ECE 875: Electronic Devices Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

Lecture 19, 21 Feb 14 Chp. 02: pn junction: HW05 solutions Double charge layers VM Ayres, ECE875, S14

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: + 0.95 V WDn = ? VM Ayres, ECE875, S14 WDp = 0.07 mm

Two ways to finish: use Method 01: VM Ayres, ECE875, S14

Use slope to find N: VM Ayres, ECE875, S14

Use intercept to find ybi: VM Ayres, ECE875, S14

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

Lecture 19, 21 Feb 14 Chp. 02: pn junction: HW05 solutions Double charge layers VM Ayres, ECE875, S14

Assume: Si at 300 K VM Ayres, ECE875, S14

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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What are the two places that you know any E info for? VM Ayres, ECE875, S14

Answer: E 02 (x = WDn) = 0 E 01 (x = 0.2 mm) = E m-02 VM Ayres, ECE875, S14

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Connect back to E m-01: VM Ayres, ECE875, S14

Get: E m-01 = simple f(WDn) VM Ayres, ECE875, S14

Find WDn: VM Ayres, ECE875, S14

Find ybi: Method 01: get relation to WD ≈ WDn VM Ayres, ECE875, S14

Find ybi: Method 02: get a value in V: VM Ayres, ECE875, S14

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