晶体管频率特性

Semiconductor Device Electronics(2007~2008年第一学期)Lecture notes at the following e-mail box:transistor2000@sina.comPassword: transistor北京工业大学电子科学与技术学科部张万荣教授主要内容1.小信号参数(h, y, z, S)和小信号等效电路2.3.混合π模型特征频率fT、总渡越时间，提高fT的方法4.功率增益和最高振荡频率，高频性能优值5.从S参数求解晶体管的一些关键参数6.课题讨论7.表征高频晶体管工作的最基本参数8.小信号应用时的（低频和高频）噪声系数9.大信号应用时的功率增益和效率10.介绍一些与本章内容有关的应用例子和最新结果，展示自己的感悟。张万荣2007 Semiconductor Device Electronics21本章的目的󰂙兼顾没学过晶体管（或本科学得不好）的同学，介绍一些频率特性的一些基本知识。󰂙适当介绍一些在科研中实用性知识。󰂙介绍最新知识，开阔视野。󰂙尽量避免大量公式推导，抽出核心知识，少而精，杂而不乱，强调基本概念，基本过程，基本意义，强调理解性记忆。应用性不强的部分精简。󰂙课堂讨论之前部分为应掌握的知识，是重点部分。课堂讨论之后部分为知识延伸部分，为了解部分。张万荣2007 Semiconductor Device Electronics3参考书󰂙《微电子技术基础----双极、场效应晶体管原理》，曹培栋编著，电子工业出版社，2001年04月。(校图书馆电子图书有，可下载)󰂙无线应用射频微波电路设计，Ulrich l. Rohde, David P. Newkirk著，刘光沽等译，电子工业出版社，2004年8月。󰂙微波晶体管放大器分析与设计，Guillermo Gonzalez著，白晓东译，清华大学出版社，2003年6月。󰂙射频电路设计，Joseph J. Carr著，电子工业出版社，󰂙2001射频电路设计年10月。---(理论与应用校图书馆电子图书有，，Reihhold可下载Ludwig, Pavel)Bretchko著，王子宇等译，电子工业出版社，2002年5月。(校图书馆电子图书有，可下载)张万荣2007 Semiconductor Device Electronics421.小信号参数和小信号等效电路在讨论BJT的频率特性时，小写符号大写下角标表示总瞬时值，大写符号大写下角标表示定态分量，小写符号小写下角标表示信号分量。依此规则，共发射极电路中输人电压的总瞬时值应表示为vBE＝VBE＋vbe（3-1）输出电流的总瞬时值则为iC=IC+ic（3-2）工作频率低，可以认为iC随vBE的变化规律与IC随VBE的变化规律qA2qVBEqVBEIEDnBniC=kTkTGe=ISe（2--23）相同，因此对于总瞬时值可写出BqvBEiC=ISekT（3－3）张万荣2007 Semiconductor Device Electronics51.小信号参数和小信号等效电路将总瞬时值表示为定态分量与信号分量之和并代人上式，则q(VBE+vbe)qVBEqvbeqvbeIC+ic=ISekT=ISekTekT=ICekTv⎡be>1时（3一96）式分母方括号中的第二项远大于第一项时，第一项可被忽略，|hhfe0fe|=⎡21/2⎢⎣1+ω2hfe0g2(C)2⎤（3一96）mDE+CTE+CTC⎥⎦张万荣2007 Semiconductor Device Electronics2211特征频率g于是|hfe|≈ω(mCDE+CTE+CTC)（3-将式中ω换成2πf，上式改写为101）|hfe|f=g(m2πC=constant（3-102）DE+CTE+CTC)特征频率是|hfe|＝1的频率，按这一定义，根据（3-102）式应有f|hgmT=fef|=2π(CDE+CTE+CTC)(3-103)上式与fβ式(下式)fgmβ=2πhfe0(CDE+CTE+CTC)比较可知fT与fβ的关系为张万荣2007 Semiconductor Device Electronics23传输延迟时间fT=hfe0fβ（3一104）另外(3-103)式所表明的|hfe|和f的乘积等于常数这一关系是十分重要的，常称之为【-6dB/倍频】变化关系，即频率相对于起始值升高一倍时，|h6dB，在lg|h曲线上对应于一直线段。fe|下降到其起始值的1/2，或者说下降fe|～lgffT的实际测量在【-6dB／倍频】范围内进行,选定频率下测出|hfe|, f与| h的乘积即为ffe|T。②传输延迟时间1）fT与τec的关系根据已推出的（示为13--1031）式，特征角频率的倒数1/ωω=(CDE+CCT可以表TE+TC)Tgm(3-105)等式右端为三个时间常数之和，它们分别是基区渡越时间τb=CDE/gm =re CDE =kT/(ICq) CDE (3-106)张万荣2007 Semiconductor Device Electronics2412传输延迟时间--τte、τtc发射结过渡(势垒)区电容充电时间τte=CTE/gm =kT/(ICq) CTE (3-107)以及集电结过渡(势垒)区电容充电时间τtc=CTC/gm =kT/(ICq) CTC(3-108)一般用τ越时间。显而易见，ec表示上述三者之和，称为传输延迟时间，或总渡fT与τec的关系是1/fT=2πτec(3-109)以上是从参数转换得来的结果；另一方面，在准静态近似下分析器件内部信号的传输过程，将有助于进一步理解τec的物理意义。输入端施加信号电压，则器件内部改变状态，从起始状态过渡到另一个稳定状态，为实现电荷的建立与消失，必将需要一定的时间，这就是延迟时间的起源。张万荣2007 Semiconductor Device Electronics25传输延迟时间从真实器件的具体结构出发，以简化假定为基础，寻找描述各个时间常数的简单解析式，竭力使分析的结果同器件的具体结构直接联系起来，同f供工具。对NPNT的测量数值直接联系起来，为分析和设计器件提晶体管，按区分析，将ττec表示为七个时间常数之和：τec=τe+τte+eb+τb+τd+τc+τtc（3－116）τe称作发射区渡越时间τte称作发射结过渡(势垒)区电容充电时间τeb称作发射结过渡(势垒)区渡越时间τb称作基区渡越时间τb =re CDE =kT/(ICq) CDEτd称作集电结过渡(势垒)区渡越时间τc代表集电结过渡区电容与集电区串联电阻RC网络形成的延迟τtc称作集电结过渡(势垒)区电容充电时间τtc=CTC/gm =kT/(ICq) CTC张万荣2007 Semiconductor Device Electronics2613传输延迟时间--发射区渡越时间τe2）发射区渡越时间τe定义:τdQ'Ee=dICτdQ'EdQ'EdVBEe=dI==CDEE/gm=CDEEreCdVBEdICQ'1E=WEqpnE(−xE)22IqDQ'=WEEPE=ApEpnE(−xE)2DIPEPEEWEIPE与IC之间的关系决定于发射极注入效率γI0=nBInB1II==PEEInB+IpE1+DPEGBI≈IPE=1−γ0=DPEGBDnBICγ0DnBGEnBGEQ'W2EDPEGBE=FEτdQ'EQ'EW2EGB2DICe=PEDnBGEdI==CIC2DnBGE张万荣2007 Semiconductor Device Electronics27传输延迟时间---发射区渡越时间τe在高β晶体管中1/β≈DPEGB/DnBGE，为便于分析问题，将这一关系代入τe式中，τe被表示为：τe=(W2E/2DPE)/β(3-184)对缓变发射区：τdQ'EQ'EW2EGBe=dI=I=FECC2DnBGE综观上述各式可知，发射区渡越时间决定于发射区宽度、发射极注入效率以及F素FE。WE愈大，γ0愈低则τe愈长。第三个影响因E的数值大小决定于发射区内建电场的方向及强度。发射区均匀掺杂，ηe＝0时FE=1。若为加速场，ηe＜0，则FE＜1。反之若为减速场（实际上双扩散器件恰同此种情况），可见ηe>0，FE>1。D.J．Rou1ston给出的用于双扩散BJT的近似表达式如下：τWEWBe=5D张万荣2007 Semiconductor Device ElectronicsnB(3-124)2814传输延迟时间---基区渡越时间τb3）基区渡越时间τbτdQ'Bb=dI=dQ'BdVBEdI=CDEB/gm=CDEBre(可直接计算得到下式)CdVBECτW2Bb=FBn2DnB(对缓变基区)pB(x)B基区附加渡越时间△τb ：npB(0)A以前假定，基区内反偏集电结边界上非平衡载流子密度nPB(WB)近似等于零，载流子必须以无限大速度进入并通C过集电结过渡区。事实上，载流子是以0WB有限速度通过集电结过渡区的，因此图3－11 推导△τnPB(WB)必然是有限的非零值。nB（WpB的基区少子分布图B）从零增大到非零值，Q’B及τB都将增大。npB(WB)=nc=JCqvl张万荣2007 Semiconductor Device Electronics29传输延迟时间--基区渡越时间τb现在考虑两种边界条件对应相同的基区少子电流密度，所以虚线与实线平行。三角形AOWB及梯形CBOWB的面积分别等于零值及非零值边界条件下的单位结面积基区少子总量。此外若再假定△npB（x）=nAOWpB(x)，则应等于平行四边形ABCWB的面积与三角形B的面积之比，即n△ττcWB2b/b=1=nc(3-130)2npB(0)WBnpB(0)考虑到基区少子电流与集电结空间电荷区电流在x＝WB处连续，可写出下列等式−qDdnpB(x)npB(0)nBdx=qDnBWW=qncvl(3-131)BnBvlpB(0)=DncnB△τb/τb=2DnBWBvWBlΔτb=v(对均匀基区)l张万荣2007 Semiconductor Device Electronics3015传输延迟时间—τeb, τd, τc,4）发射结空间电荷区渡越时间τeb定义τ为发射结过渡区自由载eb=dQBEQBEdIC流子电荷总量。可以证明τeb∝exp(-qVBE/2kT)。τeb在τec中所占比重很小，常当作其它时间常数的二级修正。5）集电结空间电荷区渡越时间τd这一个延迟时间来源于集电结空间电荷区净空间电荷随集电极电流的变化。用xmc代表集电结空间电荷区宽度，可以证明τd的表示式是τCd=xmc/2vl（3-171)6）τ迟)c(集电结过渡区电容TC与集电区串联电阻rcs引起的附加延τc＝rcsCTC张万荣2007 Semiconductor Device Electronics31传输延迟时间由于输出交流短路vce=0，上式中应用(rcs + res)代替rcs更严格的、更具有普遍意义的总延迟时间τec应表示为：τec=τe+τte+τtc+τb+△τb+τd+τcτW2eGBec=2De−ΔEV(be)/kT+kT⎛⎜AC⎞⎟nBGEqJCTE+CTCC⎜⎝AE⎟⎠τeτteτtc+W2B2DFWBxB++mc+CTCAC(res+rcs)nBvl2vlτb△τbτdτc这里的C表示单位面积的电容。AC、AE表示集电结和发射结的面积张万荣2007 Semiconductor Device Electronics3216理解1/gkT/qIm=CCTECTCresrcsEBCWeWbxmcvce=0交流短路ΔEV张万荣2007 Semiconductor Device Electronics33特征频率和截止频率--提高fT的方法③影响fT的主要因素和提高fT的方法l）基区渡越时间τbτb决定于WB、DnB以及FB。在这三个因素当中，WB是最具有决定作用的，因为它的数值可以在很大范围内变动。附加基区渡越时间△τb正比于WB，缩短△τb与缩短τb的要求是一致的。2）发射区渡越时间τe在高β晶体管中τe=(W2E/2DPE)/β影响τ）发射区宽度e的主要因素分别是I。外延平面管中WE不能任意减小，首先受电流增益要求的限制，高发射区注人效率要求宽发射区，其次从工艺上考虑。过薄的发射区会使在其上制作欧姆接触金属化层的过程过于复杂，金属层在合金化以后要能保证不穿透发射区，以避免e-b短路。为兼顾各种因素的不同要求，浅结器件一般控制张万荣2007 Semiconductor Device Electronicsxjc／xje=1.3~2.0。3417特征频率和截止频率--提高fT的方法II)发射区少子扩散系数。III）发射区杂质分布形式。从欧姆接触到发射结，发射区杂质呈递减分布所形成的内建电场对从基区注入到发射区的空穴起减速作用。IV)发射区欧姆接触的界面复合。发射区越薄，欧姆接触界面复合对τe的影响变得更为重要。3）发射结及集电结过渡区充电时间(τte及τtc)τ积过渡区电容，te∝CTE0/JCc。τtc∝CTC0/JC，CTE0代表发射结单位面电极电流密度，Jc=Ic/ATC0代表集电结单位面积过渡区电容，Jc为集E。使器件工作于高电流密度，Jc可以高至使特性退化的大电流效应未起作用。减小面积，主要是缩小发射区的宽度，而不是减小长度，因为发射区的长度决定器件的最大工作电流。张万荣2007 Semiconductor Device Electronics35特征频率和截止频率--提高fT的方法4）集电结过渡区渡越时间τd尽可能减小Xmc，为此要求提高集电区掺杂浓度，同提高最大工作电流的要求一致，却同提高击穿电压减少过渡区电容的要求矛盾。张万荣2007 Semiconductor Device Electronics3618特征频率和截止频率--提高fT的方法5）τc(集电结过渡区电容与集电区串联电阻引起的延迟时间)τ电容。减小c正比于集电区电阻率、集电区宽度及集电结单位面积过渡区Wc和提高Nc都同击穿电压要求相矛盾。