Chapter 17 - CHAPTER 17 ill(a Carriers enter the channel at the source contact and leave the channel(or are"drained" at the drain

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Unformatted text preview: CHAPTER 17 ill (a) Carriers enter the channel at the source contact and leave the channel (or are "drained") at the drain contact. _ ' (b) Channel...inversion layer beneath the MOS gate which electrically connects the source and drain. " (c) The portion of the characteristics where VD > V1332“ for a given VG (the approximately horizontal portion of the characteristics) is referred to as the saturation region of operation. (d) The depletion—inversion transition point voltage and the threshold voltage are one and the same voltage. (c) There is an additional carrier scattering mechanism in the surface channel of a MOSFET; namely, surface scattering. With increased scattering the mobility decreases. (f) The square-law name arises from the fact that 1133;“ varies as the square of V1333; in this first-order formulation (see Eq. 17.22). (g) The bulk-charge theory gets its name from the fact that source—to—drain variations in the depletion-layer or "bulk" charge are modeled correctly in the formulation. ' (h) 1]) versus V3 with VD held constant. 6) _ 810 , _ 310 Ed = — ’ gm — _'_"" 8V1) Vg=constant _ aVG VD=constant (j) The source and drain islands in a MOSFET supply the minority carriers required to obtain a low-frequency characteristic. Under inversion conditions minority carriers merely use the surface channel to flow laterally into and out of the MOS gate area in response to the applied ac signal. 17»! 17.2 (a) 051: = %tn (NA/n1) ‘= 0.02591n(1015/10‘0) = 0.298V VT = 2¢F+KJ£Q “NA 0,: ...(17.1a) K0 K360 = (2x0 298) i "2 ' (3‘9) (11.8)(8.85><10'14) VT = 0.800 v (b) In the square-law theory 2— C ‘ [Dsat = :1 ° (VG—V192 ...(17.22) -14 Co = K080 = 2 6_90X10‘8F/cm2 x0 (5x106) -3 -8 2 1,le: (5x10 )(800)(6.9X10 )(2—0.8) = 0.397.111; (2)(5x10‘4) (c) In the bulk-charge theory we must first determine VDsm using Eq.(17.29). We know (:21: and VT from pm (a), but must compute Vw before substituting into the V1353: expression. 1/2 _]4 WT: [mm (2%)] = [(2)(11.3)(8.85><10 )(2)(0.298) = 0382!“ WA (1.6x10‘19)(1015) -I9 15 -5 Vw E qNAW-r : (1.6X10 )(10 )(8.82><10 ) flimsy Co (6.90X10'3) Noting that VG — VT : 1.20V, substituting into Eq.(17.29) then gives . m U = _ (1.20) ( (0.205) fl _ (0.205) } VIM 1.20 0.205 {[————(2)(0298) + 1+——-(4)(0_298) tau—(“(0298) 17-2 or V1353“ = 1.06V ...smaller than Vow of square—law theory as expected Now __ -3 -8 Z #nCo ___ W = 5.52x104 amps/V2 L (5x104) Finally, substituting into Eq.(17.28) gives 1133;” if VD = V9531. Thus ' 2 1953;: (5.52x10-4) (1.20)(l.06) — (1'26) A (1.06) 3f2_ ($0.06)] 3 (0'205)(0'298)[i1+(2)(0.298)) (1+ (4)(O.298)i Insat = 0.349inA ¢=bulle charge result (smaller than the square-law result as expected) (d) Clearly here the device is biased below pinch-off. From Table 17.1 we note that both the square-law and bulk-charge theories reduce to the same result if VD = 0. _zng ‘ L gd (VG — VT) = (5.52x10'4)(2 -0.8) = 0.662mS (e) In the square-law theory, V1353“: VG — VT. Thus VDsat = 120‘! and VD = 2V. Since VD > VDsat, the device is saturation (above-pinch—off) biased, and from Table 17.1 =zmg L gm (VG — VT) = 0.662mS ...same as gd of part ((1) (f) In part (c) we calculated the bulk-charge V1353“: 1.06V. Since VD > V1352“, the device is above-pinch-off biased, and from Table 17.1 __ZEuCo ' L gm vpsa. = (5.52x10-4)(1.06) = 0.585mS (g) For the applied VG = 2V, VDSm = 1.20V in the square-law theory and VDSM = 1.06V in the bulk-charge theory. Since in either case VD < VDsm, we can utilize the second form of Eq.