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# HW5 - ECE 3040A 1 2 5 Georgia Institute of Technology...

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Unformatted text preview: ECE 3040A 1. 2. 5. Georgia Institute of Technology School of Electrical and Computer Engineering Homework 5 Due: Friday 996/2008 in class (20 points) Pierret 3.18. (20 points) Pierret 3.22. (20 points) Pierret 3.24. (30 points) Electrostatic analysis of a linearly graded junction: For a linearly graded junction, the doping proﬁle can be represented as ND-NA = a x, where a (in units of cm'4) is called the grading constant. The extent of the junction is -Wr’2 < x < WXZ. For this junction, ﬁnd a. Electric ﬁeld E (x), electric potential V(x), and built—in potential Vbi. Also plot E (x) and V(x). b. The width of the junction (W) in terms of Vbi and the applied voltage VA. 0. Junction capacitance C}. (15 points) A Si p+-n step junction is doped with ND: 10IS cm'3 on the 11 side. Calculate the junction capacitance per unit area with a reverse bias of V A = -10 V. 3.18 The earth is hit by a' mYsterious ray that momentarily Wipes 01“ all minomy Gigi-5' Majority carriers are unaffected. Initially in equilibrium and not affected by roortl- 3: T-ha uniformly doped silicon wafer sitting on your (1551‘ ‘5 gawk by the my at time I F ' a wafer doping is N",L = 10Wcm3. 1'“ = 10-6 56°: and T = 300 K“ (a) What is A” at I = 0+? 0 = 0+ is an imperceptible fraction of a second after t = 0.) (b) Does generation or recombination dominate at t = 0*? Explain. - ' ' . . . — + ‘ (c) Do low-level injectiOn conditions extst 1nsrde the wafer at t — 0 ? Explan- (d) Starting from the apprOpriate differential equaliml. derive Anna) for r > 0‘ 3.22 As pictured in Fig. P322, the x > 0 portion of an inﬁnite semiconductor is illumi- nated with light- The light generates GL = 1015 electron-hole pairslcm3-sec uniformly throughout the x > 0 region of the bar. CL = 0 for): < 0, steady state conditions prevail, the semiconductor is silicon. the entire bar is uniformly doped with ND = Iﬂlsfcnﬁ. ‘r — ,andT=300K. - +—-—> x o . Figure P322 (a) What is the hole concentration at x = — 9e? Explain. (b) What is the hole concentration at x —f +00? Explain. (c)- Do low-lech injection conditions prevail? Explain. (d) Determine op“ (x) for all x. NOTE: (1) Separate dpnh) expressions apply for x > 0 and x < 0. (2) Both Apn and ddpnldx must be continous at x = 0. 3.23 CdS is the most widely uSed material for constructing commercial photoconductors operating in the visible portion of the spectrum. The CdS photoconductor has a high se'n- sitivity and its spectral response closely matches that of the human eye. A model VT333 CdS Photoconductor is pictured in Fig. P3 .23. _ 3 24 The equilibrium and steady state conditions before and after iltumination of a semi- conductor are characterized by the energy band diagrams shown In Fig. P3 .24. ‘3'" = 309K, :1 = lO‘olcm3 fl, = 1345 cmZIV-sec, and up = 458 crnli’V-sec. From the information i ‘J n . provided, determine D (a) no and p0, the equilibrium carrier concentrations. (b) n and p under steady state couditions. (c) ND. ' ‘ ' 'u ' t d9 Ex lain (d) Do we have “low-level injection" when the semiconductor 151 umina e . p . (e) What is the resistivity of the semiconductor before and after illumination? E. E: ' E‘ F” o 313 eV ............. _- Fr E. E. .. (a) Before ' (b) After Figure P3324 W‘VZ'JR')‘ ...
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• Fall '07
• HAMBLEN
• Semiconductor device fabrication, Extrinsic semiconductor, Ion implantation, steady state conditions, cadmium sulfide

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