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Understanding Subthreshold Swing and MOSFET Operation in Electrical Engineering

This lecture by Prof. Virginia Ayres explores key aspects of MOSFET operation, particularly focusing on subthreshold swing in n-channel MOSFETs. It covers the challenges of turn-off states, leakage current, and diffusion issues, alongside relevant examples and definitions. The importance of subthreshold swing as a performance metric to minimize MOSFET leakage is discussed, demonstrating the necessity for precise voltage control. Additionally, the lecture touches on sensor technologies, including chemical ion and temperature sensors, enhancing the applicability of these concepts in real-world electronics.

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Understanding Subthreshold Swing and MOSFET Operation in Electrical Engineering

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

  2. Lecture 40, 18 Apr 14 • Chp 06: MOSFETs • Aspects of realistic MOSFET operation (n-channel p-substrate) • Subthreshold swing: • definition 01 • example • definition 02 • example • Chp 14: Sensors • Chemical ion sensors • Temperature sensors • Mechanical sensors VM Ayres, ECE875, S14

  3. Motivation: It is hard to turn a device OFF. ID when the MOSFET is supposed to be OFF is called leakage current. How do you turn the MOSFET OFF: (n-channel) Reduce VG below threshold. No inversion layer. Want: ID = 0. But leakage current is still a problem: why: diffusion and EHP formation can’t be stopped. Subthreshold swing S is a metric for turning a MOSFET device OFF Test conditions: use a small VDS to get a current ID running. Then see how that current responds to changes in VG VM Ayres, ECE875, S14

  4. If the bottom distortion is examined carefully, it is small but it doesn’t = exactly 0. Small currents matter. Definition 01 for Subthreshold swing S: S = DVG/decade ID = 1/slope, not slope VM Ayres, ECE875, S14

  5. bias S = 100 mV/decade ID DVG = 10210-3 V = 0.1 V Decade ID: starts where: (ID, VG) ID = 10-7A, when VG = VT = 0.5 V Actual ID : finishes where: (ID, VG) Find finish ID = ?? A, when VG = 0 V Goal ID : finishes where: (ID, VG) ID = 10-13 A, when VG = 0 V Find start VG = VT + DVT = ?? VM Ayres, ECE875, S14

  6. bias Example: try changing device to a MOSFET with: NA = 5 x 1015 cm-3 d = 10 nm = 100 Angstroms Effective insulator charge = 4 x 1010 q C cm-2 Keep: S = 100 mV/decade ID DVG = 10210-3 V = 0.1 V Set up answer to same questions: ID = 10-13 A, when VG = 0 V Find start VG = VT + DVT = ?? Find finish ID = ?? A, when VG = 0 V Find first: what else?? VM Ayres, ECE875, S14

  7. Answer: New MOSFET New VT bias S = 100 mV/decade ID DVG = 10210-3 V = 0.1 V Decade ID: Find: starts where: (ID, VG) ID = 10-7A, when VG = VT = ?? V Actual ID : finishes where: (ID, VG) Find finish ID = ?? A, when VG = 0 V Goal ID : finishes where: (ID, VG) ID = 10-13 A, when VG = 0 V Find start VG = VT + DVT = ?? VM Ayres, ECE875, S14

  8. Find VT: n-channel: - - + + signs: VM Ayres, ECE875, S14

  9. Find VT: -0.95 V VM Ayres, ECE875, S14

  10. Streetman and Banerjee, Chp. 06, p. 286: VM Ayres, ECE875, S14

  11. New MOSFET New VT bias S = 100 mV/decade ID DVG = 10210-3 V = 0.1 V Decade ID: Find: starts where: (ID, VG) ID = 10-7A, when VG = VT = -0.215 V Actual ID : finishes where: (ID, VG) Find finish ID = ?? A, when VG = 0 V Goal ID : finishes where: (ID, VG) ID = 10-13 A, when VG = 0 V Find start VG = VT + DVT = ?? VM Ayres, ECE875, S14

