒LW_______________________________________ 10.48 From Problem 10.37, 111.1=n K mA/V 2(a) ()()[]{}22DS DS T GS n GS mL V V V V K V g --∂∂= ()()()()1.02111.12==DS n V K so 222.0=mL g mA/V (b) (){}2T GS n GS ms V V K V g -∂∂=()()()45.05.1111.122-=-=T GS n V V K so 33.2=ms g mA/V _______________________________________10.49From Problem 10.38, 961.0=p K mA/V 2(a) ()()[]{}22SD SD T SG p SGmL V V V V K Vg -+∂∂= ()()()()1.02961.02==SD p V K or 192.0=mL g mA/V (b) ()[]2T SG p SGms V V K V g +∂∂=()()()35.05.1961.022-=+=T SG p V V K or 21.2=ms g mA/V_______________________________________10.50 (a) oxa s C N e ∈=2γNow ()()814101501085.89.3--⨯⨯=oxC 710301.2-⨯=F/cm 2 Then()()()()716141910301.21051085.87.11106.12---⨯⨯⨯⨯=γ 5594.0=γV 2/1 (b) ()3890.0105.1105ln 0259.01016=⎪⎪⎭⎫⎝⎛⨯⨯=fpφV (i)()()()()()2/1161914105106.13890.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯⨯=--dT x510419.1-⨯=cm()m ax SDQ ' ()()()5161910419.1105106.1--⨯⨯⨯=710135.1-⨯=C/cm 2 ()fp FB oxSDTO V C Q V φ2max ++'= ()3890.025.010301.210135.177+-⨯⨯=-- 7713.0=VL WC K ox n n 2μ=()()()()2.12810301.24507-⨯=410452.3-⨯=A/V 2 or 3452.0=n K mA/V 2 For 0=D I , 7713.0==TO GS V V V For 5.0=D I ()()27713.03452.0-=GS V 975.1=⇒GS V V (c) (i) For 0=SB V , 7713.0==TO T V V V (ii) 1=SB V V,()()[1389.025594.0+=∆T V()]389.02-2525.0=V024.12525.07713.0=+=T V V (iii) 2=SB V V,()()[2389.025594.0+=∆T V ()]389.02-4390.0=V210.14390.07713.0=+=T V V (iv) 4=SB V V,()()[4389.025594.0+=∆T V()]389.02-7294.0=V501.17294.07713.0=+=T V V _______________________________________10.51()3473.0105.110ln 0259.01016=⎪⎪⎭⎫⎝⎛⨯=fp φ V[]fpSBfpT V V φφγ22-+=∆()()[5.23473.0212.0+=()]3473.02- or114.0=∆T V VNow T TO T V V V ∆+= 114.05.0+=TO V 386.0=⇒TO V V _______________________________________ 10.52 (a) ()()814102001085.89.3--⨯⨯=ox C710726.1-⨯=F/cm 2oxds C N e ∈=2γ ()()()()715141910726.11051085.87.11106.12---⨯⨯⨯⨯= 2358.0=γV 2/1 (b) ()3294.0105.1105ln 0259.01015=⎪⎪⎭⎫⎝⎛⨯⨯=fnφV []fn BS fnT V V φφγ22-+-=∆()()[BS V +-=-3294.022358.022.0()]3294.02- 39.2=⇒BS V V_______________________________________10.53(a) +n poly-to-p-type 0.1-=⇒ms φV ()288.0105.110ln 0259.01015=⎪⎪⎭⎫⎝⎛⨯=fp φValso 2/14⎥⎦⎤⎢⎣⎡∈=a fp s dTeN x φ()()()()()2/115191410106.1288.01085.87.114⎥⎦⎤⎢⎣⎡⨯⨯=-- or410863.0-⨯=dT x cm Now()()()()4151910863.010106.1m ax --⨯⨯='SDQ or()81038.1m ax -⨯='SDQ C/cm 2 Also()()814104001085.89.3--⨯⨯=∈=ox ox ox t C or81063.8-⨯=ox C F/cm 2 We find ()()91019108105106.1--⨯=⨯⨯='ss Q C/cm 2 Then ()fp ms oxss SD T C Q Q V φφ2m ax ++'-'=()288.020.11063.81081038.1898+-⎪⎪⎭⎫ ⎝⎛⨯⨯-⨯=--- or 357.0-=T V V(b) For NMOS, apply