EECS 40 Midterm Exam 2, Spring 2000 - Microelectronic Devices, Exams of Electrical Engineering

Download EECS 40 Midterm Exam 2, Spring 2000 - Microelectronic Devices and more Exams Electrical Engineering in PDF only on Docsity! Page 1 UNIVERSITY OF CALIFORNIA, BERKELEY College of Engineering Department of Electrical Engineering and Computer Sciences EECS 40 Spring 2000 Introduction to Microelectronic Devices Prof. King MIDTERM EXAMINATION #2 April 6, 2000 Time allotted: 80 minutes NAME: ______________________________________ ____________________ (print) Last First Signature STUDENT ID#:____________________ 1. This is a CLOSED BOOK EXAM. However, you may use 2 pages of notes and a calculator. 2. Show your work on this exam. MAKE YOUR METHODS CLEAR TO THE GRADER. 3. Write your answers clearly in the spaces (lines, boxes or plots) provided. Numerical answers must be accurate to within 10% unless otherwise noted. 4. Remember to specify the units on answers whenever appropriate. 5. Do not unstaple the pages of this exam. SCORE: 1 __________ / 20 2 __________ / 30 3 __________ / 25 4 __________ / 25 Total: __________ / 100 EECS40 Midterm Exam #2 Spring 2000 Page 2 Physical Constants Description Symbol Value Electronic charge q 1.602 x 10-19 C Permittivity of vacuum εo 8.854 x 10-14 F/cm Boltzmann’s constant k 8.62 x 10-5 eV/K Thermal voltage at 300K kT/q 0.026 V Properties of Silicon at 300K Description Symbol Value Thermal velocity vth 107 cm/s Relative permittivity εr 11.7 Intrinsic carrier density ni 1.45 x 1010 cm-3 Electron and Hole Mobilities in Silicon at 300K Conversion Factors 1 eV = 1.602 x 10-19 J 1 µm = 10-4 cm = 10-6 m Farad = Coulomb / Volt Henry = Volt / (Ampere/second) Watt = Volt x Ampere Joule = Watt x second electron mobility hole mobility EECS40 Midterm Exam #2 Spring 2000 Page 5 Problem 2: Transient Response [30 points] a) In the circuit below, the switch has been in the closed position for a long time. i) Find the value of vR just after the switch opens (t = 0+). [3 pts] vR (0+) = __________ V ii) How much energy is dissipated in the 1 kΩ resistor after the switch is opened? [2 pts] Energy dissipated = __________ J b) In the circuit below, the 5 µF capacitor is initially charged to 5 V (vC1(0-) = 5 V). (The 1 µF capacitor is initially uncharged.) The switch is then closed at time t = 0. What is the final value of vC1? [5 pts] Final value of vC1 = __________ V 5 V opens at t = 0 +_ 5 kΩ 1 kΩ1 µH + _ vR 5 µF closes at t = 0 2 kΩ + _ vC1 1 µF EECS40 Midterm Exam #2 Spring 2000 Page 6 Problem 2 (continued) c) The following is a circuit model for an NMOS inverter, in which the transistor is turned on at time t = 0: i) What is the value of vC at t = 0-? [3 pts] vC (0-) = __________ V ii) What is the value of iNMOS at t = 0+? [3 pts] iNMOS (0+) = __________ A iii) What is the final value of vC? [3 pts] final value of vC = __________ V iv) Neatly sketch the graph of iNMOS for all t, labelling the axes. [5 pts] v) Write an equation for iNMOS as a function of time, for t > 0. [6 pts] Equation for iNMOS : ________________________________________ Rload RNMOS VDD +_ VDD = 