( 17.37). HuVD_ (800)“) 409an 17-3 (c) inversion layer outline (increasing toward drain) 17-4 (M f zero width VT (volts) MATLAB program script... %Problem 17.4...VT vs. NA with x0 as a parameter %Initialization clear: close %Constants and Parameters q=1.6e—19; e0=8.85e—14: kT=0.0259; ni=l.0e10: KS=11.8: KO=3.9; NA=logspace(14,l8); ‘ xo=[l.Oe—6 2.0e—6 5.0e~6 1.0e—5]: %VT Computation zF=kT.*log(NA./ni); for i=lz4, xoo=xo(i): VT: 2 .*@E+((Ks*xoo)/KO).*sqrt{(4 .*q.*NA.*oF)./(Ks*e0)): semilogx(NA,VT): axis([1.0e14,1.0e18,0,3]) hold on end grid: xlabel(‘NA (cm-3)'): ylabel(‘VT (volts)') text(l.1el7,1.25,'xo=10“—6cm'): text(1.le15,l.75,'xo=10‘-5cm'); hold off 17-5 2.5 r i . . . , . . . . . . . . . . . . . . . . . . . . . . “E . . . . . . . . . . . . . . . . . . . . . . . . . ‘ . _ . . . . . . . . , . .. :- 5 2 s 5 5m=1e~956m 5 E ': E E 5 5 ENA-1e'+1alca-n35 . . . . A . “5 . . . . . . . .._‘ . . . . . "2. . . . . . . . ..: . . . . . . . . ..: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ‘ .— . . . . . . . . . . i . . . . . . . . . . . . . . . r . e . . . . . . . . . r . . . . . . . . - . . . . . . . . . . - . . . . v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .‘ E . . . , i . . . . . . . i r r . ‘ . . . . , . . . i A . . . . . i . i . . . . . . . . . . . . . . i . . . . . . - q . . . . . . . L . . . . . . . . . . . . . . . v . . . . . . . . . . .. g. > 2 . . . . . i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V . . . . . . . . . . . r . . . . . A . . . . . . . . . . .. 13 ..... .4 ,,,,,, ,f ....... “g ....... s ........ .é ........ “g ........ 4 ...... ..f ........ .g ...... H La ....... .... ....... ....... ........ ........ ........ ________ .3 .... ._ 3 ~ 1200 220 240 250 230 300 320 340 350 380 400 TM The threshold voltage is seen to decrease in an almost linear fashion with increasing T. MA‘I‘LAB program script... %Problem 17.5...VT vs. T %Initialization clear: Close %C0nstants and Parameters q=1.6e—19: k=8.617e—5: e0=8.85e-14: KS=11.8: KO=3.9: T=linspace(200,400): kT:k.*T; xo=input('Input the oxide thickness in cm, x0 = '): NA=input(‘Input the Si doping in cm—3, NA = '): %ni versus T %Constants A=2.510e19: Eex=0.0074; %Band Gap vs. T EGO=1.17: 17—6 a=4.730e—4: b=636: EG=EGO-a.*(T.‘2)./(T+b): %Effective mass ratio (mnr=mn*/m0, mpr=mp*/m0) mnr=1.028 + (6.116-4).*T — (3.098-7).*T.‘2: mpr=0.610 + (7.83e-4).*T - (4.463-7).*T.‘2: %Computation of :11 ni=A.*((T./300) .“(1.5)) .* ( (mnr.*mpr) ."(0.75) J .*exp(—(EG—Eex) ./ (2 .*k.*T) ): ' 95W Computation gF=kT. *logmA. lni}; VT: 2 .*¢F+ ( (KS*xo} fKO) .*sqrt ( (4 .*q.*NA.*;aF) ./ (KS*e0)); plot (T,VT) : grid x1abel("I' (K) '): ylabe1('VT (voltsl') text {342, 2. 37, ['xo=' , num23tr (x0) , ' cm'1) text (342, 2 . 32, ['NA=‘ , num2$tr (NA) , ' /cm3'1) 17.6 - Differentiating Eq.(l7. 