Lecture 16 OUTLINE The MOS Capacitor contd Electrostatics

Lecture 16 OUTLINE • The MOS Capacitor (cont’d) – Electrostatics Reading: Pierret 16. 3; Hu 5. 2 -5. 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 | xo Ec p-type Si 4. 8 e. V Mobile carriers (holes) accumulate at Si surface EE 130/230 A Fall 2013 |qf. S| is small, 0 Lecture 16, Slide 2 EFS Ev

Accumulation Layer Charge Density VG < VFB From Gauss’ Law: GATE - - - VG + _ + + + xo Qacc (C/cm 2) p-type Si EE 130/230 A Fall 2013 (units: F/cm 2) Lecture 16, Slide 3

Depletion (n+ poly-Si gate, p-type Si) M VT > VG > VFB q. Vox O S W Ec GATE VG + _ - - - p-type Si Ec= EFM Ev Si surface is depleted of mobile carriers (holes) => Surface charge is due to ionized dopants (acceptors) EE 130/230 A Fall 2013 qf S 3. 1 e. V + + + Lecture 16, Slide 4 4. 8 e. V q. VG 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… EE 130/230 A Fall 2013 Lecture 16, Slide 5

Voltage Drops in Depletion (p-type Si) From Gauss’ Law: GATE + + + VG + _ - - - Qdep (C/cm 2) p-type Si EE 130/230 A Fall 2013 Qdep is the integrated charge density in the Si: Lecture 16, Slide 6

Surface Potential in Depletion (p-type Si) • Solving for f. S, we have EE 130/230 A Fall 2013 Lecture 16, Slide 7

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. This is the threshold condition. VG = VT (The surface is n-type to the same degree as the bulk is p-type. ) EE 130/230 A Fall 2013 Lecture 16, Slide 8

MOS Band Diagram at Threshold (p-type Si) M q. Vox qf. F Ec= EFM Ev EE 130/230 A Fall 2013 Lecture 16, Slide 9 O S WT qf. F qf s Ec EFS Ev q. VG

Threshold Voltage • For p-type Si: • For n-type Si: EE 130/230 A Fall 2013 Lecture 16, Slide 10 C. C. Hu, Modern Semiconductor Devices for ICs, Figure 5 -8

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) EE 130/230 A Fall 2013 Lecture 16, Slide 11 R. F. Pierret, Semiconductor Device Fundamentals, p. 575

Inversion Layer Charge Density (p-type Si) EE 130/230 A Fall 2013 Lecture 16, Slide 12

f. S and W vs. VG (p-type Si) 2 f. F f S: 0 VG accumulatio V depletion. V inversio FB T n n W: accumulatio VFB depletion. VT inversio n n EE 130/230 A Fall 2013 Lecture 16, Slide 13

Total Charge Density in Si, Qs (p-type Si) depletion 0 accumulatio VFB n accumulatio n 0 VT depletion VFB VT inversio n VG accumulatio depletion n inversio n VG 0 accumulatio n 0 depletion VFB EE 130/230 A Fall 2013 VT inversio n VFB VT VG Qinv slope = -Cox Lecture 16, Slide 14