SB V and T V shifts in apositive direction, so for 0=T V , we want 357.0+=∆T V V. So[]fp SB fpoxa s T V C N e V φφ222-+∈=∆or()()()()81514191063.8101085.87.11106.12357.0---⨯⨯⨯=+ ()()[]288.02288.02-+⨯SB V or[]576.0576.0211.0357.0-+=SB V which yields 43.5=SB V V_______________________________________10.54 Plot_______________________________________10.55 (a)()T GS oxn m V V L C W g -=μ()T GS oxoxn V V t L W -∈=μ ()()()()()65.0510*******.89.340010814-⨯⨯=--or26.1=m g mS Nowsm m m s m m m r g g g r g g g +=='⇒+='118.01which yields⎪⎭⎫⎝⎛-=⎪⎭⎫ ⎝⎛-=18.0126.1118.011m s g r or 198.0=s r k Ω (b) For 3=GS V V, 683.0=m g mS Then ()()602.0198.0683.01683.0=+='m g mS or 88.0683.0602.0=='m m g g which is a 12% reduction._______________________________________10.56 (a) The ideal cutoff frequency for no overlap capacitance is,()222L V V C g f T GS n gs m T πμπ-==()()()24102275.04400-⨯-=π or 17.5=T f GHz (b) Now ()M gsT m T C C g f +=π2 where ()L m gdT M R g C C +=1 We find()()4410201075.0--⨯⨯=ox gdT C C()()814105001085.89.3--⨯⨯= ()()4410201075.0--⨯⨯⨯ or1410035.1-⨯=gdT C F Also ()T GS oxn m V V LC W g -=μ()()()()()()84144105001021085.89.34001020----⨯⨯⨯⨯= ()75.04-⨯or3108974.0-⨯=m g SThen ()1410035.1-⨯=M C ()()[]331010108974.01⨯⨯+⨯- or 1310032.1-⨯=M C F Now()()W L C C ox gsT 41075.0-⨯+= ()()814105001085.89.3--⨯⨯= ()()44410201075.0102---⨯⨯+⨯⨯ or1410797.3-⨯=gsT C F We now find ()M gsT mTC C g f +=π2 ()1314310032.110797.32108974.0---⨯+⨯⨯=π or 01.1=T f GHz _______________________________________10.57 (a) For the ideal case()4610221042-⨯⨯==ππυL f ds Tor 18.3=T f GHz(b) With overlap capacitance (using the values from Problem 10.56), ()MgdT mT C C g f +=π2 We findds ox m W C g υ= ()()()()86144105001041085.89.31020---⨯⨯⨯⨯= or3105522.0-⨯=m g S We have()L m gdT M R g C C +=1 ()1410035.1-⨯=()()[]331010105522.01⨯⨯+⨯- or 1410750.6-⨯=M C F。
半导体物理与器件(尼曼版)第15章(免费下载)
PD ,rated =来自Tj ,max − Tamb
θ dev − case
=
a
or
PD ,rated = 16.7 W
a
227
om
f f f f f
VDS = VDD − I D R = 40 − I D (10) We find VGS = 5 V , I D = 0.25 A , VDS = 37.5 > VDS ( sat )
课
Ron
which yields VDS = 3.92 V and
aw .c
F 1 + 1 + 1 I = 5 = V (1.288) H 18 . 3.6 2.2 K
I 2 = 1.08 A , P2 = 4.19 W I 3 = 1.77 A , P3 = 6.85 W or V = 3.88 V Then I 1 = 2.16 A , P1 = 8.38 W be . x10 cm N D ≈ 15
I 3 = 1.505 A
Semiconductor Physics and Devices: Basic Principles, 3rd edition Solutions Manual 15.13 15.11 (b) In saturation region, I D = Kn VGS − VT
后 答
Also Tdev − Tcase = PD ⋅ θ dev − case = (20)(1.75) = 35 so Tcase = Tdev − 35 = 136 − 35 or Tcase = 101° C
