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1、下载可编辑卷 A学期： 2011至 2012学年度第1 学期一、 Fill in the blanks with the proper concepts and formula for the contents of Chapter I.The volume 体积 of a parallelepiped平行六面体 with axes 轴a1, a2 , a3is defined定义 by ：；Please write out the five 2D Bravais lattices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;The possible 14 prim
2、itive cells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;Fortheplanewhose interceptsare4,2,3,thereciprocals倒 数are1/4 、 1/2 、1/3,the smallest three integers整数 having the same ratio比率 are3、 6、4.The cube faces of a cubic crystal立方晶体的立方体面are二、 Expr
3、ession and the calculation for the contents of Chapter II.1） Please write out three vectors向量 of the reciprocal lattice倒格子 :b1 ,b2 , b3 .by usingvectorsa1 , a2 , a3 。b1=(2 ) ·(a2*a3)/(a1· (a2*a3) ）b2=(2 ) · (a3*a1)/(a1 ·(a2*a3) ）b3=(2 ) ·(a1*a2)/(a1· (a2*a3 ）2) Calculat
4、e计算 the volume of the primitive cell of fcc lattice面心立方晶格：晶格基矢 aai , b aj , cak体积 V=a.(bc)a3原胞基矢 a1a ( jk ), a2a (k i ), a3a (i j )222a3体积a1.(a2a3 )4三、 Derivation for the contents of the contents of Chapter III.Please deriveout the van der Waals-London Interaction范德瓦尔斯伦敦相互作用from the linearharmonic o
5、scillators model.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：.专业 .整理 .下载可编辑12121212yl 0p1CX 1p22CX 22m22m令 yl1 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e2e2e2e2yl1X 2R X1R X 2RRX1在 X1 X 2R 的近似下，将上式展开，使得到最低级近似表达式为2
6、e2 X1 X 2yl1R3通过简正模变换： X s1( X1X 2 ); X a1( X1X 2 )22并解出 X1 和 X2： X11（ X sXa ); X 21( X sX a )22同时取 yl1 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,P11（ Ps Pa), P21 (PsPa)22Ps2121 (c2则总哈密顿量可以写成 ylyl 0yl11(c2e3 ) Xs2 【1Pa 22e3 ) Xa 2 2m2R2m2R2e2112e212e22可得来。振子的两个频率为W=( c) / m2W0.R31(3 )(R3）2R8其中， W0=（
7、c/m)(1/2)该系统的零点能量为 1s)由于存在相互作用，这个值比未。的值 2-1/2W0低V（ WWa2V=1 （WsWa)W 0.1 2e2 ) 2A )28(R3R6四、 Expression and the explanation fr the contents of Chapter IV.o1) Pleasewriteout the dispersionrelation色散关系of (q)fortwo atoms 原子 PerPrimitiveBasis 每个原始依据, and explain the physical meaning of the formula公式 .五、 C
8、oncepts and the derivation for the contents of Chpater V.1)What is theDebye model 德拜模型 and Debye T3 lawT3法 ? What is the concept概念 of Debyetemperature ?2)Please derive theDensity of State in Three Dimension三维状态密度 .专业 .整理 .下载可编辑六、 Derivations for the contents of Chapter VI.1) Please derive the formul
9、a 公式 of energy levels of free electrons 自由电子的能量水平 in one dimension 维 .2) Please derive thethe Hall coefficient霍尔系数 of Hall effect.七、 Explanation and derivation for the contents of Chapter VII.Please explainthe origin of the energy gap, and write outthe free electron bandsfor 110direction of wavevect
10、or space.Solution:olthe origin of the energy gap is the two standing waves and pile up electors at different regionsand therefore the two waves have different values of the potential energy ,Ihtsis the originof the energy gap.2)the free electron bands for 110 direction of wavevetor space isEnergy ba
11、ndGa/2（000）（ k x ky 0)10000k x2ky22,3100,100222（ / a)（ kx2）ky24,5,6,7010,010,001,001（2/ a)28,9,10,11110,101,110,10112,13,14,15110,101，110，10116,17,18,19011,011,011,011八、 Concepts and the explanation for the contents of Chapter VIII.1) A holeacts in applied electric and magnetic fields as if it has a
12、 positive charge+e. Thepossible reasons in five stepsare:Solution： 1） k hke, the electrons in the full band the total wave vector iszero:k02）（ kh)e(k ）.he let the valerve band energy zero point in the conduction bandabove.专业 .整理 .下载可编辑3） VhVe, the velocityof the hole is equal to the velocityof the m
13、issing electron.4） m hme, theeffectivemassisinverselypropertionald2/ dk 2 , and for the hde band ,this has the opposite sum to that for an electron in the valence band.5)dk he(E1 Vh XB), this come from the equation of motiondtctothecrrvaturedk e-e( E1Vh XB),dtc2) Please explian the physical meaning
14、of energy-k relation of following three semiconductor materials 半导体材料 .卷 B学期： 2011至 2012学年度第1学期一、 Fill in the blanks with the proper data or concepts in Chapter I.Solid state physics largely concerned主要关注: (1） crystals晶体(2)electrons incrystals;Atomsdensity密度：n a10 23 atoms / cm 3n e10 28 29electrons