④fT随集电极电流、电压的变化小电流段，τ而Ite反比于Ic变化，因Ic增加到c增大总渡越时间减小fτT升高。te远小于其它时间常数之和时，τec趋近于常数，fT达到最高值。随着Ic继续增大，fT出现下降趋势是由于有效基区的纵向扩展效应开始起作用。VCB增加，fT增加的原因：VCB增加，xmc增加①WB下降→τC下降。③电场增加，速度增加。b下降；②TC下降→τcVCB增加，fT下降的原因：VCB增加，v →vl，xmc增加→τd增加张万荣2007 Semiconductor Device Electronics37α截止频率和超相移测量表明，BJT的共基极正向|hf b|电流增益的模|hfb|随频率上升而hf b0逐渐减小（如图3--24所示）。若hf b0hfb0代表|hfb|的低频值，通常将21/2|hfb|下降到hfb0／21/2的频率叫做共基极正向电流增益截止频率。0fαf直流下：图3－24 |hfb|随频率的变化∂2npB(x)pB0*⎛WB⎞∂x2−npB(x)−n基区输L2=0运系数β0=sech⎜⎟nB⎜⎝LnB⎟⎠交流下：∂2npB1(x)2C⎛1+jωτ1/2nB⎞∂x2−CnBnpB1(x)=0nB=⎜⎜⎝L2⎟nB⎟⎠模仿直流解β*=sech(Csech⎛⎜W⎜B1+jωτ⎞nBWB)=nB⎟张万荣2007 Semiconductor Device Electronics⎝LnB⎟⎠3819α截止频率和超相移1利用sech(x)=π∞⎡n=1⎢⎣1+4x2⎤(2n−1)2π2⎥⎦化简β*sech(CnBWB)β*=0sech(WB/LnB)ω*−jmω'β*b=β0e1+jωm=π2ω'8−1b其中ω'=2.44DnBbW2=(1+m)2DnBBW2B−jmω本征注入效率等于1时，ωα=α0eαα≈β*1+jωω(3-201)α张万荣2007 Semiconductor Device Electronics39α截止频率和超相移ω2.44Dα=ω'nB2b=W2=(1+m)DnB2（3—201a）BWB当ω=ωα时，α下降到低频值的1/ 21/2，因此ωα即为α截止角频率。如模仿hhfe0fehfe=1+jω/ωβ写出α=α01+jωωα−jmω（3—201）式分子中的eωα代表（3—201）式相对于上式的附加相移。所以m被称作超相移因子。超相移因子物理意义：少子注入基区，要经τ’建立起准稳态分布。理论计算表明，对均匀基区τd的驰豫时间才能’’d=0.19(τ’τd+ b) ，τd＝0.23 τb=mτb，因此表示建立起准稳态分布所需的驰豫时间与对发射极扩散电容充放电延迟时间之比。张万荣2007 Semiconductor Device Electronics4020共基极接法与共射极接法的增益的频率特点如果τB远大于总渡越时间中其它时间常数之和，fT≈1/2πτB，同时根据（3—201a）求出fα=（1＋m）fT=1.22fT，说明fα是大于fT的。根据(3-104)，fiT=fβhfe0，fβ＝fT/hfe0ib1b2因此，fβ<< fα, 说明共射极截止频率远i远低于共基极截止频率，特征频率略小于e共基极截止频率。即随频率的增加β值的ic1下降要比α值下降得快。这是因为在交流ic2下，交流电流的矢量满足i移的增加，ie=ic+ib。如图所表示的那样。随ic相b迅速增大，且i略有下降而ib增大的幅度比ic减小的幅度大。β=ic/ib中icb急剧增大，而α=ic/ie仅与ic下降有关而与相移无关。故随频率的升高β下降比α快得多。这一点在实际中有重要意义，它说明共基极接法晶体管比较适合于宽带放大电路，而共射极接法晶体管比较适合于选频放大电路。张万荣2007 Semiconductor Device Electronics414 功率增益和最高振荡频率i1i+h112+Rgvehgg1h12v221i1h22v2L-h参数小信号等效电路-在输入端接入信号源eg，内阻为Rg，在输出端接负载gL,功率增益为：Gp=P0/Pi＝v2i2/egi1由h参数方程v1=h11i1+hi=h12v2=hii1+hrv2221i1+h22v2=hfi1+hov2 （3-9）Gv22i2h21gLp=e=gi1(h22+gL)[(h11+Rg)(h22+gL)−h12h21]张万荣2007 Semiconductor Device Electronics4221共射极高频最大有效功率增益根据电路理论，为得到最大功率增益，须使晶体管的负载与其输出导纳相匹配，并使信号源内阻与其输入电阻相匹配。在这种条件下，最大有效功率增益为：G'h221MA=h⎛1−h2（3--237）11h22−⎜⎜1+12h21⎞⎟⎝h11h22⎟⎠适用于晶体管共发射极、共基极和共集电极三种接法。•双极晶体管的共发射极高频最大有效功率增益GBJT的β高，rMAEπ=1/gπ= β/gm，很大，π电路中rπ认为是断开的r0认为也是断开的rμ认为也是断开的简化的等效电路如图3—37所示张万荣2007 Semiconductor Device Electronics43在上述等效电路上，rbb'b'CTCe—c短接求出：bch=vbeCi=r(1)1IIgiebb'+ωCC=rbb'+≈rbb'mvb'ebjπ+μjω(CDE+CTE+CTC)hfe≈ωT/jωe令基极开路求出：hvbe=vb'eCμCTCre=v==≈0cevceCπ+CμCDE+CTE+CTChicoe=v=ωTCμ+jωCμ=ωTCTC+jωCTCce代入（3-237）式得出GMAE=ωT4ω2r=fTbb'CTC8πf2rbb'C（3—243）TC张万荣2007 Semiconductor Device Electronics4422若计入晶体管的寄生参数，其中发射极引线电感Le是影响最大的寄生参数之一。最大有效功率增益修改为GMAE=fT8πf2(rbb'+πfTLe)C(3-249)TC从中直接看出GMAE与fT成正比，与rbb’与CTC成反比，同时还与工作频率的平方成反比，工作频率升高一倍，功率增益下降到初始值的四分之一，呈现--6dB／倍频变化。GMA(dB)G-6dB/倍频pdB=10lg(PO/Pi)ffM张万荣2007 Semiconductor Device Electronics45最高振荡频率和高频性能优值4．最高振荡频率和高频性能优值f>fβ，GMAE随频率的变化服从-6dB／倍频规律，最高振荡频率是指-6dB/倍频关系外推到GMAE=1的频率，通常用fM表示，fM代表BJT接成振荡器或放大器工作时可能达到的频率上限。在（3—249）式中令GMAE=1得出f2=fTm8π(rbb'+πfTLe)C(3-250)TC然后再将上式代回（3—249）式，得出GMAE·f2＝f2M (功率增益带宽积、高频性能优值) (3-251)由(3-250)和(3-251)可见，对于给定的晶体管，GMAEf2 是个常数，它仅仅决定于晶体管本身的参数，它反映了晶体管在高频运用时的功率放大能力，其值越大，就越能在高频下进行足够的功率放大。故称为晶体管的高频优值。张万荣2007 Semiconductor Device Electronics4623工作条件(I，V)对晶体管功率增益的影响GMAEGMAE(dB)IC恒定(dB)Vce恒定V ceIC(1)工作电压对功率增益的影响：在低压下，Vce增大将使①xfmc增大、CTC减小；②有效基区宽度Wb减小，它将使rb和T都增大。为考察二者对GMA的影响，变换(3-249)G=1MAE8πf2(rL基极电阻re)CTCb近似地看作与基区宽度bb'/fT+πW的减小fb成反比，但fT随Wb减小的平方关系上升，即随W、rbT上升比rb增加要快，所以r是下降的。可见Cb/fTTCb的变化结果都使GMA上升。当Vce升高时，由于集电结基区侧的杂质浓度远高于集电区的杂质浓度，张万荣2007 Semiconductor Device Electronics47工作条件(I，V)对晶体管功率增益的影响使得xmc向基区侧的扩展部分x小，即x1的增大速度比xmc增大速度要1/xmc下降。其结果使基区有效宽度减小不明显，rb、fT变化均不大，只有CTC随反压略减，所以GMA上升不明显。(2)工作电流对功率增益的影响：曲线的变化规律是由于fT随电流的增加先上升后下降的结果。提高功率增益和最高振荡频率的途径：从（3—250）式明显看出，fM与fT、rbb’、CTC有关，f正比于fMT；反比于r，⑴需要设法提高bb’CTC，而这三个参数相互之间是有关联的。为提高fMfT(前面已讨论)；⑵降低rbb’(前面已讨论），且浅结扩散有利于减少R□b，外基区浓硼扩散(见下页)；⑶降低CTC。还要注意减小极间分布电容及延伸电极形成的电容。还应尽可能减小发射极引线电感，合理选用管壳结构。张万荣2007 Semiconductor Device Electronics4824几点讨论：外基区浓硼扩散ωfGMAE=T4ω2r=Tbb'CTC8πf2rbb'CGMAE·f2＝f2MTCRGmax=(fmax/foper)2rb1=SEOB1/12LE集电结过渡区电容CTC=FCAECTC0=FCSELECTC0rbb’CTC∝S21E fm∝(fT)1/2/SE若8πr>fT则fbb'CTCM> fTf= fT时GMAE>1若18πr1(1−|S211|2>|S12S21|1−|S22|>|S12S21|Δ=S11S22−S12S21另一种K>1和B2221=1+|S11|−|S22|−|Δ|>0潜在不稳定的晶体管，01且|Δ|>1）12|K=1−|S11|2−|S22|2+|Δ|22|SS12S21|Δ=11S22−S12S21最大稳定功率增益(K=1)，GMSG=|S21|/|S12|张万荣2007 Semiconductor Device Electronics6432求解转换器截止频率fs(|S21|2=1(0dB)时的频率)(10log|S21|2)晶体管的（插入）增益GO=|S21|2Insertion power gain50 Ω系统中功率转换功率增益张万荣2007 Semiconductor Device Electronics65求解增益带宽频率fT(|hfe|2=1时的频率) (10log|h21|2)h−2S2121=(1−S11)(1+S22)+S12S21张万荣2007 Semiconductor Device Electronics6633求解最大振荡频率fmax(是晶体管最大可用功率增益（GGA,max）或最大单向传输功率增益TU,max等于1时的频率)G|S21|T,max=GP,max=GA,max=|S|(K−K2−1)12=1−|S211|−|S222|+|Δ|2K2|SΔ=S11S22−S12S2112S21|GTU,Max=111−|S|S221|11|21−|S22|2张万荣2007 Semiconductor Device Electronics67举例—实测微波SiGeHBT张万荣2007 Semiconductor Device Electronics6834输入共扼匹配下的功率增益|S2G=21|1−|S11|2张万荣2007 Semiconductor Device Electronics69输出共扼匹配下的资用功率增益G=|S21|21−|S22|2张万荣2007 Semiconductor Device Electronics7035单向功率增益1/2|S/S−1|2U=2112K|S21/S12|−Re(S21/S12|张万荣2007 Semiconductor Device Electronics71张万荣2007 Semiconductor Device Electronics7236课堂讨论在器件生产实际中如何才能得到具有良好频率特性的晶体管？善意提示：认真讨论，争先发表、充分发挥自己的见解，发现自己的差距，不讨论与本课题无关的话题。先在小组内讨论，组长汇总意见。其它同学补充，最后教师总结发言。希望能进一步巩固所学知识，能融会贯通，有所收获。一节课讨论，另一节课作总结。讨论提示：•表征频率特性的两个重要参数是特征频率fT和最高振荡频率fm。•减小载流子的总渡越时间是提高晶体管特征频率fT的前提条件。•寄生或分布参数也影响特征频率fT和最高振荡频率fm。•工作电压和电流影响晶体管的频率特性。张万荣2007 Semiconductor Device Electronics73课堂讨论—续1•表征频率特性的两个重要参数是特征频率fT和最高振荡频率fm。☆电流增益的极限频率－－fT。☆功率放大的最高频率－－fm。•减小载流子的总渡越时间是提高晶体管特征频率fT的前提条件。总延迟时间τec应表示为：τec=τe+τte+τtc+τb+△τb+τd+τcτW2eGB−ΔEV(be)/kTkT⎛Aec=2De+⎜C+CC⎞⎟nBGEqJC⎜⎝TETCAE⎟⎠τW2eτteτtc+BWBxmc2DFB+++CTCAC(res+rcs)nBvl2vlτb是主要成分τb△τbτdτc张万荣2007 Semiconductor Device Electronics7437课堂讨论---续2这里的C表示单位面积的电容。AC、AE表示集电结和发射结的面积。•基极电阻和输出电容对晶体管的最高振荡频率fm有着重大影响。f2=fTm8πrbb'CTCrbb’CTC∝S2E fm∝(fT)1/2/SE由此可见，fM随SE减小而升高，为提高fM应该不断地减小发射区宽度。尤其对于工作到微波范围的BJT，这是个起决定作用的尺寸。高频大功率管常采用浓硼扩散来减小外基区电阻。基极电阻的减小会减弱集边效应，有利于提高输出功率。张万荣2007 Semiconductor Device Electronics75课堂讨论---续3•寄生或分布参数也影响特征频率fT和最高振荡频率fm。