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ECE 875: Electronic Devices
Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University
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Lecture 19, 21 Feb 14 Chp. 02: pn junction: HW05 solutions
Double charge layers VM Ayres, ECE875, S14
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As grown n-type epitaxial layer
Find the thickness of the depletion region WDn formed in the n-type epitaxial layer Under bias condition: Vrev = -1 V, for which WD is biggest. Given WDp-max = 0.07 mm. Find WDn-max Vext = Reverse: -1 V As grown n-type epitaxial layer p+ substrate Equilibrium: 0 V Forward: V WDn = ? VM Ayres, ECE875, S14 WDp = 0.07 mm
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Two ways to finish: use Method 01:
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Use slope to find N: VM Ayres, ECE875, S14
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Use intercept to find ybi:
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For mixed type pn doping, find: WD ybi E max NA-(x) and ND+(x) E (x)
2nd easiest to find: Easiest to find: VM Ayres, ECE875, S14
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Lecture 19, 21 Feb 14 Chp. 02: pn junction: HW05 solutions
Double charge layers VM Ayres, ECE875, S14
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Assume: Si at 300 K VM Ayres, ECE875, S14
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For mixed type +n1n2 doping, find: WD ybi E max NA-(x) and ND+(x)
E (x) VM Ayres, ECE875, S14
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VM Ayres, ECE875, S14
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What are the two places that you know any E info for?
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Answer: E 02 (x = WDn) = 0 E 01 (x = 0.2 mm) = E m-02
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VM Ayres, ECE875, S14
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Connect back to E m-01: VM Ayres, ECE875, S14
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Get: E m-01 = simple f(WDn) VM Ayres, ECE875, S14
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Find WDn: VM Ayres, ECE875, S14
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Find ybi: Method 01: get relation to WD ≈ WDn
VM Ayres, ECE875, S14
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Find ybi: Method 02: get a value in V:
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Solution: backtrack: Potential drop: ybi = ybi: set value = relation which is f(WDn) WDn is related to E Solve for E m-01 = E max VM Ayres, ECE875, S14
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