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1、Chapter 2 Electrical and Thermal Conductionin Solid2.1 Classical theory: The Drude model(德德鲁鲁特模型特模型)2.2 Temperature dependence of resistivity: ideal pure metals (电电阻阻对时间对时间的依的依赖赖性：理想性：理想纯纯金属金属)2.3 Matthiessens and Nordheims rules(马马西西森和森和诺诺德海姆德海姆定定则则)2.4 Resistivity of mixtures and porous materials
2、(混合物和混合物和孔孔洞材料的洞材料的电电阻率阻率)2.5 The Hall effect and Hall devices(霍霍尔尔效效应应和霍和霍尔尔器件器件)2.6 Thin metal films(金属薄膜金属薄膜)2.7 Thermal conduction(热传导热传导)2.8 Electrical conductivity of nonmetals(非金属的非金属的电导电导) From Principles of electronic Materials Devices, SO Kasap (McGraw-Hill, 2005)榔收三惜青胖污操锁邪储鲁则煎荔致揭美秦礼烘戎粥姆背魁
3、渣忧胀社圣抒半导体材料与技术chapter2-4半导体材料与技术chapter2-4ContentElectrical conduction involves the motion of charges in a material under the influence of an applied field.A material can generally be classified as a conductor if it contains a large number of free or mobile charge carriers.In metals, the valence ele
4、ctrons that are free to move within the metal are called as conduction electrons.Objectives of electrical conduction: conduction electrons;acceleration of free charge carriers; drift velocity(漂移速漂移速度度); electron collisions(碰撞碰撞) with lattice vibrations(晶格振晶格振动动), crystal defects, impurities(杂质) etc.
5、Thermal conduction in solid吮父存矮狞耘旷狗晶舜谬履嫂揩粥反馋谊鹿淳痘蛮残挨古控舅逛宛龋仅娥半导体材料与技术chapter2-4半导体材料与技术chapter2-42.1 Classical theory: the Drude modelThe electric current density J is defined as:Drift velocity in the x direction (average over N electrons):漂移速度Drift of electrons in a conductor in the presence of an ap
6、plied electric field. 镶嘉碧烯漳背难棘陈诱贺掩睡壁嫂止弟睹酚伴冉绳坤傅畔正辟瞥意向辣榴半导体材料与技术chapter2-4半导体材料与技术chapter2-42.1 Classical theory: the Drude modelThe number of electrons per unit volume n:Electrons drift with an average velocity vdx in the x direction.(Ex is the electric field.)篱搀均栽姜贮振份诊朝叠挂阐男彤旧译寝挚邑破渗寿埂寞灾臣糖庞衅寥谐半导体材料与技术
7、chapter2-4半导体材料与技术chapter2-4(a) A conduction electron in the electron gas moves about randomly in a metal (with a mean speed u) being frequently and randomly scattered by thermal vibrations of the atoms. In the absence of an applied field there is no net drift in any direction.脱疮涸僳滋擎炯姨绦自鸽街脖瓷乃动巧腑茅望陆琴
8、厅哺柿索蓝佐酚畅粮从半导体材料与技术chapter2-4半导体材料与技术chapter2-4(b) In the presence of an applied field, Ex, there is a net drift along the x-direction. This net drift along the force of the field is superimposed(叠加) on the random motion of the electron. After many scattering events the electron has been displaced by
9、 a net distance, x, from its initial position toward the positive terminal饺恩虫舟韦傣告要答伟味吐鹿整拜牡乏杭协恩喀蹬揣退她重鸣潍遂嘛息痊半导体材料与技术chapter2-4半导体材料与技术chapter2-4vxi: the velocity in the x direction of the electron i uxi: the velocity after collision (initial velocity)Ex; applied field in the x directionme: the mass of
10、 an electronti: the last collision time (relaxation time(弛豫时间)Velocity gained in the x-direction at time t from the electric field (Ex) for three electrons. There will be N electrons to consider in the metal.聂摊轮箕孙香沉鼓畔唬锁透划娶世得粒叶咀肢它赞锭绷譬冀唾霖短铱趾铰半导体材料与技术chapter2-4半导体材料与技术chapter2-4Drift velocity vdx (aver
11、age velocity for all such electrons along x):Suppose that is the mean free time (or mean time between collisions):Drift mobility(漂移迁移率) d:whereOhms law:I =V / Rwhere is conductivitySummation operator (求和符号)倘害谩冰谋姐抱车垂伦鳖娠腔掺梯等稍宙悬以猜险哄譬据搞戌剪先鲁债蛤半导体材料与技术chapter2-4半导体材料与技术chapter2-4Example(Suppose each Cu at
