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Understanding MOSFETs: Theory and Characteristics of n-Channel and p-Channel Devices

This lecture by Professor Ronald L. Carter covers essential theories and characteristics of n-channel and p-channel MOSFETs. It dives into the details of fully biased n-MOS capacitors, the calculation methods for threshold voltages (VT), and the impact of substrate bias on VT, known as the body effect. The session includes diagrams illustrating energy bands, channel modulation, and effects on current conduction, along with practical examples from semiconductor device physics, guided by references to key textbooks in the field.

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Understanding MOSFETs: Theory and Characteristics of n-Channel and p-Channel Devices

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  1. EE 5340Semiconductor Device TheoryLecture 27 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

  2. Fully biased n-MOScapacitor VG Channel if VG > VT VS VD EOx,x> 0 e- e- e- e- e- e- n+ n+ p-substrate Vsub=VB DeplReg Acceptors y 0 L

  3. MOS energy bands atSi surface for n-channel Fig 8.10**

  4. Computing the D.R. W and Q at O.S.I. Ex Emax x

  5. Q’d,max and xd,max forbiased MOS capacitor Fig 8.11** xd,max (mm)

  6. Fully biased n-channel VT calc

  7. n-channel VT forVC = VB = 0 Fig 10.20*

  8. Fully biased p-channel VT calc

  9. p-channel VT forVC = VB = 0 Fig 10.21*

  10. n-channel enhancementMOSFET in ohmic region 0< VT< VG Channel VS = 0 0< VD< VDS,sat EOx,x> 0 e-e- e- e- e- n+ n+ DeplReg p-substrate Acceptors VB < 0

  11. Conductance ofinverted channel • Q’n= - C’Ox(VGC-VT) • n’s= C’Ox(VGC-VT)/q, (# inv elect/cm2) • The conductivity sn = (n’s/t) q mn • G = sn(Wt/L) = n’s q mn(W/L) = 1/R, so • I = V/R = dV/dR, dR = dL/(n’sqmnW)

  12. Basic I-V relationfor MOS channel

  13. I-V relation for n-MOS (ohmicreg) ohmic ID non-physical ID,sat saturated VDS VDS,sat

  14. Universal draincharacteristic ID VGS=VT+3V 9ID1 ohmic saturated, VDS>VGS-VT VGS=VT+2V 4ID1 VGS=VT+1V ID1 VDS

  15. Characterizing then-ch MOSFET VD ID D G B S VGS VT

  16. Substrate bias effect on VT (body-effect)

  17. Body effect data Fig 9.9**

  18. Low field ohmiccharacteristics

  19. MOSFET circuitparameters

  20. MOSFET circuitparameters (cont)

  21. MOSFET equivalentcircuit elements Fig 10.51*

  22. MOS small-signal equivalent circuit Fig 10.52*

  23. MOS channel-length modulation Fig 11.5*

  24. Analysis of channellength modulation

  25. Channel length mod-ulated drain char Fig 11.6*

  26. Implanted n-channel enhance-ment MOSFET (ohmic region) 0< VT< VG e- channel ele+ implant ion Channel VS = 0 0< VD< VDS,sat EOx,x> 0 n+ n+ e-e- e- e- e- ++++++++++++ DeplReg p-substrate Acceptors VB < 0

  27. Range Si & SiO2 Al Si3N4 DRP Si Al & SiO2 Si3N4 Ion implantation*

  28. “Dotted box” approx**

  29. Calculating xi andDVT

  30. If xi ~xd,max

  31. Calculating VT

  32. Vt per Eq. 9.1.23 in M&K for a MOSFET with an 87-nm-thick gate oxide, Qff/q = 1011 cm-2, N’ = 3.5 X 1011 cm-2, and Na = 2 X 1015 cm-3. Both VS and VB = Figure 9.8 (p. 441) Implanted VT

  33. Mobilities**

  34. Substrate bias effect on VT (body-effect)

  35. Body effect data Fig 9.9**

  36. M&K Fig. 9.9 (Eq. 9.1.23)

  37. Subthresholdconduction • Below O.S.I., when the total band-bending < 2|fp|, the weakly inverted channel conducts by diffusion like a BJT. • Since VGS>VDS, and below OSI, then Na>nS>nD, and electr diffuse S --> D Electron concentration at Source Concentration gradient driving diffusion

  38. Band diagram along the channel region of an n-channel MOSFET under bias, indicating that the barrier qΦB at the source depends on the gate voltage. M&K Fig.9.10 (p.443)

  39. Measured subthreshold characteristics of an MOS transistor with a 1.2 μm channel length. The inverse slope of the straight-line portion of this semilogarithmic plot is called the drain-current subthreshold slope S (measured in mV/decade of drain current). M&K Fig. 9.11 (p.444)

  40. Subthresholdcurrent data Figure 10.1** Figure 11.4*

  41. Mobility variationdue to Edepl Figures 11.7,8,9*

  42. Velocity saturationeffects Figure 11.10*

  43. References * Semiconductor Physics & Devices, by Donald A. Neamen, Irwin, Chicago, 1997. **Device Electronics for Integrated Circuits, 2nd ed., by Richard S. Muller and Theodore I. Kamins, John Wiley and Sons, New York, 1986

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