17) with respect to VD with VG held constant yields a]; mac aVD chconsmm L (VG — VT— VD) 33‘ 0 Solving we obtain VG- VT~ VDsal = 0 VDsal = VG — VT (ftp dy 1110') I ' [D = I {.Ipydl‘dz = Z! Jl’ytit’ ‘ (17.821') 0 (Note that ID is defined to be positive flowing mn-ofthe drain.) JP 5 pr E qpppgy E «(($in (17.7') 17-7 d¢ Atom 11) = —Z—— q #p(x,y)p(x.y)dx (17.8b") dy 0 r W) QPO’) = (If P(X.y)dx (17-3') 0 q ICU) “ = _... (x, ( , )dx (17.4') #p @0010 #p 3’)pr _ ma 1 = ._z __ 17. ' D _ 1sz1: dy ( 9) L VD I [Ddy = [DL = 4] Epme (17.10') 0 o 25 If” (NOTE 1/ <0 h'h _ ___p_ I D_ , W 10 , ID _ L [0 de¢ gives ID the correct sign.) (“'11) Aantc "—' —AQscmi E “Q? (17-12.) Aékam = CB(VC'“v59 (17-133 Qp s —C0(Vg—VT) (17.14') em») a —Co(vG— VT— ¢) (17.16) T > .. ID = Z ‘“PC°[(vG—VT)VD_ van] "’0 2 VD “ VD“ (17.17') L ...V(; s VT Now that Eq.(l7.l7') is the same as the text Eq.(l7.17) except ,l—ln —-> lip and there is a polarity reversal in the inequalilics specifying the range of valEd VD and V0 values. 17-8 me : =o § 2 Eve-VT: v ...y____.__ ,.__......._-_._..._..--._..— _._._.__.-........ I D,'(ZpCoJL) VD (volts) MATLAB program script... %Problem 17.8...effective mobility per Eq. (17.5) %ID—VD Characteristics [/1 Square—Law Theory $1nitialization clear: close '1Let VGT = 'G - VT; texHB, IDOsat+D.2, 'VG-VT=4V'I fer UGT=¢:—l:l, textt4.5,IDOsat+0.2,‘theta=fl'l %Primary Corputacion _ text(4.5,IDlsat+0.2,‘theta=0.05/V') VD=1inspa:e(O,VGT ; hold on IDO=VGT.*vfl—VD.*VD./2; else, IDOsat=VGT*UGT/2; plottVD,IDO,'g-*',VD,ID1,'rU: IDO=IIDG,XDOSat§; $Labeling of VG-VT curves < 4 Im= wanna—vs. "VD./2} ./(1+0.05*'VGT); if var-=3, IDlsata (VGT‘VG‘S‘i?) I (1+0.05*VGT): text (3, IDOSat‘. +0.2, ‘VG—VT’JV') ,' IDI=[IDE,II)15at?; elseif VGT==2, ' VD=[VD,9]: textlB,IDOsat+0.2,'VG-VT=2V'); $Plottinq and Labeling else, if VG'I':=-—‘., text (8, 100551: +0.2, 'VG-VT=1V'I: plot(VD,IDU,‘q—-',VD,IDI,'r'): grid and axistlo 10 0 ICE) and xlabeH'VD (volts) - r,- ylabelt'lD/(ZpCo/L) ') "end 17-9 -o 1 2,2 (:1) From Fig. P179 we note in general that VG = VD+VB 01' VD = VG~VB In the square-law formulation V1338: = VG - VT. If V]; = VTR, then VD = Vg—VTIZ > V053; and the MOSFET is always biased into saturation. Noting ID = 0 if VG < VT or VD < V112, and using Eq.(17.22), we conclude ZL—lnCo 2L (Va—VT)2 = 2”“C° if It) (VD—VT/Z)2 ---VD > VT/2“ and ID = 0 ...VD < VT/Z (b) If VB = ZVT, then VD = Vg—ZVT < Vg—VT = VDsal and the MOSFET is always biased in the linear region of operation. The device turns on for V5 > VT or VD > —VT and is therefore on for all VD 2: 0. Using Eq.(17.17) we obtain ID ..—. Zinc) [(VG—VT)VD — Vail] = ZHHCO [(VD+VT)VD — Vigil] _ 25200 (v52 + VTVD) = ZEC" [(‘V13+Vi~)2 — Vii --~VD 2 0 ID Note that both curves have the same general shape; the part (b) curve is simply shifted to the left and displaced downward. 17—10 17,1!) 0' 5 10 I I ' 15 VG — VT (volts) The above 1]) versus VG—VT characteristics were arrived at as follows: _ (i) Suppose we systematically increase VGA/T from zero with VD held constant. Initially VD is greater than VG—VT and the device is in saturation. (Use is being made of the square— law theory.) Thus initially ZEnCo ID = Inga: = (VG — VT)2 and we conclude ID varies as the square of Vg—VT if Vg—VT < VD. (ii) When VG—VT becomes equal to V1), the device moves into the linear region of