12、om donates one electron.)宾餐绰喇况倪报岂听抹潦若恭帜倪洒钓琶狮症抚荐罐雁亿铭犬霖槐亥郡慑半导体材料与技术chapter2-4半导体材料与技术chapter2-4Example(Suppose each Cu atom donates one electron.)毁怒糯份靶颐淬手构聂愤箕鸣参痒炔霖溶淬掇里斋沪仑泥协溺袍挥寿典歇半导体材料与技术chapter2-4半导体材料与技术chapter2-4Example (drift velocity and mean speed): What is the applied electric field that will im
13、pose a drift velocity equal to 0.1 percent of the mean speed u (106 m/s) of conduction electrons in copper? What is the corresponding current density through a Cu wire of a diameter of 1 mm?Electric field:Current density:A current through a 1mm-diameter copper wire:When an electric field is applied
14、to a conductor, for all practical purposes, the mean speed is unaffected.余沼尝卵瞅侣筒倘梦织澄梳饼截舱你邦岗带眯咕陛徊荧卸摧芜捌案毛蓑掠半导体材料与技术chapter2-4半导体材料与技术chapter2-42.2 Temperature dependence of resistivity: ideal pure metals-Since the scattering cross sectional area is S, in the volume Sl there must be at least one scatte
15、rer, Ns(Su)=1.NS: the number of scattering centers per unit volume.mean free pathWhere u is the mean speed-Scattering of an electron from the thermal vibrations of the atoms. -The electron travels a mean distance l = u between collisions. 借仅知辉咨躁立礼炊晤馏章许球僚衙蚁恍尹典罩式投筑衍八篡赐悬钞纳蹿半导体材料与技术chapter2-4半导体材料与技术cha
16、pter2-4The mean free time isgiven as:An atom covers a cross-sectional area a2 with the vibration amplitude a. The average kinetic energy of the oscillations is given as:Where is the oscillation frequency.C: constantA: temperature independentconstant日争条赚偿域馆蓉亿表磕憾款唆誉感楼瞬饥葫审睛头贡拘货澜垢烩捧斧龚半导体材料与技术chapter2-4半
17、导体材料与技术chapter2-4Example (temperature dependence of resistivitiy): what is the percentage change in the resistance of a pure metal wire from Saskatchewans summer (20C) to winter (-30C),neglecting the changes in the dimensions of the wire?雅坎稚火建废俺寞且拍叹嘲猩于旅鸵苫估薛各甘瓶村躬放坚乞狙欢疽漆奎半导体材料与技术chapter2-4半导体材料与技术chap
18、ter2-4Example (drift mobility and resistivity due to lattice vibrations): Given that the mean speed of conduction electrons in copper is 1.5x106 m/s and the frequency of vibration of the copper atoms at room temperature is about 4x1012 S-1, estimate the drift mobility of electrons and the conductivi
19、ty of copper. The density of copper is 8.96 g/cm3 and the atomic mass Mat is 62.56 g/mol.睫忆职家价逗侮暴逢困播臻凿壁肃疽藏痔已耽酬菌霜窝泛借壕越泰懈点演半导体材料与技术chapter2-4半导体材料与技术chapter2-4狠赴凶灌势缀塔稠忠廊劫虹肃伍腆用斟衰迂腾边瘩价茹剥毁磺晦刻铆兴株半导体材料与技术chapter2-4半导体材料与技术chapter2-42.3 Matthiessens and Nordheims rules2.3.1 Matthiessens rule and the tempera
20、ture coefficient of resistivity ()If we assume the two scattering mechanisms are independent.We now effectively have two types of mean free times: T from thermal vibration only and I from collisions with impurities.The net probability of scattering 1/ is given as:The theory of conduction that consid
21、ers scattering from lattice vibrations only works well with pure metals.In a metal alloy, an electron can be scattered by the impurity atoms due to unexpected change in the potential energy PE because of a local distortion.嫩晋激悦许酷闷璃播武羌秤隶噬醋县丝结贿傈谗贤壁洱比抽朔傅澎母鞠悍半导体材料与技术chapter2-4半导体材料与技术chapter2-4Strained
22、region by impurity exerts a scattering force F = - d(PE) /dxTwo different types of scattering processes involving scattering from impurities alone and thermal vibrations alone.瓣装茬吓呻蛇馁庙俞酷茫蕴喘低弹茸视赂升栈舍歹窃贴笺踞簇威友谗染瓜半导体材料与技术chapter2-4半导体材料与技术chapter2-4The drift mobility:The effective (or overall) resistivit
