EE4800 CMOS Digital IC Design & Analysis
Lecture 3
MOS Transistor Device Characteristics
Zhuo Feng
3.1
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Outline
■ Introduction
■ MOS Capacitor
■ NMOS I-V Characteristics
■ PMOS I-V Characteristics
■ Gate and Diffusion Capacitance
■ Nonideal Transistor Behavior
■ Process and Environmental Variations
3.2
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Introduction
■
■
So far, we have treated transistors as ideal switches
An ON transistor passes a finite amount of current
► Depends on terminal voltages
► Derive current-voltage (I-V) relationships
■
Transistor gate, source, drain all have capacitance
► I = C (DV/Dt) -> Dt = (C/I) DV
► Capacitance and current determine speed
■
3.3
Also explore what a “degraded level” really means
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
MOS Capacitor
■ Gate and body form MOS capacitor
■ Operating modes
► Accumulation
polysilicon gate
silicon dioxide insulator
Vg < 0
+
-
► Depletion
p-type body
► Inversion
(a)
0 < V g < Vt
+
-
depletion region
(b)
V g > Vt
+
-
(c)
3.4
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
inversion region
depletion region
Terminal Voltages
■
Mode of operation depends on Vg, Vd, Vs
► Vgs = Vg – Vs
► Vgd = Vg – Vd
► Vds = Vd – Vs = Vgs - Vgd
■
Source and drain are symmetric diffusion terminals
► By convention, source is terminal at lower voltage
► Hence Vds  0
■
■
NMOS body is grounded. First assume source is 0 too.
Three regions of operation
Vg
► Cutoff
► Linear
► Saturation
Vgs
Vs
3.5
+
Vgd
-
+
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
-
Vds
+
Vd
NMOS Cutoff
■ No channel
■ Ids = 0
Vgs = 0
+
-
g
s
d
n+
n+
p-type body
b
3.6
+
-
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Vgd
NMOS Linear
■
■
Channel forms
Current flows from d to s
Vgs > Vt
► e- from s to d
■
■
g
+
-
Ids increases with Vds
Similar to linear resistor
+
-
s
d
n+
n+
Vgd = Vgs
Vds = 0
p-type body
b
Vgs > Vt
g
+
s
d
n+
n+
p-type body
b
3.7
+
-
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Vgs > Vgd > Vt
Ids
0 < Vds < Vgs-Vt
NMOS Saturation
■ Channel pinches off
■ Ids independent of Vds
■ We say current saturates
■ Similar to current source
Vgs > Vt
+
-
g
+
-
d Ids
s
n+
n+
p-type body
b
3.8
Vgd < Vt
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Vds > Vgs-Vt
I-V Characteristics
■ In Linear region, Ids depends on
► How much charge is in the channel?
► How fast is the charge moving?
3.9
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Channel Charge
■
MOS structure looks like parallel plate capacitor while
operating in inversion
► Gate – oxide – channel
■
■
■
Qchannel = CV
C = Cg = eoxWL/tox = CoxWL
V = Vgc – Vt = (Vgs – Vds/2) – Vt
polysilicon
gate
W
tox
L
n+
n+
SiO2 gate oxide
(good insulator, eox = 3.9)
p-type body
gate
Vg
+
+
Cg Vgd drain
source Vgs
channe
Vs
Vd
l
+ n+
n+ Vds
p-type body
3.10
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Cox = eox / tox
Vgc=(Vgs+Vgd)/2
=Vgs-Vds /2
Carrier velocity
■ Charge is carried by e■ Carrier velocity v proportional to lateral E-field
between source and drain
■ v = mE (m is called mobility)
■ E = Vds/L
■ Time for carrier to cross channel:
►t=L/v
3.11
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
NMOS Linear I-V
■ Now we know
► How much charge Qchannel is in the channel
► How much time t each carrier takes to cross
Qchannel
I ds 
t
W
 mCox
L
V  V  Vds
 gs t
2

Vds 

  Vgs  Vt 
Vds
2


3.12
V
 ds

Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
W
 = mCox
L
NMOS Saturation I-V
■ If Vgd < Vt, channel pinches off near drain
► When Vds > Vdsat = Vgs – Vt
■ Now drain voltage no longer increases current
V
I ds   Vgs  Vt  dsat
2


3.13

V

2
gs
 Vt 
V
 dsat

2
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
NMOS I-V Summary
■
Shockley 1st order transistor models (long-channel)


0

 
V
I ds    Vgs  Vt  ds
2


2


Vgs  Vt 


2
3.14
Vgs  Vt
V V  V
 ds
ds
dsat

Vds  Vdsat
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
cutoff
linear
saturation
Example
■ We consider a 0.6 mm process
► From AMI Semiconductor
► tox = 100 Å
2.5
► m = 350 cm2/V*s
■ Plot Ids vs. Vds
► Vgs = 0, 1, 2, 3, 4, 5
► Use W/L = 4/2 l
2
Ids (mA)
► Vt = 0.7 V
Vgs = 5
1.5
Vgs = 4
1
Vgs = 3
0.5
0
0
Vgs = 2
Vgs = 1
1
2
3
Vds
 3.9  8.85  1014   W 
W
W
2
  mCox   350 

