L01-pn结的频率特性与开关特性

1/22半导体器件原理主讲人：蒋玉龙本部微电子学楼312室，65643768Email:[e-mail]第一章pn结的频率特性与开关特性1.1半物要点回顾1.2pn结的频率特性1.3pn结的开关特性3/221.1半物要点回顾1重要公式c()[]kTEENnFCC−−=exp0()[]kTEENpVFV−−=exp0dedxdnqDJnn=扩EqnJnnμ=漂dxdpqDJpp−=扩EqpJppμ=漂⎥⎦⎤⎢⎣⎡−⎟⎠⎞⎜⎝⎛=1expkTqVJJsf2/102⎟⎟⎠⎞⎜⎜⎝⎛−=NVVqdDrεε耗尽g()[]()pnLxkTqVpxp−−=Δexp1exp)(04/22++++++++--------PNVV=0EcpEcnEvpEvnEfpEfnqVD+-++++----PNVV0EcpEcnEvpEvnEfpEfnqVq(VD–V)++++++++++++------------PN-+VV0EcpEcnEvpEvnEfpEfnqVq(VD-V)pp0nn0np0pn0-XpXnXp(x)n(x)pp0nn0np0pn0-XpXnXpp0nn0np0pn0-XpXnX－非平衡p-n结的能带图－电压完全降在势垒区重要图像--非平衡p-n结的能带图1.1半物要点回顾25/22EcpEcnEvpEvnEfpEfnqVDEcpEcnEvpEvnEfpEfnqVq(VD–V)pp0nn0np0pn0-XpXnXp(x)n(x)pp0nn0np0pn0-XpXnX⎟⎠⎞⎜⎝⎛−==−kTqVnnxnDnppexp)(00⎟⎠⎞⎜⎝⎛−==kTqVppxpDpnnexp)(00⎟⎠⎞⎜⎝⎛−−=kTVVqpxpDpn)(exp)(0⎟⎠⎞⎜⎝⎛=kTqVpxpnnexp)(0⎥⎦⎤⎢⎣⎡−⎟⎠⎞⎜⎝⎛=Δ1exp)(0kTqVpxpnn⎟⎟⎠⎞⎜⎜⎝⎛−−Δ=ΔpnnLxxxpxpexp)()(无限厚样品的稳态扩散解0)()(npxpxp−=Δnxx注入到N区的非平衡空穴⎥⎦⎤⎢⎣⎡−⎟⎠⎞⎜⎝⎛=−Δ1exp)(0kTqVnxnpp⎟⎟⎠⎞⎜⎜⎝⎛+−Δ=ΔnppLxxxnxnexp)()(注入到P区的非平衡电子－正向偏压下的非平衡少子重要图像--非平衡p-n结的能带图1.1半物要点回顾36/22EcpEcnEvpEvnEfpEfnqVq(VD–V)EcpEcnEvpEvnEfpEfnqVq(VD-V)pp0nn0np0pn0-XpXnXpp0nn0np0pn0-XpXnX－反向偏压下的非平衡少子⎥⎦⎤⎢⎣⎡−⎟⎠⎞⎜⎝⎛=Δ1exp)(0kTqVpxpnn⎥⎦⎤⎢⎣⎡−⎟⎠⎞⎜⎝⎛=−Δ1exp)(0kTqVnxnpp⎟⎟⎠⎞⎜⎜⎝⎛−−−=ΔpnnLxxpxpexp)(0⎟⎟⎠⎞⎜⎜⎝⎛+−=ΔnppLxxnxnexp)(000)()(nnnnppxpxp−=−=Δ⎟⎟⎠⎞⎜⎜⎝⎛−−Δ=ΔpnnLxxxpxpexp)()(⎟⎟⎠⎞⎜⎜⎝⎛+−Δ=ΔnppLxxxnxnexp)()(0VkTVq=0抽取00)()(ppppnnxnxn−=−−=−Δ1.1半物要点回顾4重要图像--非平衡p-n结的能带图7/22前提：－小注入－突变耗尽层条件（耗尽层外电中性）－忽略势垒区中载流子的产生、复合－非简并重要图像--理想p-n结的J-V关系0pppnΔ0nnnpΔpp0nn0np0pn0-XpXnXnpJJJ+=JpJnJnJp-XpXnXJ=Jp+Jn)()()()(pnnpnnnpxJxJxJxJJ−+=+=⎥⎦⎤⎢⎣⎡−⎟⎠⎞⎜⎝⎛=Δ1exp)(0kTqVpxpnn⎟⎟⎠⎞⎜⎜⎝⎛−−Δ=ΔpnnLxxxpxpexp)()(⎥⎦⎤⎢⎣⎡−⎟⎠⎞⎜⎝⎛=Δ−==1exp|)(0kTqVpLqDdxpdqDxJnppxxpnpn0()exp1nnppnqDqVJxnLkT⎡⎤⎛⎞−=−⎜⎟⎢⎥⎝⎠⎣⎦⎟⎟⎠⎞⎜⎜⎝⎛+=AninDpipsNLnqDNLnqDJ22⎥⎦⎤⎢⎣⎡−⎟⎠⎞⎜⎝⎛=1expkTqVJJsAipNnn20=DinNnp20=电流密度扩散电流组成1.1半物要点回顾58/22第一章pn结的频率特性与开关特性1.1半物要点回顾1.2pn结的频率特性1.3pn结的开关特性9/221.2pn结的频率特性11.2.1交流小信号下的pn结少子分布tVVtVωcos)(10+=(V1V0)V1exp(iωt)[]kTtqVptxpnnn)(exp),(0=~V0V1cosωtxn-xp[]{}1)(exp0−kTtqVpn⎥⎦⎤⎢⎣⎡⎟⎠⎞⎜⎝⎛=)exp(expexp100tikTqVkTqVpnω⎥⎦⎤⎢⎣⎡+⎟⎠⎞⎜⎝⎛≈)exp(1exp100tikTqVkTqVpnω)exp(expexp00100tikTqVpkTqVkTqVpnnω⎟⎠⎞⎜⎝⎛+⎟⎠⎞⎜⎝⎛=)exp()()(10tixpxpnnnnω+=边界条件EcpEcnEvpEvnEfpEfnqVq(VD–V)px−nx10/221.2pn结的频率特性21.2.1交流小信号下的pn结少子分布扩散区内)exp()()()(10tixpxpxpnnnω+=连续性方程pnnnpnptxpxtxpDttxpτ022),(),(),(−−∂∂=∂∂直流分量满足Q0)()(00202=−−∂∂pnnnppxpxxpDτ∴[][]pnnpntixpxtixpDttixpτωωω)exp()()exp()()exp()(12121−∂∂=∂∂0)(1)(1212=⎟⎟⎠⎞⎜⎜⎝⎛+−xpidxxpdDnpnpτω0)()(2'1212=−pnnLxpdxxpd这里pppiLLωτ+=1'EcpEcnEvpEvnEfpEfnqVq(VD–V)px−nx11/221.2pn结的频率特性31.2.1交流小信号下的pn结少子分布边界条件⎟⎠⎞⎜⎝⎛=kTqVpkTqVxpnnn0011exp)(0)(1=∞np⎟⎟⎠⎞⎜⎜⎝⎛−−='11exp)()(pnnnnLxxxpxppppiLLωτ+=1'0)()(2'1212=−pnnLxpdxxpd无限厚样品的稳态扩散解12/221.2pn结的频率特性41.2.2扩散电流)exp()()()(10tixpxpxpnnnω+=直流⎥⎦⎤⎢⎣⎡−⎟⎠⎞⎜⎝⎛=Δ−=1exp)(000kTqVLpqDdxxpdqDJpnpxnppn交流[])exp()()exp()()('111tiLxpqDdxtixpdqDtJpnnpxnppnωω=−=电子扩散电流交流分量)exp()()('11tiLxnqDtJnppnnω−=⎟⎟⎠⎞⎜⎜⎝⎛−−⎥⎦⎤⎢⎣⎡−⎟⎠⎞⎜⎝⎛=ΔpnnnLxxkTqVpxpexp1exp)(000⎟⎟⎠⎞⎜⎜⎝⎛−−='11exp)()(pnnnnLxxxpxpnnniLLωτ+=1'13/221.2pn结的频率特性51.2.2扩散电流总电流交流分量)()()(111tJtJtJnp+=)exp()()('1'1tiLxnqDLxpqDnppnpnnpω⎥⎦⎤⎢⎣⎡−+=)exp(exp110001tikTqViLnqDiLpqDkTqVnnpnppnpωωτωτ⎟⎠⎞⎜⎝⎛⎥⎦⎤⎢⎣⎡+++=()()[])exp(112/12/11tiiJiJkTqVnnppωωτωτ+++=14/221.2pn结的频率特性61.2.3交流小信号导纳()()[]2/12/11111)cos()(nnppiJiJkTqAtiVtAJviYωτωτω+++==≡CiGYω+≡A：pn结面积()()()[])exp(112/12