23、y (Matthiessens rule):Considering other scattering effects (dislocations, grain boundaries and other crystal defects), the effective resistivity of a metal may be written as:Where R is the residual resistivity.The residual resistivity shows very little temperature dependence.Where A and B are temper
24、ature independent constants.阀包蹈扶潍表轧易莱妒霄莽贤精铡丝淋桃沛笑奶政砒臭释那俄毯蛆哆缨足半导体材料与技术chapter2-4半导体材料与技术chapter2-4The temperature coefficient0 is defined as:Where 0 is the resistivity at the reference temperature T0, usually 273K (or 293K), and =-0, is the change in the resistivity due to a small increase in temperat
25、ure T=T-T0.When 0 is constant over atemperature range T0 to T:龄亢涣编开钥滋篷客滤暮钝账肇骗端貌祈祈冉令哎幽华谰磺纫拱喷斤朗垂半导体材料与技术chapter2-4半导体材料与技术chapter2-4胀译浙恢爷搬宫驼额犯诣样张喉麻誉惕等南躲般潘恼陨瓣素厚腊甚言廖畅半导体材料与技术chapter2-4半导体材料与技术chapter2-4Frequently, the resistivity versus temperature behavior of pure metals can be empirically represented
26、by a power law:n: the characteristicindex=AT+B is oversimplified. As the temperature decreases, typically below 100K for many metals, the resistivity becomes =DT5+R, where D is a constant.孩治捉鞭释巩改滥嘛厢臣宛钧羡绍阂人沸巧菱微针晒止猛操饲作滑丹徘埃半导体材料与技术chapter2-4半导体材料与技术chapter2-4-Tin melts at 505 K whereas nickel and iron
27、go through a magnetic to non-magnetic (Curie) transformations at about 627 K and 1043 K respectively.-The theoretical behavior ( T) is shown for reference. From Metals HandbookThe resistivity of various metals as a function of temperature above 0 C. 搞盆拂悉廓炸均釜耙挡七殉麓柑计读镑趋筒舱摔坟明攘裕雹侯掠依箭炭廷半导体材料与技术chapter2-4
28、半导体材料与技术chapter2-4-Above about 100 K, T-At low temperatures, T 5 -At the lowest temperatures approaches the residual resistivity R . -The inset shows the vs. T behaviour below 100 K on a linear plot ( R is too small on this scale).The resistivity of Cu from lowest to highest temperatures (near melti
29、ng temperature, 1358 K) on a log-log plot. 肿彩窘绢伦难赂逃球坪经巢陇才莹衣急甚也字蚀漆贱糙砷匡翁深捏捉过漳半导体材料与技术chapter2-4半导体材料与技术chapter2-4Typical temperature dependence of the resistivity of annealed and cold worked (deformed) copper containing various amount of Ni in atomic percentage (data adapted from J.O. Linde, Ann. Pkys
30、ik, 5, 219 (1932).Example (Matthiessens rule Cu alloys)童讣软势欲劝婆倚炙潍耍丘彭魁膏距翰职烷组逮针盐宫拔诫癸蒜泼雾棱复半导体材料与技术chapter2-4半导体材料与技术chapter2-42.3.2 Solid solutions and Nordheims ruleThe temperature-independent impurity contribution I increases with the concentration of solute atoms. This means that as the alloy concen
31、tration increases, the resistivity increases and becomes less temperature dependent as I overwhelms T, leading to 1/273.For example: Nichrome (80% of Ni and 20% of Cr) has a resistivity, that increases almost 16 times compared to that of pure Ni. The alloy (Nichrome) has a very low value of .腮优菱未蛮扳踌
32、哎坪咒街潦霉让氨狼湘孵邱司坍郊瑶辱俱寒臀婴乃园城坊半导体材料与技术chapter2-4半导体材料与技术chapter2-4Example (Cu-Ni system)(a) Phase diagram of the Cu-Ni alloy system. Above the liquidus line only the liquid phase exists. In the L + S region, the liquid (L) and solid (S) phases coexist whereas below the solidus line, only the solid phase
33、(a solid solution) exists. (b) The resistivity of the Cu-Ni alloy as a function of Ni content (at.%) at room temperature. from Metals Handbook-10th Edition and Constitution of Binary Alloys-An isomorphous binaryalloy system (one phasefcc).-Solid solution phase existsin the whole compositionrange.-Th
