ee3161 spring10 lecture note 6

Its common to assume that the fermi level on the

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Unformatted text preview: ) = ND ￿ n(−xp ) = n2 /NA i NA ND n2 i ￿ kT Vbi = ln q EE3161 Semiconductor Devices Sang-Hyun Oh 21 UNIVERSITY OF MINNESOTA Exercise: p-n+ junction Compute the built-in voltage Vbi of p-n+ step junction. It’s common to assume that the Fermi level on the heavily doped side is positioned at the band edge, i.e. EF=EC in a n+ material. qVbi = (EC − EF )p−side = Eg /2 + (Ei − EF )p−side n+ region p region p(p−side) = NA = ni e(Ei −EF )/kT Eg Vbi = + kT ln 2q 22 Ei − EF = kT ln EE3161 Semiconductor Devices Sang-Hyun Oh ￿ NA ni ￿ ￿ NA ni ￿ UNIVERSITY OF MINNESOTA Quantitative Relationships: for E(x) Step Junction with VA (applied voltage)=0 Note that E=0 everywhere outside of the depletion region. Therefore, one obtains for the p-side of the depletion region: ￿ x −qNA /KS ￿0 , −xp ≤ x ≤ 0 dE qND /KS ￿0 , 0 ≤ x ≤ xn = dx 0, x ≤ −xp and xn ≤ x dE = − ￿ −qNA , −xp ≤ x ≤ 0 qND , 0 ≤ x ≤ xn ρ(x) = 0, x ≤ −xp and xn ≤ x 0 dE dx = dx ￿ E (x) 0 ￿ x −xp qNA ￿ dx KS ￿0 23 qNA E (x) = − (xp + x) KS ￿0 EE3161 Semiconductor Devices Sang-Hyun Oh UNIVERSITY OF MINNESOTA Solution for E(x) Similarly on the n-side ￿ 0 x dE dx = dx ￿ 0 dE = ￿ E (x) ￿ xn x qND ￿ dx KS ￿0 qND E (x) = − (xn − x) KS ￿0 0 ≤ x ≤ xn E (0)p−side = E (0)n−side EE3161 Semiconductor Devices Sang-Hyun Oh NA xp = ND xn 24 UNIVERSITY OF MINNESOTA Maximum E-field Emax qND qNA =− xn...
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This note was uploaded on 02/24/2010 for the course EE 3161 taught by Professor Prof.sang-­hyunoh during the Spring '10 term at University of Minnesota Crookston.

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