Exam 1 Solutions - Microelectronic Circuits | ECE 3040, Exams of Electrical and Electronics Engineering

Download Exam 1 Solutions - Microelectronic Circuits | ECE 3040 and more Exams Electrical and Electronics Engineering in PDF only on Docsity! ECE 3040 Microelectronic Circuits Exam | February 20, 2008 Dr. W. Alan Doolittle Print your name clearly and largely: S OQ ly Yan S Instructions: Read all the problems carefully and thoroughly before you begin working. You are allowed to use | new sheet of notes (1 page front and back) as well as a calculator. There are 100 total points. Observe the point value of each problem and allocate your time accordingly. SHOW ALL WORK AND CIRCLE YOUR FINAL ANSWER WITH THE PROPER UNITS INDICATED. Write legibly. If 1 cannot read it, it will be considered a wrong answer. Do all work on the paper provided. Turn in all scratch paper, even if it did not lead to an answer. Report any and all ethics violations to the instructor. Good luck! Sign your name on ONE of the two following cases: 1 DID NOT observe any ethical violations during this exam: lL observed an ethical violation during this exam: First 33% Multiple Choice and True/False (Circle the letter of the most correct answer or answers ) -_ On\y 1.) (3-points) True False Various energy bandgaps can be produced in research laboratories This 2 using either MOCVD or MBE tools but these tools are not suited for large scale manufacturing / (due to theixowsgrowth rates resulting from the atom by atom layering they implement . ~~ 2.) G-poinisf Truc r False: The bandgap results from the splitting of energy levels, typically the s and p subs bias of atoms. 3.) (3-points) True a ‘The term (1-f(E)), where f(E) is the fermi distribution function, describes the-probability that a state at energy E is occupied. 4) (3-poinsy Trusr False: Since both energy and momentum must be conserved when electron- hole recombination happens, indirect semiconductors require a phonon (lattice vibration) to allow the transiti cur. 5.) pe Tae False: Strong atomic bonds lead to large energy bandgaps. 6.) (3-points{_True or False: The density of states predicts that at energies equal to the bandgap energy (E= e there is no available state for electrons to occupy. 7.) (3-points\ True or False: Impact ionization occurs under very high electric fields when electrons slam into atoms and knock free another electron. fet 1S False Select the best answer or answers for 6-10: 8.) (4-points) The minority carrier diffusion equation ... a.) ... can predict drift currents . OD cannot be used when drift current is present ©.) ... can determine the majority carrier concentrations if one also uses the law of the junction to _-—~ felate n to p. ( 4.) ).. is a simplification of the current continuity equation. -) ... is something I really do not understand and thus I might not pass this exam! 9.) (4-points) The valence electrons ...? a.}- Disappear when the crystal is formed. _b3)Participate in bonding the crystal’s atoms together, c.) Can be captured by an acceptor thus creating a free hole. a) Cannot be promoted into the conduction band unless they are in a direct bandgap material. 10.)(4-points) The following energy band diagram indicates the material is: a.) Degenerate and n-type E, b.) In equilibrium ¢)Non-degenerate n-type Ec- 3kT / Degenerate and p-type an low level injection ) Non-degenerate p-type g.) In steady state seruj? i4 Solution 1S 6 ne Pulling all the concepts together for a useful purpose: 14.) (30-points) An infinite length of GaN semiconductor is grown in a Clemson University epitaxy reactor. In the middle of the growth, the Clemson student drops his gold wedding ring in AA : the growth system creating midgap y t impurities, enhancing Shockley - Read 9-14" An if 0 - Hall recombination, resulting in a region of very ‘high Ssecombination. In this defective region, the minority carrier lifetime is 0.0 seconds indicating zero excess minority carriers in this region. Next to this defective region is a region of very high minority carricr lifetime, 10_ c nanoseconds. The sun has been shining uniformly on the entire semiconductor (including x=infinity ) for more than 10 seconds and is uniformly absorbed, generating Jel7 extra C electron-hole pairs per cm per second in the defect free region. If the semiconductor is held C«- at room temperature (27 degrees C), determine the minority carrier diffusion current density at all positions in the semiconductor. Assume a minority carrier er mobility of 4.0 cm ?/Vsec. Defect Free Region 1 Since (O¥ee PI? NOns, soe = °° ty ro, sean” adn, An, A= A, 4! = VNOZE cm Voce Given: 0= D,— 34-4 General Solution is: An © fe = Ae - dx” t, Nae @aAn, An, . | “ =F Gin Given: 0=D,—"-—*.+G, General Solution is: An, (x)= de + Be Pr wblemn de q,, ’ _ d°An, —_ Given: 0= D, —— General Solution is: An, (x) = A+ Bx dx” Lat), tn. . d’An, 2 _s Given: 0=D, 5—+G, General Solution is: An, (x) = Ax’ + Bxt+C > BAKO cw dx OO Fum °An, G Given: 0=D,—* +G,,, f(x) General Solution is: An, (x) =| — 222 x)dx |+ Bx+C "he 10 p D ay “| N 10 & dAn, An, 0) . Given: sot General Solution is: An, \t)=An,(t=O)e -* k= \ di A= Am=9) — Lh give pee! AGiven: 0=-—£+G, General Solution is: An, =G,t, > lo fo c ohete CFR PESO H be | Ae K=O) Qpad fRey > iw Miaos hy Carries Pasion Use this page for additional work. Angls)= Ne. Be Lhe, Since @ x20 Lrylx)= 0 Sry (a) =O Since @xn 0 Brplk)= On, BIO ter Ang (x) +e be Cin ite. At Br 6c.tn, is Togerber =v A > 6. oy Lng ls) = 6.4, CI -—e ee “) ag le) Mal) oP" cme? x70 Dye Jn (c= £0 ee X20 nzhot dn & p. oe Lor x 70 ole old ax ax =? J. (x)= QO For X20 4 On6.D pr O forxeo J Ge): E bis Alem ea PPP oe A hin® =O