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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 NDNA = 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 Gigi5'
Majority carriers are unaffected. Initially in equilibrium and not affected by roortl 3: Tha
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'“ = 106 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 lowlevel 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 electronhole pairslcm3sec 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 lowlech 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 cmZIVsec, and up = 458 crnli’Vsec. 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 “lowlevel 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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