And Tcase − Tsnk = PD ⋅ θ case − snk = (20)(0.8) = 16° C so Tsnk = Tcase − 16 = 101 − 16 or Tsnk = 85° C
半导体物理学
K空间等能面
在k=0处为能带极值
E(k)E(0) 2k2 2mn*
导带底附近
2k2 E(k)E(0) 2mp*
价带顶附近
K空间等能面
以 间任k 一x 、矢k y 量、k代z 表为波坐矢k标轴构成 k 空间，k 空
金刚石型
闪锌矿型
半 导 体 有: 化 合 物 半 导 体 如GaAs、InP、ZnS
练习
1、单胞是基本的、不唯一的单元。（ ）
2、按半导体结构来分，应用最为广泛的是 （ ）。
3、写出三种立方单胞的名称，并分别计算 单胞中所含的原子数。
4、计算金刚石型单胞中的原子数。
电子壳层
原子的能级
不同支壳层电子
在周期性势场内，电子的平均速度u可表示 为波包的群速度
u dv dk
E hv u 1 d E dk
E(k)
E(0)
h2k2 2mn*
u
k
m
* n
自由电子的速度
微观粒子具有波粒二象性
p m0u
E p2 2m0
(r,t)Aei(Krt)
p K
E hv
u k m0
半导体中电子的加速度
半导体物理学
半导体物理学
教材:
《半导体物理学》(第七版)，刘恩科等编著， 电子工业出版社
参考书：
《半导体物理与器件》（第三版）， Donald A.Neamen著，电子工业出版社
半导体物理学
课程考核办法 :
本课采用开卷笔试的考核办法。 总评成绩构比例为：平时成绩10%； 期末
考试90%
2、实际情况的半导体材料与理想的半导体材料有 何不同？
半导体物理与器件(Neamen)
漏源I-V特性定性分析
对称n沟 结 图3.1对称 沟pn结JFET的横截面 对称 的横截面
漏源电压在沟道区产生电场，使多子从源极流向漏极。
13·1·1 pn-JFET
• ID的形成：（n沟耗尽型）
与MOSFET比较
两边夹 厚度几~十几 厚度几 十几 微米
对称n沟 结 图3.1对称 沟pn结JFET的横截面 对称 的横截面 结型:大于 绝缘栅:10 结型 大于107 ，绝缘栅 9～1015 。 大于
13·1·1 pn-JFET
（2） ID—VDS关系
漏源I-V特性定性分析
线性区 VDS较小：
VDS增大：
VDS较大：
增加到正好使漏 端处沟道横截面 积 =0 夹断点：沟道横 截面积正好=0
过渡区
13·1·1pn-JFET
漏源I-V特性定性分析
• 饱和区：（ VDS 在沟道夹断基础上增加）
ID存在，且仍由导电沟道区电特性决定
13·1·1pn-JFET
V 3、 GS足够小
漏源I-V特性定性分析
VGS
VGS↓= VP使上下耗尽层将沟道区填满， 沟道从源到漏
I 彻底夹断， D＝0 ，器件截止。
结论：栅结反偏压可改变耗尽层大小，从而控制漏电流大小。
13·1·1pn-JFET
• N沟耗尽型JFET的输出特性： • 非饱和区： – 漏电流同时决定于栅源电 压和漏源电压 • 饱和区： – 漏电流与漏源电压无关， 只决定于栅源电压
• pn JFET • MESFET 所用知识：半导体材料、PN结、肖特基势垒二极管
JFET基本概念
• 基本思路：加在金属板上 的电压调制（影响）下面 半导体的电导，从而实现 AB两端的电流控制。 • 场效应：半导体电导被垂 直于半导体表面的电场调 制的现象。 • 特点：多子器件，单极型 晶体管
半导体物理与器件Neamen
16
1.3空间晶格
金刚石结构
1.3.4 金刚石结构
Байду номын сангаас
17
1.3空间晶格
四面体结构
金刚石结构
18
1.3空间晶格
金刚石晶格
金刚石结构
19
1.3空间晶格
闪锌矿结构（GaAs）
不同原子构成的四面体
金刚石结构
20
1.3空间晶格
金刚石结构
21
1.4原子价键
离子键 （NaCl 库仑力）
课程主要内容
固体晶格结构：第一章 量子力学：第二章~第三章 半导体物理：第四章~第六章 半导体器件：第七章~第十三章
1
绪论
什么是半导体
按固体的导电能力区分，可以区分为导体、半导体和绝缘体
表1.1 导体、半导体和绝缘体的电阻率范围
材料 电阻率ρ(Ωcm)
导体 ＜ 10-3
半导体 10-3～109
如在绝缘衬底上制备的硫化镉(CdS)薄膜，无光照时的电 阻为几十MΩ，当受光照后电阻值可以下降为几十KΩ 此外，半导体的导电能力还随电场、磁场等的作用而改变
3
1.1半导体材料
元素半导体（Si、 Ge） 化合物半导体（双元素，三元素等）
4
1.2固体类型 半导体的晶体结构
一、晶体的基本知识 长期以来将固体分为：晶体和非晶体。
共价键 (H2 共用电子对) 金属键 (Na 电子海洋)
范德华键 （弱 HF 电偶极子 分子内非健结合的力）
存在分子或
22
1.4原子价键
硅原子和硅晶体
23
1.5固体中的缺陷和杂质
晶格振动 点缺陷 （空位和填隙） 线缺陷
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饱和蒸汽密度表表中压力为绝对压力，密度单位为kg/m3温度(t)℃压力(P)MPa 密度(ρ)温度(t)℃压力(P)MPa 密度(ρ)1000.10130.59771280.2543 1.4151010.10500.61801290.2621 1.4551020.10880.63881300.2701 1.4971030.11270.66011310.2783 1.5391040.11670.68211320.2867 1.5831050.12080.70461330.2953 1.6271060.12500.72771340.3041 1.6721070.12940.75151350.3130 1.7191080.13390.77581360.3222 1.7661090.13850.80081370.3317 1.8151100.14330.82651380.3414 