q2_spr01_soln - Spring 2001 6.012 Microelectronic Devices...

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Unformatted text preview: Spring 2001 6.012 Microelectronic Devices and Circuits Prof. J. A. del Alamo April 18, 2001 — Quiz #2 problem grade SOLUTlONJ Name: Recitation: General guidelines (please read carefully before starting): 0 Make sure to write your name on the space designated above. 0 Open book: you can use any material you wish. 0 All answers should be given in the space provided. Please do not turn in any extra material. If you need more space, use the back page. 0 You have 120 minutes to complete your quiz. 0 Make reasonable approximations and state them, i.e. quasi—neutrality, depletion approxima— tion, etc. 0 Partial credit will be given for setting up problems without calculations. NO credit will be given for answers without reasons. 0 Use the symbols utilized in class for the various physical parameters, i.e. um I D, E, etc. 0 Every numerical answer must have the proper units next to it. Points will be subtracted for answers without units or with wrong units. 0 Use (1) = 0 at no = pa = n,- as potential reference. I Use the following fundamental constants and physical parameters for silicon and silicon dioxide at room temperature: n,- = 1 x 1010 cm-3 kT/q = 0.025 V q = 1.60 x 10-19 C 6.9 = 1.05 x 10—12 F/cm 601; = 3.45 X 10‘13 F/cm (1b) ( 5 points) We want this inverter to have an average propagation delay tp = 1 ns when driving a CL = 1 pF capacitive load. Calculate Wn and WP. '\ TN AVLYW PKIVLA?»,‘t:°M M: . ‘ cbvm, CLVDD ‘ ‘ M *r ’i‘fm“tl’wl ’ 1L 1 + w 1 J ,u.‘ (9,; L Vb» 0’“) J ,M (ax (Van 4 V'l’rl Ln L, T Cl.va 1-K i W? ' ' 3 - -r._—_.’-———' — ' I (on Wf w“ AnLVoh—thll WP (VNH' 7') J>\v\w& [hr Wp '- Cl-L Vm Ln WP ’ ) _ wp -. ,_,.__..—— ,_ . + _....»-—--—x - 2 6-.» W H” MMLVDD 'V'h) #9 WWW?!" l9"1 x C u ' l / V 'L zu‘zjuo'huo'q «MU-WV UNI") WW‘ wt \AD‘VQ VHLJ' Ga 3h3‘5l9-'z '1 L (A; z __r - t if; (a P/Lvu *3; )Q).\°‘¥ \Auvw :A—I - w“ -_ _ _, I.) /A'~ 1. ( 25 points) You are given a CMOS inverter with the following parameters: VT” = 0.5 V tog,- = 10 nm Mn = 400 cm2/V - s VT? 2 —1 V An = AP = 0.1 V“1 M, = 200 cm2/V - s VDD=5V Ln=Lp=1um (1a) (5 points) Calculate the ratio Wp/Wn so that VM = 2.5 V. J rv ‘ ‘ . M ‘1 cram P k, . . L) \VTV‘". 1:; (VD) vmt lv. P )+ L“ LL'l‘ VJ lulu (av liz_( VM'VTH ilk 7.5-9,: 7, L” Vm-Vm'tvrp 5-1.5-) ) - TM); marlin D “(VJ 4, W JM C [:11 = 51‘ r 74 Wr/“P L. - ____. m fil‘nc" w‘n/Ah Mu WP : & M LY: 2.; 3e (1c) (10 points) Estimate N M L and N M H for. this inverter. We Mom. in: J+£r+ g) kemvwfivj #4». «Ha? W“ «)- VI; w" “4- 1AV\—. (VWM-t fiwp) (Tonlln‘fl : 0}M 3m? : ‘fiw. "71M? 2 '1” + l )0m + 3:.) row “P w” c./(V v "i? [./4(VM+V.) EN“ 4‘ M‘ Tu)"' LP/‘P tP _ z w IL - m M“ U (VM‘VTW? )‘u + if“? [/1 (-VM“ V11!) ILA LL ' -— -— V v _ __ L ‘LVM’VTK) + w“ A“ ( M+ 1P) : E— ’ (23-04 ) 4» LR; (Lg-b) t “.1 A“ 1, a, I _ L a L (VM'V‘h) + LVM+V1r) 0' n'r) 4‘ I-7 (7'1 ') Wt «0w v)! 4'“ J‘mwb'd‘ 4°”MJM 1” NM Vim-V I-ZJ’ NML.