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Unformatted text preview: EF,P EF,N Reverse bias VA < 0 EF,P EF,N EE3161 Semiconductor Devices Sang-Hyun Oh 33 UNIVERSITY OF MINNESOTA Boltzmann’s Law
Walls at uniform temperature T P+dP n(h) dh P Ideal gas
Unit area of cross-section dh n(h) = n0 e−mgh/kT
h f (E (h)) ∝ e−E (h)/kT This is an example of the Boltzmann distribution: The density of gas at any point is proportional to e
EE3161 Semiconductor Devices Sang-Hyun Oh -(energy)/kT
34 UNIVERSITY OF MINNESOTA Q: Fermi-Dirac vs. Boltzmann Nondegenerate f (E ) = 1 1 + e(E −EF )/kT
Fermi-Dirac ≈ 1 e(E −EF )/kT = e−(E −EF )/kB T ∝ e−E/kT
Boltzmann EE3161 Semiconductor Devices Sang-Hyun Oh 35 UNIVERSITY OF MINNESOTA Boltzmann Distribution in PN Junction
Electron energy Density n(electron) x x p(hole) From Boltzmann law: The ratio of carriers on the two sides of the junction is given by
Np (p side) = e−qV /kT Np (n side) Nn (n side) = eqV /kT Nn (p side) (Electron potential energy) = -qV (Hole potential energy) = qV
EE3161 Semiconductor Devices Sang-Hyun Oh 36 UNIVERSITY OF MINNESOTA PN Exercise: p-i-n diode P
xi − 2 i
xi 2 N The p-i-n diode shown above is a three-region device with a middle region that is intrinsic. Assuming that p- and n- regions are uniformly doped (NA and ND), qualitatively sketch (a) charge density, (b) electric ﬁeld, (c) electrostatic potential inside the device, (d) the energy band diagram under equilibrium. What is the built-in voltage drop between p and n?
EE3161 Semiconductor Devices Sang-Hyun Oh 37 UNIVERSITY OF MINNESOTA PIN Diode x x Electric ﬁeld Potential x x Energy band diagram
EE3161 Semiconductor Devices Sang-Hyun Oh 38 UNIVERSITY OF MINNESOTA...
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