固體物理往年試題

卷：至年度1期一inblankswithChaptervolume體積ofaparallelepiped行六面體axes軸isdefined定義：；lattices布維子as:方晶、角格長(zhǎng)晶、心方格斜晶格

正;cells胞:單斜格簡(jiǎn)單立晶格、心方格面立晶、角格六晶、單斜格底單斜晶、單交格底正晶、心交格面正晶、單角晶格體四晶格;reciprocals倒數(shù)1/4、1/2整數(shù)ratio比率3、6、4.Thecubefacesofacubiccrystal立方晶體的立方體面are二、Expressionof1）向量thelattice倒格子:。）））2)Calculate計(jì)oflattice面心方格：晶基矢體積V=原胞矢體積三、DerivationforthecontentsofthecontentsofChapterIII.PleasederiveoutthevanderWaals-LondonInteraction德瓦爾斯倫敦相互作用fromthelinearharmonicoscillatorsmodel.性諧振子模型解：作為一個(gè)模型，考慮兩個(gè)值距為R的全同線性諧振子和2，每個(gè)振子帶有一個(gè)正電荷（+e）和一個(gè)負(fù)電荷（-e），正負(fù)電荷之間的距離分別為和X2，粒子沿X軸振動(dòng)，動(dòng)量分別用R1和R2表示，力常量為。在未受個(gè)數(shù)擾作用時(shí)，該系統(tǒng)的哈密頓量為：令表示兩個(gè)振子之間的庫(kù)倫相互作用能，核間坐標(biāo)為，于是有在的近似下，將上式展開(kāi)，使得到最低級(jí)近似表達(dá)式為通過(guò)簡(jiǎn)正模變換：并解出和：同時(shí)取的近似形式，是系統(tǒng)的中哈密頓量對(duì)角化，可以得出這兩種模式相聯(lián)系的動(dòng)量和則總哈密頓量可以寫(xiě)成可得來(lái)。頻率為其中，W0=（c/m)^(1/2)該系統(tǒng)的零點(diǎn)能量為由于存在相互作用，這個(gè)值比未?！鱒=四、ExpressionandtheexplanationforthecontentsofChapterIV.1)Pleasewriteoutthedispersionrelation色散關(guān)系ω(q)fortwoatoms原子PerPrimitiveBasis每個(gè)原始依據(jù),andexplainthephysicalmeaningoftheformula公式..五、ConceptsandthederivationforthecontentsofChpaterV.WhatistheDebyemodel德拜模型andDebyeT3lawT3?Whatistheconcept概念ofDebyetemperature?PleasederivetheDensityofStateinThreeDimension維狀態(tài)密度.六、DerivationsforthecontentsofChapterVI.Pleasederivetheformula公式ofenergylevelsoffreeelectrons自由電子的能量水平inonedimension維.PleasederivethetheHallcoefficient霍爾系數(shù)ofHalleffect.七、ExplanationandderivationforthecontentsofChapterVII.Pleaseexplaintheoriginoftheenergygap,andwriteoutthefreeelectronbandsfor[110]directionofwavevectorspace.Solution:oltheoriginoftheenergygapisthetwostandingwavesandpileupelectorsatdifferentregionsandthereforethetwowaveshavedifferentvaluesofthepotentialenergy,Ihtsistheoriginoftheenergygap.2)thefreeelectronbandsfor[110]directionofwavevetorspaceisEnergybandGa/2π（000）（0)100010,16,17,18,19八、ConceptsandtheexplanationforthecontentsofChapterVIII.1)Aholeactsinappliedelectricandmagneticfieldsasifithasapositivecharge+e.Thepossiblereasonsinfivestepsare:Solution：1）theelectronsinthefullbandthetotalwavevectoriszero:2）letthevalervebandenergyzeropointintheconductionbandabove3）thevelocityoftheholeisequaltothevelocityofthemissingelectron.4）theeffectivemassisinverselypropertionaltothecrrvatureandforthehdeband,thishastheoppositesumtothatforanelectroninthevalenceband.5)thiscomefromtheequationofmotion2)Pleaseexplianthephysicalmeaningofenergy-krelationoffollowingthreesemiconductormaterials導(dǎo)體材料卷學(xué)期：

