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EE 105 - Fall 2010 - Salahuddin - Midterm 1 (solution)

EE 105 - Fall 2010 - Salahuddin - Midterm 1 (solution) -...

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Unformatted text preview: UNIVERSITY OF CALIFORNIA, BERKELEY College of Engineering Department of Electrical Engineering and Computer Sciences BB 105: Microelectronic Devices and Circuits MIDTERM EXAMINATION #1 Time allotted: 60 minutes NAME: So: g a; 0% g STUDENT ID#: INSTRUCTIONS: Fall 2010 1. SHOW YOUR WORK. (Make your methods clear to the grader!) Specially, while using chart, make sure'that you indicate how you have got your numbers. For example, if reading off mobility, clearly write down what doping density that corresponds to. 2. Clearly mark (underline or box) your answers. 3. Specify the units on answers whenever appropriate. SCORE: 1 2 3 Total /14 /16 [15 I45 PHYSICAL CONSTANTS Descrigtion Symbol Value Electronic charge q 1.6><10'I9 C Boltzmann’s constant k 8.62xi0'5 eV/K Thermal voltage at VT = 0.026 V 300K kT/q USEFUL NUMBERS VT 111(10) = 0.060 V at T=300K exp( 30) ~ 1013 23 1 1 De letion re ion Width: W = "— —+— p g q (Na Nd PROPERTIES OF SILICON AT 300K Description Symbol Value Band gap energy E3 1.12 eV Intrinsic carrier in 1010 crn'3 concentration Dielectric permittivity agi 1.0x10'l2 F/crn )(Vbl ‘ VAppfied) Electron and Hole Mobilities in Silicon at 300K nmbility (anzflt’s) WENJWIJL. ML“! Li I ii)” 10M 10‘5 19‘“ ., .... LLLIV‘VJ uglm. :._ ,LLLL-,....L.-L Wi- s Lil % -11; ,_3.. 1017 1018 1019 1020 [Vd-i- ill-:1“mthis}[all[ggliggfltjflifjn (c1313) Prob 1. [14 pts] (a) Assume that a Si sample has been doped with Ga (which is a group ill element). (i) Will the electron density increase or decrease if one increases temperature? Why? [Zpt] (ii) Wiil the hole density increase or decrease if one increases temperature? Why? i2ptl ‘ch we an; in scent-(221w l we ' acefiPlW ‘3 ”(fl .\ \ “)7 [t WET” will mcxrease 01$ Yil' increases Mini/t 6w, ,y _ in are as l n g it’,,i’i’i[)(1"t/‘O1‘i'txtY'zg 0‘) l0: ”Gm will not: depend or} WWW) Q’m‘i”""w (b) Assume that a Si sample has a hole concentration which increases linearly over a distance of 1.6 pm from an initial value at x=0 to a final value of 10]l5 cm'3 at x=1.6 um. it is known that the absolute value of maximum current density in this sample is 10.4 lit/cm2 and the average mobility of holes throughout this sample can be approximated to be 400 cmz/V-sec. Find out the hole concentration at x=0. Can you think of a situation (e.g. for a practical device) where such a profile of hole concentration may appear? {4 pt] 35”” 3’: (Lb? £5??? ../"/ \ El; . ”Mirwewjmha. u , ,f/l/Ir 1 ‘11 le ’JVP X CL, x '\A X {D 4 {1371/ /'A! l by“ — \ \T 4 am y 0 x: I EX“) F- [Cl “:5 fizz-ml) [i a l‘LMo xqomo‘ofléx A ‘lD'F ’ ’__,;__W alcflwmmmn ' l‘ 6 7i l M M. 5*” w 20‘? p at o) »- KNEWMCW : ‘0‘ ~> ya a”. 