f2m=fT8π(rbb'+RE+πfTLe)CC管壳和封装，极间电容，键合电容，杂散电容，延伸电极形成的MOS电容(现代微波管它占总C线电感Le(要求短、粗)，发射极镇流电阻C的50~75%)。发射极引R•E。工作电压和电流影响晶体管的频率特性。张万荣2007 Semiconductor Device Electronics7638表征高频晶体管交流特性的最基本参数•S参数•特征频率fT=hfe×fmeas。应用到共射宽带低通放大器后，fT为增益带宽积。它影响高频增益。要求好的高频噪声性能时，器件的fT应高。在设计电路时并不用fT，但它仍是晶体管的优值。•最高振荡频率fmax(它也是晶体管的优值。)f|Y21|max≈16π2RbbC2beCGbcmax=(fmax/foper)张万荣2007 Semiconductor Device Electronics77表征高频晶体管工作的最基本参数•小信号应用时的功率增益和噪声系数Gmax, |S21|2, 噪声因子=输入信号的信噪比/输出信号的信噪比噪声系数的值中只有一个与特定输入阻抗有关，这个唯一的最小值是最小噪声系数NFmin•大信号应用时的功率增益和效率放大器的最大有用输出功率常受到输出功率1dB压缩点PPout-1dB（线性的上限）的限制。效率（集电极）Pin张万荣2007 Semiconductor Device Electronics7839张万荣2007 Semiconductor Device Electronics79效率从广泛意义上讲，效率是指RF输出功率Pout与输入电路的直流和RF功率总和的比值，记为η。η≡PoutPDC+Pin对振荡器而言，是没有输入功率的，而对放大器中的晶体管而言，它的最大RF输入功率可用功率增益和输出功率简单计算得到。因此，上式中Pin参数是多余的。输入晶体管的的直流功率大部分是被集电极损耗的。因此可把“效率”更贴切地定义为集电极效率ηC=Pout/PDC张万荣2007 Semiconductor Device Electronics8040power-added efficiency (PAE)PAE≡Pout−Pin=η⎛1⎞PC⎜⎜1−⎟DC⎝GP⎟⎠where ηC=Pout/Ppower from the power supply, PDCis the collector efficiency, Pis the ac input power from DCis the DC the high-frequency power generator, Pinoutis the ac output power at the load.张万荣2007 Semiconductor Device Electronics81晶体管的噪声白噪声区张万荣2007 Semiconductor Device Electronics8241晶体管的低频噪声HBT的1/f噪声源主要是基极电流1/f噪声S比于Iα(IIB。1/f噪声正BB为基极电流)，反比于发射极面积AE：SIB=KAIα1BEfK是与工艺相关的常数，对典型SiGeHBT，α≈2 。低频转角(corner)频率fLC(在f=fLC下，1/f噪声S2qIIB等于散粒噪声B)。fKIBKJCLC=2qA=E2qβ减小fLC，就要减小K因子，增大β，减小工作电流密度。张万荣2007 Semiconductor Device Electronics83晶体管的高频噪声晶体管的高频噪声特性也可用高频转角频率fHC表征，其定义为噪声是白噪声2倍时的频率，fHC可粗略表示为ffαfTHC≥β≈β为了提高工作频率，就要提高f或晶体管的特征频率HC，其有效途径是提高共基极截止频率fαfT。事实上，晶体管的最小噪声系数可表示为张万荣2007 Semiconductor Device Electronics8442晶体管的高频噪声(1)若f>fCH，忽略n/β项，IC/VT=gm, 变为Fmin−1=nfβ+f2gm(Re+Rb)T≈ff2gm(Re+Rb)T在f>fT/β的频率区域，随频率的增加，F迅速增加，(F1/2min（即正比于[(min-1)～f曲线斜率为[(2gmRB)/fT]R)1/2B/fT]），因此低RB、高f的噪声性能的关键。T是取得好因此我们看出，要取得好的高频噪声特性，需要同时得到高β，高fT和低RB。张万荣2007 Semiconductor Device Electronics8643典型的台面型HBT结构示意图张万荣2007 Semiconductor Device Electronics87张万荣2007 Semiconductor Device Electronics8844张万荣2007 Semiconductor Device Electronics89Microphotograph of the six-finger DaimlerChrysler SiGeHBT.张万荣2007 Semiconductor Device Electronics9045张万荣2007 Semiconductor Device Electronics91张万荣2007 Semiconductor Device Electronics9246EBCE张万荣2007 Semiconductor Device Electronics93InPSHBTsand DHBTs张万荣2007 Semiconductor Device Electronics9447张万荣2007 Semiconductor Device Electronics95张万荣2007 Semiconductor Device Electronics9648张万荣2007 Semiconductor Device Electronics97张万荣2007 Semiconductor Device Electronics9849Cross section of a millimetre-wave III-V HEMT device张万荣2007 Semiconductor Device Electronics99Cross section of a millimetre-wave III-V HEMT deviceFigure B1 –Cross section of a millimetre-wave III-V HEMT device. Current flows from the source to the drain in the high mobility buried channel under the Schottkygate contact. The gate sits in a recess to improve the current modulation in the device.张万荣2007 Semiconductor Device Electronics10050Lumped element equivalent circuit of millimetrewaveIII-V HEMTFigure B2 –element equivalent Lumped circuit mapped onto the physical structure of a millimetrewaveIII-V HEMT.The challenge in optimisinga III-V HEMT for millimetre-wave applications is to minimisevarious elementsin the equivalent circuit such as the source and drain resistances, Rsand Rd and the gate resistance Rg.From this equivalent circuit, a number of RF figures of merit can be derived.张万荣2007 Semiconductor Device Electronics101Performance of SiGeHBTs-f Tvs. BVCE0400 SiGe HBT InP DHBTz InP SHBTH300G GaAs HBT y,cneu200 Johnson Limit(1965)qerf ffotu100C0051015202530Breakdown voltage, VSiGe HBTs show considerably lower BVCE0than III-V HBTs.The low breakdown voltage is a serious obstacle for high-power SiGe HBTs.张万荣2007 Semiconductor Device Electronics10251The Johnson Limit on RF BJT Performance张万荣2007 Semiconductor Device Electronics103TheEvolution ofRF Transistors 1000*InP HBTGaAs pHEMTInP HEMTAlGaAs/GaAs HEMTGaAs MESFETzH100InP HBTGInP HEMT , TAlGaAs/GaAs HEMTf , xGe BJTmaf10Si BJTfmaxfT*Transferred substrate119601970198019902000Important Trends:Year•Continuous increase of the frequency limits, i.e. f(wide bandgaptransistors)Tand fmax(III-V’s)•Increase of output power •Low-cost RF transistors for consumer mass markets (Si-based)张万荣2007 Semiconductor Device Electronics10452Trend of the best-achieved fTfor various transistorsJae-Sung Rieh, BasanthJagannathan, SiGeHeterojunctionBipolar Transistors and Circuits Toward Terahertz Communication Applications, IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 52, NO. 10, OCTOBER 2004,pp.2390-2408张万荣2007 Semiconductor Device Electronics105Device Merit Parameter Comparison张万荣2007 Semiconductor Device Electronics10653BV vscut-off frequency张万荣2007 Semiconductor Device Electronics107触发器静态分频器张万荣2007 Semiconductor Device Electronics10854张万荣2007 Semiconductor Device Electronics109The implanted extrinsic base structure and Raised extrinsic basestructureETX: epitaxialtransistorRXB:raisedextrinsic baseFigure 8ETX structure (top) and RXB structure (bottom). The RXB structure eliminates the unwanted effects from the deep implant, including the excess capacitance and diffusion effects on the intrinsic base region.