1.8641110.14810.85281390.3513 1.9151120.15320.87981400.3614 1.9671130.15830.90751410.3718 2.0191140.16360.93591420.3823 2.0731150.16910.96501430.3931 2.1291160.17460.99481440.4042 2.1851170.1804 1.0251450.4155 2.2421180.1863 1.0571460.4271 2.3011190.1923 1.0891470.4389 2.3611200.1985 1.1221480.4510 2.4221210.2049 1.1551490.4633 2.4841220.2114 1.1901500.4760 2.5481230.2182 1.2251510.4888 2.6131240.2250 1.2611520.5021 2.6791250.2321 1.2981530.5155 2.7471260.2393 1.3361540.5292 2.8161270.2467 1.3751550.5433 2.8861560.5577 2.958184 1.0983 5.6291570.5723 3.032185 1.1233 5.7521580.5872 3.106186 1.1487 5.8771590.6025 3.182187 1.1746 6.0031600.6181 3.260188 1.2010 6.1311610.6339 3.339189 1.2278 6.2641620.6502 3.420190 1.2551 6.3971630.6666 3.502191 1.2829 6.5531640.68353.586192 1.3111 6.6711650.7008 3.671193 1.33976.8121660.7183 3.758194 1.3690 6.955 1670.7362 3.847195 1.39877.100 1680.7544 3.937196 1.42897.248 1690.7730 4.029197 1.45967.398 1700.7920 4.123198 1.49097.551 1710.8114 4.218199 1.52257.706 1720.8310 4.316200 1.55487.864 1730.8511 4.415201 1.58768.025 1740.8716 4.515202 1.62108.188 1750.8924 4.618203 1.65488.354 1760.9137 4.723204 1.68928.522 1770.9353 4.829205 1.72428.694 1780.9573 4.937206 1.75978.868 1790.9797 5.048207 1.79599.045 180 1.0197 5.160208 1.83269.225 181 1.0259 5.274209 1.86999.408 182 1.0496 5.391210 1.90779.593 183 1.0737 5.509211 1.94629.782 212 1.98529.974231 2.849114.25 213 2.024810.17232 2.901014.52 214 2.065010.37233 2.954614.78 215 2.105910.57234 3.008515.05 216 2.147410.77235 3.063115.33 217 2.189610.98236 3.118515.61 218 2.232311.19237 3.174615.89 219 2.275711.41238 3.231616.18 220 2.319811.62239 3.289216.47 221 2.364511.84240 3.347716.76 222 2.409812.07241 3.407017.06 223 2.455912.30242 3.467017.37 224 2.502612.53243 3.527917.68 225 2.550012.76244 3.589717.99 226 2.598113.00245 3.652218.31 227 2.646913.24246 3.715518.64 228 2.696313.49247 3.779718.97 229 2.746613.74248 3.844819.30 230 2.797514.00249 3.910719.64过热蒸汽密度表过热蒸汽是对应于当时压力下的饱和温度而言的，同样压力下的蒸汽，在饱和点的温度就是饱和温度。
高于饱和的温度的蒸汽就是当时压力的过热蒸汽。
可以高1℃，也可以10℃100℃等。
它们的压力是一样的，但它们过热度不同也就是温度不同时的焓植、墒值、密度等性质不一样。
表中压力为绝对压力，密度单位为kg/m3压力(Mpa)温度（℃）150170*********0.100.51640.49250.47070.45070.43230.150.77810.74120.70790.67770.65000.20 1.04230.99180.94660.90560.86840.25 1.3089 1.2444 1.1869 1.1349 1.08490.30 1.5783 1.4990 1.4287 1.3653 1.30790.40 2.1237 2.0141 1.9166 1.8297 1.75130.50 2.6658 2.5380 2.4121 2.2997 2.19920.80 4.3966 4.1676 3.9350 3.7400 3.53741.10 6.1313 5.8332 5.5342 5.2356 4.98101.407.87857.51637.1540 6.7913 