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Unformatted text preview: You must provide your name on the answer sheet. In addition, you are asked to voluntarily “provide” your social security number in order to verify your identity and avoid confusion between “two students“ with the same name. Your social security number is sought for identification purposes pursuant to Public Law 93—579 and is being used as part of a system of "student" records that has been in effect prior to 1970. If you do not want to provide your social security number, you must write on the answer form an alternative identifier. [An alternative choice “would be” the University ‘Net-ID’ (network identification name) or the 9-digit blue number on each person's I—card]. ECE 440 H Spring 2006 Name s-al’n Net ID# Section ECE 440 - EXAM N0. 1 Thursday February 23, 2006 7:00-8:30 p.m. ROOM ASSIGNMENTS Room 100 MSEB K.C. Hsieh Section C, J. Tucker, Section E, S. Bishop Sections X and G Conflict Exam #1 — Thursday, Feb. 23, 2006, 4:00-5:30 p.111. Room 245 Everitt Lab. NOTE: This is a closed book and closed notes exam. Unless stated otherwise, do your work on the page of the problem and if necessary on the preceding blank page. It is mandatory that proper units be included exglicitly along with the numerical value for each term in a quantitative calculation, showing how the units of the final answers are derived. Failure to do this will result in an credit. Circle our answer. Be neat! For each roblem ou must show complete work and indicate your reasoning. No credit will be given if you do not Show the complete work and describe our racednre even if the answer is correct. Write your name, ID#, and section on this page and Sign below. Signature: Your Exam Score: l. A silicon sample is doped with 8x1014 Sb atoms/cm3. The donor level is 59 meV away from the conduction band edge, i.e. EC-ED=5 9 meV. (a) (10 points) Determine the electron and hole concentrations at 300 K under equilibrium conditions, and sketch 3 energy band diagram. Label clearly EC, EV, EF, and Bi. Assuming that 131 coincides with the center of the band gap, and the band gap energy is 1.1 eV at 300 K. N >>n MAX 360k on Wm adfwfw'fiw Layer a N I a W I =- 5 ml W; 2 gum/3 rev he z 8119'“ 0"" Ep‘bx n°=n‘Wf—-—:';}"_‘ “L (b) Assume that the F ermi—Dirac statistics applies to electrons in energy bands as well as with impurities. At temperature Th, half of the antimony atoms are ionized. Answer the following questions. (bl) (4 points) Is Th higher or lower than 300 K and why? . ‘~ . . 1 at l'kMW'C-S lM-m . Wwfi tau $6!» twfmd'scL I2 szVK-S a): 300K mos-r shun” atonws chm-J4” “gave” Mmdmsldlew” l - “‘41- CW: 6. 1MPW ‘5 3 1:3de mm 390K WM cm;é,a, 90 TL (b2) (5 points) Sketch a schematic band diagram for the material system at temperature Th. Label ciearly EC, EV, ED, BF, and E1. Assuming that E coincides with the center of the band gap, and the band gap energy increases to 1.12 eV at temperature Th. n __L —' - “: U - b - aw “i “W “WEE?” z p t qumw 5:" W at?» .---.--._-_ _______, E". (b3) (6 points) Estimate the physical number of this particular temperature Th. Assume that . . . . . _ 18 the intrinsic carrier concentration ni : JNCNV exp(—Eg /2kT)72.31xlO exp(-Eg/2kT). -v (1:111, nurde=¢xioZ§ M Ewe: EF “'54: h” =n,- in: ) :8 "Eg/z (EF'Ei) “ma—"W an. (J 43%; Edi-Ea : .3! 0 ________..._. My 2 x1 mpfi m, ) l Fifi-’9) ‘3 63/2 55/2. *(Ef-‘E‘l -‘- 2.3mm “low [g -0.05? = 2,3tflo £10? .6“- ” gush/MAI [sunk = :HOK __-——--‘—' «tamer-aw =r Th: asamw 2. A small Si bar at 300 K is uniformly doped with phosphorous to a density of 6‘211016/0m3 as sketched below. L=O.1 cm (a) (7 points) Determine the average drift velocity Vx of the carriers (including sign) in Gin/5.. plan a. 4L . _-.- aa___ _‘.’_. segmo 9.1 1 V)f .jAns 3‘ vs Macaw s (b) (5 points) Use your result in part (a) to calculate the current density (Afomz) inside the bar. ‘ (c) (7 points) Calculate the conductivity of the bar and its resistance for a cross—sectional area of (100 pm) 2. 6:ZHDMH : IMHO—15c. icxiokbcmdic 3w =16? elm)" I = A-6'{~ : (Ivoxlo‘l‘om )2 X 153%?