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MOS Capacitor Electrostatics

This lecture covers the electrostatics of the MOS capacitor, including voltage drops in the system, band diagrams for n-type and p-type Si, and the depletion and accumulation regions. It also discusses the threshold condition and strong inversion in p-type Si.

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MOS Capacitor Electrostatics

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  1. Lecture 16 OUTLINE • The MOS Capacitor (cont’d) • Electrostatics Reading: Pierret 16.3; Hu 5.2-5.5

  2. Bulk Semiconductor Potential, fF • p-type Si: • n-type Si: Ec Ei qfF EF Ev Ec EF |qfF| Ei Ev EE130/230M Spring 2013 Lecture 16, Slide 2

  3. Voltage Drops in the MOS System • In general, where qVFB = FMS = FM – FS Vox is the voltage dropped across the oxide (Vox = total amount of band bending in the oxide) fsis the voltage dropped in the silicon (total amount of band bending in the silicon) • For example: • When VG = VFB, Vox = fs = 0, i.e. there is no band bending EE130/230M Spring 2013 Lecture 16, Slide 3

  4. MOS Band Diagrams for n-type Si Decrease VG toward more negative values  the gate electron energy increases relative to that in the Si • Inversion • VG < VT • Surface becomes p-type decrease VG decrease VG • Accumulation • VG > VFB • Electrons accumulate at surface • Depletion • VG < VFB • Electrons repelled from surface EE130/230M Spring 2013 Lecture 16, Slide 4

  5. MOS Band Diagrams for p-type Si increase VG increase VG VG = VFB VG < VFB VT > VG> VFB EE130/230M Spring 2013 Lecture 16, Slide 5

  6. + + + + + + - - - - - - Accumulation (n+ poly-Si gate, p-type Si) M O S VG < VFB 3.1 eV | qVox | Ec= EFM GATE Ev |qVG | xo |qfS| is small,  0 + VG Ec _ p-type Si 4.8 eV EFS Ev Mobile carriers (holes) accumulate at Si surface EE130/230M Spring 2013 Lecture 16, Slide 6

  7. + + + + + + - - - - - - Accumulation Layer Charge Density VG < VFB From Gauss’ Law: GATE xo + VG _ Qacc (C/cm2) p-type Si (units: F/cm2) EE130/230M Spring 2013 Lecture 16, Slide 7

  8. + + + + + + - - - - - - Depletion (n+ poly-Si gate, p-type Si) M O S VT > VG > VFB qVox W Ec GATE EFS qfS 3.1 eV Ev qVG + VG _ Ec= EFM p-type Si Ev 4.8 eV Si surface is depleted of mobile carriers (holes) => Surface charge is due to ionized dopants (acceptors) EE130/230M Spring 2013 Lecture 16, Slide 8

  9. Depletion Width W (p-type Si) • Depletion Approximation: The surface of the Si is depleted of mobile carriers to a depth W. • The charge density within the depletion region is • Poisson’s equation: • Integrate twice, to obtain fS: To find fs for a given VG, we need to consider the voltage drops in the MOS system… EE130/230M Spring 2013 Lecture 16, Slide 9

  10. + + + + + + - - - - - - Voltage Drops in Depletion (p-type Si) From Gauss’ Law: GATE + VG _ Qdep (C/cm2) Qdep is the integrated charge density in the Si: p-type Si EE130/230M Spring 2013 Lecture 16, Slide 10

  11. Surface Potential in Depletion (p-type Si) • Solving for fS, we have EE130/230M Spring 2013 Lecture 16, Slide 11

  12. Threshold Condition (VG = VT) • When VG is increased to the point where fs reaches 2fF, the surface is said to be strongly inverted. This is the threshold condition. VG = VT • (The surface is n-type to the same degree as the bulk is p-type.) EE130/230M Spring 2013 Lecture 16, Slide 12

  13. MOS Band Diagram at Threshold (p-type Si) M O S qVox WT qfF Ec EFS qfF qfs Ev qVG Ec= EFM Ev EE130/230M Spring 2013 Lecture 16, Slide 13

  14. Threshold Voltage • For n-type Si: • For p-type Si: EE130/230M Spring 2013 Lecture 16, Slide 14

  15. + + + + + + - - - - - - Strong Inversion (p-type Si) As VG is increased above VT, the negative charge in the Si is increased by adding mobile electrons (rather than by depleting the Si more deeply), so the depletion width remains ~constant at W = WT WT r(x) M O S GATE x + VG _ p-type Si Significant density of mobile electrons at surface (surface is n-type) EE130/230M Spring 2013 Lecture 16, Slide 15

  16. Inversion Layer Charge Density (p-type Si) EE130/230M Spring 2013 Lecture 16, Slide 16

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