张万荣2007 Semiconductor Device Electronics11055The implanted extrinsic base structure and Raised extrinsic basestructureComparison of the IBM SiGeHBT device structures illustrates how improvements in device structure may provide increases in the figure of merit, futilized the same device structure, often referred to as the max. Through several generations of technology, IBM has epitaxialtransistor (ETX).Its identifiable structural characteristic is an extrinsic base implanted into the SiGeepitaxialfilm. Through careful analysis, depending heavily on 2D simulations [34], it was determined that this structure has some significant limitations. Implants into the silicon create lattice defects, which affect the diffusion of the intrinsic base boron, increasing B and thus reducing device performance. This limits how close the implant may be placed to the intrinsic device, and thereforecreates a lower limit on the achievable base resistance, RBB. The implanted extrinsic base also extends deep into the silicon and intersects the collector implants at a high concentration, which results in high CCB. Shown in Figure 8 are the ETX structure and the structure IBM is pursuing with a raised extrinsic base (RXB)to substantially reduce Rmay be placed in close proximity to the intrinsic device, thus BBand CCB. The raised extrinsic base has less influence on the intrinsic dopantdiffusion and reducing RCBBwithout impact to fT. It also has a minimal junction depth, and, as such, has a relatively small Initial results on the RXB structure demonstrate its benefits over the ETX structure. While retaining CB.the fTperformance of a structure without a self-aligned extrinsic base (indicating no influence of the extrinsic base on the intrinsic base), the base resistance has been reduced by a factor of approximately 2, and CCBhas been maintained constant compared to a previous-generation device of similar area, with lower fFigure 9T. This results in simultaneous f).Tand fmaximprovements between generations of more than 80% (张万荣2007 Semiconductor Device Electronics111The implanted extrinsic base structure and Raised extrinsic basestructureFigure 9Comparison of cutoff frequencies between SiGe7HP fT120-GHz device with ETX structure and next-generation fT210-GHz device, with vertically scaled profile and new RXB structure. (MAG maximum available gain; U unilateral matched power gain.)张万荣2007 Semiconductor Device Electronics11256Summary of IBM SiGeBiCMOSand rfCMOS technology张万荣2007 Semiconductor Device Electronics113Schematic cross-section of the 375-GHz SiGeHBTJae-Sung Rieh, BasanthJagannathan, SiGeHeterojunctionBipolar Transistors and Circuits Toward Terahertz Communication Applications, IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 52, NO. 10, OCTOBER 2004,pp.2390-2408张万荣2007 Semiconductor Device Electronics11457Fig. 1. Schematic of the new raised extrinsic base SiGeHBT.B. Jagannathan,Self-Aligned SiGeNPN Transistors With 285 GHz fManufacturableTechnology, IEEE ELECTRON DEVICE LETTERS, VOL. 23, NO. 5, MAY 2002, MAXand 207 GHz fTin a pp.258-261.张万荣2007 Semiconductor Device Electronics115Self-Aligned SiGeNPN Transistors With 285 GHz fMAXand 207 GHz fTin a ManufacturableTechnology, IEEE ELECTRON DEVICE LETTERS, VOL. 23, NO. 5, MAY 2002, pp.258-261.MSGMAGf2×G=fm2-10lg100=20dBFig. 3. (a) f T; fMAX(U extraction) and fSiGeNPN device. (b) Mason’s unilateral power gain (U) and maximum available power gain MAX(MAG extraction) versus collector current for 0.12×2.5 um2versus frequency at peak fTcurrent.张万荣2007 Semiconductor Device Electronics11658Self-Aligned SiGeNPN Transistors With 285 GHz fTechnology, IEEE ELECTRON DEVICE LETTERS, VOL. 23, NO. 5, MAY 2002, pp.258-261.MAXand 207 GHz fTin a ManufacturableFig. 4. (a) f (|hTversus collector current for small 0.12 ×0.5 um SiGeNPN device. (b) Current gain 21|) and Mason’s unilateral power gain (U) versus frequency at peak f Tcurrent.张万荣2007 Semiconductor Device Electronics117SiGeHBTswith cut-off frequency of 350GHz(IEDM2002)张万荣2007 Semiconductor Device Electronics11859SiGeHBTswith cut-off frequency of 350GHz(IEDM2002)张万荣2007 Semiconductor Device Electronics119SiGeHBTswith cut-off frequency of 350GHz(IEDM2002)张万荣2007 Semiconductor Device Electronics12060SiGeHBTswith cut-off frequency of 350GHz (IEDM2002)张万荣2007 Semiconductor Device Electronics121张万荣2007 Semiconductor Device Electronics12261张万荣2007 Semiconductor Device Electronics123张万荣2007 Semiconductor Device Electronics12462张万荣2007 Semiconductor Device Electronics125张万荣2007 Semiconductor Device Electronics12663张万荣2007 Semiconductor Device Electronics127张万荣2007 Semiconductor Device Electronics12864MOSFETs张万荣2007 Semiconductor Device Electronics129SiRF MOSFETsFig. 1. Evolution of the record cutoff frequency fTand the recordmaximum frequency of oscillation fmaxof RF SiMOSFETsversus time.From: Frank Schwierz, JuinJ. Liou. RF transistors-Recent developments and roadmap toward terahertz applications. Solid-State Electronics 51 (2007) 1079–1091张万荣2007 Semiconductor Device Electronics13065SiRF MOSFETsITRS: International Technology Roadmap for SemiconductorsFig. 2. Best reported fand fmaxITRS 2005 targets for SiTand fmaxperformance of SiMOSFETsversus gate length, together with the fMOSFETs.T张万荣2007 Semiconductor Device Electronics131SiRF MOSFETsFig. 3.fTand fmaxtargets for SiMOSFETsversus year as specified in the 2003 and 2005 issues of the ITRS.张万荣2007 Semiconductor Device Electronics13266SiRF MOSFETsTo achieve the fTtargets, SiRF MOSFETsare required to show a constant ffT·L product of 9 GHz ·um. The average electron velocity in the channel. For T·L product can be related to the comparison, the best experimental InPHEMTs(with gate lengths between 80 and 500 nm) show a much higher fT·L product in the range of 20–50 GHz ·um. In other words, the fact that the electron transport is slower in SiMOS channels compared to that in the InGaAschannels of InPHEMTsis taken into account in the targets.Nevertheless, currently it is not clear if the fand fMOSFETscan be achieved. TThe simulations mentioned above either fully maxtargets for Sineglected or underestimated parasitic elements that could deteriorate the frequency performance. The smaller the transistors become, the more significant is the effect of parasitic elements(such as contact and series resistances, stray and fringe capacitances) on transistor performance.Fig. 4. Simulated cutoff frequencies of double-gate and single-gate SOI MOSFETs.张万荣2007 Semiconductor Device Electronics133SiRF MOSFETsFig. 5. Reported noise performance of SiMOSFETsand the ITRS target (specified only at a frequency of 5 GHz for SiMOSFETs).