Lecture 30 OUTLINE The MOS Capacitor Electrostatics Reading

Lecture #30 OUTLINE The MOS Capacitor • Electrostatics Reading: Chapter 16. 3 1 Spring 2007 EE 130 Lecture 30, Slide 1

Bulk Semiconductor Potential, f. F • p-type Si: Ec EF • n-type Si: EF qf. F Ei Ev Ec |qf. F| Ei Ev 2 Spring 2007 EE 130 Lecture 30, Slide 2

Voltage Drops in the MOS System • In general, where q. VFB = FMS = FM – FS Vox is the voltage dropped across the oxide (Vox = total amount of band bending in the oxide) fs is 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 3 Spring 2007 EE 130 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 decrease VG • Accumulation – VG > VFB – Electrons accumulate at surface decrease VG • Depletion – VG < VFB – Electrons repelled from surface • Inversion – VG < VT – Surface becomes p -type 4 Spring 2007 EE 130 Lecture 30, Slide 4

Biasing Conditions for p-type Si increase VG VG = VFB VG < VFB increase VG VT > VG > VFB 5 Spring 2007 EE 130 Lecture 30, Slide 5

Accumulation (n+ poly-Si gate, p-type Si) M VG < VFB 3. 1 e. V O S | q. Vox | Ec= EFM GATE - - - VG +_ Ev |q. VG | + + + |qf. S| is small, 0 Ec p-type Si 4. 8 e. V EFS Ev Mobile carriers (holes) accumulate at Si surface 6 Spring 2007 EE 130 Lecture 30, Slide 6

Accumulation Layer Charge Density VG < VFB From Gauss’ Law: GATE - - - xo + + + VG +_ Qacc (C/cm 2) p-type Si (units: F/cm 2) 7 Spring 2007 EE 130 Lecture 30, Slide 7

Depletion (n+ poly-Si gate, p-type Si) M VT > VG > VFB q. Vox O S W Ec GATE VG +_ qf. S 3. 1 e. V + + + - - - p-type Si q. VG Ec= EFM Ev 4. 8 e. V Si surface is depleted of mobile carriers (holes) => Surface charge is due to ionized dopants (acceptors) 8 Spring 2007 EE 130 Lecture 30, Slide 8 EFS Ev

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 f. S: To find fs for a given VG, we need to consider the voltage drops in the MOS system… 9 Spring 2007 EE 130 Lecture 30, Slide 9

Voltage Drops in Depletion (p-type Si) From Gauss’ Law: GATE + + + VG +_ - - - Qdep (C/cm 2) p-type Si Qdep is the integrated charge density in the Si: 10 Spring 2007 EE 130 Lecture 30, Slide 10

Surface Potential in Depletion (p-type Si) • Solving for f. S, we have 11 Spring 2007 EE 130 Lecture 30, Slide 11

Threshold Condition (VG = VT) • When VG is increased to the point where fs reaches 2 f. F, 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 12 Spring 2007 EE 130 Lecture 30, Slide 12

MOS Band Diagram at Threshold (p-type Si) M q. Vox qf. F O S WT qf. F qfs Ec EFS Ev q. VG Ec= EFM Ev 13 Spring 2007 EE 130 Lecture 30, Slide 13

Threshold Voltage • For p-type Si: • For n-type Si: 14 Spring 2007 EE 130 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 GATE r(x) M O S + + + VG +_ - - - x p-type Si Significant density of mobile electrons at surface (surface is n-type) 15 Spring 2007 EE 130 Lecture 30, Slide 15

Inversion Layer Charge Density (p-type Si) 16 Spring 2007 EE 130 Lecture 30, Slide 16