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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. O. S. V G < V FB. 3.1 eV. | qV ox |. E c = E FM. GATE. E v. |qV G |. x o.

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Lecture 16
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

+

+

+

+

+

+

-

-

-

-

-

-

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

EE130/230A Fall 2013

Lecture 16, Slide 2


Accumulation layer charge density

+

+

+

+

+

+

-

-

-

-

-

-

Accumulation Layer Charge Density

VG < VFB

From Gauss’ Law:

GATE

xo

+

VG

_

Qacc (C/cm2)

p-type Si

(units: F/cm2)

EE130/230A Fall 2013

Lecture 16, Slide 3


Depletion n poly si gate p type si

+

+

+

+

+

+

-

-

-

-

-

-

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)

EE130/230A Fall 2013

Lecture 16, Slide 4


Depletion width w p type si
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…

EE130/230A Fall 2013

Lecture 16, Slide 5


Voltage drops in depletion p type si

+

+

+

+

+

+

-

-

-

-

-

-

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

EE130/230A Fall 2013

Lecture 16, Slide 6


Surface potential in depletion p type si
Surface Potential in Depletion (p-type Si)

  • Solving for fS, we have

EE130/230A Fall 2013

Lecture 16, Slide 7


Threshold condition v g v t
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.)

EE130/230A Fall 2013

Lecture 16, Slide 8


Mos band diagram at threshold p type si
MOS Band Diagram at Threshold (p-type Si)

M

O

S

qVox

WT

qfF

Ec

EFS

qfF

qfs

Ev

qVG

Ec= EFM

Ev

EE130/230A Fall 2013

Lecture 16, Slide 9


Threshold voltage
Threshold Voltage

  • For n-type Si:

  • For p-type Si:

C. C. Hu, Modern Semiconductor Devices for ICs, Figure 5-8

EE130/230A Fall 2013

Lecture 16, Slide 10


Strong inversion p type si

+

+

+

+

+

+

-

-

-

-

-

-

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)

EE130/230A Fall 2013

Lecture 16, Slide 11

R. F. Pierret, Semiconductor Device Fundamentals, p. 575


Inversion layer charge density p type si
Inversion Layer Charge Density (p-type Si)

EE130/230A Fall 2013

Lecture 16, Slide 12


F s and w vs v g p type si
fS and W vs. VG(p-type Si)

2fF

fS:

0

VG

accumulation

depletion

inversion

VFB

VT

W:

0

VG

accumulation

depletion

inversion

VFB

VT

EE130/230A Fall 2013

Lecture 16, Slide 13


Total charge density in si q s p type si
Total Charge Density in Si, Qs(p-type Si)

depletion

inversion

0

VG

accumulation

VFB

VT

accumulation

depletion

inversion

accumulation

depletion

inversion

VG

0

VFB

VT

VG

0

VFB

VT

accumulation

depletion

inversion

VG

0

Qinv

VFB

VT

slope = -Cox

EE130/230A Fall 2013

Lecture 16, Slide 14


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