Lecture 16

1. Lecture 16 ANNOUNCEMENTS • Wed. discussion section (Eudean Sun) moved to 2-3PM in 293 Cory • HW#9 is posted online. OUTLINE • MOS capacitor (cont’d) • 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 (x=0) 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 < VFB) are comprised of holes and/or donor ions. Inversion VGB < VTH Depletion VTH<VGB < VFB Accumulation VGB > VFB -tox -tox -tox Xd,max Xd 0 0 0

9. PMOS Q-V , C-V depletion inversion accumulation accumulation depletion inversion

10. The channel charge density is equal to the gate capacitance times the gate voltage in excess of the threshold voltage. MOSFET in ON State (VGS > VTH) 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 x=0, for an NMOSFET).

11. For small VDS, the MOSFET can be viewed as a resistor, with the channel resistance depending on the gate voltage. MOSFET as Voltage-Controlled Resistor • 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 VDS<VGS-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 (VDS>VGS-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.

18. Drain Current Saturation (Long-Channel MOSFET) • For VDS > VGS-VTH:

19. MOSFET Regions of Operation • When the potential difference between the gate and drain is greater than VTH, the MOSFET is operating in the triode region. • When the potential difference between the gate and drain is equal to or less than VTH, the MOSFET is operating in the saturation 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?