“ r mo it = 7.6?Ma-2Afl R: _V_ =_13_‘L~—-——- * 3°“- : 7.58xio‘1A-r (d) (6 points) If a second ddping with boron at 3x1016/Cm3 is added to the initial phOSphorous doping of 6x1016/cm3, how would the following quantities be affected (higher or lower) and Why? . . 15 Gamer densrryz LOW heme hoeup—NA = 3:004; 16 Mobility: LOW 19me 85 wave Cflkfllwwcfi) it‘d/WW9»; (“4*N4:$x‘°/‘:f) '13 “MIR mob: EU I. dWl Resistance: Hljkw bcww. r?) be?!» éawq uww A silicon sample that is uniformly doped with 1 x 1016 /crn3 As atoms is continuously illuminated (steady state) with light that generates a spatially uniform concentration of electron hole pairs (BI-IF) An = Ap = 4 x 1014 cm‘3. Assume that In = 'cp r— 5 tts and that T: 300K. (a) (2 points) Determine the optical generation rate gop (form—s) during the steady-state illumination. Fw- cm n—‘t‘fyu, Say-WPLL , Mics wt. 11M w‘wwH} wn‘ws. H: AF =¢x1023 << thlxwéj) So Lcw-«iuwe WW‘M lwlats 4F 4310iq‘4w3 9 l? _~_- . 1-. _____ 2 -_.—...—_.—-.—-——-— "—' XIO .4? go? 1-? =3) 80f I} fl‘o'bSM W34“ (b) (4 points) Determine no , p0 , and the total steady—state concentrations of electrons (a) and holes in the sample. lb . . m and = lxw C.’ Nd »"l--) ” °‘ 43 10 9 = n“ = AUX"? 2 2.25m: Po X, Wu {.3 a: H’ atom:- .oer rt: haw-53;; = new" “('0 “H I é 1;. Mn ML _ .= +4 = LLDCIO 1-4er 4: +340 P- [Jo-+5?“ P. P /3 (c) (4 points) Calculate the resulting steady—state positions of the quasi—Fermi levels relative to E; , that is, F” - El- and 15- — Fp. n Fn‘EC Pt= :wf’ ‘ ‘fu [b Lafitte _. FL -... ———.._—__—.—-: =1? F'rbc t {QT-J“ n; _ 0.023? an. I‘mmm 0.334.89/ I EFF? fun. Map—E:— 1U- ,z- - «tum =,t<+w :r E; F,» ts£~—;1L;~—fi-fl$? Imam H (d) (4 points) Draw a simple band gap diagram for this Si sample and sketch in (and label) the positions of the quasi—Fermi levels relative to El- (assume E; is located at mid—gap). (6) Assume that at a point in time (t = 0) the steady—state illumination ceases abruptly, and the excess carrier concentrations begin to decay (recombine). (cl) (5 points) Determine sufficient data points to plot the decay of n(t) and p(t) as a function of time from t = 0 to 20 us on the empty graph provided, (e2) (6 points) Referring to part (b) above, mark and label the positions of the steady-state concentrations of the majority carriers and minority carriers at t = 0, and indicate the contributions of the photoaexcited EHP, An and Ap, to these total, steady—state concentrations. - t - -x/tP £n(t)=-Ay\g /t"‘ (afimaymt) luau?“ Cu" 7i») - '4 HF -% a? e P : 41:10.! :1 0.367?= M14110 43 «to 2. SFUFWIHI 34173 5': 496 G 3 = lf-Klemiafill-‘ig = (Mm; 4;; 1. q" :4mom‘ 140.0183 : isng/cma = 4X10”): 9.1353 3* g-‘HKIO'ZQ 6p<Jr=15MJ=4P€- Jrcrwwml’fi' FzPD-fgffli) fL=ho+8mH lb 1 a“ [OIXKOIL — Li- I c . _ mum — 1"” "’ Vii-3203* ,1, t nit) 10 A ‘T’ E O V — 3‘ to'5 U) : 4mg“ a, m. D “Haida (D B PoTSIHt) I g S‘HXIDB :3 CD [511110 U K 13 "- Lu W 7.33Xio 1:. [9 0 2'4 6 8101214161820 Timeous) 4. Shown below is the band structure of a non—uniformly doped Si sample at room temperature. With reference to this diagram, answer the following questions with comprehensive explanations. Toss—Q2. "—QSS'W {r 0.15 8V 0.2 EV O 0.5 cm 1.5 cm (a) (4 points) Determine the net current through the sample. The not WYM “‘0 W bwsem SWQ L}, M WM“: tfiwhalleI-Mm. (b) (6 points) What is the direction and magnitude of the electric field at x = 0.5 cm? I aE-L’tiv' £- 3 &x 90:05am - 4(0'35wfl‘6w) (we. HM {amt the“: 75am an.“ lama?“ ‘4‘ 0-5“ ) y g 1% - :: (AF—v— Cw. —- . 3 x (III—WIM- Mm a M01 W “"2 fl“ POEM (o) (8 points) Determine the carrier concentrations at x=0.5 em. (1X XW’ISM tA‘EF 2 EL'EF : (5):”; WP( 0" ) ‘3l3x16?3 Pf“ W? k 0.02:1 0M 2. 3 - h“ — ISHD 3 N-$:*3 4: (d) (7 points) Assuming that the hole mobility is 400 omz/V—s, what is the diffusion component of the hole current at X = 0.5 cm? AH ark W .. 3-? = o - 3;, *5? . # ~de :. — .— I] — Man1 v Tf.l3><w xtwox 9.5' ll —5 = ._ 2.13 m ‘ &<deflw 454%. «fowM “U .3113 £132— Om -. 10 ...
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