半导体物理课堂

1、PowerPoint2003,第八章,1,半导体物理学习题,第八章,8,1,8,2,8,3,8,4,8,7,8,8,8,9,8,10,2,8,1,导出使表面恰为本征时的表面电场强度，表面电荷密度,和表面层电容的表达式,P,型硅,解答,P,型硅,能带不弯,0,p,A,p,N,表面本征时,0,S,V,s,s,n,p,由公式,8-17,得,2,0,exp,exp,s,i,s,s,p,A,qV,n,qV,n,n,kT,N,kT,由公式,8-18,得,0,exp,exp,s,s,s,p,A,qV,qV,p,p,N,kT,kT,ln,ln,s,A,A,s,s,S,B,i,i,qV,N,N,kT,n,p,V

2、,V,kT,n,q,n,3,其中,0,12,2,2,4,2,0,10,4.6,10,10,10,s,s,qV,qV,p,s,kT,kT,p,n,qV,N,cm,e,e,kT,p,1,0,0,2,0,0,1,2,18,18,2,10,2,1,1,2,2(ln,10,10,ln,10,s,s,qV,qV,p,p,s,s,s,kT,kT,p,p,s,A,i,s,n,n,qV,qV,qV,F,e,e,kT,p,kT,p,kT,qV,N,kT,n,qV,N,cm,kT,其中,18.42,0,8,16,8,0,10,10,10,s,s,qV,qV,p,kT,kT,p,n,e,e,p,4,P,型硅表面本征，

3、能带下弯,0,0,0,S,s,s,V,E,Q,1,1,2,2,1,1,2,2,0,1,0,2,1,1,2,2,2,2,2,2,ln,1,1,1,2,1,2,2,ln,s,s,s,s,s,s,s,D,D,rs,rs,rs,A,s,S,s,D,D,D,i,qV,qV,p,rs,rs,kT,kT,s,D,p,s,D,rs,rs,D,A,s,D,D,i,qV,qV,kT,kT,E,F,V,kT,qL,kT,L,q,kT,kT,N,kT,Q,F,V,qL,L,q,L,q,n,n,C,e,e,L,p,qV,L,kT,kT,L,N,qV,L,L,n,其中,1,2,rs,A,kT,N,2,q,返回,5,8,2

4、,8,0.24,i,s,n,S,cm,V,V,求,时耗尽层的厚度,解答,3,14,2,2,0,0,8,6,10,2,2,ln,0.55,ln,0,0,d,A,B,s,B,i,A,i,rs,d,x,x,rs,cm,cm,N,kT,V,V,V,V,q,n,N,q,d,V,x,kT,dV,x,A,dx,n,q,dx,q,dV,x,x,x,A,x,dx,D,D,D,查图,4,15,得,N,所以为表面耗尽,N,对于,n,型硅,积分得,N,边界条件,场强为,即,6,0,2,0,2,d,rs,rs,q,dV,x,x,x,dx,q,x,V,x,x,D,D,N,N,再积分，得,B,0,2,0,0,0,0,2,2

5、,0,2,d,d,rs,d,rs,s,d,rs,x,x,V,x,q,B,x,q,V,x,x,x,q,x,V,x,2,D,d,D,D,边界条件,时,体内电势为,N,则,N,N,处为表面势，即,7,1,12,0,2,19,14,6,3,7,14,5,2,0.24,2,11.9,8.85,10,1.6,10,6,10,10,7.26,10,0.726,5.5,10,7.56,10,s,rs,d,D,d,V,F,m,x,q,m,m,m,N,cm,x,cm,D,N,若,返回,8,8,3,对于,MOS,电容,2,i,S,O,的厚度为,0,1000,d,0,A,n,型硅,5,cm,计算室温,27,o,下的平

6、常电容,0,FB,C,C,解答,2,3,14,20,12,0,23,8,66,5,9,10,9,10,11.9,3.8,8.85,10,0.026,1.38,10,A,D,D,rs,ro,N,N,cm,N,cm,m,F,m,kT,eV,k,T,K,由式,中,用,代替,9,1,0,0,2,2,2,0,1,1,FB,ro,rs,rs,D,C,C,kT,q,N,d,1,12,23,2,19,2,20,10,2,1,3.8,11.9,8.85,10,1.38,10,300,1,11.9,1.6,10,9,10,1000,10,1,0.69,1,0.439,返回,10,8,4,导出理想,MIS,结构的开

