CMOS Transistors
Outline
• Qualitative Description of CMOS
Transistor
• gm/ID Design
• Biasing a transistor Using gm/ID
Approach
• Design Using Cadence
A Crude Metal Oxide
Semiconductor (MOS) Device
Positive charge attract
P-Type Silicon is
negative charges
slightly conductive.
to interface between
insulator and silicon.
The gate
draws no current!
V2 causes movement
of negative charges,
thus current.
V1 can control the
resistivity of the channel.
A conductive path is created
If the density of electrons is
sufficiently high.
Q=CV.
An Improved MOS Transistor
(provide electrons)
(drain electrons)
n+ diffusion allows
electrons move
through silicon.
Typical Dimensions of MOSFETs
tox is made really thin
to increase C, therefore,
create a strong control of Q by V.
These diode must
be reversed biased.
A Closer Look at the Channel
Formulation
Need to tie substrate to GND
to avoid current through PN
diode.
(OFF)
(ON)
VTH=300mV to 500 mV
Free electrons appear at VG=VTH.
Positive charges repel the holes
creating a depletion region, a region free of holes.
Channel Resistance
As VG increases, the density of electrons increases, the value of
channel resistance changes with gate voltage.
Drain Current as a function of
Drain Voltage
Resistance determined by VG.
Drain Current as a function of
Gate Voltage
Higher VG leads to a lower channel resistance, therefore larger slope.
Length Dependence
The resistance of a conductor is proportional to the length.
Dependence on Oxide
Thickness
Q=CV
C is inversely proportional to 1/tox.
Lower Q implies higher channel resitsance.
Width Dependence
The resistance of a conductor is inversely proportional to the cross
section area.
A larger device also has a larger capacitance!
Channel Pinch Off
• Q=CV
– V=VG-VOXIDE-Silicon
• VOXIDE-Silicon can change along the
channel! Low VOXIDE-Silicon implies less Q.
VG-VD is sufficiently large
to produce a channel
No channel
VG-VD is NOT sufficiently large
to produce a channel
Electrons
are swept
by E to drain.
Drain can no longer affect the drain current!
Regions
(No Dependence on VDS)
No channel
Determination of Region
• How do you know whether a transistor
is in the linear region or saturation
region?
– If VDS>(VGS-VTH) and VGS>VTH, then the
device is in the saturation region.
– If VDS<(VGS-VTH) and VGS>VTH, then the
device is in the linear region.
Graphical Illustration
Limited VDS Dependence
During Saturation
As VDS increase,
effective L decreases,
therefore, ID increases.
Pronounced Channel Length
Modulation in small L
Transconductance
• As a voltage-controlled current source, a MOS transistor
can be characterized by its transconductance:
• It is important to know that
What Happens to gm/ID when W
and ID are doubled?
Body Effect
The threshold voltage will change when VSB=0!
Experimental Data of Body
Effect
The threshold voltage will increase when VSB increases.
Small Signal Model for NMOS
Transistor
PMOS Transistor
IV Characteristics of a PMOS
Small Signal Model of PMOS
Small Signal Model of NMOS
gm/ID Design Approach
gm/ID Design Flow
Specs
Design
Equations
(Analytical
)
gm/Id Data Set
(Emprical)
gm/ID Design Optimization
W/L Ratios
(F. Silveira, JSSC,
1996.)
Intuition
gm
gds
gm/ID
g /g
2gm
2gds
gm/ID
g /g
2gm
2gds
gm/ID
g /g
gm/ID Data Set
•
•
•
•
•
•
gm/gds
gm/gmbs
ID/W
Cgd/Cgg
Cgs/Cgg
….more
(F. Silveira, JSSC,
1996.)
Design Example
Calculation
Initially assume that gmro is large!
(gm is determined)
gm/gds
(50)
Current Density
Biasing an MOS Transistor
Using gm/ID technique
Section 7.1
J.Ou
Sonoma State Univeristy
Basic Analysis
Use 1.2 V
(Modified Ex 7.1)
Design Equations
Assumption: VDD=1.2 V
Transistor Information:
Type: 120 nm
Specify VDS
Note var1_1 is ‘vsd’ if pmos is used
Note var2_1 is ‘vns’ if nmos is used.
In this example, is initially unknown, so
we will assume that it is 0.0
Interpolation
Since the database base
can not be so large as to keep
all possible values of vds/vsb,
we have to interpolate based on
existing values, which are available
On 0.1 V interval.
Current release: need to enter
inBias <= the minVar1 and maxVar1.
minVar=maxVar-0.1
Browse Database
dBrowse2D(25, 'pfet', '15.0u', 'vsd', 0.3, 0.4, 0.353, 'vns', 0.5, 0.6, 0.577, 'vth')
Variable name=dBrowse2D(gmoverid, type, length,
var1, minVar1, maxVar1,inBias1,
var2, minVar2, maxVar2,inBias2,
‘parameter’
)
Valid parameters:
gmovergds, gmovergmbs, vth, ft, gmoveridft, idoverw, vod, region, fndbderiv
cgdovercgg,cddovercgg, cgsovercgg, csbovercgg, cdbovercgg,
ron, vdsat, rseff, rdeff
type: nfet, pfet
length: {'120n' '180n' '250n' '350n' '600n' '800n' '1.0u' '2.0u' '3.0u' '4.0u' '5.0u'
'6.0u' '7.0u' '8.0u' '9.0u' '10.0u' '15.0u' '20.0u'} (text string)
Iteration
• Start with
– length=‘120nm’
– gmoverid=20
– VDS=VDD/2, VSB=0
• Calculate
–
–
–
–
–
–
–
–
–
–
–
vod_1
vth_
vgs_1
vx (gate voltage)
vs (source voltage)
ID
Idoverw
W
RD
Vd
Vds=Vd-Vs
Iteration Example
Design Iterations
Iteratio
n
VS
IDS
W
RD
Vds
0
0.1 V
392uA
53.06
um
1.529K
ohms
0.207 V
1
0.321
322 uA
45.16
um
1.89
Kohms
0.278 V
2
0.340
340.4
uA
46.86
um
1.762
Kohms
0.259
3
0.335
335 uA
46.44
1.788
Kohms
0.265
Matlab & Simulation
Parameters
Matlab
Cadence
W
46.56 um
46 um
Vx
0.857 V
0.857 V
ids
336.8 uA
339 uA
gm
6.7 mS
6.80 mS
gm/ids
19.94
20.05
Vs
0.336 V
0.339 V
Vd
0.6 V
0.593 V
Vds
0.263 V
0.257V
Vth
0.5 V
0.497 V
Circuit Design Using
Cadence
J.Ou
Start Cadence
Start Cadence
Create New Cellview
Add Instance
Add a Resistor
Add Ground
Add Power
Add Wire
Done!
Start ADE L
Start DC Analysis
Netlist and Run
Annotate DC Node Voltages
Model Library Setup
DC Voltage Annotated
Component Display
Display DC Operating Point
Click on the device to display
values!
Save State