Lecture_13

Lecture_13 - PN Junctions Summary Midterm Results p-n...

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1 Prof. J. S. Harris 1 EE243. Semiconductor Optoelectronic Devices (Winter 2010) Midterm Results p-n junction diodes •Depletion approximation •Forward current •Other currents in diodes •Generation-recombination •Recombination •Photocurrent •Tunneling Practical diode structures •p-i-n diodes •Heterostructure diodes •Schottky diodes •Ohmic contacts PN Junctions Summary Prof. J. S. Harris 2 Midterm Results
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2 Prof. J. S. Harris 3 EE243. Semiconductor Optoelectronic Devices (Winter 2010) Form of conduction and valence band edges in real space for a junction between p and n regions in same material in depletion approximation Obvious that value of built-in voltage, V bi is separation of the Fermi levels (chemical potentials) between the n and p materials. This remains true, even for degenerate doping V bi is also difference in energy (in eV) between conduction band edges (or the valence band edges) on either side of the junction In practice, Fermi levels (chemical potentials) in n and p materials usually within several k B T of "bottom" of conduction or top of valence bands, hence V bi almost always relatively close numerically to the bandgap energy, E g (in eV), of material. pn homojunction depletion approximation Prof. J. S. Harris 4 EE243. Semiconductor Optoelectronic Devices (Winter 2010) De±ne junction at a point x = 0 Edge of depletion layer on p -side is at a point -x p Edge of depletion layer on n -side is at a point x n Density of acceptors on the p -side is N A Density of donors on the n -side is N D . Because effectively zero mobile carriers in depletion region Net charge densities are entirely from ionized dopant atoms hence from Maxwell ʼ s equations in depletion region on the p - side (- X p < x < 0) (4.43) (4.44) and on the n -side (0 < x < x n ) where E x is the electric ±eld dE x dx = ρ ε = e r o N A dE x dx = = e r o N D Depletion layer width at zero bias
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3 Prof. J. S. Harris 5 EE243. Semiconductor Optoelectronic Devices (Winter 2010) Field must be zero just inside conducting p and n materials, so E x = 0 at x = -x p and x = x n De±ne ±eld at x = 0 to be some value E max ,formally integrating Eq. (4.43) gives and similarly for the n- side of the junction (4.45) (4.46) (4.47) i.e. dE x 0 E o = eN A ε r o dx x p 0 E max = eN A r o x p E max = eN D r o x n Depletion layer width at zero bias (2) Prof. J. S. Harris 6 EE243. Semiconductor Optoelectronic Devices (Winter 2010) Now integrate ±eld to obtain voltage (since dV/dx = -E x ) Voltage from edge of depletion region on p -side, up to junction is and similarly, voltage from junction to edge of depletion layer on n -side is (4.49) (4.48) V p = eN A 2 r o x p 2 V n = eN D 2 r o x n 2 Depletion layer width at zero bias (3)
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4 Prof. J. S. Harris 7 EE243. Semiconductor Optoelectronic Devices (Winter 2010) We know that, at zero bias deFning total depletion layer width, w d , we have, substituting from Eq. (4.51)
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This note was uploaded on 06/05/2010 for the course EE 243 taught by Professor Harris,j during the Winter '10 term at Stanford.

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Lecture_13 - PN Junctions Summary Midterm Results p-n...

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