6.42881.709.84649.36889.24738.41307.93522.0011.629511.098510.567610.03669.50542.5015.189014.451613.715012.977612.24063.0018.416817.570916.724315.877615.03673.5022.700821.571320.442719.313118.22664.0027.164025.747024.330322.912921.49544.5030.385228.916327.447525.978424.50965.0035.424333.629331.834230.038428.24336.0043.895441.747539.598837.450835.30207.0056.720153.699150.678047.656144.63528.0065.471362.180058.888355.596852.30619.0084.545779.826175.106170.386365.666510.0108.6250102.028995.434688.841282.248612.5158.3464148.7516139.1578129.5629119.978115.0206.4175194.4276182.4477170.4577158.476617.5250.3934236.6910222.8603209.1592195.456820.0327.8165309.9521291.2953273.4409255.578621.5384.6647363.2975341.9027320.5455299.1880压力(Mpa)温度（℃）2502702903103300.100.41560.40010.38570.37240.36000.150.62460.60100.57950.55940.54040.200.83420.80270.77360.74650.72140.25 1.0445 1.00480.96820.93430.90270.30 1.2540 1.2077 1.1634 1.1224 1.08440.40 1.6780 1.6152 1.5554 1.5000 1.44900.50 2.1081 2.0255 1.9495 1.8802 1.81470.80 3.4110 3.2718 3.1453 3.0283 2.92151.10 4.7460 4.5445 4.3612 4.1943 4.04101.40 6.1147 5.8437 5.5945 5.3794 5.17771.707.52197.1830 6.8607 6.5815 6.33092.008.97448.53508.14477.80617.49552.5011.503610.879410.35009.88889.48063.0014.184213.337712.635911.997911.51433.5017.053015.924315.016314.256513.85014.0020.077818.660317.499716.552715.74904.5023.040721.571720.102818.933317.93085.0026.448324.653222.858021.422120.25086.0033.154131.006228.857426.709125.05027.0041.613338.592235.570432.548830.22318.0049.014545.723142.431639.139935.84859.0060.946556.210051.507746.787742.068010.075.654365.769962.467659.664849.280212.5110.384295.776991.196481.603472.0105 15.0146.4967127.6820122.5268110.536998.5531 17.5181.6261163.4280154.2312140.3919126.689520.0236.9271219.0574201.2031182.5462164.683921.5277.7931256.4260235.0688213.6739192.3164压力(Mpa)温度（℃）350370*********0.100.34840.33750.32720.31760.30860.150.52300.50660.49120.47670.46310.200.69800.67590.65530.63600.61780.250.87320.84560.81980.79550.77260.30 1.0488 1.01560.98450.95520.92770.40 1.4010 1.3563 1.3144 1.2753 1.23770.50 1.7545 1.6983 1.6456 1.5961 1.54980.80 2.8227 2.7305 2.6440 2.5595 2.48841.10 3.9030 3.7700 3.6512 3.5384 3.43351.40 4.9945 4.8290 4.6673 4.5220 4.38571.70 6.0998 5.7779 5.6936 5.5120 5.34412.007.2186 6.9619 6.7290 6.5117 6.31302.509.11398.78028.47508.19387.93323.0011.049410.630810.24939.90009.57753.5013.028612.616212.052811.630811.24254.0015.053914.439213.886213.307712.99914.5017.127916.401815.752715.145114.66795.0019.262718.410817.656516.982716.37196.0023.700622.557021.562920.690019.90627.0028.403727.010025.633024.522423.40218.0033.417931.482529.869828.496927.29139.0038.808336.321734.304432.294731.159310.044.756041.527439.000636.934435.1684 