Midterm Solutions (2)

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Electrical Engineering

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Jan 9, 2024

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E C E 121B Midterm Name: ________ _ Read the question and the possible answers before attempting any calculations. Write your name on the front of each page (tests may be separated for grading purposes). This test is closed book. You may use a calculator and a single 8.Sx 11 sheet (back and front) of formulas. This can include the sheet that I provided to you earlier with your own formulas on the back. Secdon 1: Muldple choice (50%) (50 pts.) Circle the correct answer. Any problem with multiple answers circled will be marked wrong! There is no pardal credit on the multiple choice questions. Some of the answers are obvious by looking. Look and think before calculating! - 1. (4 pts.) Two otherwise identical transistors on the same wafer have equal base transit times but are biased at two different collector currents such that Ic1 = 2}o. What is the ratio of the diffusion capacitances of the two transistors, Co1/Co2? a. 1 C. 1/2 d. 1/4 ) C V= G, ➔ C o< Qa. µ"'"� tAKA. y s -to Jo .,."':s ea.rie:s+ ;"�;'hvt.. , :::r. -= Qg :I. e. CK. Qa C. - 'T-t- So C,n � pz. -= Ic.;£ 2 2. (4 pts.) An npn transistor has a common emitter current gain(�) of 1000, and a unity current gain cutoff frequency ( ft) of 100 GHz. What is the approximate minority carrier lifetime in the base? - 3. a. IO nanosec b. 0.3 µsec + Vcr,2 Jg 2 :.- 1£1 So I c. 2, � pJ J � ft (pi g ,) - � p. 'Z.. 1 ,. , (4 pts.) Two identical transistors are hooked up as shown above. Common- emitter current gain of each is I 00. Assuming they are both in forward active mode, what is the approximate ratio of Ic2/ls1? b. 10 C. 100 d. 1000

1.0E+OO 1.0E-01 1.0E-02 1.0E-03 1.0E-04 1.0E-05 .s 1.0E-06 _j 1.0E-07 1.0E-08 1.0E-09 1.0E-10 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 VEa (Volts) .1c .. i. ,o - 4. (4 pts.) The Gummel plot shown is for a silicon npn transistor with base doping of N a = 10 15 . What is the approximate value of the common emitter current gain (P) at a collector current of 10 mA. IO "" ), = l O • / D - 3 P,, :- / o :3 a.1 b. 1000 c.100 � - 5. ( 4 pts.) At high current, the current gain of the transistor in problem 4 has been -::: ,o reduced by... r\O n icl e a. l .I c. a. Collector Resistance � b. Input Series Resistance c. Generation Recombination o. High Level Injection 1nJ,•c41i-le.S H, 5 '°' �t l,.�e.�11\ - 6. (4 pts.) An ideal transistor is biased in common emitter mode. If the collector current is 20 mA, the common emitter current gain is 100, and the load resistance is 50 n, what is the approximate small signal voltage gain? G3) b.2000 c.20 d.4000 -l 20 •IO - 5 0 -3 2" • ,o ,If °'\+� o ""Sk ; ,., rlAr �;es Y-e.sisn."ce.. C4\,,\.s-e.s 1,., --t-,Q C.'4r'1e.. (-i. +lrc. -' r � 1J ;+ Joes ,to+ ,-eJu.ce c.'4ue�.,. .5ct.,',, UCLA Henry Samueli SEAS

Name: --- - --- -- 12 10 8 + u 4 2 I 0 0 - .-. 0.5 ' I 1.5 VcE (Volts) Is = 50 µA Is = 40 µA 0 2 2.5 7. (4 pts.) Referring to the common-emitter le-Vee chara � ic above. The transistor with the above characteristic is biased from � supply (Vee = 2.5V) with a 250 Q load. V BE is chosen such that the base current is 25 µA. What is the approximate collector-emitter voltage (VcE) across the transistor? a. 0.1 V C. 0.4 V d. 0.6V - 8. ( 4 pts.) The transistor with Ic-V CE as shown above with the same 250 Q load and biased such that le = 4 mA. What minimum LiVsE (change in VsE) is required to d1ive the transistor into saturation? a. l V b. 2.5 V . 0.02 V d.0.5 V I -f I >J I\ ,.., } 0 11 5 -j-� /o�J. J,·., e... not(:_ -:rhi:.t- "' c = ,'t'I-\-,.,. .... A _-, r\ 1 ,·l'\ 5 ;�-tv.:"t)oV"\: '/.:,u. "ee.d 1 s +o dou.lol-e. --f..) .5 e..t i°o'\"h Sc::;.--\...,.-c,-t--i.)"' l;, 1,1 --t- 1..i i's C::.>'l e,cpMetlii·c.J +;:, .... c"h·o"' o+ 1 B = 20 )"A -f..o Sc;+-....r�--h·Z)" I5 -::,- L/O Y'- A- � ½.IJ.; T 1B2 = l/0 )-< A- =- .J..o e �V, /kT I I) I � ').o rA -== J_D e � (v2 - v, )/4, 2 = e 9 VBc; 5.::> i'+ 01\JI + .. lJ � -lc\,\J v\-\: Yi vol-,._s. See ar1� G--um ,,..e I ?lo-t- � ye,.,, •--hi l J:ke >eG-ti..,,2.] J5 � 0 _o\A zsi:> =- ,o,,,A