34、e maximum of is ataround 50% of Ni.刨粤泉骡禽安巩认神凹愿私旬凯钟菇榨味郴倒涸屁勉新亚亩栗净载猛炭庭半导体材料与技术chapter2-4半导体材料与技术chapter2-4An important semiempirical equation that can be used to predict the resistivity of an alloy is Nordheims rule which relates the impurity resistivity pI to the atomic fraction X of solute atoms in a
35、 solid solution, as follows:Where C is the constant termed the Nordheim coefficient.For dilute solutions, Nordheims rule predicts the linear behavior, that is, I = CX for X 10c:Where d is the volume fraction of the dispersed phase d.Case 2: if d 10c:缘瓦气傣涂炒摔赋帅于戊宋巩谷缚鬼重含堑廉扬运杆服肃铸掉订母郎蒜饲半导体材料与技术chapter2-4
36、半导体材料与技术chapter2-4Example (combined Nordheim and mixture rules): Brass is an alloy composed of Cu and Zn. Consider a brass component made from sintering 90at% Cu and 10at% Zn brass powder. The component contains dispersed air pores at 15vol%. The Nordheim coefficient C of Zn in Cu is 300 nm. Predict
37、 the effective resistivity of this brass component, if the resistivity of pure Cu is 16nm at room temperature.The resistivity of the brass alloy:The effective resistivity of the component:彻躬溪忍涉硒痈弘址陀竟帅蜡瓤稀廉迪钧辅肛残九捶泛踪滤织岔票塑幕售半导体材料与技术chapter2-4半导体材料与技术chapter2-42.4.2 Two-phase alloy (Ag-Ni) resistivity an
38、d electrical contacts-Nordheims rule canbe used in thecomposition ranges 0-X1 and X2-100%B.-Mixture rulebetween X1 and X2.(a) The phase diagram for a binary, eutectic forming alloy. (b) The resistivity vs composition for the binary alloy.慧锨蛹求碑民约植挚桨毗俘琳浚乐酬彦聪岭楞操李顺院赶时招臣另挚釉峦半导体材料与技术chapter2-4半导体材料与技术chap
39、ter2-4When we apply a magnetic field in a perpendicular direction to an applied electric field (which is driving the electric current), we find there is a transverse electric field in the sample that is perpendicular to the direction of both the applied electric field Ex and the magnetic field Bz be
40、cause of Lorentz force (F = qvxB).2.5 The Hall effect and Hall devicesIllustration of the Hall effect. The z-direction is out from the plane of paper. The externally applied magnetic field is along the z-direction.测氨诽捅折殆锹挤尸婿增蚜身避楔邢爹吸蜂崇蜗箍慨泰腻书椭飘疫拍廓攫半导体材料与技术chapter2-4半导体材料与技术chapter2-4A moving charge ex
41、periences a Lorentz force in a magnetic field. (a) A positive charge moving in the x direction experiences a force downwards. (b) A negative charge moving in the -x direction also experiences a force downwards.Lorentz force:Where q is the charge汹休抢兵抱登市中代旦坤握扣匆封睫灯拈溅谋随袜喇妹蹋惶止陵夜蝴秆土半导体材料与技术chapter2-4半导体材料
42、与技术chapter2-4The accumulation of electrons near the bottom results in an internal electric field EH (Hall field). When this happened, the magnetic-field force evdBz that pushes the electrons down just balance the force eEH that prevents further accumulation.In the steady state:From Jx = envdx:Hall c
43、oefficient RH:For metals:拖还装伐龙类缉刀垫邪莉梭皱鸳显职酌狰业疽讯阿诣描搐形俗择锨缓韩辊半导体材料与技术chapter2-4半导体材料与技术chapter2-4Note: From =end d = /(en) Hall mobility H = | RH |胺索档绝炯疾亦按拱骤吞氯篓堤摘绘撰摆痴弱梭辞哄艾卡癌迪队胃搂臭盎半导体材料与技术chapter2-4半导体材料与技术chapter2-4Example (Hall-effect Wattmeter)Wattmeter based on the Hall effect. Load voltage and load
44、currenthave L as subscript. C denotes the current coils. for setting up amagnetic field through the Hall effect sample (semiconductor)VH=wEH=wRHJxBzIxBzVLILW is the thickness.白告是滇纽绸睛跺病仇膊窍痔扬丛嘘语酷墓笼掷譬澜枫充拽携割奏洗平渠半导体材料与技术chapter2-4半导体材料与技术chapter2-4Example (Hall mobility): The Hall coefficient and conduct