5 V Rload = 90 kΩ RNMOS = 10 kΩ Cload = 10 nF t=0 Cload + _ vC iNMOS EECS40 Midterm Exam #2 Spring 2000 Page 7 Problem 3: Op-Amp Circuits [25 points] Assume the op-amps in this problem are ideal. a) Consider the following circuit: i) Find an expression for Vo as a function of Va. [6 pts] Expression for Vo : ________________________________________ ii) Find Vo for Va = 2 V. [3 pts] Vo = __________ V iii) For what values of Va will the op-amp be saturated? [6 pts] Values of Va for which the op-amp will be saturated: __________________________________ +_ 20 kΩ 40 kΩ + _ +_ 20 kΩ 10 kΩ 6 V + _ VoVa 15 V -15 V EECS40 Midterm Exam #2 Spring 2000 Page 10 Problem 4 (continued) b) If a diode is operated only within a small range of forward-bias voltages, its behavior can be accurately modelled by a resistor, whose value is dependent on the bias voltage. Derive an expression for the diode “small-signal” resistance: in terms of the saturation current Is, the bias voltage V, and the absolute temperature T. [5 pts] Rdiode = ________________________________________________________ c) Plot vL vs. VIN for -10 V < VIN < 10 V on the axes provided, for the circuit below. Note that the diode is a perfect rectifier. Label the axes. [5 pts] Rdiode ∂I ∂V ------    1–= VIN +_ 5 kΩ 10 kΩ + _ vL +_2 V vL VIN H a noto at 40 EECS40 Midterm Exam #2 | > OLU Tle Ns Spring 2000 Problem 1 Circuits with Dependent Sources [20 points] a) Find ¥,. {4 pts] le + sma (ft) LO kK S40K0 10 i, 1k OF, - 0 — DKA Current divider formula’ (= jen? Foun") V,=_—/O0 Vv = |mA Vp 210i xf(OkR j= 10< 1 mANCIDKIL) = - /00 7 b) In the circuit below, the independent source values and resistances are known. Use the nodal analysis technique to write 3 equations sufficient to solve for V,, ¥,, and V, To receive credit, you must write your answer in the box below. [6 pts] fg DO NOT SOLVE THE EQUATIONS! Doty Le suptrn ode * R> f 10: : reference. node : Va , L= 2 => Value of dependent vo ba ge | faurce. = fOg = 10 (a/R, ) Write the nodal equations here: Note that phe ihty tiskrramrrrs in fhese €9 uathiors are Va Va —V Wa V, V4, ——— _ b c. Node a: fyat Ry t en O pe? SOL ‘ | real Vb ~ Va Vb + Van 1 Me =O “FP Supernod€: fe» ~ Re v Ry 7 MV VerM, = lO relahonziug wae fo Mependiend souete! Page 3 EECS40 Midterm Exam #2 Spring 2000 Problem 1 (continued) c} Consider the following circuit: 3k x, ON y 1k2 Wy > MM 8 mv) Vy it TKQ vy SVSkQ ‘ob i) Find the voltage /,». [5 pts] , AV , Fy Vin 60 Vv 1 ER. FO-Wn . 7 We Applying KCL to node x* “3,5 = L420 = Ale, at FER FO ~Ux = Dye =? VRE TV - av : , . V ty > Get imA 5 tat O => Vig= Uy = 200, (BkA)= 60 ii) What is the current /, when the terminals a and b are shorted together? [3 pts] ZO, =2ROmA hie aA ig -le mA Te |p . 2kn iby Current Ayvider formule : b oe BRL t ~ Oe —7D = a jpn pen! 20 mA ) 1S mA iti) Draw the Thevenin Equivalent Circuit. [2 pts] Vn = Ve c= Vi, b from pat ti) Thevenin Equivalent Circuit: Voc. VAb from port fe) | a Ky, 7 Fe 4 | Tee ta om part fst) ' kA | _ _ bev v 60 / i | i | | | | | ob Page 4 EECS40 Midterm Exam #2 Spring 2000 Problem 3: Op-Amp Circuits [25 points] Apply KCL at (-) node: Assume the op-amps in this problem are ideal. a) Consider the following circuit: Va Vn ms Vo 7 Yn ideal op-amp technique! 