至

學(xué)年度第1

學(xué)期一、FillintheblankswiththeproperdataorconceptsinChapterI.Solidstatephysicslargelyconcerned要關(guān)注:(1）crystals晶體electronsincrystals;density度：；vector移矢量：vsa1、a2、a3/；ofa行面體is：；2D:正方晶、六晶格、長(zhǎng)方晶、有長(zhǎng)晶和斜晶格;system:角晶系;

三斜、單、正交、立方、四角、六角和三Forthearetheare1/3、1/1、1/2,theare（263）.Thecubefacesofacubicare（100）（010）(001)(00)(00)和（00）二、fortheof1）outthreevectorofthe.Explain:Pleaseverify驗(yàn)證relation:.體積theofbcclattice：三、ofconstant馬德常數(shù)theinfinite無(wú)限的ions子alternatingsign交替的跡象一維鏈be::四、of1)1D其中C是最鄰面間力量M是個(gè)原的質(zhì)。onis2)Whatisthelongwavelimit長(zhǎng)波極限r(nóng)esult結(jié)果getfromthislimit?一維單原子鏈、一維雙原子鏈中，q的取值都只在一定范圍之內(nèi)。（一維單原子鏈：,一維雙原子鏈：），長(zhǎng)波極限就是取值趨向于范界時(shí)的情況。研究的意義在于了解極限情況下格波振動(dòng)頻率的情況。Or當(dāng)qa<<1時(shí)，將cosqa展開(kāi)并取得近似，可得1-.由此色散系度為表明在長(zhǎng)波極限下，頻率與波長(zhǎng)成正比。五、ExplanationsforcontentsofChapterV.1)WhatistheDebyemodelandDebyeT3law?WhatistheconceptofDebyetemperature?Solution:1)DebyemodelisthelowoftheMheDebyemodel,theallowmodelvectorssmallerthantheK2)DebyeT3lawiswhenT《，U=，thatcanobtain3)Debyetemperaturecandefine2)PleaseexplainthephysicsmenaningofUmklappProcesses:UP過(guò)程：Solution:Tothethermalnesistivityofelectrons,whichhavemoreimportanteffectthreephononprocessesisn’t,itis,GisreriprocallatticevectorscalledUmklappprocesses.Intheprocessestheenergyisconstant.Thephononvector,inthefirst,Brillouinzoneshasphysicsmenaning.TheumklappprocessescanletthephononvectorbacktothefirstBrillouinzones.六、DerivationforthecontentsofChapterVI1)Pleasederivetheformulaofenergylevelsoffreeelectronsinonedimension.請(qǐng)導(dǎo)出一維自由電子能級(jí)的公式Solution:Forschrodingerequation,wecanobtain,whereistheelectronorbitalenergy.ToinfintlepotentialboundaryconditionsWecanobtainwhereAisaconstant,sothatwecanobtainenergy3)PleasederivethetheHallcoefficientofHalleffect.導(dǎo)出霍爾效應(yīng)的霍爾系數(shù)Solution:Tothestateelectricfieldsteadystate,thetimederivativeiszero,thenVx=,,,whereiseyctotionfrequency,when,Wecanget.AndtheHallcoffinientdefinedis,wecanusedtoget.七、ExplanationandthederivationforthecontentsofChapterVII.Pleaseexplaintheoriginoftheenergygap,andwriteoutthefreeelectronbandsfor[111]directionofwavevectorspace.解釋能隙的起源，并寫(xiě)了[111]方向的波矢空間的自由電子帶。八、DeravationandthecalculationforthecontentsofChapterVIII第八章.1)Startingfromthedefinitionofgroupvelocityvg,pleasegivetheeffectmassm*describedbytheenergybandvswavevectork.從群速的定義，請(qǐng)把影響質(zhì)量*的能帶與波矢描述3)Basedontheconceptoftheeffect