7、启电压随温度变化的关系式,解答,1,2,0,8,52,4,ln,A,s,rs,A,B,B,i,N,kT,Q,qN,V,V,q,n,由式,得,0,0,0,ro,C,d,与温度无关,0,0,1,2,0,0,2,4,ln,2,ln,s,T,s,B,A,rs,A,i,A,i,Q,V,V,V,V,C,N,N,kT,n,N,kT,C,q,n,11,1,3,3,2,2,15,2,4,2,2,0,4.82,10,0,g,g,E,kT,E,kT,p,n,i,c,v,g,g,g,m,m,n,N,N,e,T,e,m,dE,E,E,T,dT,返回,12,8,7,计算下列情况的平带电压的变化,氧化层均匀分布正电荷,三角

8、行分布，金属附近高，硅附近低,三角形分布，金属附近低，硅附近高,并假设单位面积的总离子数为,2,12,10,cm,N,s,氧化层厚度为,0.2,m,9,3,0,r,解答,电荷均匀分布，面密度,2,12,10,cm,q,q,N,Q,s,s,13,0,0,s,0,0,0,0,0,d,d,s,s,Q,x,dx,dx,d,N,q,Q,x,d,d,体密度,由面密度求体密度,0,0,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,19,1,2,4,12,1,1,2,2,2,2,1,0.2,10,1.6,10,4.6,2,3.9,8.85,1,1,0,0,d,d,FB,S,s,ro,s,

9、ro,x,x,V,dx,xdx,d,C,d,C,d,C,d,Q,N,q,N,q,d,C,cm,cm,C,V,c,d,F,m,14,分布如图,x,0,d,x,m,x,0,0,0,0,0,0,0,0,12,12,17,3,6,0,2,3,0,0,2,0,0,0,0,0,10,2,2,10,10,0.2,10,8,10,2,1,2,m,m,m,m,m,d,d,m,m,m,s,s,m,m,s,m,x,x,q,d,x,q,d,d,x,dx,x,dx,d,q,N,cm,d,q,x,d,d,d,q,x,d,x,d,N,N,d,d,c,q,cm,由面密度求,即,0,15,0,0,2,0,0,0,3,2,2,0

10、,0,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3,2,2,1,1,3,2,6,6,3.09,3,d,FB,d,m,m,m,m,S,m,m,m,r,S,r,x,x,V,dx,C,d,d,d,x,x,qdx,q,C,d,d,C,d,d,N,d,d,d,d,q,d,q,d,q,C,C,N,d,q,V,16,体电荷密度,0,m,x,xq,d,0,0,0,0,2,0,0,0,0,0,0,0,2,0,0,0,2,3,3,0,2,2,0,0,0,0,0,0,0,0,0,2,0,0,2,2,2,2,1,1,1,3,2,2,6.2,3,d,d,m,m,

11、s,s,s,s,m,d,d,m,m,FB,s,FB,r,q,q,d,x,dx,xdx,N,q,d,d,d,N,N,d,N,q,x,xq,x,d,d,d,q,x,x,V,dx,x,qdx,d,C,d,C,d,C,d,N,qd,V,V,解得,返回,17,8,8,试导出下列情况下快表面态中单位面积电荷的表达式,位于禁带中央处,i,E,的单能级表面态，单位面积内的,表面态数为,ss,N,均匀分布于整个带的表面态，即,ss,N,E,const,以上两题，假定表面态是受主型的，即当该表面态被,一个电子占据时带负电，空着时为电中性,解答,1,1,1,F,sA,sA,sA,E,E,kT,f,E,e,g,受主型

