固体物理习题解答：Chapter 8 problems

1.Impurityorbitsa)ThedonorionizationenergyWeestimatetheionizationenergyandtheorbitradiusbyBohrtheoryofthehydrogenatom:(page222)Forindiumantimonide,dielectricconstant=18,electroneffectivemassme*=0.015m.b)Theradiusofthegroundstateorbitc)TheminimumdonorconcentrationTheoverlapeffectsoccurwhentheaveragedistancebetweenthedonorsdissmallerthanthediameterofthedonororbits2ad.Thentheminimumdonorconcentration2.Ionizationofdonorsa)TheconcentrationofconductionelectronsWhenassumenoacceptoratomsarepresentandthatEg>>kBT,theconcentrationofconductionelectronsisgiven(page226)b)TheHallcoefficient(page164)3.HalleffectwithtwocarriertypesFromtheequationsofmotion,wehavethecurrentdensityofthecarriers:Forelectrons,Assumetheappliedmagneticfieldisalongzaxis,andtheappliedelectricfieldisalongxaxis.Thegeometryissimilarasshowninpage165.ThenForholes,whereInsteadystateInthelimit<<1,neglecttheterm()2.Theni.e.Thecurrentdensityinx-directionInthelimitEy<<Ex,TheHallcoefficientwhere isthemobilityratio.4.CyclotronresonanceforaspheroidalenergysurfaceConsidertheenergysurfaceThevelocityThestaticmagneticfieldinthex-yplaneTheequationofthemotionTheequationofthemotionSetthesolutionsoftheequationsiswhereThenForanuntrivial

Cx,Cy,andCzi.e.Thus5.MagnetoresistancewithtwocarriertypesAssumeappliedthemagneticfieldisalongzaxis,ThedriftvelocityofonekindchargecarriersqisForelectronsq=e,andforholesq=e.ThenthevelocitiesofthecarriersForelectrons:Forholes:ThecurrentdensityForelectrons:Forholes:whereInthelimitofverystrongfield,c>>1,Forelectrons:Forholes:Thetotalcurrentdensityi.e.a)SetThenb)Assumetheappliedelectricfieldisalongxdirection.Atste