固體物理往年試題

1、卷 A 學(xué)期： 2011 至 2012 學(xué)年度第 1 學(xué)期一、Fill in the blanks with the proper concepts and formula for the contents of Chapter I. The volume體積 of a parallelepiped平行六面體 with axes軸 is defined定義 by： ；Please write out the five 2D Bravais lattices布拉維格子 as : 正方晶格、六角晶格、長方晶格、有心長方晶格和斜方晶格 ;The possible 14 primitive cells

2、原胞 are : 簡單三斜晶格、簡單立方晶格、體心立方晶格、面心立方晶格、三角晶格、六角晶格、簡單單斜晶格、底心單斜晶格、簡單正交晶格、底心正交晶格、體心正交晶格、面心正交晶格、簡單四角晶格和體心四角晶格 ;For the plane whose intercepts are 4,2,3, the reciprocals倒數(shù) are 1/4、1/2、1/3 ,the smallest three integers整數(shù) having the same ratio比率 are 3、6、4 . The cube faces of a cubic crystal 立方晶體的立方體面are 二、 Exp

3、ression and the calculation for the contents of Chapter II.1）Please write out three vectors向量 of the reciprocal lattice倒格子: .by using vectors 。 b1=(2)·(a2*a3)/(a1·(a2*a3)）                    

4、;    b2=(2)·(a3*a1)/(a1·(a2*a3)）                          b3=(2)·(a1*a2)/(a1·(a2*a3）2) Calculate計(jì)算 the volume of the primitive cel

5、l of fcc lattice面心立方晶格：晶格基矢體積V=原胞基矢體積三、 Derivation for the contents of the contents of Chapter III. Please derive out the van der Waals-London Interaction范德瓦爾斯倫敦相互作用 from the linear harmonic oscillators model.線性諧振子模型解：作為一個(gè)模型，考慮兩個(gè)值距為R的全同線性諧振子1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X1和X2，粒子沿X軸振動，動量分

6、別用R1和R2表示，力常量為C。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)振子之間的庫倫相互作用能，核間坐標(biāo)為R，于是有在的近似下，將上式展開，使得到最低級近似表達(dá)式為通過簡正模變換：并解出X1和X2：同時(shí)取的近似形式，是系統(tǒng)的中哈密頓量對角化，可以得出這兩種模式相聯(lián)系的動量Ps和Pa,P1則總哈密頓量可以寫成可得來。振子的兩個(gè)頻率為W=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。的值2-1/2V=四、Expression and the explanation for the contents of Chapter IV.1) Please wri

7、te out the dispersion relation 色散關(guān)系of (q) for two atoms原子 Per Primitive Basis每個(gè)原始依據(jù) , and explain the physical meaning of the formula公式.五、 Concepts and the derivation for the contents of Chpater V. 1) What is the Debye model德拜模型 and Debye T3 lawT3法? What is the concept概念 of Debye temperature?2) Plea

8、se derive the Density of State in Three Dimension三維狀態(tài)密度.六、Derivations for the contents of Chapter VI. 1) Please derive the formula公式 of energy levels of free electrons自由電子的能量水平 in one dimension維.2) Please derive the the Hall coefficient 霍爾系數(shù)of Hall effect.七、Explanation and derivation for the content

9、s of Chapter VII. Please explain the origin of the energy gap, and write out the free electron bands for 110 direction of wavevector space.Solution:olthe origin of the energy gap is the two standing waves and pile up electors at different regions and therefore the two waves have different values of

10、the potential energy ,Ihtsis the origin of the energy gap.2) the free electron bands for 110 direction of wavevetor space is Energy band Ga/2 （000） （0)1 000 0 2,3 100,00 4,5,6,7 010,00,001,00 8,9,10,11 110,101,10,10 12,13,14,15 10,16,17,18,19 八、Concepts and the explanation for the contents of Chapte

11、r VIII. 1) A hole acts in applied electric and magnetic fields as if it has a positive charge +e. The possible reasons in five steps are: Solution：1）the electrons in the full band the total wave vector is zero:2） let the valerve band energy zero point in the conduction band above3） the velocity of t

12、he hole is equal to the velocity of the missing electron.4） the effective mass is inversely propertional to the crrvature and for the hde band ,this has the opposite sum to that for an electron in the valence band.5)this come from the equation of motion 2) Please explian the physical meaning of ener