张万荣2007 Semiconductor Device Electronics13467SiRF MOSFETsObviously, for small widths the output power increases with increasing Wexpected. Then, totas however, for a certain optimum gate width the output power peaks and eventually decreases for larger WtotFig. 6. Output power of RF SiMOSFETsin 65-nm standard logic technology as a function of gate width, after [20]. The symbols are experimental results and the lines are a guide for the eye.张万荣2007 Semiconductor Device Electronics135SiRF MOSFETsThe 250-nm devices deliver higher output powers up to 14 GHz since they can be operated at higher voltages. The operating voltage is 1 V for the 65-nm transistors and 2.5 V for the 250-nm devicesFig. 7. Maximum output power of 65 and 250-nm RF SiMOSFETsin standard logic technology as a function frequency, after [20]. The symbols are experimental results and the lines are a guide for the eye.张万荣2007 Semiconductor Device Electronics13668SiGeHBTsFig. 8. frange of the best reported frequency performance of SiGeTand fmaxtargets (lines with symbols) for SiGeHBTstogether with the area indicating the HBTs. For comparison, an area indicating the record frequency performance of conventional SiBJTsis also shown.张万荣2007 Semiconductor Device Electronics137SiGeHBTsA problem of SiGeHBTsis that, for a given cutoff frequency, the breakdown voltage (here we discuss the emitter–collector breakdown voltage BVCEO) is relatively low, i.e., lower than that for III–V HBTs.The highest reported fT·BVCEOproduct for experimental SiGeHBTsis 570 GHz ·V [24] compared to the ITRS targets of 630 GHz ·V in 2010 and 740 GHz ·V in 2020.The fSiGeT·BVspikeCEOproduct can be increased by a in the emitter [28].[28].Choi LJ, Van HuylenbroeckS, PiontekA, Sibaja-Hernandez A, KunnenE, Meunier-BeillardP, et al. On the use of a SiGespike in the emitter to improve the fproduct of high-speed SiGeHBTs. IEEE T·BVCEOElectron Dev Lett2007;28:270–2.Fig. 9. Reported cutoff frequency as a function of the collector–emitter breakdown voltage BVtogether with the fCEOT–BVCEOtargets.张万荣2007 Semiconductor Device Electronics13869III–V TransistorsFor gate lengths above 0.2 um, the cutoff frequencies of all transistor types increase with shrinking gate length and the fperformance trends correspond to the order of Tthe mobility: InPHEMTsand GaAsmHEMTshave the channels with the highest mobility and also show the highest cutoff frequencies, followed by GaAspHEMTs. SiMOSFETs, on the other hand, have the channels with the lowest mobility and show the lowest fT’s. Below 100 nm gate length, however, the trend changes. At these gate lengths, the cutoff frequencies of SiMOSFETsare above those of GaAspHEMTs. Moreover, for GaAspHEMTsfwith further decreasing gate length. Around Tdecreases 30 nm gate length, the fTof InPHEMTsshows a tendency to saturate, while for SiMOSFETsthe increase of fTis still almost unbowed.Fig. 10. Reported cutoff frequency of III–V HEMTsand SiMOSFETsversus gate length. The lines are a guide for the eye.张万荣2007 Semiconductor Device Electronics139III–V TransistorsThe fmaxdata in Fig. 11 show that above 100 nm gate length the III–V HEMTsshow much higher fmaxcompared to SiMOSFETs. Below 100 nm, for decreasing gate length the fmaxof the III–V HEMTsstarts to decline while that of SiMOSFETsstill continuously increases. Astonishingly, at 30 nm, the best SiMOSFETsshow the highest fmaxof all RF field-effect transistors!Fig. 11. Reported maximum frequency of oscillation of III–V HEMTsand SiMOSFETsversus gate length.张万荣2007 Semiconductor Device Electronics14070III–V TransistorsClearly the targets for GaAsmHEMTsare higher and increase faster compared to those for InPHEMTs. This suggests that more efforts will be spent on research and development of GaAsmHEMTsthan on InPHEMTsFig. 12. ITRS fTtargets for low-noise III–V HEMTsvs. time. The numbers at the lowest curve indicate the gate length(nm) at which the target has to be achieved and are valid for the three HEMT types shown in the Figure.张万荣2007 Semiconductor Device Electronics141III–V TransistorsThe targets for GaAsmHEMTsare more challenging than for InPHEMTs.Fig. 13. ITRS targets for the minimum noise figure at a frequency of 26 GHz versus time for low-noise III–V HEMTs.张万荣2007 Semiconductor Device Electronics14271III–V TransistorsTaking a look on the GaAsHBT data from Fig. 14 it can be seen that these transistors show considerably lower fand f Tmaxcompared to SiGeHBTs.InPHBTsare the fastest bipolar transistorsFig. 14. Maximum frequency of oscillation versus cutoff frequency of III–V and SiGeHBTs. SHBT: single HBT, DHBT: double HBT.张万荣2007 Semiconductor Device Electronics143III–V TransistorsTwo issues are worth mentioning: (a) The targets for SiGeHBTsare lower than for InPHBTs, but the difference becomes smaller towards the end of the roadmap (2011: 450 GHz for InPHBTsvs. 425 GHz for SiGeHBTs). (b) The expected emitter width for a given year is much smaller for SiGeHBTsthan for InPHBTs. It should be noted that the InPtargets are in ‘‘yellow cells’’until 2008 and then in ‘‘red cells’’until the end of the roadmap, while the SiGeHBT targets are in ‘‘yellow cells’’starting from 2008.Fig. 15. fmaxtargets for InPand SiGeHBTsversus time. The numbers indicate the expected emitter width(nm).张万荣2007 Semiconductor Device Electronics14472Why are advanced Si-based RF transistors that fast?considering theelectron mobility data from Table 3 leads to the conclusionthatIII–V transistors should be much faster than Sitransistors since the electron mobility in Si, and especially in MOS inversion channels, is inferior comparedto GaAsand InGaAs.the speed of short-gate FETsis not much affected by the mobility since along most of the channel the velocity is saturated.Based on a recently developed new conceptual view on the MOSFET it is argued that the carrier transport even in extremely short FET channels is strongly influenced by the carrier injection velocity at the source end of the channel, which in turn is related to the carrier effective mass and thus to the mobility [52]. From this point of view, III–V FETsagain should have an edge due the higher mobility compared to Si.