operation. In the linear region : Zine}, I [(VG—VT)VEi- vé/zi 1D and ID varies linearly with ifs—VT. (iii) With increased VD, one stays on the voltage-squared part of the curve for a longer and longer range of voltages. Once Vg—VT > VB, :1 linear region whose slope increases with increasing l-"D is observed. l7wll (a) dq) . J’N = JNr = wrung: = -Q.unngr- (17-7) If the z-direction points from the surface into the bulk, 2t: [D = —J [1M dde = — 2nrJNr dz ...zc is the channel depth 0 2t: = -—21trfl (-— I pnn dz (17-8.) dr 0 Since the second quantity enclosed in parentheses above is just EDQN, we can write —_ :1 ID = —27t1rtthIq—ggi ' (17.9') r2 r2 VD I 1—D = i;- = LITE-1n (r2/r1) = flan] QNdfib (17-10') r I’ and VD _ __ 2n * . 1D — mob/r1) flu] QNd¢ (17-11) The change in geometry does not modify Eqs.(17.12) through (17.16). Thus QN = —Co(VG—VT-¢) and _ 2n — _ _ 2 In — Fug/r1) uncoka VTWD V00] 17—12 (b) Setting r2 = r1 + L, we can write In (rQ/rl) = h1(rljr:L) = 1n(1+L/r1) If L/rl << 1 ln(1 +L/r1) = (L/r1)-—%-(Ur1)2+--- 3 Url Thus 2,]; _) 2an = ; In(r2/r1) L L and one obtains the usual 19 — VD result. 17. 12 (a) Utilizing the Eq. (17.22) square-law result, Z Enco 2 I = V —- V Dsat 2L ( G T) and 1mm Hum [ vG— Vrm 2 InsatoooK) ‘ Enooom VG.— mom Assuming II“ has the same temperature dependence as p“ (and neglecting any differences in the effective mobility as a function of temperature that may result from operating at slightly different VG — VT points), we obtain the computational expression Imam = yum [ Vo—VTm ]2 IDsal(300K) #n(300K) VG —- VT(300K) 17-13 ID rllln...nr...nuhliv mlo , ' ' ' ' .5 200 220 am 260 250 300 m 340 sea son not: 200 m 240 250 zoo zoo :20 am 350 aao mo T(K) 1”th The results here are rather interesting. If the device is VG biased far above turn-on, then the V3 — VT term in the part (a) expression becomes approximately unity and the characteristics exhibit essentially the same temperature dependence as the mobility — generally decreasing with temperature. However, the threshold voltage change with temperature is sufficiently large that a totally different Insal temperature-dependence is observed if the chosen V6 is only slightly greater than VT. -—- The change in the degree of surface inversion becomes more important than the change in mobility. It should be noted that in performing the computations the tin value in N A—doped Si was assumed to be the same as that in equivalently ND-doped Si. MA'IIAB program script... %Problem 17.12...IDsat(T)/IDsat(300K) vs. T %Initialization clear; close %Constants and Parameters q;1.6e—19; k=8.617e-5: Ks=11.8: ' Ko=3.9; ' e0=8.859—l4; T=linspace(200,400,101); %Note: T(51J=300K: kT=k.*T: xo=1.0e-5: NA=1.0e16: VG=input{'Input gate voltage in volts, VG = '); 17-14 %ni versus T %Constants A=2.510e19; Eex=0.0074; %Band Gap vs. T EGO=1.17: a=4.730e—4: b=636: EG=EGO—a.*(T.“2)./(T+b); %Effective mass ratio (mnr=mn*/m0, mpr=mp*/m0) mnr=1.028 + (6.116-4).*T - (3.092-7).*T.“2; mpr=0.610 + (7.83e-4).*T - (4.46a-7).*T.‘2: %Computation of ni ni=A.*((T.f300).‘(1.5)).*((mnr.*mpr).”{0.75)).*exp(—(EG—Eex)./(2 .*k.*T}); . %VT Computation oF=kT.*log(NA./ni): VT= 2 .*oF+((KS*xo)/KO).*sqrt((4 .*q.*NA.