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Explore the intricacies of the MOS capacitor system, including band diagrams, biasing conditions, depletion, accumulation, and inversion phenomena in p-type and n-type silicon. Learn about voltage drops, depletion width, and surface potential in this lecture summary.
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OUTLINE The MOS Capacitor Electrostatics Reading: Chapter 16.3 Lecture #30 EE130 Lecture 30, Slide 1
Bulk Semiconductor Potential, fF • p-type Si: • n-type Si: Ec Ei qfF EF Ev Ec EF |qfF| Ei Ev EE130 Lecture 30, Slide 2
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 Lecture 30, Slide 3
MOS Band Diagrams (n-type Si) Decrease VG (toward more negative values) -> move the gate energy-bands up, relative to 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 Lecture 30, Slide 4
Biasing Conditions for p-type Si increase VG increase VG VG = VFB VG < VFB VT > VG > VFB EE130 Lecture 30, Slide 5
+ + + + + + - - - - - - Accumulation (n+ poly-Si gate, p-type Si) M O S VG < VFB 3.1 eV | qVox | Ec= EFM GATE Ev |qVG | |qfS| is small, 0 + VG Ec _ p-type Si 4.8 eV EFS Ev Mobile carriers (holes) accumulate at Si surface EE130 Lecture 30, Slide 6
+ + + + + + - - - - - - Accumulation Layer Charge Density VG < VFB From Gauss’ Law: GATE xo + VG _ Qacc (C/cm2) p-type Si (units: F/cm2) EE130 Lecture 30, Slide 7
+ + + + + + - - - - - - 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 Lecture 30, Slide 8
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: Depletion Width W (p-type Si) To find fs for a given VG, we need to consider the voltage drops in the MOS system… EE130 Lecture 30, Slide 9
+ + + + + + - - - - - - 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 Lecture 30, Slide 10
Surface Potential in Depletion (p-type Si) • Solving for fS, we have EE130 Lecture 30, Slide 11
Threshold Condition (VG = VT) • When VG is increased to the point where fs reaches 2fF, the surface is said to be strongly inverted. (The surface is n-type to the same degree as the bulk is p-type.) This is the threshold condition. VG = VT EE130 Lecture 30, Slide 12
MOS Band Diagram at Threshold (p-type Si) M O S qVox WT qfF Ec EFS qfF qfs Ev qVG Ec= EFM Ev EE130 Lecture 30, Slide 13
Threshold Voltage • For p-type Si: • For n-type Si: EE130 Lecture 30, Slide 14
+ + + + + + - - - - - - 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 + VG x _ p-type Si Significant density of mobile electrons at surface (surface is n-type) EE130 Lecture 30, Slide 15
Inversion Layer Charge Density (p-type Si) EE130 Lecture 30, Slide 16