12.562.417856.149651.821248.501545.8023 15.086.568874.584066.834161.553057.5137 17.5116.3142100.817685.322876.618570.571120.0151.1200137.7965108.543094.494585.327621.5171.8651150.0074128.1614106.636095.1366压力(Mpa)温度（℃）450470*********0.100.30000.29190.28420.27690.27000.150.45020.43810.42700.41560.40520.200.60050.58420.56880.55000.54000.250.75070.73160.71130.69250.67570.300.89890.88560.85400.83200.81080.40 1.2035 1.1708 1.1396 1.1102 1.08210.50 1.5036 1.4648 1.4258 1.3888 1.35370.80 2.4171 2.3500 2.2869 2.2274 2.17201.10 3.3345 3.2402 3.1529 3.07102.99021.40 4.2575 4.3496 4.2291 3.9157 3.81431.70 5.1863 5.0374 4.8972 4.7665 4.64082.00 6.1203 5.9419 5.7811 5.6204 5.47252.507.67777.49377.28107.0799 6.86373.009.26428.85608.60208.36108.13303.5010.884210.551210.25009.94999.67764.0012.508712.183511.757011.416911.09944.5014.150713.700913.288012.895012.53155.0015.813915.301714.802114.385913.97496.0019.198118.549517.956017.402916.89127.0022.663521.867521.146020.469919.85068.0026.017025.264024.395023.590522.85739.0029.873328.463727.710026.767625.906810.033.644732.300231.096030.011629.0164 12.543.543141.588439.880038.353736.9936 15.054.249751.526549.194047.124945.3087 17.565.933162.180759.052056.342753.987520.078.775973.685869.601066.060263.067421.587.093981.018476.166772.137668.7108压力(Mpa)温度（℃）5505705900.100.26340.25710.25120.150.39530.38600.37680.200.52710.51460.50260.250.65910.64400.62840.300.79130.77240.75400.40 1.0556 1.0303 1.00620.50 1.3204 1.2887 1.25850.80 2.1164 2.0290 2.01681.102.9170 2.8449 2.77741.40 3.7183 3.6271 3.54011.70 4.5230 4.4116 4.30562.00 5.3322 5.1989 5.07452.50 6.6858 6.5177 6.35823.008.04867.84377.64983.509.41979.17778.94804.0010.800310519110.25334.5012.189411.868311.56505.0013.588513.226712.88506.0016.411915.965715.54407.0019.274518.735018.23148.0022.174221.540020.95009.0025.112424.377123.694910.028.100027.255726.473812.535.741434.607233.554115.043.668042.193640.834917.551.898550.023748.326920.060.449358.125356.040221.565.737063.113260.7719乙烯饱和蒸汽压与温度的关系(lgP=6.74756-585/(T+255))温度T（℃）lgP饱和蒸汽压力P（bar)-100 2.973366452 1.237521803-99 2.99756 1.308417692-98 3.02144535 1.382393739-97 3.045028354 1.459535834-96 3.068314717 1.539930514-95 3.09131 1.62366492-94 3.114019627 1.710826761-93 3.136448889 1.801504273-92 3.158602945 1.895786178-91 3.180486829 1.993761645-90 3.202105455 2.095520251-89 3.223463614 2.201151942-88 