*oF)./(Ks*e0)); %Mobility Computation %Fit Parameters NDref=1.3el7; TNref=2.4; unmin=92; Tumin=*0.57: un0=1268: Tun0=—2.33; an=0.91; Ta=—0.146;_ %Mobility Calculation NDrefT=NDref*(T./300).“TNref; unminT=pnmin.*(T./300).‘Tumin; pn0T=un0.*(T./300).‘TpnO: anT=an.*(T./300).*Ta; pn=pnminT+pn0T./(1+(NA./NDrefT).‘anT); %IDsat Computation and Plot %IDratio=IDsat(T)lIDsat(3OOK) and pnratio=pn(T)/pn(300K); pnratio=pnlun(51): - IDratio=unratio.*((VG—VT)/(VG«VT{51))l.‘2: %Plotting result ' plot(T,IDratio,T,unratio,'g——'); grid xlabel('T (K)'): ylabel('ID ratio...or...mobility ratio'} %Key text(302,2.25,{'VG = ',num25tr(VG),‘V']) x=[302,312}: y1=[2.15,2.15]: y2=[2.05,2.05] hold on: plot(x,yl,x,y2,'g~-') text(314,2.15,'IDratio') text(3l4,2.05,'mobility ratio') hold off 17-15 17.13 With R3 and RD taken into account, the channel voltages at y=0 and y=L become V(0) = IDRS and V(L) = VD - IDRD. Inserting the revised voltage limits into Eq. (17.10), and likewise modifying Eq. (17.11), we obtain Z— VD—IDRD ID = ——:‘—“I Qthp (17.11') IDRs where in the square-law theory QN = —Co(VG - VT- (0) (17-16) Substituting the Eq. (17.16) expression for QN into Eq. (17.11') and integrating yields 2“ c ' v 1 2 I 2 ID = “2 °{(VG~VT)tVD—ID(Rs+RD)i—L%Dfi‘2~+( D23) ] or , z- c v 1 R R 2- . ID =- “If °i(VG—InksmvntvD-ID(Rs+RD)1J—Pfliififl} (17.17) Tuming next to the modification of Eq. (17.21), we note that when VD = VDsat, QN(L) = 0, (KL) = VDsal—IDWRD, and from Eq. (17.16), 0 = -Co[VG - VT — (VDsar-IDsatRDH 01' VDsat—IDsatRD = VG— VT (17-21.) Finally. setting VD = Vpsm and ID = [mm in Eq. (17.17'), and simplifying the result using Eq. (17.21'), one obtains ZEnCo 19m = (VG—Insatks —VT)2 ' (1722') Note that replacing VD by VD—ID(R3+RD) and VG by VGFIDRS in Eqs. (17.17), (17.21), and (17.22) does indeed yield Eqs. (17.17'), (17.21'), and (17.22'). 17-16 11,14 Following the text suggestion, we set QNUL) = 0 in Eq.(17.27) when V(L) = VD -—) V133“. one) =—co [VeVersarVw(f1"+vDsa_./2' cm: —1)] 5st 0 , 01' VG~ Vr- VDsat‘VW“ 1 + Vow/24’}? -1) = 0 Manipulating the preceding into a form which can be solved for VDsa; we note VG — V’I‘ + Vw- VDsat = Vw 91+ VDsat/Z‘PF Squaring vfiw — ave—mm)va + (VG-VT+Vw)2 = V3», + V\2NVDsar/2¢F 01' 2 V Veal—[5% + 2(VG—VT+Vw)] Vow + (VG—VeVWF _— Va, = 0 Solving the quadratic equation gives _ IR 2 2 2 V V vpsat = AY- + (VG — VT + Vw) i {[41 + (VG-VT‘FVW)] — WwVfiVw)2 + Viv} 44)}: 4¢F 2 2 2 "ll/‘2 = Vg—VT+Vw(1+Xw— +251(vG—VT+VW)+V3VJ 4% 445p 49?}: v v 2 v VG—VT “'2 = VGFVT+Vw(l+v-W— in(—w— +2—33— 4¢F 4991: 44151: 2991: _ 2119 = Vg—VT+Vw 1+—Y-W-—)in VG VT+{1+fiV-) 4¢1= 2¢F 4¢F Note that if the (+) root is chosen VDsm(+root) > VG —— VT. Choosing the (—) root on the other hand yields Vpsat < {VG — VT). As discussed in the text, in the bulkvcharge formulation, part of the change in the gate charge goes into balancing changes in the depletion-layer charge. Thus, there is less inversion-layer charge at a given VG relative to the square-law formulation. Consequently V953; occurs at a lower voltage than VG — VT. We choose the (—) root and slightly rearrange our result to finally obtain Eq.