张万荣2007 Semiconductor Device Electronics145Why are advanced Si-based RF transistors that fast?An interesting study comparing the potential of different materials for fast transistors has been done by Fischettiand Laux[53]. They concluded that the III–V semiconductors with their small effective mass (and thus high mobility) suffer from low densities of states near the bottom of the conduction band. A smallernumber of available states means that a larger change of the Fermi level, and thus a largervariation of the gate voltage, will be needed to achieve a certain variation of the sheet electron concentration nShin a FET channel.[53]Fischetti MV, LauxSE. Monte carlosimulation of transport in technologically significant semiconductors of the diamond and zincblendestructures –Part II: submicrometerMOSFETs. IEEE Trans Electron Dev 1991;38:650–60.张万荣2007 Semiconductor Device Electronics14673Why are advanced Si-based RF transistors that fast?The drain currentIchannel, nDof a FET is related to the sheet carrier concentration in the Sh, by:(1)where vis the carrier velocity and Wis the gate width.The FET’stransconductancegm, defined as the variation of the drain current caused by a variation the gate–source voltage VGS, can then be expressed as:(2)From (2) it can be seen that for a large transconductancenot only a high v(i.e., fast carriers) is needed, but a large dnSh/dVand high peak velocities), GSas well. While the III–V materials offer high electron velocities (high mobilitiesIII–V FETssuffer from a smaller dnSh/dVGScompared to SiFETsdue to the lower density of states of the III–V materials. This drawback of the high-mobility III–V semiconductors is meanwhile well established and is considered in several studies assessing the potential of III–V semiconductors as possible channel materials for future VLSI MOSFETs[54–56].[54] RahmanA, KlimeckG, LundstromM. Novel channel materials for ballistic nanoscaleMOSFETs–band structureeffects. Tech Dig IEDM, paper 26.2; 2005.[55] SaraswatKC, Chui CO, Kim D, KrishnamohanK, PetheA. High mobility materials and novel device structures for high performance nanoscaleMOSFETs. Tech Dig IEDM, paper 26.2; 2006.[56] Thompson SE, SuthramS, Sun Y, Sun G, ParthasarathyS, ChuM, Nishida T. Future of strained Si/semiconductors in nanoscaleMOSFETs. Tech Dig IEDM, paper 27.1; 2006.张万荣2007 Semiconductor Device Electronics147Why are advanced Si-based RF transistors that fast?The gate–source capacitance of the intrinsic FET normalized to the gate width, C’GS;int, is given by:(3)From (2) and (3) it becomes clear that both the transconductanceand the intrinsic gate–source capacitance depend on dnSh/dVGS. In other words, a largeintrinsic gate–source capacitance per unit gate width is one of the preconditions for a largetransconductance. The deteriorating effect of a low density of states on C’GS;intis called loss of gate capacitance[53].[53]Fischetti MV, LauxSE. Monte carlosimulation of transport in technologically significant semiconductors of the diamond and zincblendestructures –Part II: submicrometerMOSFETs. IEEE Trans Electron Dev 1991;38:650–60.The cutoff frequency can be expressed as:(4)where gRis the source series resistance.dsis the drain conductance, CGSand CGDare the gate–source and gate-drain capacitances, and S张万荣2007 Semiconductor Device Electronics14874Why are advanced Si-based RF transistors that fast?Sometimes, neglecting CGD, gds, and RS, Eq. (4) is further simplified to:(5)A frequently used approximation for fmaxis:(6)where Riis the charging resistance for CGSand RGis the gate resistance.On first view, an inspection of Eqs. (4) and (6) leads to the conclusion that, in order to design afast FET with high fTand fmax, the transconductanceshould be aslargeas possible while all other components including CGSshould be minimized. While this in general is correct, the gate–source capacitance needs a closer inspection. As has been shown above, a large dnSh/dVGS, and thus a large intrinsic gate–source capacitanceper unit gate width C’needed for a large transconductance. On the other hand, the overall gate–source capacitance CGS;int(the unit is F per cm gate width), is GS(unit F) should be small. This is achieved by making the gate short thus minimizing the intrinsic portion of Cfringing, stray, and pad capacitances.GS, and by minimizing the external parasitic components of the gate–source capacitance, such as 张万荣2007 Semiconductor Device Electronics149Why are advanced Si-based RF transistors that fast?To realize short-gate FETswith good RF performance it is inevitable to suppress short-channel effects (such as poor saturation of the output ID–Vconductance gDScharacteristics resulting in a large drain positive effect of the short gate, and the RF performance suffers. Eqs. (4) and (6) clearly indicate the ds). Otherwise the short channel effects may compensate, or even overcompensate, the negative effect of gds on fTand fmax.Experiences have shown that the drain conductance in short-gate FETscan be kept small when the ratio L/dG-Ch(dG-Ch is the distance between the gate and the channel of the transistor) is large [6,57,58]. In other words, for very short gates extremely thin barriersbetween the gate and the channel are needed. Table 4 compares the barriers of GaAspHEMTs, InPHEMTs, and SiMOSFETs. Clearly, with respect to the L/dG-Chratio, the SiRF MOSFET has an edge compared to the III–V HEMTs.[6] SchwierzF, LiouJJ. Modern microwave transistors –theory, design, and performance. New Jersey: Wiley; 2003.