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

2. Lecture 27, 19 Mar 14
Chp 04: metal-insulator-semiconductor junction: GATES
Examples
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4. Chp. 04: MOS: Gate Chp. 03: Interconnect Chp. 01: Si Chp. 02: pn
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5. Use energy band diagram to find:
p-type Si
Use energy band diagram to find:
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6. Use energy band diagram to find: Electron concentration in channel
p-type Si
Use energy band diagram to find:
Electron concentration in channel
V requirements: battery = $
E –field/Vi across the insulator: breakdown not good
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7. Usual approach: Q(x) E (x) V  y(x) Everything else
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8. Usual approach: = d E dx The total charge density is
The Electric field is a function of the charge density.
The potential is proportional to the Electric field
The surface charge is:
= d E dx
∞ means deep in substrate
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9. Example 01 (will be a continuing problem):+
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10. Answer: = 2.32 x 104 cm-3 In forward bias: b = 38.6 V-1 @ r.t.
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11. Example: what is the electron concentration at x = 0?
= 2.32 x 104 cm-3
In forward bias:
b = 38.6 r.t.
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12. Answer: need yp = yp(x) = 2.32 x 104 cm-3 In forward bias:
b = 38.6 r.t.
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13. Can find potential yp(at x=0) using strong inversion condition:
2 x yBp =
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ys = yp(x=0)

14. Example:
Evaluate ys in strong inversion condition for example problem 01 with NA = 4 x 1015 cm-3
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15. Answer:
yp(x = 0) =
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16. To find yp(x) (and therefore concentration) must use this approach:
Q(x)
E (x)
V  y(x)
Everything else
Will get E -field first and also wanted to know that
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17. Electric field and potentials: in inversion:
Breakdown info here
concentration info here
New: the potential drop across the (ideal) insulator Vi
Metal = battery potential: V
p-type Semiconductor potential: yp(x)
Semiconductor surface potential:
ys = yp(x=0)
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19. LD : the Debye length
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20. Example:
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21. Answer:
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22. Can easily find E (x=0) = E s:
Take the square root of E 2 in eq’n 10 and use yp(x=0) = ys to evaluate:
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23. Can easily find Q(x=0) = Qs:
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24. Example:
Evaluate Qs for ys = 0.67 V
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25. Answer:
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28. s
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29. Note that an important part of the concentration we’d like to know could be defined as charge/area under the Gate (different than usual units)
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30. Example:
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31. Answer:
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