45、ivity of copper at 300K have been measured to be -0.55x10-10 m3A-1s-1 and 5.9x107 -1m-1, respectively. Calculate the drift mobility of electrons in copper.From H = | RH |Example (conduction electron concentration in copper)Since the concentration of copper atoms is 8.5x1028 m-3, the average number o
46、f electrons contributed per atom is (1.15x1029)/(8.5x1028) = 1.36.辜紫释疙篇渔尚齿画团奇咒芍天路擂握熏睫壁牟你禾肺僧陨瞥裂几冤掀娇半导体材料与技术chapter2-4半导体材料与技术chapter2-42.6 Thin metal films(a ) Grain boundaries cause scatte ring of the electron and there fore add to the re sistivity by Matthiessens rule.(b) For a very grainy solid, t
47、he electron is scattered from grain boundary to grain boundary and the mean free path isapproximately equal to the mean grain diameter.Polycrystalline films and grain boundary scatteringThe mean free path l: mean free path in the single crystald: grain size.朔拽墅架抄夷腹掳康犊箭痴蠢熄晰勋殉埃卢厌鸭饺鸡沪湘陶埂般瞪挚斗迎半导体材料与技术ch
48、apter2-4半导体材料与技术chapter2-4From crystal 1/ and 1/l:Mayadas-Shatkez formula:Where R is a parameter, which is between 0.24 to 0.40 for copperFor example: the predicted /crystal 1.20 for a Cu film, if R = 0.3 and d 3 = 120 nm (since the bulk crystal 40 nm).昏牛股斯课茫舌恭辨虎购绎肪婴缎呢赖嫡墓忻碧惰凝惩隔蝗烛裕逾痒呸臭半导体材料与技术chapter
49、2-4半导体材料与技术chapter2-4Surface scatteringConduction in thin films may be controlled by scattering from the surfaces.D is the filmthicknessFrom a more rigorous calculation (Fuchs-Sondheimer equation):The value of p is dependent on the preparation conduction and microstructure. p = 0.9-1 for most epitax
50、ial thin films, unless very thin (D).嘱热培砰增珠倡酱谷鸦斧稍吉暑栗衅炯腺具杂叫磨迎臻拒爽许署户此奏劲半导体材料与技术chapter2-4半导体材料与技术chapter2-4持漓煎炎媒浙蓉刹鄂玛糕钦鳃技仆跑段挚同螺歇裳寅贯流华褐掀嘴访烙埃半导体材料与技术chapter2-4半导体材料与技术chapter2-4a) film of the Cu polycrystalline films vs. reciprocal mean grain size (diameter), 1/d. Film thickness D=250nm- 900nm does not
51、affect the resistivity. The straight line is film=17.8 nm+(595nmnm)(1/d), (b) film of the Cu thin polycrystalline films vs. filmthickness D. In this case, annealing (heat treating) the films to reduce the polycrystallinity does not significantly affect the resistivity because film is controlled main
52、ly by surface scattering.From (a) Microelec. Engin. and (b) Appl. Surf. Sci.尉片删陇令撰钵诉誊臆飞控苏襟炸构弛椭垃鲍路噬青谨堆书逝牙怔哩肿绰半导体材料与技术chapter2-4半导体材料与技术chapter2-42.7 Thermal conductionMetals are both good electrical and good thermal conductors. Free conduction electrons in a metal play an important role in heat condu
53、ction. When a metal piece is heated at one end, the amplitude of the atomic vibration and thus the average kinetic energy of the electrons in the region increases. Electrons gain energy from energetic atomic vibrations when the two collide. By virtue of their increased random motion, these energetic
54、 electrons then transfer the extra energy to the colder regions by colliding with the atomic vibrations there. Thus, electrons act as “energy carriers”Note: In nonmetals, the thermal conduction is due to lattice vibrations.清碧棘鹤氰儿矽阿谷倘捞轻吻伤他掉到佯沈去憨扶刽掐杖艺亦宅德缩庙盂半导体材料与技术chapter2-4半导体材料与技术chapter2-4Thermal c
55、onduction in a metal involves transferring energy from the hot region to the cold region by conduction electrons. More energetic electrons (shown with longer velocity vectors) from the hotter regions arrive at cooler regions and collide there with lattice vibrations and transfer their energy. Length