12、界面态的空穴分布函数为,18,1,1,1,1,1,1,F,sA,F,sA,F,sA,E,E,kT,sA,sA,sA,sA,E,E,E,E,kT,kT,e,g,f,E,f,E,ge,e,g,单位面积上的电荷量为,电子的分布函数为,1,F,i,E,E,E,E,i,SA,F,i,kT,kT,E,E,E,E,F,i,F,i,kT,kT,ss,s,E,E,kT,i,D,i,D,A,A,i,i,qN,qn,A,ge,n,n,N,n,e,e,N,N,p,N,n,e,e,n,s,s,Q,型,型,19,1,1,ss,ss,i,A,i,D,A,qN,qN,n,p,n,N,g,g,n,N,s,s,s,s,代入,式得

13、,Q,型材料,Q,型材料,电子占据能量为,E,得表面态的几率为,1,1,1,F,sA,sA,sA,E,E,kT,ss,ss,g,f,E,e,g,N,E,N,const,E,Q,在整个禁带中单位能量间隔的表面态数,20,1,c,c,F,v,v,ss,g,sA,sA,ss,g,E,E,ss,ss,ss,sA,E,E,E,E,kT,g,g,N,E,dE,dE,E,f,E,N,E,dE,E,N,E,qN,E,dE,Q,q,f,E,dE,E,E,ge,在,范围内为,其上占据的电子数为,总的表面电荷量为,21,1,ln,1,1,F,F,E,E,E,E,c,F,c,F,kT,kT,E,E,E,E,v,F,v

14、,F,kT,kT,E,E,kT,E,E,F,kT,e,e,ss,ss,ss,e,e,g,g,e,u,E,E,kT,du,e,d,u,dE,dE,du,kT,kT,u,qN,qN,kT,kT,u,Q,du,E,gu,u,E,gu,令,则,0,0,0,0,c,F,c,F,F,v,v,F,E,E,E,E,c,kT,kT,c,E,E,E,E,kT,kT,v,v,N,n,N,e,e,n,p,p,N,e,e,N,22,0,0,0,0,1,ln,1,1,1,ln(1,v,ss,ss,ss,c,g,c,v,ss,ss,p,g,N,qN,kT,Q,qN,N,E,g,n,p,N,N,n,Q,qN,讨论：对于本征半

15、导体,1,1,1,ln,ln,2,v,F,c,F,c,i,E,E,E,E,kT,kT,ss,ss,ss,ss,ss,E,E,kT,g,g,e,e,qN,kT,qN,qN,kT,Q,qN,g,E,E,ge,23,对于一般半导体,0,0,0,0,0,0,1,ln,1,c,F,c,F,F,v,v,F,E,E,E,E,c,kT,kT,c,E,E,E,E,kT,kT,v,v,v,ss,ss,ss,c,g,N,n,N,e,e,n,p,p,N,e,e,N,p,g,N,qN,kT,Q,qN,N,E,g,n,24,对于非简并,p,型或,n,型总有,0,0,0,1,1,ln(1,c,v,c,ss,ss,ss,g,

16、ss,ss,p,N,N,n,N,qN,kT,Q,qN,g,p,n,E,Q,qN,型,n,型,返回,25,8-9,对,16,3,10,A,N,cm,氧化层厚度,0,1,d,m,的硅栅控,二极管，计算,21,下其开启电压,与反压的关系。取,T,V,0,FB,V,解答,0,0,0,2,2,FB,s,k,B,q,T,s,T,s,k,B,V,V,V,V,V,V,Q,V,V,V,V,V,C,说明此系统为理想模型,表面势,时,26,16,10,1,0,2,0,0,0,ln,2,0.026,10,2,ln,0.052,6,2.3,0.41,1,1.5,10,0.696,2,2,A,B,i,B,s,A,dm,r

17、s,k,B,dm,A,rs,N,kT,V,q,n,V,V,Q,qN,x,V,V,x,qN,C,d,27,0,0,1,0,2,0,1,1,0,2,2,0,0,1,4,19,16,14,2,14,2,ln,2,2,ln,2,ln,2,2,2,ln,ln,10,2,1.6,10,10,11.7,8.85,10,0.696,3.8,8.85,10,0,A,dm,A,T,k,i,A,rs,k,i,A,k,rs,A,i,A,A,A,rs,k,k,rs,i,i,k,qN,x,N,kT,V,V,C,q,n,N,kT,V,d,q,n,N,kT,V,qN,q,n,d,N,N,kT,kT,qN,V,V,q,n,q,

