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

2. Lecture 32, 31 Mar 14 Chp 06: MOSFETs
pn junctions/Depletion regions (examples) Channel Current IDS (n-channel p-substrate)
VM Ayres, ECE875, S14

3. Chp. 04: MOS: Gate Chp. 03: Interconnect Chp. 01: Si Chp. 02: pn n-p-n
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4. Qs ys ys For examples: VGate Si @ r.t.
Substrate is p-type with NA = 4 x 1015 cm-3
Matches Fig. 4.5
Does not match Fig (b) Qs ys ys
VGate
VM Ayres, ECE875, S14

5. Example: What kind of pn junction is this: forward bias, reverse bias or equilibrium?
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6. Answer: Equilibrium: earth to earth. Continue Example: Find WD
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7. Answer:
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8. Example: M-O-S depletion region is identified
Example: M-O-S depletion region is identified. Find full inversion. + VG
-  gnd
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9. VM Ayres, ECE875, S14

10. WD = WDmax = WDm for low frequency operation
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11. From Lec 31: Fig 4.8 (a): after strong inversion, increase Qm  increase Qn while QDep and therefore WD stay the same.
Low frequency
High frequency,
Slow ramp
High frequency,
Fast ramp
WDmax is bigger
WDmax is biggest
Qn layer; no time to form at all
Qn smaller
Qn biggest
VM Ayres, ECE875, S14

12. n=channel p-substrate “knee” in Vfor  strong inversion.
For VG less than value for strong inversion:
Can find ys(VG) as in Pr using equivalent of Fig 4.10 (b).
Note: this is Fgi. 10 (b). C-V in Fig (a) shows that this  low frequency operation. ys
VGate
Warning: Fig is for NA = 1 x 1016 cm-3 not our example!
VM Ayres, ECE875, S14

13. Example: Is there an electric field across the channel region?
Sub-question: “across” in which direction? + VG
-  gnd +
VDS
-  gnd
VM Ayres, ECE875, S14

14. First check coordinate system:
Chp. 04: MOS: Gate
Chp. 03: Interconnect
Chp. 01: Si
Chp. 02: pn
n-p-n
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15. First check coordinate system:
Take “across”  Drain-Source: E (y)  “0” < y < length of channel L L z
Width = Z y
SiO2 x
Width of gate/ charge sheet under gate in a MOSFET is called “Z”. It is a dimension in e.g., cm. Don’t confuse with atomic number.
VM Ayres, ECE875, S14

16. Answer: Yes. There are (different) electric fields in both the y and x directions.+ VG
-  gnd +
VDS
-  gnd
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17. E (y) is due to the potential drop across the channel:
Answer:
E (y) is due to the potential drop across the channel:
e-’s move by F = q E (y) drift motion in the channel. + VG
-  gnd +
VDS
-  gnd
VM Ayres, ECE875, S14

18. Example: Is the shaded region an E (y) -field region or a pn junction depletion region?+ VG
-  gnd
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19. Answer: Mixed. May have different field properties than channel.
See Pr + VG
-  gnd
VM Ayres, ECE875, S14

20. Same here, see Pr. 02. + VG
-  gnd
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21. Note that Qn = Qn(y) in the Fig.+ VG
-  gnd +
VDS
-  gnd
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22. Example: What kind of pn junction is this: forward bias, reverse bias or equilibrium? Assume VDS is on, as shown. + VG
-  gnd +
VDS
-  gnd
VM Ayres, ECE875, S14

23. Answer: Reverse bias. Continue Example: Find WD for Vrev = -6V.+ VG
-  gnd +
VDS
-  gnd
VM Ayres, ECE875, S14

24. Answer:
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25. Answer: Drain pn junction with VDS on Source pn junction with VDS on
VM Ayres, ECE875, S14

26. The bigger depletion region at the Drain end leads to a physical pinch, which leads to saturation current. IDS  free Qn . Qn  Qn(y)
VM Ayres, ECE875, S14

27. Lecture 32, 31 Mar 14 Chp 06: MOSFETs
pn junctions/Depletion regions (examples) Channel Current IDS (n-channel p-substrate)
VM Ayres, ECE875, S14

28. Channel current IDS Units-based guess:
Need a length. Multiply by channel length L or channel width Z? ?
VM Ayres, ECE875, S14

29. Channel current IDS Units-based guess:
Need a length. Multiply by channel length L or channel width Z? ?
Answer: IDS = Z Qn vel
=> dIDS = Z dQn(y) vel(y) some dy
then IDS =Sum up (integrate) dIDS
VM Ayres, ECE875, S14

30. Charge sheet model: to deal with Qn(y)
Constant mobility model: to deal with vel(y)
VM Ayres, ECE875, S14

31. Result of Charge sheet model:
Result of constant mobility model:
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32. Result of Charge sheet model:
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33. Example:
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34. Channel width Z changes, channel length L stays the same
Therefore: You fabricated a new device with a different gate dimension.
VM Ayres, ECE875, S14

35. Example: For the new device, Z = ? to do the specified job.
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36. Answer: Given: device 01 is a “Square” MOSFET: Length L = width Z
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37. Answer:
Did not change the Drain or Gate batteries as well as the gate length
VM Ayres, ECE875, S14

38. Answer:
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39. Answer:
Dividing info from two readings to get rid of common unknowns is a standard approach.
VM Ayres, ECE875, S14