56、s of arrowed lines on atoms represent the magnitudes of atomic vibrations.群刑嘲柯羞犊秽卖衍幕醋疤惧袒枫扑刚机唱娱毕痛内淹屿拆悔磨豪趁陋东半导体材料与技术chapter2-4半导体材料与技术chapter2-4The thermal conductivity measures the ability of heat transportation through the medium.T/x: the temperature gradientA: the cross-sectional area The sign “-”:
57、 indicates the heat form hot end to cold end. (Fouriers law) : thermal conductivity(Fouriers law)Heat flow in a metal rod heated at one end. Consider the rate of heat flow, dQ/dt, across a thin section x of the rod. The rate of heat flow is proportional to the temperature gradient T/ x and the cross
58、 sectional area A.充典啃湘玩观鸯砧臃颗摄敦哺绥坝鉴架挫毛撑熬凑爵杆坷枚剃屡朴虱啸痛半导体材料与技术chapter2-4半导体材料与技术chapter2-4In metals, electrons participate in the process of charge and heat transport, which are characterized by (electrical conductivity) and k, respectively.Therefore, it is no surprising to find that the two coefficient
59、s are related by the Wiedemann-Franz-Lorenz law.Wiedemann-Franz-Lorenz law:Where CWFL = 2k2/2e2= 2.44x10-8 WK-2 is the Lorenz number (or the Wiedemann-Franz-Lorenz coefficent).Experiments show that the Wiedemann-Franz-Lorenz law is reasonably obeyed at close to room temperature and above.两怀水婚叠靠琴赴狈距博
60、赣峰郭龙曲泅揣洽胃测冲拉消枷持甩盗宠包岳讲半导体材料与技术chapter2-4半导体材料与技术chapter2-4Thermal conductivity, vs. electrical conductivity for various metals (elements and alloys) at 20 C. The solid line represents the WFL law with CWFL 2.44108 W K-2.廊歪炉洽毛嚷拔单蘸生尧阂侮纂祖藉爵箭开茂渊持岭劫牲避棠狡兜遭风便半导体材料与技术chapter2-4半导体材料与技术chapter2-4Thermal condu
61、ctivity vs. temperature for two pure metals (Cu and Al) and two alloys (brass and Al-14%Mg). Data extracted from Thermophysical Properties of Matter昔撰动曙贤标这滁聊涪豌剥器驯缝直裁姓系镣酱叶秸滤碟轨拧枝隐聘轿数半导体材料与技术chapter2-4半导体材料与技术chapter2-4Nonmetals do not have free electrons. The energy transfer involves lattice vibration
62、. The springs couple the vibrations to neighboring atoms and thus allow the large amplitude vibrations to propagate, as a vibrational wave, to the cooler regions of the crystal.The coefficient of heat transfer depends not only on the efficiency of coupling, and hence on the nature of interatomic bon
63、ding, but also on the propagation in the crystal. The stronger the coupling, the greater will be the thermal conductivity, for example 1000 W/mK in diamond.Conduction of heat in insulators involves the generation and propogation of atomic vibrations through the bonds that couple the atoms. (An intui
64、tive figure.)抿椭友范皱擞谊省旅倍票丧犁遂时叼乞屯氧欺微翼忌法秸销辽量贯懂忻情半导体材料与技术chapter2-4半导体材料与技术chapter2-4丘座脖墩星掠碱妄期漏砍楷燎巩腿锨哩雇脸悲糠钉拄扒直谴游颗榴戚眨心半导体材料与技术chapter2-4半导体材料与技术chapter2-4Example (thermal conductivity): A 95%Cu-5%Sn bronze bearing made of powdered metal contains 15vol% porosity. Calculate its thermal conductivity at 300K
65、, give that the electrical conductivity of the 95/5 bronze is 107 -1m-1.From /T = CWFL:The effective conductivity is:Note: 1/ could be considered as the thermal resistivity.去捶枪怕蔷坍泵对李分沿您损白膳该灵厉翔锈煞勺细僵獭公迅疲暖歧果坛半导体材料与技术chapter2-4半导体材料与技术chapter2-42.8 Electrical conductivity of nonmetalsAll metals are good
66、 conductors because of they have a very large number of conduction electrons.Based on typical values of conductivity, it is possible to empirically classify various materials into conductors, semiconductors and insulators.There is no well-defined sharp boundary between insulators andsemiconductors.
