Connected - Microelectronic Devices and Circuits - Solved Exam, Exams of Microelectronic Circuits

Download Connected - Microelectronic Devices and Circuits - Solved Exam and more Exams Microelectronic Circuits in PDF only on Docsity! UNIVERSITY OF CALIFORNIA, BERKELEY Coilege of Engineering Department of Electrical Engineering and Computer Sciences EE 105: Microelectronic Devices and Circuits Fall 2007 MIDTERM EXAMINATION #1 Time allotted: 80 minutes NAME: SOLUTIONS (print) Last First Signature STUDENT ID#: INSTRUCTIONS: 1. Use the values of physical constants provided below. 2. SHOW YOUR WORK. (Make your methods clear to the grader!) 3. Clearly mark (underline or box) your answers. 4. Specify the units on answers whenever appropriate. PHYSICAL CONSTANTS Description Symbol Value PROPERTIES OF SILICON AT 300K Electronic charge q 16xloP?c D Boltzmann’s constant k —-8.62x10%eV/K _ Band gap energy Thermal voltage at 300K. p= k7/q = 0.026 V Intrinsic carrier concentration Ki Dielectric permittivity sj 1.0x10"? Fem Note that Vp In(10) = 0.060 V at 7=300K Electron and Hole Mobilities in Silicon at 300K SCORE: 1 425 2 125 3 130 Total: 780 Page |  Fol Prof. Li 2007 [ce10s Mipterm *41 Securions “ Problem t {25 points]: Semiconductor Basics a) Consider a Si sample of length 10 uum and cross-sectional area lum’, uniformly doped with 10" cm’ arsenic, maintained at T= 300K. | Voit is applied across its length, as shown below: 1 Voit +-)= V7 7 1 pm + ietalli 10 | etal contact “mn contact 4) What are the electron and hole concentrations, # and p, in this sample? [4 pts] Arsenic is a donor in silicon =) Np= 10m? Nye 0 Since Ny > Na) this Sample is ne Pope. n= Np~Ng = 108, 3 A 12 ae - n2 pe nA = em 0 tema = 120 cow ii) Estimate the resistance of this sample. [5 pts] From ploton Page | uy, = 300 cm? Ves ! cesistuity = Benny spp ™ an since. N>>p OZ D~ tim tox po bem = 20003. L resistance R= 0A =(0.02 n-em) (2 1x 107? om iii) Qualitatively (no calculations required), how would the resistance of this sample change if it were to be additionally doped with 2x10'* cm™ boron? Explain briefly. [4 pts} Boron is an acceptor in sificon => Ngr2xiolF ean 4 The sample woulol be converted te po type rnottrrek : oft = ~ = 12-38 Clame majority -cacrite with hele concentration P®Ng~Mp = 10cm Came: major ty: beboce ), Since the hole mobs itty is lower than the electron mobi ity, tre resizlance of the sample. weuled racréase » ©) i) Accurately sketch on the plots below the /,-Mcr and /c-Vcr characteristics (for OV < Vog < SV) of an NPN BIT operating at 7’ = 300K with Js = 5x10™ A, 6 = 200, and Vy = SV, biased at Mpg, = 0.72V. [6 pts] Note that ¢° 7206 = 197, fg [uA] 4g [MA] 100+. F 10 80 — 8 60+ ee 6 40 ++ eee 4 20+ 2 0 +—_+—_+—_ +" "+> i: 0 9 1 2 3 «4 «6 ‘ e—— BIT 15 in deep seduyehian. (re< pre) for Vee < 0672V _ BEN e. 2.7 te¢ (lt = -) =(Ex10"* A) e -(en"™)bvo"V(as ) = for Vo 2 Ov, Tc¥ SmA For Veg = SY, Te = 1OmA ii) Draw the small-signal model for this BIT, biased at 3; = 0.72V and Vo:=2.5V. [6 pts] Indicate numerical values for the small-signal parameters, and label the transistor terminals. (Nate: ro = Va/Te nominal Where Lc pominat 18 the collector current for Veg << Va) At Veg =2EV, I= SmA (14220) = . me. SKA | 5 Am Vr Qesev = 0129 @ 200 wo | & memento ee gon > «O 1" Gm> eas = o4 6402. Doziye Bren A IS . | gE Steg te enn naan) Page 5 Problem 3 [30 points]: BJT Amplifiers a) Consider the BJT amplifier stage shown below, operating at 7= 300K with a bias current fc = 0.1mA. Assume fy = 1x0°A, 8= 100, V= 3¥02 Vee =3V Tf Iy<<,, 10ka Ry Te then V, V, “gee (2Y) By Vi=tv oat oo, eka Check assumption i By-1¥ T= 200 nh >> Ig = = i) What is the value of Ri? [pts] Mer = Vee - Tete ~ Te Pe Veet, (Rethe) tor te Vy In (S)=o.028 ba \ pow 0.026 tn (10) = l2xg.02 28 Ln (ie)=0,72V ve a * tH a u a¢ P Tet ie m= <OlimA Vin~ Ver IN -G.72V + = 7 b nena \ Ve = Ver + Te Re => Ree mao oxo 8A 228 kr | ii) For what range of Ac values is the BJT operating in the active mode? [4 pts] For the BIT +y be ia achve mete, Vout > Vy: = _ Vee“ Viv Vee ~ Te Re 2 Vy => Re s << ce re = ZOKsL iii) Draw (in the box provided) the most simplified circuit that can be used for AC analysis to determine 4,, for Rc = 10 kQ, C; is large, so that its impedance is negligible at the small-signal frequency of interest. Labe| indicate-numerical_valuesfor the various circuit elements, but DO NOT SOLVE FOR A,. [6 pts] Por Ac analysis: * Short Nec +o @ND * Short Cy + at loka Skt Sy yee 2 vy Vin, b) Consider the circuit below: i) Is this a common emitter, common base, or emitter follower circuit? Justify your answer. [2 pts] * Input signal is applied -to the enutlte, . =) Commen base topolo3y * Output signal is taken fromthe coffector, SS ii) Derive expressions for the voltage gain (4,), input resistance (R,,), and output resistance (R,y.). [LO pts] ‘You may assume that the capacitors C, and C, are large, so that their impedances are negliaible a You may assume that the capacitors C, and Cy, are large, so that their impedances are negligible at the small-signal frequency of interest. You may also neglect the Early effect (ie. assume /’, With the capacitors Sherted, the cireut+ becomes: Ke Ret Re iii) Describe one-of the design trade-offs involved, when selecting the value of Rc. pss ‘To achieve high voltage gaia, Re Should be large — bet then & large Ry results in larger Rout (which is andesirable for an amph fer) anol reduced headroom (Uinuting the Page 7 . ; y output voltage sutiey ),