[57] TserngHQ, Kim B, SaunierP, Shih HD, KhatibzadehMA. Millimeter-wave power transistors and circuits. MicrowJ 1989;32(April):125–35.[58] Frank DJ, TaurY, Wong H-S. Generalized scale length for twodimensionaleffects in MOSFETs. IEEE Electron Dev Lett1998;19:385–7.张万荣2007 Semiconductor Device Electronics15075Why are advanced Si-based RF transistors that fast?A thin barrierleads to an additional desirable effect related to the ratio ofthe intrinsic to the external parasitic portion of the gate–source capacitance which will be discussed in the following. Letus for simplicity assume an RF FET where the carriers travel with a constant velocity (which we call the effective velocity veff) through the channel and that the carrier sheet concentration ngm becomes:Shalong the channel is constant. Then, the transconductance(7)The intrinsic gate–source capacitance CGS,intcan either be considered as the variation of the gate charge caused by a variation of the gate–source voltage (dQG/dVGS), or be approximated by assuming a parallel plate capacitor with the gate and channel acting as plates and the barrier as the dielectric:(8)where ebaris the dielectric constant of the barrier and dbaris the barrier thickness. Note that C=C’W.GS;intGS;int·张万荣2007 Semiconductor Device Electronics151Why are advanced Si-based RF transistors that fast?Now we consider a FET with an overall gate–source capacitance Cgate–source capacitance CGSconsisting of the intrinsic effects. Using (5) and expressing CGS,intand of a parasitic component CGS,parthat includes fringe, stray, and pad GS,intby the plate capacitor formulation from(8), we arrive at:(9)for a transistor with a given gate length L and gate width W, the intrinsic component of Cterm in the brackets of the denominator in Eq. (9)) should be largewhile the parasitic portion of CGS(the first (second term) should be small. In other words, a largeeGSthe parasitic portion of the gate–source capacitance on the overall RF performance. Table 5 compares bar/dbaris desirable since it reduces the effect of typical er,bar/dbarratios (er,baris the relative dielectric constant of the barrier) of state-of-the-art GaAsHEMTs, InPHEMTs, and SiMOSTFET. Similar as in Table 4 we observe a clear advantage ofthe SiMOSFET.张万荣2007 Semiconductor Device Electronics15276Why are advanced Si-based RF transistors that fast?The above discussion leads to the conclusion that, concerning the fT–fmaxperformance, the SiMOSFET takes advantage of–the high density of statesin the Siconduction band (which is higher than in the high-mobility III–V materials),–its generic device structure with the very thin barrier(i.e., gate oxide) between gate and channel.This compensates for the poor transport properties, in particular the low mobility, of the MOS inversion channels.Experiences show that, if experimental RF FETswith the same basic structure and of similar channel materials are compared, the speed in terms of fand fbehaves roughly as the mobility of the channel material:T–Sinmax-channel MOSFETsshow much higher channel mobilitiesand also higher fand fthan Sip-channel MOSFETswith the same gate length.T–InPmaxHEMTsand GaAsmHEMTswith their high mobilityInhaving In0.53Ga0.47As channels offer higher fTand fmaxthan GaAspHEMTs0.2Ga0.8As channels with lower mobility.张万荣2007 Semiconductor Device Electronics153Why are advanced Si-based RF transistors that fast?If, however, FETswith differentbasic structures (e.g.,MOSFETvs. HEMT) are compared, other issues such as the immunity against short-channel effects and the ebar/dbarratio, additionally have to be taken into consideration.Let us finally take a look on HBTsand on the reasons for the speed advantage of SiGeHBTscompared to GaAsHBTs. The cutoff frequency of bipolar transistors can be expressed as [6]:(10)where τECis the emitter–collector transit time. This transit time is the sum of several delay times including the base transit time τsmall τBwhich is related to the base thickness wB. A small wBresults in a bipolar transistor can be approximated by [6]:Band is therefore desirable for a fast transistor. The maximum frequency of oscillation of a (11)where RBis the base resistance and Cresulting small τCBis the collector–base capacitance. Thus, a thin base and a Bis desirable for a high fTand a high fmaxas well, provided the base resistance can be kept low.张万荣2007 Semiconductor Device Electronics15477Why are advanced Si-based RF transistors that fast?Typical GaAsHBTsshow base dopingsin the range of 1019–1020cm-3and the base thickness is about 30–70nm. SiGeHBTs, on the other hand, usually show higher base dopings(up to several times 1020cm-3) and base thicknesses around 10nm are quite common. For state-of-the art SiGeHBTs, the as-grown thickness of the SiGebase can be as small as 2nm [59]. Such thin base layers result in extremely small TB. Additionally, the Geprofile in the SiGebase can begradedleading to a strong built-in fieldthat accelerates the electrons on their way through the base to the collector. This ensures a small base transit timeof SiGeHBTseven if the base thickness is not scaled to the limit.The high base doping in SiGeHBTsguarantees a small base resistance Reven for very narrow base layers, what is beneficial for fBcontribute to the ability to realize extremely thin and highly doped base layers in SiGemax, see Eq. (11). Several factors HBTs. First, the dopantsolubilityin Siand in the ‘‘Si-like’’compound SiGeis larger than in III–V compounds. Furthermore, the incorporation of carbon in the SiGebase (SiGe:C) causes a strong suppression of the boron outdiffusionfrom highly doped and thin SiGebase layers. This leads to the situation that the base of SiGeHBTsafter all processing steps is not much thicker than the as-grown SiGebase layer.The ability to form very thin and highly doped SiGebaselayers with simultaneously small base resistance is one of the main reasons for the fact that SiGeHBTsoutperform GaAsHBTsin terms of fTand fmax.