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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.
- Spring '10