1. ECE 875: Electronic Devices
Prof. Virginia Ayres
Electrical & Computer Engineering
Michigan State University

2. Lecture 19, 21 Feb 14 Chp. 02: pn junction: HW05 solutions
Double charge layers
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3. 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 = ?
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WDp = 0.07 mm

4. Two ways to finish: use Method 01:
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5. Use slope to find N:
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6. Use intercept to find ybi:
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7. 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

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

9. Assume: Si at 300 K
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10. For mixed type +n1n2 doping, find: WD ybi E max NA-(x) and ND+(x)
E (x)
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11. VM Ayres, ECE875, S14

12. What are the two places that you know any E info for?
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13. Answer: E 02 (x = WDn) = 0 E 01 (x = 0.2 mm) = E m-02
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14. VM Ayres, ECE875, S14

15. Connect back to E m-01:
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16. Get:
E m-01 = simple f(WDn)
VM Ayres, ECE875, S14

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

19. Find ybi: Method 02: get a value in V:
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20. 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