  12. VT = -0.215 V

  13. VT = -0.215 V

  14. New MOSFET New VT bias S = 100 mV/decade ID DVG = 10210-3 V = 0.1 V Decade ID: Find: starts where: (ID, VG) ID = 10-7A, when VG = VT = -0.215 V Actual ID : finishes where: (ID, VG) Find finish start: ID = 10-5 A, when VG =0V Find finish ID = 10-13 A, when VG = - ## V Goal ID : finishes where: (ID, VG) ID = 10-13 A, when VG = 0 V Find start VG = VT + DVT = ?? VM Ayres, ECE875, S14

  15. VT-new = -0.215 V + DVT VT = -0.215 V

  16. Lecture 40, 18 Apr 14 • Chp 06: MOSFETs • Aspects of realistic MOSFET operation (n-channel p-substrate) • Subthreshold swing: • definition 01 • example • definition 02 • example • Chp 14: Sensors • Chemical ion sensors • Temperature sensors • Mechanical sensors VM Ayres, ECE875, S14

  17. Definition 01 for Subthreshold swing S: S = DVG/decade ID Definition 02 for Subthreshold swing S: VM Ayres, ECE875, S14

  18. Definition 02 incorporates analysis of an important problem in turning a MOSFET OFF: stopping diffusion current few e- Lots of e- Lots of e- VM Ayres, ECE875, S14

  19. Two points: 1. few e-: in depletion region, not charge sheet: x-dependence Lots of e- Lots of e- 2. VDS = extra depletion region in real OFF VM Ayres, ECE875, S14

  20. Investigate the diffusion current issue: These are the source and drain ends of the channel, not the n+ regions VM Ayres, ECE875, S14

  21. Investigate the diffusion current issue: VM Ayres, ECE875, S14

  22. Investigate the diffusion current issue: Diffusion current: VM Ayres, ECE875, S14

  23. Diffusion current ID = f(ys)  VG: ID Surface potential is related to VG: Examine change in ID per change in VG starting with change in ys per change in VG VM Ayres, ECE875, S14

  24. VM Ayres, ECE875, S14

  25. Influence of interface traps: VM Ayres, ECE875, S14

  26. VM Ayres, ECE875, S14

  27. New MOSFET New VT bias Consistent? S = 100 mV/decade ID DVG = 10210-3 V = 0.1 V Decade ID: Find: where: (ID, VG) ID = 10-7A, when VG = VT = -0.215 V Actual ID : finishes where: (ID, VG) Find start: ID = 10-5 A, when VG =0V Find finish ID = 10-13 A, when VG = - ## V Goal ID : finishes where: (ID, VG) Find finish ID = 10-13 A, when VG = 0 V Find start VG = VT + DVT = + ## V VM Ayres, ECE875, S14

  28. Did Cox and/or CD change? VM Ayres, ECE875, S14

  29. Did Cox and/or CD change? Yes. Example: Find S for this device. Assume room temperature operation at 300 K. VM Ayres, ECE875, S14

  30. Answer: 3.45 x 10-7 F cm-2 2.5 x 10-8 F cm-2 VM Ayres, ECE875, S14

  31. Answer: 3.45 x 10-7 F cm-2 2.5 x 10-8 F cm-2 S 3.45 x 10-7 F cm-2 0.0259 eV e

  32. Units: Definition 01 for Subthreshold swing S: S = DVG/decade ID Definition 02 for Subthreshold swing S: S VM Ayres, ECE875, S14

  33. Lecture 40, 18 Apr 14 • Chp 06: MOSFETs • Aspects of realistic MOSFET operation (n-channel p-substrate) • Subthreshold swing: • definition 01 • example • definition 02 • example • Chp 14: Sensors • Chemical ion sensors • Temperature sensors • Mechanical sensors VM Ayres, ECE875, S14

  34. What has changed from a conventional MOSFET? Choices: Gate Insulator Channel Substrate VM Ayres, ECE875, S14

  35. What has changed from a conventional MOSFET: Gate Insulator Channel Substrate VM Ayres, ECE875, S14

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