(17.29). . “- VGA/T V_ 21B V \ VDsat"VG—VT-Vw{[ 2¢p +(1+-‘W3—WFH —(1+Ew1;)l 17*17 12,15 The required computer program and a sample output is reproduced below. IDI(Z|JCOJL) VD (volts) MATLAB program script... %ID-VD Characteristics /// Bulk-Charge Theory %InitializatiOn clear; close %Constants and Parameters q=1.60e-19: e0=8.85e—14; kT=0.0259; ni=1.0e10; KS=11.8: KO=3.9; NA=input('input the doping in cm—3, NA = '): xo=input('input the oxide thickness in cm, xo = '); %Computed Parameters aF=kT*log(NA/ni); WT=sqrt((4*KS*e0*zF)/(q*NA)): Co=KO*e0/xo; V'W=q*NA*WT/Co: 17-18 11,15 (Solution not supplied.) 1 2.! Z (Solution merely involves straightforward mathematical manipulations.) 12.18 (a) Given VD = 0, then 4502) = 0 and (3.9)(sssx10-14x2) QNtany) =-co(Vc.~vT) =1??- (VG-VT) = 0 5x10-6 = -1.38X10'7coullcm2 (b) gait/13:0 = Z‘unco (VG — VT) ' ...making use of Table 17.1 = _ZEnQN = (70x10‘4)(550)(1.38x10'7) L 7x104 - = 7.59x10-4s 11,12 lV-d is the same in ideal p-channel and n—channel MOSFETS with the same 10 and bulk doping concentration. Thus, with the devices also equivalently biased, one concludes from . Table 17.] that the same gm's will result if Lp ‘9" Ln ‘1" where the subscripts indicate the channel type. This same conclusion is reached whether one uses the square-law theory or bulk-charge theory and whether the devices are biased below or above pinch-off. Next, examining the first form of Eq.(17.37), we again quite generally conclude that Cow-channel) must equal Co(n-ehannel) for the fmax values to be the same. Since Co = K OEOZLI'IO, we therefore require : ZnLn 17-20 %ID—VD Computation and Plot for VGT=4:—1:1, %VGT = VG - VT; %Compuation A=VGT/(2*9F); B=1+vw/(4*oF): VDsat=VGT-VW*(sqrt(A+B“2)—B): VD=linspace(0,VDsat); ID1=VGT.*VD-VD.*VD/2: VDF=VD./(2*oF): IDZ=(4/3)*VW*6F.*((1+VDF).‘1.5*(1+1.5*VDF)); ID=ID1-ID2: IDsat1=VGT.*VDsat-VDsat.*VDsat/2: VDFsat=VDsat./(2*6F); IDsat2=(4/3)*VW*oF.*((1+VDFsat).‘l.5-(1+1.5.*VDFsat)): IDsat=IDsat1—IDsat2: VD=[VD,9]: ID=[ID,IDsat]; %Plotting and Primary Labeling if vsr=4, ' plot(VD,ID); grid: axis([0 10 0 10]); xlabel('VD (volts)'); ylabel(‘ID/(ZuCo/L)'): text(8,IDsat+0.2,'VG-VT=4V'): hold on else, plot(VD,ID); %The following 'if' labels VG—VT curves < 4 if VGT==3, text(8,IDsat+0.2,'VG«VT=3V'): elseif VGT==2, text (8, IDsat+O . 2, 'VG-V‘I‘=2V' ) : else, text(8,IDsat+0.2,'VG-Vl=lV'): end end and hold off 17-19 Substituting Zp from the first relationship into the second relationship and simplifying, one obtains __ o=vflh tan and ZnLn En z = = r z P LP ’1‘} n The mobilities deduced from Fig. 3.53 yield II“ = l1an = 673 cmZN-sec and Hp = W2 = 229 cmzN-Sec. Thus the required p—channel device dimensions are Z = «J 673/229 x 50 = 85.7pm and L = 4229/673 x 5 = 2.92pm 11,2!) (a) Since the applied V1) is greater than zero, we infer the given MOSFET is an n-channel device. Also, at point (1) the MOSFET is biased below saturation. Thus the channel narrows near the drain but is not pinched-off. 7/ [depletion region outline 17-21 (b) In the square-law theory V9331: VG—VT. Thus . = VDgal+VT = (c) The point (2) bias corresponds to the pinch-off point. At the pinch—off point, and based on the square-law theory, the charge in the MOSFET channel goes to zero at the drain. QN(L) = 0 ((1) With VD = 4V and VG-VT = 3V, VD > VDSM = VG—VT. Consequently, for the readjusted gate voltage, the MOSFET is being operated in the saturation region. Since I psat cc (VG—V102, it follows that [Dsagl = VGI"‘V'I')2 Insaa ch—VT Here identifying the desired ID = Ipsau (Val—VT = 3V) and 11333;; = 10'3A (Veg-V1- : 5V) from the given characteristics, we conclude ID =(10'3)(%)2 = 3.6x10-4 A (e) By definition gd = dip/3V1) with VG held constant. Inspecting the given characteristic, we conclude BID/8V1) = 0 at bias point (3) and gd = 0. Alternatively, in the saturation region of operation, IDsat is not a function of VD. Consequently 811333,]an = O and gd = 0. (f) At bias point (3) the MOSFET is in the above pinch—off region of operation and from Table 17.1 @1931 = 4x19-4 5 = Z‘unc" {VGuVfi = ELM = 3‘” L Vg—VT (g) For an n—channel (p-bulk) MOSFET, one expects a lowfrequency MOS—C type characteristic similar to that displayed in Fig. 17.1363). 17—22 lLZl Making use of Table 17.1 and defining B = 2 £711ch , we conclude: 0 ."V V 3" En] G~T D fl \VGJHLVD mVC—Vravb V —V' V' .HV’ 5‘7 V £1316 T-D D G-T ‘3 lo ---VD2VG"-VT [VD WVDS¥kaT El: fl lVbuVr .HVDZIQrVT 17-23 12,22 There is of course no set answer to this question. The answer, however, should include some of the following points: Externally the J—FET and MOSFET yield similar electrical characteristics and even appear similar physically, with the terminal leads being designated the source, drain, and gate. The gate voltage in both devices determines the maximum conductance of the internal channel. However, there are major differences in the nature of the conducting channel and the substructure used to modulate the channel conductance. The J—FE'I‘ channel is a narrow piece of bulk material; in the basic transistor configuration the MOSFET channel is an inversion layer which is created by the applied gate voltage. Manipulation of the channel conductance is accomplished by reverse biasing a pn junction in the J—FET; the MOSFET channel conductance is modulated by the bias applied to the MOS structure. The first and even second-order quantitative analyses leading to the dc characteristics are quite similar for the two devices. Nonetheless, there are two complicating factors which enter the MOSFET analysis, factors which are not present in the J-FET analysis. First of all, carriers in a surface channel experience motion—impeding collisions with the Si surface which lower the mobility of the carriers and necessitate the introduction of an effective carrier mobility. Secondly, the carrier concentration and current density in the surface channel are strong functions of position, dropping off rapidly as one proceeds into the semiconductor bulk. For the device structure analyzed in the text, the carrier concentration and current density are of course constant across the J—FET channel. Both first order theofies give rise to an 1933‘ which varies (or varies approximately) as the square of the gate voltage. The general ac response and first order equivalent circuits for the two devices are identical. 17-24 ...
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This note was uploaded on 01/31/2011 for the course ECE 3085 taught by Professor Taylor during the Spring '08 term at Georgia Institute of Technology.

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Chapter 17 - CHAPTER 17 ill(a Carriers enter the channel at the source contact and leave the channel(or are"drained" at the drain

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