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1.0E+01 1.0E+00 1.0E-01 1.0E-02 1.0E-03 1.0E-04 - al 1.0E-05 - 1.0E-06 1.0E-07 1.0E-08 1.0E-09 0.00 0.50 1.00 1.50 VaE (Volts) C 9. (4 pts.) In the transistor with measured Gummel characteristic as shown above, find the approximate base shunt resistance REx in the model? � 'c. ')( c.. +7.fe c.. +s -rl.... a. 4Q b. 100 MQ d. 40.Q -fy4,u,'ii-o r a. + low .le. I< ;v 0, I == 10 7 _fl_ £.x ~ 10-8 10. (4 pts.) You've used a one dimensional simulator to solve for excess minority caniers in the neutral base of a transistor (W = 0.5 �tm). The model gives an equation for Lin(x) as follows (with x in �tm): Lin(x) = 10 10 (3.16x 2 - 103.00x + 50.71) ( / c m 3 ) What is the base transport factor? a. 1.000 UCLA Henry Samueli SEAS b. 0.985 C. 0.990 J.c <:>< slo ye. c.t vv J_ �n/2x / � ,...,, -v [0, 3 2 x -1D3 J x ::-w :o.s - ( 0 3 99. i tJ /v Jo3 0. 97

Name: 4. � ��' 3. e. "'" ��As e- }'r- C ' . \ � � 2. �o � � � � te '6 ga 1. Ee Jr-Y 'V 0. ------- Ev - l . 0 100 200 300 400 500 600 700 800 Position (mn) The plot above is a faithful band diagram of an electron device calculated using an accurate Poisson solver. The electron energy scale and position in the device are accurately depicted as are the conduction and valence bands and the quasi-Fermi levels (dotted lines). Use this graph to answer the questions below by inspection (no calculations are necessary). The dotted lines a, b and c are reference planes referred to below. 11. (2 pts.) The order of externally applied potential from greatest to least is as follows: a. V, > V,;>V, �v,;;,3) c. V,;>V, > V, d. V, > V, > Vo 12. (2 pts.) Minority carrier particle flow and current direction at bare as follows: a. particles __.. -+ current b. C. particles +-- <I- current d. particles -4--- current 13. (2 pts.) The band diagram represents the following device type: � b. HBT c. pnp BJT d. pin diode 14. (2 pts.) The neutral base width in the device is about: a.400run b. lµm c.lOnm � run J 15.(2 pts.) In going from b to c electron potential energy changes by about: � b.l.l eV c.3.l eV d.OeV elec.1Yon s �re.. r"linot";+ 'l C4r<;e v-J i" +k p- 7 yrc- 1>,se � flt'_ , b \ f' tv2..'leV +.o 1vo.1eJJ vi 1"�c.e '" Got\o�c.�o"' a.t'\ d'- 1vo�

