固体物理往年试题

第1页共9页卷A学期：2011至2012学年度第1学期一、FillintheblankswiththeproperconceptsandformulaforthecontentsofChapterI.Thevolume体积ofaparallelepiped平行六面体withaxes轴isdefined定义by：；Pleasewriteoutthefive2DBravaislattices布拉维格子as:正方晶格、六角晶格、长方晶格、有心长方晶格和斜方晶格;Thepossible14primitivecells原胞are:简单三斜晶格、简单立方晶格、体心立方晶格、面心立方晶格、三角晶格、六角晶格、简单单斜晶格、底心单斜晶格、简单正交晶格、底心正交晶格、体心正交晶格、面心正交晶格、简单四角晶格和体心四角晶格;Fortheplanewhoseinterceptsare4,2,3,thereciprocals倒数are1/4、1/2、1/3,thesmallestthreeintegers整数havingthesameratio比率are3、6、4.Thecubefacesofacubiccrystal立方晶体的立方体面are二、ExpressionandthecalculationforthecontentsofChapterII.1）Pleasewriteoutthreevectors向量ofthereciprocallattice倒格子:321,,bbb.byusingvectors321,,aaa。b1=(2π)·(a2*a3)/(a1·(a2*a3)）b2=(2π)·(a3*a1)/(a1·(a2*a3)）b3=(2π)·(a1*a2)/(a1·(a2*a3））2)Calculate计算thevolumeoftheprimitivecelloffcclattice面心立方晶格：晶格基矢kac,jab,iaa体积V=3).(acba原胞基矢)(2),(2),(2a321jiaaikaakja体积4a)aa.(a3321三、DerivationforthecontentsofthecontentsofChapterIII.PleasederiveoutthevanderWaals-LondonInteraction范德瓦尔斯伦敦相互作用fromthelinearharmonicoscillatorsmodel.线性谐振子模型解：作为一个模型，考虑两个值距为R的全同线性谐振子1和2，每个振子带有一个正电荷（+e）和一个负电荷（-e），正负电荷之间的距离分别为X1和X2，粒子沿X轴振动，动量分别用R1和R2表示，力常量为C。在未受个数扰作用时，该系统的哈密顿量为：22222121021212121yCXpmCXpml令1yl表示两个振子之间的库伦相互作用能，核间坐标为R，于是有321,,aaa第2页共9页221221221yXReXReXXReRel在RXX《21的近似下，将上式展开，使得到最低级近似表达式为321212yRXXel通过简正模变换：)(21);(212121sXXXXXXa并解出X1和X2：)(21);2121asasXXXXXX（同时取1yl的近似形式，是系统的中哈密顿量对角化，可以得出这两种模式相联系的动量Ps和Pa,P1)(212),21PaPsPPaPs（则总哈密顿量可以写成])2(21m21])2c(2121[y2322232210XaRecPaXsRePsmylyll【可得来。。振子的两个频率为W=...]2(81)2(211[]/)2[(2323202132）ReReWmRec其中，W0=（c/m)^(1/2)该系统的零点能量为)s21WaW（由于存在相互作用，这个值比未。。的值2-1/2VW低△0△V=))2(81.0)as216232RARe△（△四、ExpressionandtheexplanationforthecontentsofChapterIV.1)Pleasewriteoutthedispersionrelation色散关系ofω(q)fortwoatoms原子PerPrimitiveBasis每个原始依据,andexplainthephysicalmeaningoftheformula公式..五、ConceptsandthederivationforthecontentsofChpaterV.1)WhatistheDebyemodel德拜模型andDebyeT3lawT3法?Whatistheconcept概念ofDebyetemperature?2)PleasederivetheDensityofStateinThreeDimension三维状态密度.第3页共9页六、DerivationsforthecontentsofChapterVI.1)Pleasederivetheformula公式ofenergylevelsoffreeelectrons自由电子的能量水平inonedimension维.2)PleasederivethetheHallcoefficient霍尔系数ofHalleffect.