1% Kit? "1 x amt) 'x Mai/3 $511 :0):07 “‘5 W3 terrier/v punt/em 4mnm M 5“: “Vi? . Heavy,“ _, TMS “ll/”(L hO‘PPW W? the (/OlW/(A'U‘im loose, juncgirimq Pr mp {‘Ymfléri‘S‘l‘Tf‘. (c) Assume that a Si sample'R/flength SOO‘um at T=300°K is uniformly doped with acceptors at a concentration of 2.5 x 10wcm'3. Following that, the semiconductor is compensated such that the carrier mobility comes out to be 400 cmz/v-sec. If 5V is applied across this sample, find out the current density. [6m] . \ k r p 1 “ . . t MA summer : ssm : - 1:?— F3 r1: Moi“[email protected]'y»2,~g§7\w17ma; ,0 Lm €100 ”my/Visgg', \l 1 (m: n l r Prob 2. [16 pts] (3) [10 pts] Consider that a Si sampie has been doped as shown below: (i) Briefly state how depletion region is created at the junction. [2 pt] lo Uri/FHA * t i ' i ‘ , CJ’KO’T‘ es; holes alt-{lust ”horn {3 lo n leaumgn’mmw'm “gab“ j ’ x p N ‘ \ la“ ,s Sh'fiféi elutrons thii‘tfms ca. from Vi if} P “10““ “9 WMWL meo ”‘5’ PO {Vi/1W3 as; (ii) Find out the built in potential at T=300i<. [2 pt] K L) ’U ’034 V L 10 V“ % ”L- ‘” V‘” “4’ "Tao "i W, - “1- N 3 ‘M‘¢”“’ 1 EN 4 x O‘OQ :: (3‘84 V] 0 (iii) ifthe two sides of the sample is now shorted, do you expect a current to flow due to the built in potential? Justify your answer. {2 pt] \nm A no; beam/(st: toi‘ii/iow.i-- 0m Oittieii‘wi Wilmer: d/‘WW‘M WWY‘W owvets sent the: deali- i/iri-'*r‘i."‘€fi’t—t:“. platen/lain, x l" ”i Isl-Tim, “the bw‘ii-i‘n pai-miini towi‘lctwp to mom—M W “W“ “WW/W2 ”1 M" to rum, 0 m Mimi‘s; a; ~f"lm:i~ (iii/Lt it) uCi‘Fl‘i‘f‘i emf-if? WA Mi 'Y'Y"i\i7"f' (1W1acm:€”’1”“cfi1:enm Obi/Y rs 3 'Hn a? fim My» . (iV) Draw the charge density and electric profile for this junction. [2 pt] 3C2 charge, Partfvle. film/MC lily/id P‘m’ile‘le - (V) Qualitatively explain what happens to charge density and electric field when a reverse bias is applied as opposed to equilibrium condition. Justify your answer. [2 pt] \ The ehol’gé Will-Fla will be bottled/WA. TlM‘s tS lot cams 1?. rt. Your/m: lm‘os uncovers additional immobi‘le LhO-Wlffi 9”” ”"5 ju ncta‘cm . r' ~. .\ _ but to wa‘démd chat-«ye, profile. 'lhé peak i»"lt6lW1C 'l‘iilél ’43 lithe, \ n m h n ”Mid . ilk] 0 lie that e1 6 ch? to ' tho-Me 95 {W M lad Willa "(Ml ”‘9 - ling chm/9 c: th’M-a"l“¢3 . (b) A on junction diode will be designed such that: (i) the p side is much more heavily doped than the n side (ii) it has a built in potential of 0.72 V and (iii) at Vappned=—O.88V (reverse bias), it gives a capacitance of f‘aOfF/(um)2 (1 femto= 1045). Find out the doping concentration for acceptors and donors. Clearly state all the approximations. [6 pt] N i 1 ‘ MOJ‘ Dds _L_ N 9: M. W :2 (31,54, ({Ua"?