15、/ cm 3；Translationvector平移矢量：3translationvectorvsa1 、 a2 、 a3/T u1a1u2a2u3 a3；The volume of a parallelepiped平行六面体a1, a2 ,a3a1.(a2a3 )with axesis：；The posibble five 2D Bravais lattice are :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;Forthe plane whoseinterceptsare3,1,2,th
16、ereciprocalsare1/3 、 1/1、1/2, ,the smallest threeintegers having the same ratio are（ 263）.专业 .整理 .下载可编辑The cube faces of a cubic crystal are（ 100）（ 010）( 001) (100)(0 10)和（001）二、 Calculations for the contents of Chapter II.1） Please write out three vector of the reciprocal lattice:b1 , b2 , b3 .Expl
17、ain:b1 a2a3， a3a1， a1a22b22b32a3）a1 (a2a3）a1( a2 a3）a1( a22)Please verify验证 the relation: bi ? aj. 2ij3) Calculate the volume体积 of the primitive cell of bcc lattice：三、 Calculations and the concept explanation for the contents of Chapter III.Please calculate theMadelung constant 马德龙常数 forthe infinite
18、无限的 line of ions离子 ofalternating sign交替的迹象 for the one-dimensional chain2 ln 2. 一维链 to be :四、 Expression and exlanations for the contents of Chapter IV.1) Please write out the 1D dispersion relation of(q), and explain the physical meaning ofthe formula.1(q)= (4c / m) 2sin 1 qa , 其中 C 是最近邻平面之间的力常量，M是
19、一个原子的质量。2The special signifcance of phonon wavevetors that lie on the zone.boundaryisdevelopedfromtheformula,wecanobtainwhenq=0,w(q)=0,when1q=, w( q)( 4c / m)2a2) What is the long wave limit长波极限 and what result结果 we can get from this limit?一维单原子链、一维双原子链中，q 的取值都只在一定范围之内。（一维单原子链：,一维双原子链：），长波极限就是 q 取值趋
20、向于范围边界时的情况。研究的意义在于了解极限情况下格波振动频率的情况。Or.专业 .整理 .下载可编辑当 qa<<1 时，将 cosqa 展开并取得近似，可得 cosqa12.1- （ qa)2由此色散系度为 w 2(c / m） q2a2 表明在长波极限下，频率与波长成正比。五、 Explanations for the contents of Chapter V.1) What is the Debye model and Debye T3 law? What is the concept of Debye temperature?Solution:1)Debye model
21、is the low of the Max planck blackbody radiation solid equivalents.in the Debye model,the allow model vectors smaller than the K2)DebyeT3lawis when T， U= 3 3NKBT4 /5 3， that can obtainCv12 4Nk B (T )234 NkB (T )353)Debye temperature can definehv (6 2N )31kBV2)Please explain the physics menaning ofUm
22、klapp Processes:UP过程：Solution:To thethermalnesistivityof electrons,whichhave more important effectthreephonon processesisn tk 1k2k3 ,itisk1k 2k3G ,Gisreriprocallattice vectors calledUmklapp processes .In the processes the energy is constant .The phonon vector ,in the first ,Brillouin zoneshas physic
23、s menaning .The umklapp processes can let the phonon vector back to the first Brillouin zones.六、 Derivation for the contents of Chapter VI1) Please derive the formula of energy levels of free electrons in one dimension.请导出一维自由电子能级的公式Solution:ForschrodingerequationH,wecanobtainH H2d2HH ,where-dx22mH
24、is the electron orbital energy . To infintle potential boundary conditionsn (0 )0,n (l )0,.专业 .整理 .We can obtain下载可编辑n Asin( 2x), 1n L, where A is a constant,so that we can obtainn2energyn22n(）2mL3)Please derive the the Hall coefficient of Hall effect.请导出霍尔效应的霍尔系数Solution:Tothestateelectricfieldstea
25、dystate,thetimederivativeiszero ,then Vx=eExwc Vy ,mVyeEywc Vx , VzeEz ,wherewceB is eyctotion frequency ,whenVy0 ,mmmcWecan getEywc ExeBEx .And the HallcoffinientdefinedisRHE y ,we canmjx Busedj xnqVxne2 Ex / m to getRH1 .ne七、 Explanation and the derivation for the contents of Chapter VII.Please ex
26、plain the origin of the energy gap, and write out the free electron bands for 111direction of wavevector space.请解释能隙的起源，并写了 111 方向的波矢空间的自由电子带。八、 Deravation and the calculation for the contents of Chapter VIII第八章 .1) Startingfrom the definitionof group velocityvg , pleasegivethe effectmass m* describ
27、edby the energy band vs wavevectork. 从群速 Vg 的定义，请把影响质量m *的能带与波矢k 描述 P1353) Based on the concept of the effective mass质量 , please write out the energy of an electron电子 near the low edge边缘 of the conduction传导 band and that of an electron near the topof the valance band,respectively.P139 基于有效质量概念，请写出能靠
28、近导带低边和一个电子，在价带顶的电子，分别。.专业 .整理 .下载可编辑一、1、【马德隆常数的物理意义】在一个晶体内，其中一个离子的总电势能，可表示为一个与它距离最近的另一个离子电势能的 M倍， E=ME0，其中 E0 为两个离子的系统的电势能， M称为马德隆常数（ Madelung constant ），其值与晶体结构有关。2、【德拜温度】 1912年德拜提出以连续介质的弹性波来代表格波，将布喇菲晶格看作是各向同性的连续介质。有1 个纵波和2个独立的横波。温度愈低，德拜模型近似计算结果愈好；温度很低，主要的只有长波格波的激发。3、费米面：如果固体中有 N 个自由电子，按照泡利原理它们基态是由 N 个电子由低到高填充的 N 个量子态。 N个电子在 k 空间填充半径为 kF 球，球内包含的状态数恰 好等于 N。一般称这个球为费米球， kF 为费米半径，球的表面为费米面。二、.专业 .整理 .下载可编辑1、证明：面心立方的原胞基矢：体心立方的原胞基矢为：.专业 .整理 .下载可编辑4、一、1、爱因斯坦理论能够反映出Cv 在低温时下降的基本趋势。.专业 .整理 .