20 kQ Ra Rp veurrints Flowing inte input Hreunals = 0 ~ __ eb (V4-%%) + ‘voltages at input terminals ace equed Vo Ra * ” ” Ra 10kQ = Since tp= O, WE Can use the vo Mage — divider formula: Ry Rel => V,= Re, [Ma "Re #Ryf Ve | aa i) Find an expression for V, as a function of V,. [6 pts] This is @ aitference- am pliffer cir cutt Fuahe ich you've studied tn the lab) with Vp = Gr (G-Va) = 2(b-Va) Expression for V,: ii} Find V, for ¥, =2 V. [3 pts] V,z/2-2(2)=8V y= 8 ov iii) For what values of ,, will the op-amp be saturated? [6 pts] Ve = /2-2V,. ™ Va. = (12-Ve 4 2-15 By, V, satnrated at ISV + Vas “ETT 72 iz-(-15) 29 Vo saturated at -ISV? Va = =F Se Vv Values of V,, for which the op-amp wili be saturated: Page 7 EECS40 Midterm Exam #2 Spring 2000 Problem 3 (continued) b) In the following circuit, the op-amps are operating linearly. V out = _, R \ NN ~ oe OO “ YS inverting amplifier : Ve = “@, — Find V,,,,, in terms of V), ¥>, Ry, Ry, Rs, Ry. (10 pts] (Hint: The superposition method might be helpful here.) Find the individwued combributons of each Volta ge Sourcé = Vg = Oo, so the circurt simpli Hes to a simple +V + OV: ) * ° inverting amplitper R2 &, Cireurt simp hi ties +p simple non-inverting amp lets br ic) Set V, te OV: Add the contributions of tach source Together : 4 Ro Ry Vout = Vout + Vout = eV, TO wm (i+ 2) Ve Pe ke ~ Ri Vv ~ 3 } i¢ z ) Vo Pout = Page 8 EECS40 Midterm Exam #2 . Spring 2000 Problem 4: Semiconductor properties; p-n diodes [25 points] a) Consider a silicon sampie maintained at 300K under equilibrium conditions, uniformly doped with 1x10!° cm phosphorus atoms. The surface region of the sample is additionally doped uniformly with 3x10!° em‘? boron atoms, to a depth of 1 ym, as shown in the figure below. Phosphorus soa donor uniformly doped with 1xi0!® cm? P and Boren fs an acceptor 5x10!° cm? B a = in bem 3 - Mp = 70 em ™ hs, I P lum = /0 Yom Mg > &« 10cm? uniformly doped with 1x10!* em? P —> Np = 1078 em H ne Schematic cross-sectional view of silicon sample i) In the figure above, indicate the type of the regions (I and II) by labelling them as sq" or “p” type. [2 pts] ii) What are the electron and hole concentrations in Region 1? [5 pts] Ny > Np » anal Na >> WH; Se P* Nar Np = 8x10 = jxio'’s ¢xj0l n= F256 om? 2 a ne {A ¢sra? ) ‘6 pn en; => viz pr PXIO em? Po He 1078 = 5256 iii) What is the sheet resistance of Region I? [5 pts] ! i ® 7 bart GH OP ~ Zep p R,=_ 4458 Q/square From plot on Fage 2, LP 3250 cm efVis for Na tN, = 6 10 Fem 3 ~k te ks = = guppt iy) Suppose any voltage between 0 V and 5 V can be applied to Region I. What fixed voltage (“bias”) would you apply to Region II, to guarantee that no current would ever flow between Region J and Region II? Briefly explain your answer. [3 pts] Ta pre vent Current from Flowing we neeot to ensure that the. Region II bias voltage =__- 5 -V pon junction wil) never be r biased. Thus, the n-fope region muse o€ biased to ward ¢ Page 9 ar SV oer higher. “] = [ W-o2x10" 250) (4x10") (10-*) | = F458 SL/D