3.244565988 2.310746989-87 3.265417143 2.424395954-86 3.286021538 2.54218965-85 3.306383529 2.664219098-84 3.326507368 2.790575494-83 3.346397209 2.921350169-82 3.36605711 3.056634549-81 3.385491034 3.196520119-80 3.404702857 3.341098388-79 3.423696364 3.490460851-78 3.442475254 3.644698952-77 3.461043146 3.803904051-76 3.479403575 3.968167384-75 3.49756 4.137580036-74 3.515515801 4.312232901-73 3.533274286 4.492216653-72 3.550838689 4.677621707-71 3.568212174 4.868538196-70 3.585397838 5.065055932-69 3.60239871 5.267264379-68 3.619217754 5.475252621-67 3.635857872 5.689109333-66 3.652321905 5.908922753-65 3.668612632 6.134780653-64 3.684732775 6.366770313-63 3.700685 6.604978492-62 3.716471917 6.849491402-61 3.7320960827.100394684-60 3.747567.357773385-59 3.7628661227.62171193-58 3.7780168537.8922941-57 3.7930145458.169603011 -56 3.8078615088.45372109 -55 3.822568.744730058 -54 3.8371122399.042710902 -53 3.8515203969.347743862 -52 3.8657866019.65990841 -51 3.8799129419.979283231 -50 3.89390146310.3059462 -49 3.90775417510.63997439 -48 3.92147304310.981444 -47 3.9350611.33043041 -46 3.94851693811.68700811 -45 3.96184571412.05125073 -44 3.97504815212.42323096 -43 3.98812603812.80302063 -42 4.00108112713.19069062 -41 4.0139151413.58631088 -40 4.02662976713.98995041 -39 4.0392*******.40167727 -38 4.0517*******.82155852 -37 4.06407376115.24966029 -36 4.0763*******.68604769 -35 4.08846909116.13078485 -34 4.10050117616.5839349 -33 4.11242486517.04555995 -32 4.12424161417.51572113 -31 4.135********.9944785 -30 4.1475618.48189113 -29 4.159********.97801705 -28 4.17046748919.48291325 -27 4.181********.99663567 -26 4.19297484720.51923923 -25 4.20408173921.05077779 -24 4.21509246821.59130415 -23 4.22600827622.14087008 -22 4.23683038622.69952628 -21 4.2475623.26732241 -20 4.25819829823.84430704 -19 4.26874644124.43052773 -18 4.2792055725.02603095 -17 4.28957680725.63086212 -16 4.29986125526.24506562 -15 4.3100626.86868475 -14 4.32017410827.50176176 -13 4.33020462828.14433787 -12 4.34015259328.79645323 -11 4.35001901629.45814694-10 4.35980489830.12945706 -9 4.3695112230.81042062 -8 4.37913894731.50107358 -7 4.38868903232.20145089 -6 4.3981624132.91158646 -5 4.4075633.63151316 -4 4.41688270934.36126286 -3 4.42613142935.10086639 -2 4.43530703635.85035358 -1 4.44441039436.609753220 4.45344235337.379093141 4.4624037538.158400132 4.47129540938.947700013 4.4801181439.747017614 4.48887274140.556376775 4.4975641.375800366 4.5061806942.205310287 4.51473557343.044927468 4.52322539943.894671889 4.53165090944.75456258 9.2临界温度。