18、n,V,v,696,17,0.696,0.696,k,k,k,V,V,V,V,V,返回,28,8,10,5,m,硅,p,n,栅控二极管，其冶金结面积为,3,3,10,cm,衬底杂质浓度,16,3,10,cm,结深,氧化层厚度,0.2,m,1,s,寿命,表面复合速度,0,5,S,cm,s,平带电压,2,FB,V,V,栅极与,n,型区重叠面积为,3,2,10,cm,试计算,衬底表面分别为本征和强反型时的栅电压（室温下结,电容为零时,0,20,q,V,V,的条件,1,k,V,V,时的室温下的反向电流,在与同样的栅压下,0.4,k,V,V,时的正向电流，并求,出反向电流,正向电流和栅电压的函数关系,2

19、9,解答,0,0,2,0,s,s,s,s,i,q,s,FB,s,s,qV,qV,kT,kT,s,n,D,qV,qV,kT,kT,s,n,D,V,V,V,V,n,p,n,n,e,N,e,n,p,p,e,e,N,表面本征情况,上面式相等,2,s,s,i,qV,qV,kT,kT,D,D,n,e,N,e,N,开方，取对数得,ln,i,s,D,n,kT,V,q,N,30,16,10,0,1,1,0,2,2,0,14,8,2,0,0,4,0,0,0,0,10,ln,0.026ln,0.35,1.5,10,2,2,3.9,8.85,10,1.725,10,0.2,10,2,i,F,i,s,B,D,s,o,r

20、s,s,s,D,d,D,D,rs,s,D,rs,s,o,D,rs,rs,E,E,n,kT,V,V,V,q,q,N,Q,V,C,V,Q,qN,x,qN,qN,V,qN,C,F,cm,d,Q,d,V,qN,C,二氧化硅层中的压降,表面深耗尽,1,2,0,s,V,31,1,4,19,16,14,2,14,1,0,0,2,0,0,0,0,0,0.2,10,2,1.6,10,10,11.9,8.85,10,0.35,3.9,8.85,10,1.99,1.99,0.35,2,4.34,2,2,0.35,0.70,2,2,2,G,o,s,FB,s,B,s,o,D,rs,s,D,rs,rs,rs,V,V,V,

21、V,V,V,V,V,V,Q,d,d,V,qN,V,qN,C,表面本征时,衬底表面强反型,1,2,1,0,2,0,0,2,2,2,2,1.99,2.81,2.81,0.70,2,5.51,B,D,rs,B,rs,o,o,G,o,s,FB,V,d,qN,V,V,V,V,V,V,V,V,强反型时,32,a,0,1,2,n,0,0,0,6,38,G,R,FB,gF,gS,gd,S,gM,V,V,V,V,V,I,I,I,I,I,Q,i,2,时的反向电流,300K,或是,S,O,中正电荷或是金半功函数的作用,型衬底表面为多子积累状态,场感应结产生电流,表面界面态产生,电流,表面耗尽层,只有冶金结的反向漂流

22、电流,和产生电流,由,式,33,1,2,2,1,19,23,10,2,3,2,6,16,14,2,2,16,3,2,1.6,10,1.38,10,300,400,1.5,10,10,1,10,10,1.16,10,1.16,10,1,10,400,2,1,2,2,p,no,p,i,s,Mj,Mj,p,D,D,p,p,p,p,no,i,D,p,i,Mj,i,r,gM,D,Mj,Mj,qD,p,qkT,n,I,A,A,L,N,u,N,kT,D,L,D,p,q,n,N,cm,cm,s,qn,A,n,I,q,x,A,其中,由,查表得,0,s,D,R,D,V,V,qN,34,19,10,3,14,6,1