七、ExplanationandderivationforthecontentsofChapterVII.Pleaseexplaintheoriginoftheenergygap,andwriteoutthefreeelectronbandsfor[110]directionofwavevectorspace.Solution:oltheoriginoftheenergygapisthetwostandingwavesandpileupelectorsatdifferentregionsandthereforethetwowaveshavedifferentvaluesofthepotentialenergy,Ihtsistheoriginoftheenergygap.2)thefreeelectronbandsfor[110]directionofwavevetorspaceisEnergybandGa/2π（000）（yxkk0)1000022kyxk2,3100,1002)/2aπ（yx22k2kπ）（4,5,6,7010,010,001,0012)/2aπ（8,9,10,11110,101,110,10112,13,14,15110,101011011，，16,17,18,19110,101,110,011八、ConceptsandtheexplanationforthecontentsofChapterVIII.1)Aholeactsinappliedelectricandmagneticfieldsasifithasapositivecharge+e.Thepossiblereasonsinfivestepsare:Solution：1）,kehktheelectronsinthefullbandthetotalwavevectoriszero:0k2）.()kehh）（keletthevalervebandenergyzeropointintheconductionbandabove3）,heVVthevelocityoftheholeisequaltothevelocityofthemissingelectron.4）,mehmtheeffectivemassisinverselypropertionaltothecrrvature,/d22dkandforthehdeband,thishastheoppositesumtothatforanelectroninthevalenceband.5)),1(dkXBVcEedthhthiscomefromtheequationofmotion),1(-dkeXBVcEedth2)Pleaseexplianthephysicalmeaningofenergy-krelationoffollowingthreesemiconductormaterials半导体材料.第4页共9页卷B学期：2011至2012学年度第1学期一、FillintheblankswiththeproperdataorconceptsinChapterI.Solidstatephysicslargelyconcerned主要关注:(1）crystals晶体(2)electronsincrystals;Atomsdensity密度：323/10cmatomsna329~28/10cmelectronsne；Translationvector平移矢量：3translationvectorvsa1、a2、a3/332211uauauaT；Thevolumeofaparallelepiped平行六面体withaxesis：)aa.(a321；Theposibblefive2DBravaislatticeare:正方晶格、六角晶格、长方晶格、有心长方晶格和斜方晶格;Sevenlatticesystemare:三斜、单斜、正交、立方、四角、六角和三角晶系;Fortheplanewhoseinterceptsare3,1,2,thereciprocalsare1/3、1/1、1/2,,thesmallestthreeintegershavingthesameratioare（263）.Thecubefacesofacubiccrystalare（100）（010）(001)(100)(010)和（001）二、CalculationsforthecontentsofChapterII.1）Pleasewriteoutthreevectorofthereciprocallattice:321,,bbb.Explain:）π，）π，）π321213321132321321(2(2b(2baaaaabaaaaaaaaaa2)Pleaseverify验证therelation:.3)Calculatethevolume体积oftheprimitivecellofbcclattice：321,,aaaijjiab2第5页共9页三、CalculationsandtheconceptexplanationforthecontentsofChapterIII.PleasecalculatetheMadelungconstant马德龙常数fortheinfinite无限的lineofions离子ofalternatingsign交替的迹象fortheone-dimensionalchain一维链tobe::四、ExpressionandexlanationsforthecontentsofChapterIV.1)Pleasewriteoutthe1Ddispersionrelationofω(q),andexplainthephysicalmeaningoftheformula..ω(q)=,21sin)/c4(21qam其中C是最近邻平面之间的力常量，M是一个原子的质量。Thespecialsignifcanceofphononwavevetorsthatlieonthezone.boundaryisdevelopedfromtheformula,wecanobtainwhenq=0,w(q)=0,whenq=21)/4()(,amcqw2)Whatisthelongwavelimit长波极限andwhatresult结果wecangetfromthislimit?一维