ection 2: Problems (50%) Show your work. Full credit for the correct answer with work hown. S n ible answers (correct order of magnitude) ge t partial credit. Generous partial credit for an incorrect an wer with th correct idea if clear and brief. egative credit for irrel .evant or incorrect equations (nev r less than zero but can negate some positive credit). #1 ,. : #2. "-v-' sW b Na B = 1 Q 17 1. (50 pts.) Two ilicon npn bipolar junction tran istors are shown schematically above. # I is the "nominal" transi tor #2 differs from the nominal by having a ba e v hose width i scaled bys (scan be great r or less than one), otherwi the tran i t r are id ntical. (assume W i/ L n << 1 in both transi tor . Ignore depletion effect in the ba e ... assume Wb and sWb are the neutral ba e width . ) a) (l 5 pts.) Giv n that tran i tor #1 ha an emitt r injection effic i ncy of 1.000 and a common emitter current gain of 50 find the scale factor s that will result in transistor #2 ha ing a common emitter current gain of 00. Assume ideal beha ior and state any other a umptions clearly. G; \1€M_ -t-ho.➔ Wb 12." << ) We. k�ol,.., s t...-: I ) b-e. P-> = � �I I � -ti P-, ,_ = 1)00 � �-c, - 'Lt. 1. 50 �. 2.. 6lA.-t- 4 ex.. w So /lo == � (Continued on next page) UCL Henry Samueli E S le$ 5 ��t;" S-o sWb/2_" << ) l't'n-2 !'(, fl ; .S o. Cot;S n. "T of 1"t;1.. r� ,.__ �,c. l �-r c:4. f �-t 6t"\ >';i.e. ot k �c:. l(o 1 _J_ 'L-t.' Wb So -2.. s' - (swb) ?:-t "L �ls-* I

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b) Name: ________ _ (10 pts.) On the plot supplied below, carefully draw the excess electron concentration in the base as a function of distance from the emitter depletion region edge (0) for both transistors (and label clearly #1 and #2). (The Wb shown on the plot is the neutral base width of# 1) Assume V BE is the same for both cases with exp[ qV BE/k.T] = 101 and V B C negative with exp[qVBc/k.T] <<1. Use the same origin for both transistors, you need not plot a numerical value on either axis. Full credit for getting the ratios right between the two transistors. If ratios are not right, partial credit for getting right which one is bigger/smaller along which axis. c) (10 pts.) Derive an expression for the ratio of the emitter current of transistor #1 to the emitter current of transistor #2 for the same V BE• Your answer should be in terms of the scale factor, s, and other constants (do not replace s with the numerical value you found in part a). (only the simplest accurate expression gets full credit). /4, � I£n1 1t2 �Ibi2 1£� � d..6 t'L - cJx. x; = O JE/ :Ie>11 .6tto/Wb ::- s - � - - �ttvfiw'lfJ 2E. 2. :I.e11 i. (Continued on next page)

d) (5 pts.) Assuming the conditions in part a), evaluate the expression in c to get a numerical answer for IEillE2 - - _j_ 4 e) (10 pts) The idealized Gummel plot of device 1 is shown. Draw the idealized Gummel plot of device 2 on the same graph (to scale ... quantitatively correct). 1.0E-01 1.0E-02 1.0E-03 1.0E-04 1.0E-05 1.0E-06 1.0E-07 1.0E-08 1.0E-09 0 (Continued on next page) UCLA Henry Samueli SEAS ... ... . ·· --·-·- ··· ·-· . ' " n •••••••-•-••••••••""'' • .,._,,_,••-•-•---••••• _., • •-- ---•--•-• - . . •-·-- --·-·--·· . . '_,,.._, ., .... ___ .. _ . . •---· ... 0.2 0.4 VBE 82 · .. .. . • . ---, .. -, .. ------····-- .... ;· .·.· .. :· . ....... ............ ___ ····· . . ·-·-···---•--· 0.6 0.8 ::::: 1 C. 2 f.,'L 1c,/8; = 4._!_ If,

• Name: _ __ ___ _ _ _ f) (0 to 10 pts. EXTRA CREDIT) By assumption, in the assumed ideal case, transistor #2 has a vastly superior current gain to transistor #1. List non-ideal limitations that we discussed by name (or a short description) that affect #2 more than #1. Remember that you are given that the transistor structures differ ONLY in their neutral base width. Your score will be based on the difference between Right answers and Wrong answers (so don't just make a list of limitations ... create a numbered list of only those limitation you are reasonably sure affect #2 more than #1) You will get full credit just for the list and correct names. If you can't remember the names you will get credit if you describe the idea in words and pictures. A J J s"�� J. IA ,,; I\ ) -tlz. �:J'tet'� ., 1 w'5 look:� -G... �J or ne5 Gl""h �e ie.C:�ds oC re.J \A. ca'"S b�s� 1.u.'d-t-h . (1+ yol.4 wv-o+e do� ... 7 ° ti�� cl-s' d. S4iJ.. .... � ""� ros/-+1'>1e_ 1 yov.. d:J"";. lose "V)'l c.reJ,:+.) I. 2. 3. +I � + 2. � + :s "? + Ii/ o-r tl\oW'"' '- 3 5 7 ) ,o

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