20111ee121B_1_EE121B_HW2_soln

20111ee121B_1_EE121B_HW2_soln - .20. .. .. r 3'...

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Unformatted text preview: .20. .. .. r 3' --" - - egg-1.2201111," ‘125o'm in Boater-67.31) " oneJami-gm Physical constants: 1. Electronic charge = 1.60 X 10'£9 C II. Vacuum Permittivity = 8.85 X 10:14 Flow III. Boltzmann constant = 8.62 X 1.0"” eV/K IV. Planck constant = 6.63 x 10-34 J—s V. Electron mass in vacuum = 9.10 X 10'“ kg General assumptions in all problems uniess specifically stated otherwise: 1. Temperature m 300 K H. Semiconductor 3 Silicon a. All necessary physical parameters can be found: htt :flwww.ioffe.rssi.ru/SVAINSM/Semicond/Si/index.html Introduction: The purpose of this homework is to consolidate your fundamental knowledge of I’ijunctions in preparation for your upcoming Bipolar Junction Transistor learning. The first question analyzes the electrostatic characteristics of a PN~junction under equilibrium. The second one analyzes both the electrostatic and current behaviors of the same device under externai voltage biasing. The third question asks you to predict the PN—junction switching transient response. The forth asks you to ‘experimentally’ extract the minority carrier lifetime from a practical PN—j nnction. (Hint: use Excei or MATLAB for both questions 1 and 2) ' I. - "1) .Nij' .tgunetlen’fslibwn. . . .- aljpiOXin.'13i_t.iQn " a) Calculate the builtfiin potential V0 ..1gui‘e iii 'Z'-.iit'iidéi€ fliétmfir’:-e'éfliiibtiflfli;lfiiiéiz'ihei-fiéiiiétioti' ' ' I Using equation (5-8) of Streetman and Banerjee, V0 2:53 In (“N”) = 0. 7164. V (assuming ngnlfiwem'g'} ‘1 "t2 I b) Calcuiate the depletion layer boundaries xpg and acne, and the depletion width W Using equations (5-21), (5-2321), and (5-2313) of Streetman and Banerjee, W: m V0 w+w) :9.661x10”5cm =W=9.566x 10-7 m x“) NA+ND c WNA N A + N D 0') Calculate the electric field at the metallurgical junction Using (5-17) of Streetman, Emax = mggND-xnfl = “g” (3) Calculate the electrostatic potential at the metallurgical junction E (x) z — 3 N A x, E xno z = 9. 566 x 10"5c'm mix“) = 1.479 x 104 V/cm with x measured from the edge of the depletion region on the pwside. So, V(x) m — f E(x)dx ziNsz v(x_,,{,) = Hing-{,2 57.9.7.5.x 10*“3V which is the potential at the junction with respect to the p-side, The potetitialjat the same poi-tittwithreSpe-cft the; ties-idle. I ' HEW. r.'.t'.- - n '—-’=S.i'de) #:ng .-' V'CWLr; tip” m--Sid93'-='7J97'5 1V ' I I- I I... ' __ . 53¢)" ' 'eitéh-ithc- ’ 'ii‘g'esgdeh'sitx;électfic.fieldg-and;e'zecnostaucspetgmial:fiétween’r-the: ” a“ . - - 2) For the PN junction shown in Figure 1 under external voltage biasing, a) Calculate the depletion iayer boundaries 39,0 and xflg, and. the depletion width. Wunder a forward bias of 0.4 V W— 26 V V (1+1)-6410x10‘5 - WND x?” 3 NA + NB WNA xn" NA + ND where VA is the applied voltage (and is positive for forward bias). : 6. 347 x 16‘7cm : 6.347 x 10”“scm b) Sketch thoexcess minority carrier grofllo within the two quasi—neutral regions under a for-ward bias of 0.4 v mth 3 ail-Eh?-Squasi'éfiéfnfi'i._iiieV¢Ié3i5éiW¢¢11. ' d) Calculate the ratio of current due to hoie injection from the 19— into the nnregion to current due i0 electron injection from {he n— into the p~region under forward biases 0104 V and 0.6 V Using the equations (5-29), (5-30), (5-39), and (5-40) of Streetman and Banerjzee, n-2 11.2 _ ,3. qV/kT _ m. _5_ qV/kT ._ Ap — ND (e 1) and An — NA (8 1) qALp qALp 113 I w A = m- qu/RT — 1 P Tp p rp ND ( ) 2 I m qALn m qALn n, C qV/kT _ 1) n tn In NA We have, I L 1.” N i _ p " A = 22 In LnTpND independent of bias. e) Calculate the same ratio in d) under reverse biased of 5.0 V and 1.0.0 V Same as above ---':howf-=k1¢rifaétorsa aeizéx-pécicd std =:affs¢1i-fl’ie:fiobsérvc ram. lecture,squared: . .. . . . . . .. . . . . -- . . e'htf-Q’Figuliéf-z .2C0.11T?ii1575fh¢31-3 .becamegreasesi (pfliirj-trmiSient,_"E¢r':f¢aéhgar-inc.'i‘griWing'ieaséis; 35'31ietcii._iyi_rith a.-'_soli'd.};iine . the excected modification to the baseline trans'ieii't"('sh0Wri' as :a dashed line) arid briefly explain 'ycu'r resiflts: i(l) (a) ('3) (c) Figure 2 In - *Ufih +0 (em {a a»! v S at: me, Q a) 1;: is decreased to [p’ with IR being the same‘.» hogs Ska“; 0“ 5 r r ‘ ‘J‘ b) [R is decreased to IR ’ with I; being the same way {Siwa PM“ Wk; 10%” mg L c) 1}) is increased (maée Eonger) with both 1F and I}; being the same Mafia/ac f0 mcrim‘aim WW? %, fire wig?! wawa magi 1‘“th ion, Moira i0 Wen mm chm/{Ifaw %%{3& 1)) / so aromas side? We, wiii Mamie. 4) (Design Question) You are given a [fl-n junction diode and access to electrical measurement tools (LV measurement tools, Capacitance measurement teols, Oscifloscepes; eta). 'You..1.<n0-W.rhe- dopinss in”: the. diode» but you-do nothaY-saccesS to any tables-in book's men the in't'ernet. Devise an experiment to measure” the minority carrier-_.iife_time in the nficped region; ...
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20111ee121B_1_EE121B_HW2_soln - .20. .. .. r 3'...

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