OUTLINE

1
Lecture 16

• ANNOUNCEMENTS
• Wed. discussion section (Eudean Sun) moved to
  2-3PM in 293 Cory
• HW9 is posted online.

• OUTLINE
• MOS capacitor (contd)
• Effect of channel-to-body bias
• Small-signal capacitance
• PMOS capacitor
• NMOSFET in ON state
• Derivation of I-V characteristics
• Regions of operation
• Reading Chapter 6.2.2

2
VGB VTH (Threshold)

• VTH is defined to be the gate voltage at which
  the inversion-layer carrier concentration is
  equal to the channel dopant concentration.
• For an NMOS device, n NA at the surface (x0)
  when VGB VTH

• The semiconductor potential is
• The potential in the body (bulk) is
• At VGB VTH, the potential at the surface is
• The total potential dropped in the semiconductor
  is 2fB
• The depletion width is

Xd
-tox
0
-tox
Xd
3
Effect of Channel-to-Body Bias

• When a MOS device is biased in the inversion
  region of operation, a PN junction exists between
  the channel and the body. Since the inversion
  layer of a MOSFET is electrically connected to
  the source, a voltage can be applied to the
  channel.

VG VTH

• If the source/channel of an NMOS device is biased
  at a higher potential (VC) than the body
  potential (VB), the channel-to-body PN junction
  is reverse biased.

• The potential drop across the depletion region is
  increased.
• The depletion width is increased
• The depletion charge density (Qdep qNAXd) is
  increased.
• The inversion-layer charge density is decreased,
  i.e. VTH is increased.

4
Small-Signal Capacitance

• The MOS capacitor is a non-linear capacitor
• If an incremental (small-signal) voltage dVG is
  applied in addition to a bias voltage VG, the
  total charge on the gate is
• Thus, the incremental gate charge (dQG) resulting
  from the incremental gate voltage (dVG) is
• CG is the small-signal gate capacitance

constant charge
5
(N)MOS C-V Curve

• The MOS C-V curve is obtained by taking the slope
  of the Q-V curve.
• CG Cox in the accumulation and inversion
  regions of operation.
• CG is smaller, and is a non-linear function of
  VGB in the depletion region of operation.

6
MOS Small-Signal Capacitance Model
Depletion
Inversion
Accumulation
The incremental charge is located at the
semiconductor surface
The incremental charge is located at the bottom
edge of the depletion region
The incremental charge is located at the
semiconductor surface
7
MOS Capacitive Voltage Divider

• In the depletion (sub-threshold) region of
  operation, an incremental change in the gate
  voltage (DVGB) results in an incremental change
  in the channel potential (DVCB) that is smaller
  than DVGB
• How can we maximize DVCB/DVGB ?

8
PMOS Capacitor

• The PMOS structure can also be considered as a
  parallel-plate capacitor, but with the top plate
  being the negative plate, the gate insulator
  being the dielectric, and the n-type
  semiconductor substrate being the positive plate.
• The positive charges in the semiconductor (for
  VGB lt VFB) are comprised of holes and/or donor
  ions.

Depletion VTH ltVGB lt VFB
Accumulation VGB gt VFB
Inversion VGB lt VTH
-tox
-tox
-tox
Xd
Xd,max
0
0
0
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PMOS Q-V , C-V
depletion
inversion
accumulation
accumulation
depletion
inversion
10
MOSFET in ON State (VGS gt VTH)

• The channel charge density is equal to the gate
  capacitance times the gate voltage in excess of
  the threshold voltage.

Areal inversion charge density C/cm2

• Note that the reference voltage is the source
  voltage.
• In this case, VTH is defined as the value of VGS
  at which the channel surface is strongly
  inverted (i.e. n NA at x0, for an NMOSFET).

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MOSFET as Voltage-Controlled Resistor

• For small VDS, the MOSFET can be viewed as a
  resistor, with the channel resistance depending
  on the gate voltage.

• Note that

12
MOSFET Channel Potential Variation

• If the drain is biased at a higher potential than
  the source, the channel potential increases from
  the source to the drain.
• ?The potential difference between the gate and
  channel decreases from the source to drain.

13
Charge Density along the Channel

• The channel potential varies with position along
  the channel
• The current flowing in the channel is
• The carrier drift velocity at position y is
• where mn is the electron field-effect mobility

14
Drain Current, ID (for VDSltVGS-VTH)

• Integrating from source to drain

15
ID-VDS Characteristic

• For a fixed value of VGS, ID is a parabolic
  function of VDS.
• ID reaches a maximum value at VDS VGS- VTH.

16
Inversion-Layer Pinch-Off (VDSgtVGS-VTH)

• When VDS VGS-VTH, Qinv 0 at the drain end of
  the channel.
• ? The channel is pinched-off.
• As VDS increases above VGS-VTH, the pinch-off
  point (where Qinv 0) moves toward the source.
• Note that the channel potential VC is always
  equal to VGS-VTH at the pinch-off point.

• The maximum voltage that can be applied across
  the inversion-layer channel (from source to
  drain) is VGS-VTH.
• The drain current saturates at a maximum value.

17
Current Flow in Pinch-Off Region

• Under the influence of the lateral electric
  field, carriers drift from the source (through
  the inversion-layer channel) toward the drain.
• A large lateral electric field exists in the
  pinch-off region
• Once carriers reach the pinch-off point, they are
  swept into the drain by the electric field.

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Drain Current Saturation (Long-Channel MOSFET)

• For VDS gt VGS-VTH

19
MOSFET Regions of Operation

• When the potential difference between the gate
  and drain is equal to or less than VTH, the
  MOSFET is operating in the saturation region.

• When the potential difference between the gate
  and drain is greater than VTH, the MOSFET is
  operating in the triode region.

20
Triode or Saturation?

• In DC circuit analysis, when the MOSFET region of
  operation is not known, an intelligent guess
  should be made then the resulting answer should
  be checked against the assumption.
• Example Given mnCox 100 mA/V2, VTH 0.4V.
• If VG increases by 10mV, what is
  the change in VD?