/111tiiJiJkTqVtJnnppωωτωτ+++=交流小信号导纳定义1.2.3.1低频情况(ωτp1,ωτn1)⎥⎦⎤⎢⎣⎡⎟⎠⎞⎜⎝⎛++⎟⎠⎞⎜⎝⎛+≈nnppiJiJkTqAYωτωτ211211()()⎥⎦⎤⎢⎣⎡+++=nnppnpIIiIIkTqττω21DCiGω+≡电导扩散电容15/221.2pn结的频率特性71.2.3交流小信号导纳1.2.3.1低频情况(ωτp1,ωτn1)kTqIGF=()()⎟⎠⎞⎜⎝⎛+=+=kTqVnqLpqLkTqAIIkTqCpnnpnnppD000exp221ττ()()⎥⎦⎤⎢⎣⎡+++=nnppnpIIiIIkTqYττω21CiGYω+≡1.2.3.2高频情况(ωτp1,ωτn1)())1(2/2/iJJkTqAYnnpp++≈ωτωτ()()[]2/12/11111)cos()(nnppiJiJkTqAtiVtAJviYωτωτω+++==≡16/221.2pn结的频率特性81.2.4交流小信号等效电路GCDCTGLRs本征导纳漏导17/22第一章pn结的频率特性与开关特性1.1半物要点回顾1.2pn结的频率特性1.3pn结的开关特性18/221.3pn结的开关特性11.3.1pn结二极管的开关作用LLSRVrRVVI111≈+−=这里VS=0.6~0.7VSi0.2~0.3VGeRII=19/221.3pn结的开关特性21.3.2导通过程（以p+n结为例）LRVI11=⎟⎠⎞⎜⎝⎛+=RJIIqkTV11ln问题：trise=?（提示：求ΔQ(t)形式）EcpEcnEvpEvnEfpEfnqVq(VD–V)px−nxEcpEcnEvpEvnEfpEfnqVq(VD-V)pxnAqDIdxxpd10)(−=Δ=0x)(稳态∞→tJV0t)(xpn)(ti1I)(tV0t势垒区边界0npt=0，正脉冲电压20/22()()dxLxpqAtQpn⎥⎥⎦⎤⎢⎢⎣⎡−Δ≈∫∞exp001.3.2导通过程（以p+n结为例）⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎣⎡+⎟⎟⎠⎞⎜⎜⎝⎛−=−11ln01nptppqALeIqkTVpττEcpEcnEvpEvnEfpEfnqVq(VD–V)px−nxx0Q[]⎟⎟⎠⎞⎜⎜⎝⎛+=⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛+=→∞===→=1ln1ln01ln0101RpnpIIqkTpqALIqkTVtqkTVtτ1.3pn结的开关特性3Vj-t关系推导JV0t)(tVpQIdtdQτ−=1初始条件0)0(=Q()[]pptItQττ−−=exp1)(1少子寿命足够短，稳态得以建立近似21/221I2I−0ttRInp0tt=时间增加0np势垒区边界x01.3pn结的开关特性41.3.3关断过程（以p+n结为例）t=t00),0(lnnnJptpqkTV=00ttsLLJRVrRVVIti222)(−≈++−=−=（常数）抽取电流问题：ts=？)(tv0tt2Vstft)(tit=t0，负脉冲电压()tpkTqVpxpnnn,0exp)(0=⎟⎠⎞⎜⎝⎛=pp0nn0np0pn0-XpXnXfsoffttt+=下降时间存储时间反向恢复时间正向导通时间22/221.3pn结的开关特性51.3.3关断过程（以p+n结为例）pQIdtdQτ−−=2初始条件pIQτ1)0(=()()pppItIItQτττ221exp)(−−+=当t=ts时0)(=stQ⎟⎠⎞⎜⎝⎛+=211lnIItpsτ提高pn结开关速度途径1、I1↓I2↑ts↓2、掺Au，τp↓ts↓Q-t关系推导01=−=pQIdtdQτ