张万荣2007 Semiconductor Device Electronics155SummaryThe performance of state-of-the-art RF transistor in terms of cutoff frequency fT, maximum frequency of oscillation fmax, minimum noise figure NFmin, and output power Pouthas been reviewed and compared, and their relevance to the ITRS targets was discussed. It has been shown that the performance of SiRF MOSFETshas been improved considerably during the last few years, and that SiMOSFETswith high fTand fmaxin excess of 300 GHzand very low noise figures up to 26 GHz have been reported recently. However, more research work is needed to meet the challenging ITRS targets for the MOSFET performance (in particular the targets for fTand fmax).The performance of SiGeHBTshas also been improved considerably in recent years. The ITRS fTand fmaxtargets for SiGeHBTsare lower than those for InPHBTs, but the gap becomes smaller towards the end of the roadmap. While the role of GaAspHEMTsis expected to decline in the future, GaAsmHEMTsare becoming promising high-performance field-effect transistors for RF applications. Currently the frequency performance of GaAsmHEMTsis comparable to that of InPHEMTs, and the fT, fmax, and NFmintargets for GaAsmHEMTsare more aggressive than those for InPHEMTs.张万荣2007 Semiconductor Device Electronics15678SummaryIt has been shown in this review that the traditional opinionsregarding the role of Si-based devices among the different RF transistors are no longer valid. Both SiMOSFETsand SiGeHBTsoffer some inherent advantages concerning the device structure (extremely thin barrier between gate and channel in MOSFETs, high base doping and very thin base layers in SiGeHBTs) that compensate for the inferior transport properties in the SiMOS inversion channel and the SiGebase compared to the InGaAschannels of III–V HEMTsand the GaAsor InGaAsbase layers III–V HBTs.张万荣2007 Semiconductor Device Electronics157SummaryMuch work remains to be done, however, to develop RF transistors actually capable of THz operation. Even if some recent research papers may suggest that advanced RF transistors are close to enter the THz range [26,60,61], we are still far from the realization of three-terminal THz devices. Realistically speaking, THz operation means that a transistor should be able to amplify signals and toshow a gain sufficient for practical applications at THz frequencies. Thus, the frequency limits fTand fmaxof a transistor with an operating frequency of 1 THz have to be considerably above 1 THz. While the intrinsic devices definitively show the potential of THz operation, short-channel effects (in the case of field-effect transistors) and external parasiticsseverely degrade the overall device performance.[26] Shi Y, NiuG. Vertical profile design and transit time analysis of nano-scale SiGeHBTsfor Terahertz fT. Proc BCTM 2004:213–6.[60] RhiehJ-S, JagannathanB, Greenberg DR, et al. SiGeheterojunctionbipolar transistors and circuits toward Terahertz communication application. IEEE Trans MicrowTheory Tech 2004;52:2390–408.[61] TrewRJ. High-frequency solid-state electronic devices. IEEE Trans Electron Dev 2005;52:638–49.张万荣2007 Semiconductor Device Electronics15879SummaryNevertheless, the progress in the development of Sibased and III–V RF transistors in the past and, possibly, the exploitation of innovative device structures and new materials may open the way to the realization of transistors with real THz capability. A simulation study has predicted extremely high cutoff frequencies of HEMTswith InSbchannels[62] and experimental transistors of this type having a gate length of 85 nm showed a cutoff frequency of 340 GHz[63]. These transistors show very high cutoff frequencies already at low source–drain voltages what makes them attractive for ultra-high-speed ultra-low-power applications. Another very intriguing feature is that, in spite of the narrow bandgapof only 0.17 eVof the InSbchannel, these transistors have been operated at room temperature and at drain–source voltages up to 1 V without any indication of breakdown.[62] Herbert DC, Childs PA, Abram RA, Crow GC, WalmsleyM. Monte Carlo simulations of high-speed InSb-InAlSbFETs. IEEE Trans Electron Dev 2005;52:1072–8.[63] Ashley T, Buckle L, EmenyMT, FearnM, Hayes DG, Hilton KP,etal. Indium antimonidebased technology for RF applications. Proc Compound SemicondIC Symp2006:121–4.张万荣2007 Semiconductor Device Electronics159SummaryAnother interesting material for RF transistor is InN. Its bandgapof 0.7eV is comparable to that of Indislocation-free InNhave predicted electron mobilities0.53Ga0.47As. Simulations for around 4,000Incm2/Vs (what is comparable to the electron mobility in 0.53Ga0.47As), steady-state electron peak velocities around 5 *107cm/s (much higher than in Inovershoot [64,65]. Unfortunately, the InN0.53Ga0.47As) and a pronounced velocity technology is still in an embryonic state and operating InNRF transistors have not been realized so far. Finally, carbonbased materials [66,67] may be an interesting option for future RF transistors. Both carbon nanotubesand grapheneshow very high carrier mobilities.[64] O’Leary SK, FoutzBE, ShurMS. Eastman LF potential performance of indium-nitride-based devices. ApplPhys Lett88, paper152112; 2006.[65] PolyakovVM, SchwierzF. Low-field electron mobility in WurtziteInN. ApplPhys Lett88, paper 032101; 2006.[66] Burke PJ. AC performance of nanoelectronics: towards a ballistic THz nanotubetransistor. Solid-State Electron 2004;48:1981–6.[67] GeimAK, NovoselovKS. The rise of Graphene. Nature Mater 2007;6:183–91.张万荣2007 Semiconductor Device Electronics16080Present Status: Fast Bipolar Transistors张万荣2007 Semiconductor Device Electronics161张万荣2007 Semiconductor Device Electronics16281张万荣2007 Semiconductor Device Electronics163张万荣2007 Semiconductor Device Electronics16482

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