13、gy-k relation of following three semiconductor materials半導(dǎo)體材料 .卷 B 學(xué)期： 2011 至 2012 學(xué)年度第 1 學(xué)期一、Fill in the blanks with the proper data or concepts in Chapter I.Solid state physics largely concerned主要關(guān)注: (1）crystals晶體 (2) electrons in crystals ;Atoms density密度： ；Translation vector平移矢量： 3 translation v

14、ector vs a1、a2、a3 / ； The volume of a parallelepiped 平行六面體with axes is： ； The posibble five 2D Bravais lattice are : 正方晶格、六角晶格、長方晶格、有心長方晶格和斜方晶格 ; Seven lattice system are : 三斜、單斜、正交、立方、四角、六角和三角晶系 ;For the plane whose intercepts are 3,1,2, the reciprocals are 1/3、1/1、1/2 , ,the smallest three integer

15、s having the same ratio are （ 263 ） . The cube faces of a cubic crystal are （100）（010）( 001) (00)( 00)和（00） 二、Calculations for the contents of Chapter II.1） Please write out three vector of the reciprocal lattice: .Explain:2)Please verify驗(yàn)證 the relation: .3) Calculate the volume 體積of the primitive c

16、ell of bcc lattice：三、Calculations and the concept explanation for the contents of Chapter III. Please calculate the Madelung constant馬德龍常數(shù) for the infinite無限的 line of ions離子 of alternating sign交替的跡象 for the one-dimensional chain 一維鏈to be :四、Expression and exlanations for the contents of Chapter IV.

17、1) Please write out the 1D dispersion relation of (q), and explain the physical meaning of the formula.(q)=其中C是最近鄰平面之間的力常量，M是一個(gè)原子的質(zhì)量。The special signifcance of phonon wavevetors that lie on the zone.boundary is developed from the formula ,we can obtain when q=0,w(q)=0,when q= 2) What is the long wav

18、e limit長波極限 and what result結(jié)果 we can get from this limit?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： ），長波極限就是q取值趨向于范 圍邊界時(shí)的情況。研究的意義在于了解極限情況下格波振動頻率的情況。Or當(dāng)qa<<1時(shí)，將cosqa展開并取得近似，可得cosqa1-.由此色散系度為表明在長波極限下，頻率與波長成正比。五、 Explanations for the contents of Chapter V. 1) What is the Debye model and Deb

19、ye T3 law? What is the concept of Debye temperature?Solution:1)Debye model is the low of the Max planck blackbody radiation solid equivalents.in the Debye model ,the allow model vectors smaller than the K2) Debye T3 law is when T ，U=，that can obtain 3) Debye temperature can define 2) Please explain

20、the physics menaning of Umklapp Processes:UP過程：Solution:To the thermal nesistivity of electrons,which have more important effectthree phonon processes isnt ,it is ,G is reriprocal lattice vectors called Umklapp processes .In the processes the energy is constant .The phonon vector ,in the first ,Bril

21、louin zoneshas physics menaning .The umklapp processes can let the phonon vector back to the first Brillouin zones.六、 Derivation for the contents of Chapter VI 1) Please derive the formula of energy levels of free electrons in one dimension.請導(dǎo)出一維自由電子能級的公式Solution:For schrodinger equation ,we can obt

22、ain ,where is the electron orbital energy . To infintle potential boundary conditions We can obtain where A is a constant,so that we can obtain energy 3) Please derive the the Hall coefficient of Hall effect.請導(dǎo)出霍爾效應(yīng)的霍爾系數(shù) Solution:To the state electric field steady state ,the time derivative is zero

23、,then Vx=,where is eyctotion frequency ,when ,We can get .And the Hall coffinient defined is ,we can used to get .七、Explanation and the derivation for the contents of Chapter VII.Please explain the origin of the energy gap, and write out the free electron bands for 111 direction of wavevector space.請解釋能隙的起源，并寫了 111 方向的波矢空間的自由電子帶。八、Deravation and the calculation for the contents of Chapter VIII第八章.1) Starting from the definition of group velocity vg , please give the effect mass m* described by the energy band vs wavevector k. 從群速Vg的定義，請把影響質(zhì)量m *的能帶與波矢k描述P1