半导体器件基础答案(英文版)邓宁.pdf

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1、SOLUTIONSCHAPTER11.1.ShowthatEquation(1.6)followsfromEquation(1.3).2qSolution:Equation(1.3)isdE=dr.IntegratingbothsidesweobtainP24πεr0222qq1q⎡1⎤dE=dr=dr=−+const=E∫P∫2∫2⎢⎥P4πε0r4πε0r4πε0⎣r⎦Tofindtheconstant,weemploytheboundaryconditionthatatr=∞,EP=Evac:2−qEr(

2、)=∞=E=+const=+0constPvac4πε⋅∞0∴const=Eandvac2−qEE=−=E,Equation(1.6)Pvacvac4πε⋅∞01.2.Consideralithiumnucleus,ofcharge+3q.Calculatethefirstthree++electronenergiesforanelectroninaLiion,usingtheBohrmodel.Werepeattheanalysisthatweusedforthehydrogenatom,exceptthat

3、−19nowthechargeofthenucleusQ1isequalto3qC=+3(1.610×).Theresultsofthekeystepsare2QQ−3q12F==2244πεπrrε0023qErE()=−Pvac4πεr022mv3q−=02rr4πε0mvr=nhnn231q⎛⎞v=⎜⎟n()4πε0h⎝⎠n2()4πε0h2rn=()n23mq24mq31⎛⎞E=⎜⎟K22224()πε0h⎝⎠n491mq⎛⎞EEEE=+=−⎜⎟nPnKnvac22224()πε0h⎝⎠nThusEE=

4、−913.6(eVE)=−122eV1vacvacAnderson&Anderson12/15/04SolutionsChapter1913.6()eVandEE=−=−E30.6eV2vac2vac2913.6()eVandEE=−=−E13.6eV3vac2vac31.3.ShowthatEquations(1.12)and(1.13)followfrom(1.8)and(1.11).22mvqEquation(1.8)is:−=02rr4πε02Multiplybothsidesbyranddivideb

5、yv:2qmvr=whichfromEquation(1.11)is4πεv02qmvr==nh4πεv0Solvingtherighthandequalityforv:2qv=(Equation(1.13))4πεnh0Solvingthelefthandequalityforrsubstitutinginv:22nhnnhh()4πε04πε0nhr===(Equation(1.12)).22mvmqmq1.3.IneachofthepotentialenergydistributionsinFigure1

6、P.1,sketchthemagnitudeanddirectionoftheforceontheelectron.Anderson&Anderson22/15/04SolutionsChapter1Theforceisminusthegradientofthepotentialenergy(Equation(1.2)).1.5.ConsidertheelectronintheenergydiagramofFigure1P.2.TakingtheenergytheelectronhasatPointAasEto

7、tal,ateachoftheindicatedpositions,findthetotalenergy,thekineticenergy,thepotentialenergy,andtheelectron’svelocity.Indicatethedirectionofforce(ifany).Recallthattotalenergyisconserved.Atpoint“D”theelectroncollidesinelasticallywithsomething(perhapsanatominthecr

8、ystal).Afterthecollision,theelectron’senergyisequaltoitspotentialenergy,anditskineticenergyiszero.Itstotalenergyismuchlessthanbeforethecollision;wheredidtheextraenergygo?TheelectronatPointAisatr