= VM» M ._ 14' -—-; 7.2 V )An “3' f ‘2': - / WP - w“ ,( WP )AVI 1 a + $4M? : 1 L“ filth! H) + z r? M” (J). LD )5? r“ flut‘l + If Mr (or: §.°K* 3,9 F ' ~ P t‘vx (—5 + in 1—9 f ’ W" )4 (ex CVM‘V7h) If EL. “ .n u \NWL WL MwL wut 4"“ 1“”" H“) 7'5“ ; 'bW‘ ED “‘A "" : A? : (\- (1d) (5 points) Sketch and appropriately label the voltage transfer characteristics of this inverter. 2. (20 points) You are given the following I-V characteristics for a n—MOSFET with tom = 10 nm, W = 10 um, and L = 1 gm. The gate material is n+-doped polysilicon. The body is tied up to the source. In (A), gm = 1.4 X 10*4 A/V. In (B), go = 5.7 x 10—5 A/V. (2a) (5 points ) From (A), estimate the threshold voltage, VT. From U0, L3 QM“; [Qt-J’rAr-lkfih wn. (2b) ( 5 points) From (A), estimate the electron mobility, pm. LV\ +N. +ramv§1+§n LSJ Li‘AJLA 0") 4th 4W Ad‘s/v.4» \ \ TN *YfimA/LBY £41??th lJ FILM 33 ~_ 9 W V; L : "Ir/“n C” (VIM ‘ :1 -VT)V°J TN +(Avklfio‘fldzvtLfiVd-L L 4M: 31;) w 2— —— - — \I W $VH 'r/‘V‘ (u m ID\\I\|V\3 (M [An yvl PH )‘q l, . a x a h N = W = a—r-r‘Tr“ ‘ W C“ VD! l°u\°- ’1 ZMS‘MD x °\ w:+\n .43 [9». ; €331 - 3-v'r’;_._.l° - 3_Hf>|o') F/L-M ta,- )02|9—? rby‘m ( V95 ;/ JMJM) (2d) ( 5 points) Estimate the saturation voltage, VDssat, and the saturation current, I Dsat, corre— sponding to the characteristics in MA A MNMT.‘ Vmwt ‘- V51 'VT WM! '«rf QLSIS In L”) '. VD/Jai»; 3- 0.1 : L6 V. - w 1/ I: x Lb : —-/A.,cu LVH-VT) = _.. V°é:3hf,|o'; (3—0J4) —: H? MA 2" 2x! (2e) (5 points) From (B), estimate the Width of the channel pinch-off region, AL, at VDS = 4 V. To fit Vtmlr »,u, m me Must L V5; 'VbuJ- .(19\V}V3 [or AL v -v ’r "” , i - AL : 3,9 L ( DJ and) 2 A, Lib“: 66M ; 2,) w.) x “'3 : o.ol'3r [we or L?- 7. at JAN. LLLHMM JM’M ). 3. (20 points) An n-channel MOSFET is wired up in the form indicated below. This is an enhancement-mode device (VT > 0). Neglect channel length modulation. 'i + (33.) (10 points) In terms of usual MOSFET parameters, derive suitable equations for the I-V char- acteristics of the resulting two-terminal device. Sketch the I-V characteristics in a linear scale. F" V) VT .4“ MNFET :5 M “4 J‘+"'“i’l‘°‘4 nkiwq Jim Va-B:°LVT. TN l'V CVArtLi‘LfiA‘AAL) Ark z .- w 7. L = {1/4” cu cv-vT) Far Vc V1 4w; Mugs—f I; c...+-.H. MA 1;, I TN 1’V chcrw‘l‘crili'zlu +NM \“h 0 V,» v T \I Ifiou” rrvLH) W‘VDL ox fiber/Ll 4):er 4'“ ' £ 9m ‘KJx_ io'WAV’i LVVVMAL Lira.ch i1 (’VL‘MEI. raJ'lNr 1H4“ Lfiyt h (3b) ( 10 points ) Sketch a complete high-frequency small-signal equivalent circuit model for this two- terminal device for situations in which V > VT. Express all small-signal elements in terms of those of the MOSFET, i.e.: as a function of gm, go, 093, 09.1, Cab, etc. A If. «ML/bah c3" Hwk JmM-‘ln‘fw-vk .u'vhmw'} ()nm‘t maM aLA‘ MN'EE: 5" J‘+"‘b:"" ( “Y‘Vtmp‘gfi‘l l\w\ 44421 Uvu {or V" ‘1‘?) ha I m, Hud- r+ yJH HMV‘MVU‘ Lunch m Lu) :1 JIM/wk 1L, +H “,qu WWI ,LN r41 74 Jlurftr/ ,L. +L~L have Tkh+ b‘(4¢'b:VL5 14)“; a“, , %L W 534. Wt An 4% he“ wW-x: 4. (15 