\ 75D CVb;[email protected] 70’) “ LKJAKDAMH dQ/lm Via/P 1:) an A 9ng gw- 0L 59: q, _, QJQQL .7- W lq T“ Ha HA Va: L L“, WHITMLM (a- r"— ‘fi‘ 0 Ligtfliw =~ E'Xlog F/W‘” ‘ . W ’0‘“ 65‘ Lei/VHF)“ 3 _,, rm ”7‘21 Ham (1) Mon W vlvg'xwm X 10 WW A“; {3710 M310?” ‘3‘“ MW “”TZTW 3" waw— 215M; {1-4 a} m» «ML fifi‘ 169“ ‘xWwalgi’wm Q ELI/Lb LINK/{Mal 1:. VHF? w U {3'33 6 -:- [930)“ng ,., ((3 BLUE-,- "H/CQ Wfi‘rlv] viola.“ Elm, WM 3:, (bode. Law/10f be. olmrrgmi ( w;,,;_;;.:;. W q £5-“flgL3‘fi um M a}: UA é VMP :- --~0‘8r€s 1/0 hr; mum/L (Emma, M) Q MA at S/Ct\8r'h+bb abbfim 1W )0 y»?! +- m paii’wfimm «NW D 2 4% U '4 wa+uA: waor \ MaNbilloi MEETS-x- 53; 10 .) M: V EL 90 17me MD M IBM) (/1013 3 [9mg :04 y :0 arm Prob 3. [14 pts] (6!) [3 Pt] (i) For a BJT biased in the active mode, what are the mechanisms of carrier transport at the Base-Emitter and Base-Coiiectorjunction? [2 pt] B 053‘? . 1Q ‘r‘i’i M ilfifi'rHM‘m) DIHTAS 30% Boise cm Ir firearm—ma bvi‘i—b - (ii) What are the two major mechanisms that can contribute to the base current? What steps are taken to minimize their effects? [2 pt] m IDI‘f-i'iciisirm. 244,10 4er W (53 ‘(iflO‘r‘Yi)91\"n6’r‘i“{‘071 in my EGSE “ “ ‘ “' 7‘ ,. ”waist/a T23 mix/Jimmie cifiimc/rony Lmfli-m is much W16“ WUW‘U ’6) mam 17m, basa- Fo minrimi‘z-L YéwmbfwaHWJ base YEIQK‘OM 11;, mate S'htr‘rt O’DYHPQ'T'fi' ”*9 my)“ dtte'rmind Ligm-fmsfli‘o aniw Hffiflifflfl» (iii) How is coilector doped with respect to the base (more heavily or more tightly)? Why? [2 pt] GONE/Ltd?” CS mO'YQ [AC-9V1} U3] Oidfwi {”6 ‘M»?w»i‘m2\?-g:.. {MW/'14:) leg-fenci. ‘ (iv) What happens to the early voltage if base doping is reduced? Why? [2 pt} \ , E ,‘4 emu/HM" b01512, $0?!ch mega/m wen.) My " -‘ ’ “ W remix amt: ‘ SmaiiiZ/Y’ 1mm mm by, acidihmai r/ m (My mm (Sibel/'1‘? 03L COHiLi‘WYK-«boigg, dLochmd Ytglfia’m ‘3?qu x.” 3 Wéb Tht‘s; mamas 11¢ rum btwmz. W K) V5! 0L. § tmigm fut Y] (Hm 0'38 V6,}; 9 Th Cg . x‘ ..I_ q .. j Cit.” mom 3 “(3 MN! {inseam W1 W1 in " mm m WW5 w"-""{" ‘C ‘ J VON-age k151i drew-'9é4egfll (b) {7 pt] (i) Assume that for the transistor shown above, VBE=O.8 V, {3:2 and RE=1 k0. if to make sure ic=1 mA, ch must be at least 0.4 V, Find out the minimum Vcc that is required to get |c=1 mA. [5 pt] _ r- I , PL ' g VLB >! D 4 U V8 :2 0 8. “V EC; (.1. I" a 3?]; - K V :; Vt J V6, “VB ),0 4V ? (L (,2 :O‘¢§+ f0 E’XngVi “lg/kw Vat.» ngl— O‘4V :ng» i‘S‘" ,__ R‘%\/ (ii) Draw the small signal model for the above transistor including RE and assuming that there is an independent small signal source in series with the DC source V35. [2 pt] CL», (‘ ~W’uma,=wwfiH—.19WM% V0 (3 u, 1;. a. to W . N. l m «w .3 W0 “33...... s: was VT» 26 A” '4 ”fl;- :25 “Q” ...
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