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

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)
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
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
decrease VG
decrease VG
Accumulation
VG > VFB
Electrons accumulate at surface
Depletion
VG < VFB
Electrons repelled from surface
Inversion
VG < VT
Surface becomes p-type
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)
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 + + + + + +
3.1 eV
qfS 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)
qVox WT
qfF Ec
EFS
qfF
qfs Ev
qVG
Ec= EFM Ev
EE130/230M Spring 2013
Lecture 16, Slide 13

14. Threshold Voltage For p-type Si: For n-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