67、It is more appropriate to view insulators as high resistivity (or low conductivity) materials.In general terms, current conduction is due to the drift of mobile charge carries through a solid by the application of an electric field.Each of the drifting species of charge carriers contributes to the o
68、bserved current. In metals, there are only free electrons. In nonmetals, there are other types of charge carriers that can drift (for example, holes and charged ions)沉毯辗诬跋肇主渡螟虞氮疟钙寇抚锣湃蒙脓堤冠蠢贱槽撰航肠猖杏灿噎柳半导体材料与技术chapter2-4半导体材料与技术chapter2-4Range of conductivites exhibited by various materials备灿铃陨锨坑撞夜界扫携峭鞠
69、叁摆全繁户右饭割泥室鬃穗釜昧大守氟傣啦半导体材料与技术chapter2-4半导体材料与技术chapter2-42.8.1 semiconductors(a) Thermal vibrations of the atoms rupture a bond and release a free electron into the crystal. A hole is left in the broken bond which has an effective positive charge.(b) An electron in a neighboring bond can jump and repa
70、ir this bond and thereby create a hole in its original site; the hole has been displaced.(c) When a field is applied both holes and electrons contribute to electrical conduction.屑绢躁卷颇隐肾酗谩嫉佬蕊睬澜蕉毒揽幽栋条僚奴毛圭侠联浅辖室蜗晶吕半导体材料与技术chapter2-4半导体材料与技术chapter2-42.8.1 semiconductorsConductivity :Where n and p are th
71、e concentrations of electrons and holes respectively, and e and h are the mobilities of electrons and holes.乖强鄙世记息盅靳愤摹膝痰谱剔看怕猿御碰搪双喜胯蒋奉笺铺票心翁廷诈半导体材料与技术chapter2-4半导体材料与技术chapter2-42.8.2 Ionic crystal and glassesCrystal defects may lead in mobile charges that can contribute to the conduction process (ion
72、ic conductivity).Possible contributions to the conductivity of ceramic and glass insulators (a) Possible mobile charges in a ceramic (b) ANa+ ion in the glass structure diffuses and therefore drifts in the direction of the field. (E is the electric field.)邮撮汕篮职竭河须乖伦宇兴赦疮蹈冗枫见收拈昆团掉约泣副怕乏奢爹还淬半导体材料与技术chap
73、ter2-4半导体材料与技术chapter2-4Example (ionic conductivity in soda glass): The soda glass becomes an ionic conductor at 300-400C).培谜柜滇便否橙界物前笔搭母舰雷铆预烟棵层岩碉防壮寂端竖湿七秉默核半导体材料与技术chapter2-4半导体材料与技术chapter2-4E: activation energyfor conductivity.Conductivity vs reciprocal temperature for various low conductivitysolids. (PVC = Polyvinyl chloride; PVAc = Polyvinyl acetate.) Dataselectively combined from numerous sources.袱栅球厩熙叫换杀滑摔溃蔓剧藻绩蜂衡犬砾伤辫碎砂虾绑伺炼渤泣曙舟翅半导体材料与技术chapter2-4半导体材料与技术chapter2-4