points) An NMOS inverter with a resistor pull up was miswired and ended up as sketched below. R=1 KQ CL The parameters of the transistor are: ,unCoz = 50 MA/V2, W/ L = 5, and VT z: 1 V. Neglect channel length modulation in this problem. (4a) (5 points ) For V,- N = O, in What regime is the transistor biased? How much is VOUT? (numerical answer empected). \ ‘ :u 5, V J- l For vwla 4H lrwmrl-cv H cv‘l" H) M p\ (Mul') ' In errun low} 'l'lnrmril" +H “killer “Ml VMT "° ‘ (4b) (10 points) For V; N = 5 V, in What regime is the transistor biased? How much is VOUT? (you can leave the result in the form of an equation Where VOUT is the only unknown). \ \ . For sz§v, JWL 4VAMCI+" H “" JK'LVY‘G-fim' HV‘LL VH) :o V “(VT)- ‘. TN. L'VrLVJ‘ \\bw.‘m.j Wavgk Hot 4(akl—TI‘VY' I) L 5 4 v 1).],- ZD '1 52, (VINFVDUT—V—J - 159'” ( 5' “‘7' '- .. ,»- —? 1,", : V" ' »_ IO V9.7 )7, SvaL 7,", > 7—D wL M‘WL 0’ w V9v+1r M V.» + '(o=” TN lutvh’ob :J 5. (20 points) In a certain pn junction diode at room temperature at a particular forward bias voltage, the current supported by hole injection into the n-side of the diode is 100 MA. The quasi—neutral width of the n—side of the diode is wn — 1:” = 1 pm. The hole diffusion coefficient is 10 cmz/s. The pn junction area is 10 ,umz. Make and state suitable approximations. (5a) ( 5 points) Estimate the hole concentration at the space-charge region edge of the n quasi—neutral region. ( numerical answer empected TH Lvrrun‘l’ lJ fivflk L)‘_ 9L! ) Lr" L—t- wn’ih LAVIW; fur“): -( -v ' lam-X“) \° *\ Pb‘m) - Ln( = L—D—P—fl ’— (“3le 1*DP WNW”; Nuo‘Yx 1° (5b) ( 5 points) Estimate the velocity at which holes are injected at the edge of the n quasi-neutral region (numerical answer expected). . 5+ _ ML can bvn Q . ’FH— 4w ery '4 Wk \vah"N~*r'~J nylw Zr. " a A P Solvlvns V“ '. ,_ -—6 .. V L1“) ' Ly, I‘ lQDxlD _ oJ LW/ P ' *jfifi ‘ I I 1A pun) L5,le x n: )- 6.3x|a" (5c) ( 5 points) Estimate the hole flux arriving at the surface of the n quasi-neutral region. ( numerical answer expected). \ \ arrIVIVVS om “Ami ,3. Mm “do”; -I» in V\ guah‘onvinvl res/I‘D»- «F 7+: a? TM/ :1 Lean,“ Wu anA +W" fire. infio‘i‘td 1N \MJL «\vx is 4N JAM NRA 7:4me qu 4N Jy‘Au»f—b\er‘,L r142“. (Lat/k M Jvr‘au, long”- Mu I F (04“ > F 0(a): .5.— = ._ _,‘|o P .) P A? 53 :o' 3‘ \. 6 “in (5d) ( 5 points) Estimate the diffusion capacitance associated with hole storage in the n quasi-neutral region. (numerical answer expected). ' TN, \A‘i‘l, twink; J‘me‘ ;V\ 4N n—QNvL TI : 1' ~H 7' g ~I“! 62?: Tr 1r : LWM'XK) 1» L U“ ) .. Mono": Sti° C 2D,: 7,; l6 TN; Mq/tcyv‘sm Laytfikxfi‘e‘hk \II', -n/ . .. 1 C]? r '3" Q = S,.‘ : Zx\°‘ F L? P can ...
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This note was uploaded on 07/20/2009 for the course ELECTRICAL 6.012 taught by Professor Prof.jesúsdelalamo during the Fall '05 term at MIT.

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q2_spr01_soln - Spring 2001 6.012 Microelectronic Devices...

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