1. Lecture 21 OUTLINE The MOSFET (cont’d) P-channel MOSFET
CMOS inverter analysis
Sub-threshold current
Small signal model
Reading: Pierret 17.3; Hu 6.7, 7.2

2. P-Channel MOSFET The PMOSFET turns on when VGS < VT
Holes flow from SOURCE to DRAIN
 DRAIN is biased at a lower potential than the SOURCE
In a CMOS technology, the PMOS & NMOS threshold voltages are usually symmetric about 0, i.e. VTp = -VTn VG
VDS < 0
IDS < 0
|IDS| increases with
|VGS - VT|
|VDS| (linear region) VS VD
GATE ID P+ P+ N VB
EE130/230A Fall 2013
Lecture 21, Slide 2

3. Long-Channel PMOSFET I-V
Linear region:
Saturation region:
m = 1 + (3Toxe/WT) is the bulk-charge factor
EE130/230A Fall 2013
Lecture 21, Slide 3

4. CMOS Inverter: Intuitive Perspective
CIRCUIT
SWITCH MODELS
VDD
VIN
VOUT S D G
VDD
VDD Rp
VOUT = 0V
VOUT = VDD Rn
Low static power consumption, since
one MOSFET is always off in steady state
VIN = VDD
VIN = 0V
EE130/230A Fall 2013
Lecture 21, Slide 4

5. Voltage Transfer Characteristic
N: sat
P: sat
VOUT
N: off
P: lin C
VDD
N: sat
P: lin A B D E
N: lin
P: sat
N: lin
P: off
VIN
VDD
EE130/230A Fall 2013
Lecture 21, Slide 5

6. CMOS Inverter Load-Line Analysis
VGSp=VIN-VDD – +
VIN = VDD + VGSp –
VDSp=VOUT-VDD +
VOUT = VDD + VDSp
IDn=-IDp
increasing
VIN
VIN = 0 V
VIN = VDD
IDn=-IDp
increasing
VIN
VOUT=VDSn
VDD
VDSp = 0
VDSp = - VDD
EE130/230A Fall 2013
Lecture 21, Slide 6

7. Load-Line Analysis: Region A
VGSp=VIN-VDD – + –
VDSp=VOUT-VDD +
IDn=-IDp
VIN  VTn
IDn=-IDp
VOUT=VDSn
VDD
EE130/230A Fall 2013
Lecture 21, Slide 7

8. Load-Line Analysis: Region B
VGSp=VIN-VDD – + –
VDSp=VOUT-VDD +
IDn=-IDp
IDn=-IDp
VDD/2 > VIN > VTn
VOUT=VDSn
VDD
EE130/230A Fall 2013
Lecture 21, Slide 8

9. Load-Line Analysis: Region D
VGSp=VIN-VDD – + –
VDSp=VOUT-VDD +
IDn=-IDp
IDn=-IDp
VDD – |VTp| > VIN > VDD/2
VOUT=VDSn
VDD
EE130/230A Fall 2013
Lecture 21, Slide 9

10. Load-Line Analysis: Region E
VGSp=VIN-VDD – + –
VDSp=VOUT-VDD +
IDn=-IDp
VIN > VDD – |VTp|
IDn=-IDp
VOUT=VDSn
VDD
EE130/230A Fall 2013
Lecture 21, Slide 10

11. MOSFET Effective Drive Current, IEFF
M. H. Na et al., IEDM Technical Digest, pp , 2002 V1 V2 V3
CMOS inverter chain:
IEFF =
IH + IL 2 V1
TIME
VDD
VDD/2 V2 V3
tpLH
tpHL
IDsat
GND
VDD S D
VIN
VOUT
CMOS
inverter: IH
VIN = VDD
NMOS DRAIN CURRENT IL
VIN = ½VDD
0.5VDD
VDD
NMOS DRAIN VOLTAGE = VOUT
EE130/230A Fall 2013
Lecture 21, Slide 11

12. Propagation Delay, td
C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Fig. 6-20
VDD
CMOS inverter chain:
Voltage waveforms:
VDD
td is reduced by increasing IEFF and reducing load capacitance C
EE130/230A Fall 2013
Lecture 21, Slide 12

13. Sub-Threshold Current
For |VG| < |VT|, MOSFET current flow is limited by carrier diffusion into the channel region.
The electric potential in the channel region varies linearly with VG, according to the capacitive voltage divider formula:
As the potential barrier to diffusion increases linearly with decreasing VG, the diffusion current decreases exponentially:
EE130/230A Fall 2013
Lecture 21, Slide 13

14. Sub-Threshold Swing, S log ID VGS VT
Inverse slope is subthreshold swing, S
[mV/dec]
NMOSFET Energy Band Profile
increasing E
distance
n(E)  exp(-E/kT)
Source
Drain
increasing
VGS
EE130/230A Fall 2013
Lecture 21, Slide 14

15. VT Design Trade-off Low VT is desirable for high ON current:
IDsat  (VDD - VT) <  < 2
But high VT is needed for low OFF current:
log ID
Low VT
VT cannot be aggressively reduced!
High VT
IOFF,low VT
IOFF,high VT
VGS
EE130/230A Fall 2013
Lecture 21, Slide 15

16. How to minimize S?
EE130/230A Fall 2013
Lecture 21, Slide 16

17. MOSFET Small Signal Model (Saturation Region)
Conductance parameters:
A small change in VG or VDS will result in a small change in ID
low-frequency:
high-frequency:
R. F. Pierret, Semiconductor Device Fundamentals, Fig
EE130/230A Fall 2013
Lecture 21, Slide 17

18. Parasitic Components EE130/230A Fall 2013 Lecture 21, Slide 18
R.S. Muller & T.I. Kamins, Device Electronics for Integrated Circuits, Fig. 8.12

19. MOSFET Cutoff Frequency, fT
The cut-off frequency fT is defined as the frequency when the
current gain is reduced to 1.
input current =
vG here is ac signal
CG is approximately equal to the
gate capacitance,  W L Cox
output current =
At the cutoff frequency (wT = 2pfT):
Higher MOSFET operating frequency is achieved by decreasing the channel length L
EE130/230A Fall 2013
Lecture 21, Slide 19