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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 squarelaw name arises from the fact that 1133;“ varies as the square of V1333; in this
firstorder formulation (see Eq. 17.22). (g) The bulkcharge theory gets its name from the fact that source—to—drain variations in the
depletionlayer 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 lowfrequency 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 squarelaw 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 bulkcharge 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 qNAWr : (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) 172 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;: (5.52x104) (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 squarelaw result as
expected) (d) Clearly here the device is biased below pinchoff. From Table 17.1 we note that both
the squarelaw and bulkcharge 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 squarelaw theory, V1353“: VG — VT. Thus VDsat = 120‘! and VD = 2V. Since
VD > VDsat, the device is saturation (abovepinch—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 bulkcharge V1353“: 1.06V. Since VD > V1352“, the device is
abovepinchoff biased, and from Table 17.1 __ZEuCo
' L gm vpsa. = (5.52x104)(1.06) = 0.585mS (g) For the applied VG = 2V, VDSm = 1.20V in the squarelaw theory and VDSM = 1.06V in the bulkcharge theory. Since in either case VD < VDsm, we can utilize the second form of
Eq.( 17.37). HuVD_ (800)“) 409an 173 (c) inversion layer outline (increasing
toward drain) 174 (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 (cm3)'): ylabel(‘VT (volts)') text(l.1el7,1.25,'xo=10“—6cm'): text(1.le15,l.75,'xo=10‘5cm'); hold off 175 2.5 r i . . . , . . . . . . . . . . . . . . . . . . . . . . “E . . . . . . . . . . . . . . . . . . . . . . . . . ‘ . _ . . . . . . . . , . .. : 5 2 s 5 5m=1e~956m 5
E ': E E 5 5 ENA1e'+1alcan35 . . . . 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=8.85e14: 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=EGOa.*(T.‘2)./(T+b):
%Effective mass ratio (mnr=mn*/m0, mpr=mp*/m0)
mnr=1.028 + (6.1164).*T — (3.0987).*T.‘2:
mpr=0.610 + (7.83e4).*T  (4.4637).*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 mnofthe drain.) JP 5 pr E qpppgy E «(($in (17.7') 177 d¢ Atom
11) = —Z—— q #p(x,y)p(x.y)dx (17.8b")
dy 0 r
W)
QPO’) = (If P(X.y)dx (173')
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? (1712.)
Aékam = CB(VC'“v59 (17133
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. 178 me : =o § 2 EveVT: 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, 'VGVT=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 VGVT 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,'VGVT=2V');
$Plottinq and Labeling else, if VG'I':=—‘., text (8, 100551: +0.2, 'VGVT=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 179 o 1 2,2
(:1) From Fig. P179 we note in general that VG = VD+VB 01' VD = VG~VB In the squarelaw 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 voltagesquared 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 (177)
If the zdirection 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 (178.)
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; = LITE1n (r2/r1) = ﬂan] QNdﬁb (1710')
r I’ and VD
_ __ 2n * .
1D — mob/r1) ﬂu] QNd¢ (1711) 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) squarelaw 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) 1713 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 turnon, 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 temperaturedependence 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 NDdoped 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=8.617e5: Ks=11.8: ' Ko=3.9; ' e0=8.859—l4; T=linspace(200,400,101); %Note: T(51J=300K:
kT=k.*T: xo=1.0e5: NA=1.0e16: VG=input{'Input gate voltage in volts, VG = '); 1714 %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 + (6.1164).*T  (3.0927).*T.“2;
mpr=0.610 + (7.83e4).*T  (4.46a7).*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 1715 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 squarelaw theory
QN = —Co(VG  VT (0) (1716)
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—InksmvntvDID(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 — (VDsarIDsatRDH
01' VDsat—IDsatRD = VG— VT (1721.) 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'). 1716 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 + (VGVT+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 + (VGVT‘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+vW— in(—w— +2—33—
4¢F 4991: 44151: 2991:
_ 2119
= Vg—VT+Vw 1+—YW—)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
depletionlayer charge. Thus, there is less inversionlayer charge at a given VG relative to
the squarelaw 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—VTVw{[ 2¢p +(1+‘W3—WFH —(1+Ew1;)l 17*17 12,15
The required computer program and a sample output is reproduced below. IDI(ZJCOJL) VD (volts) MATLAB program script...
%IDVD Characteristics /// BulkCharge Theory %InitializatiOn
clear; close %Constants and Parameters q=1.60e19: 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: 1718 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)(sssx1014x2) QNtany) =co(Vc.~vT) =1?? (VGVT) =
0 5x106 = 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 
= 7.59x104s
11,12 lVd is the same in ideal pchannel 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 squarelaw theory or bulkcharge theory and whether the devices are biased
below or above pinchoff. Next, examining the ﬁrst form of Eq.(17.37), we again quite generally conclude that
Cowchannel) must equal Co(nehannel) for the fmax values to be the same. Since
Co = K OEOZLI'IO, we therefore require : ZnLn 1720 %ID—VD Computation and Plot
for VGT=4:—1:1, %VGT = VG  VT;
%Compuation
A=VGT/(2*9F); B=1+vw/(4*oF):
VDsat=VGTVW*(sqrt(A+B“2)—B):
VD=linspace(0,VDsat);
ID1=VGT.*VDVD.*VD/2:
VDF=VD./(2*oF):
IDZ=(4/3)*VW*6F.*((1+VDF).‘1.5*(1+1.5*VDF));
ID=ID1ID2:
IDsat1=VGT.*VDsatVDsat.*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,'VGVT=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, 'VGV‘I‘=2V' ) :
else,
text(8,IDsat+0.2,'VGVl=lV'):
end
end
and
hold off 1719 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 cmZNsec and Hp =
W2 = 229 cmzNSec. 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 nchannel device. Also, at point (1) the MOSFET is biased below saturation. Thus the channel
narrows near the drain but is not pinchedoff. 7/ [depletion region
outline 1721 (b) In the squarelaw theory V9331: VG—VT. Thus
. = VDgal+VT = (c) The point (2) bias corresponds to the pinchoff point. At the pinch—off point, and based
on the squarelaw theory, the charge in the MOSFET channel goes to zero at the drain. QN(L) = 0 ((1) With VD = 4V and VGVT = 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 (VegV1 : 5V)
from the given characteristics, we conclude ID =(10'3)(%)2 = 3.6x104 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 = 4x194 5 = Z‘unc" {VGuVﬁ = ELM = 3‘” L Vg—VT (g) For an n—channel (pbulk) 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 TD D GT
‘3 lo VD2VG"VT [VD WVDS¥kaT
El: ﬂ lVbuVr .HVDZIQrVT 1723 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 secondorder 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 JFET 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. 1724 ...
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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.
 Spring '08
 Taylor

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