1. Lecture 20 OUTLINE The MOSFET (cont’d)
Long-channel I-V characteristics
Reading: Pierret 17.2; Hu 6.6

2. Derivation of NMOSFET I-V
VD > VS
Current in the channel flows by drift
Channel voltage VC(y) varies continuously between the source and the drain
Channel inversion charge density W
EE130/230A Fall 2013
Lecture 20, Slide 2
R. F. Pierret, Semiconductor Device Fundamentals, Figs. 17.6

3. 1st-Order Approximation
If we neglect the variation of Qdep with y, then
where VT is defined to be the threshold voltage at the source end:
The inversion charge density is then
EE130/230A Fall 2013
Lecture 20, Slide 3

4. NMOSFET Current (1st-order approx.)
Consider an incremental length dy of the channel. The voltage drop across this region is
in the linear region
EE130/230A Fall 2013
Lecture 20, Slide 4

5. Saturation Current, IDsat (1st-order approximation)
C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Figure 6-16
IDS saturates when VD reaches VG-VT
 Set VD = VG-VT in the equation for ID
EE130/230A Fall 2013
Lecture 20, Slide 5

6. Problem with “Square Law Theory”
Ignores variation in depletion width with distance y:
where
EE130/230A Fall 2013
Lecture 20, Slide 6

7. Modified (Bulk-Charge) I-V Model
In linear region:
In saturation region:
EE130/230A Fall 2013
Lecture 20, Slide 7

8. MOSFET Threshold Voltage, VT
The expression that was previously derived for VT is the gate voltage referenced to the body voltage that is required reach the threshold condition:
Usually, the terminal voltages for a MOSFET are all referenced to the source voltage. In this case,
and the equations for IDS are
EE130/230A Fall 2013
Lecture 20, Slide 8

9. The Body Effect Note that VT is a function of VSB:
where g is the body effect parameter
When the source-body pn junction is reverse-biased, |VT| is increased. Usually, we want to minimize g so that IDsat will be the same for all transistors in a circuit.
EE130/230A Fall 2013
Lecture 20, Slide 9

10. MOSFET VT Measurement
VT can be determined by plotting IDS vs. VGS, using a low value of VDS
IDS
VGS
EE130/230A Fall 2013
Lecture 20, Slide 10

11. Long-Channel MOSFET I-V Summary
In the ON state (VGS>VT for NMOS; VGS<VT for PMOS), the inversion layer at the semiconductor surface forms a “channel” for current to flow by carrier drift from source to drain
In the linear region of operation (VDS < (VGSVT)/m):
In the saturation region of operation (VDS > (VGSVT)/m):
EE130/230A Fall 2013
Lecture 20, Slide 11