23、9,16,6,5,11,1.6,10,1.5,10,10,2,11.9,8.85,10,0.7,1,2,10,1.6,10,10,1.2,10,4.73,10,5.68,10,56.8,u,0,1,G,R,V,V,V,时的反向电流,14,11,11,1.16,10,5.68,10,5.68,10,k,s,gM,I,I,I,b,20,1,G,R,V,V,V,V,时的反向电流,由,1,知强反型时,35,即,20,5.51,5.51,1,6.51,R,V,V,V,栅下,n,型表面处为强反型状态,少子空穴堆积,0,gs,I,界面态表面产生电流,表面耗尽区产生电流,0,gd,I,反向电流,14,11,1

24、.16,10,5.68,10,Rg,gM,gF,s,sF,s,gM,I,I,I,I,I,I,I,由上式算得,36,0,1,14,6,2,19,16,6,5,11,1,2,2,2,2,2,11.9,8.85,10,0.35,2,1,1.2,10,1.6,10,10,1.2,10,4.73,10,5.68,10,56.8,i,i,s,gF,dm,s,dm,Fj,Fj,i,s,rs,B,R,Fj,D,n,qn,A,I,q,x,A,x,qn,A,V,V,qN,u,20,1,G,F,V,V,V,V,时的反向电流,37,11,11,10,5.68,10,5.68,10,1.136,10,113.6,2,R

25、g,gM,gF,s,sF,gM,gF,s,sF,s,I,I,I,I,I,I,I,u,I,I,I,可略,a,0,0.4,G,F,V,V,V,时流,p,n,结的正向电,0,2,G,FB,V,V,V,Q,n,区表面为多子积累状态，只考虑,冶金结的正向扩散电流和复合电流即可；又因是,p,n,结，可视为单向注入，即主要是空穴扩散电流,38,0,0.4,14,14,6,0.026,8,1,1,1.16,10,1,1.16,10,4.80,10,5.57,10,F,F,qV,p,n,kT,d,pd,Mj,p,qV,kT,s,qD,p,I,I,A,e,L,I,e,e,p,n,结的势垒复合电流,2,2,F,qV

26、,i,kT,rM,Mj,D,qn,I,A,x,e,39,1,0,2,1,14,2,19,16,5,0.4,19,10,3,5,0.026,2,6,11,8,2,2,11.9,8.85,10,0.7,0.4,1.6,10,10,2.0,10,1.6,10,1.5,10,10,2.0,10,2,10,2.4,10,2191,5.26,10,rs,D,F,D,D,rM,V,V,x,qN,cm,I,e,0,0.4,G,F,V,V,V,时,8,7,5.57,5.26,10,1.08,10,F,d,rM,I,I,I,40,b,20,0.4,G,F,V,V,V,V,时的,F,rF,rM,d,dF,I,I,I

27、,I,I,在,1,求过强反型时,5.51,20,5.51,G,T,V,V,V,V,V,显然为,n,型表面强反型,未加冶金结电压时，强反型表面势为,2,s,B,V,V,冶金结加上正向偏压后表面势降低为,2,2,0.35,0.4,0.3,s,B,F,V,V,V,场感应结,1,0,2,2,0.35,2,0.4,rs,dm,D,x,qN,41,1,14,15,2,19,16,2,11.9,8.85,10,0.3,2.0,10,1.6,10,10,cm,场感应结正向复合电流,2,8,1,5.26,10,2,F,qV,kT,dm,rF,i,FJ,rM,x,I,qn,A,e,I,总的正向电流感应结复合电流,

28、rF,I,冶金结复合电流,rM,I,冶金结空穴扩散电流,d,I,感应结空穴扩散电流,dF,I,其中,d,I,dF,I,2,rF,rM,d,I,I,I,8,8,8,7,5.26,10,5.26,10,5.57,10,2,2.19,10,42,c,求反向电流，正向电流与栅压的关系,冶金结耗尽层宽度为,1,0,2,2,rs,D,D,D,V,V,x,qN,外加反压时,0,k,V,V,外加正压时,0,F,V,V,设感应结耗尽层的厚度为,d,x,绝缘层电容为,0,C,平带电压为,FB,V,表面势为,s,V,则有,0,s,G,FB,s,Q,V,V,V,C,43,2,0,2,0,0,2,2,D,d,s,s,D,rs,D,d,D,d,G,FB,rs,qN