120
m
A
/
V
 L 
8
L
100

10
L

 
3.15
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
4
5
PMOS I-V
■ All dopings and voltages are inverted for PMOS
■ Mobility mp is determined by holes
► Typically 2-3x lower than that of electrons mn
► 120 cm2/V*s in AMI 0.6 mm process
■ Thus PMOS must be wider to provide same current
► In this class, assume mn / mp = 2
► *** plot I-V here
3.16
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Capacitance
■
■
Any two conductors separated by an insulator have
capacitance
Gate to channel capacitor is very important
► Creates channel charge necessary for operation
■
Source and drain have capacitance to body
► Across reverse-biased diodes
► Called diffusion capacitance because it is associated with
source/drain diffusion
3.17
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Gate Capacitance
■ Approximate channel as connected to source
■ Cgs = eoxWL/tox = CoxWL = CpermicronW (minimum L)
■ Cpermicron is typically about 2 fF/mm
polysilicon
gate
W
tox
n+
L
n+
SiO2 gate oxide
(good insulator, eox = 3.9e0)
p-type body
3.18
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Diffusion Capacitance
■ Csb, Cdb
■ Undesirable, called parasitic capacitance
■ Capacitance depends on area and perimeter
► Use small diffusion nodes
► Comparable to Cg
for contacted diff
► ½ Cg for uncontacted
► Varies with process
3.19
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Ideal vs. Simulated nMOS I-V Plot
■ 65 nm IBM process, VDD = 1.0 V
Ids (mA)
Simulated
Vgs = 1.0
Ideal
1200
Velocity saturation & Mobility degradation:
Ion lower than ideal model predicts
1000
Ion = 747 mA @
Channel length modulation: V = V = V
gs
ds
DD
Saturation current increases
with Vds
Vgs = 1.0
800
Vgs = 0.8
600
Velocity saturation & Mobility degradation:
Saturation current increases less than
quadratically with Vgs
400
Vgs = 0.8
Vgs = 0.6
200
Vgs = 0.6
Vgs = 0.4
0
Vds
0
3.20
0.2
0.4
0.6
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
0.8
1
ON and OFF Current
■ Ion = Ids @ Vgs = Vds = VDD
► Saturation
Ids (mA)
1000
Ion = 747 mA @
Vgs = Vds = VDD
800
Vgs = 1.0
600
Vgs = 0.8
400
Vgs = 0.6
200
■ Ioff = Ids @ Vgs = 0, Vds = VDD
Vgs = 0.4
0
Vds
0
0.2
► Cutoff
3.21
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
0.4
0.6
0.8
1
Electric Fields Effects
■ Vertical electric field: Evert = Vgs / tox
► Attracts carriers into channel
► Long channel: Qchannel  Evert
■ Lateral electric field: Elat = Vds / L
► Accelerates carriers from drain to source
► Long channel: v = mElat
3.22
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Mobility Degradation
■ High Evert effectively reduces mobility
► Collisions with oxide interface
3.23
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Velocity Saturation
■ At high Elat, carrier velocity rolls off
► Carriers scatter off atoms in silicon lattice
► Velocity reaches vsat
▼ Electrons: 107 cm/s
▼ Holes: 8 x 106 cm/s
► Better model
3.24
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Vel Sat I-V Effects
■ Ideal transistor ON current increases with VDD2
2
W Vgs  Vt 

 Vgs  Vt 
L
2
2
2
I ds  mCox
■ Velocity-saturated ON current increases with VDD
I ds  CoxW Vgs  Vt  vmax
■ Real transistors are partially velocity saturated
► Approximate with a-power law model
► Ids  VDDa
► 1 < a < 2 determined empirically (≈ 1.3 for 65 nm)
3.25
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
a-Power Model
 0

V

I ds   I dsat ds
Vdsat


 I dsat
3.26
Vgs  Vt
cutoff
Vds  Vdsat
linear
Vds  Vdsat
saturation
I dsat  Pc

V

2
gs
 Vt 
a
Vdsat  Pv Vgs  Vt 
a /2
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Channel Length Modulation
■ Reverse-biased p-n junctions form a depletion region
► Region between n and p with no carriers
► Width of depletion Ld region grows with reverse bias
► Leff = L – Ld
■ Shorter Leff gives more current
► Ids increases with Vds
► Even in saturation
GND
Source
VDD
Gate
VDD
Drain
Depletion Region
Width: Ld
n
+
3.27
L
Leff
p GND
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
n
+
bulk Si
Channel Length Modulation
I ds 

V

2
gs
 Vt  1  lVds 
2
■ l = channel length modulation coefficient
► not feature size
► Empirically fit to I-V characteristics
3.28
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Threshold Voltage Effects
■ Vt is Vgs for which the channel starts to invert
■ Ideal models assumed Vt is constant
■ Really depends (weakly) on almost everything else:
► Body voltage: Body Effect
► Drain voltage: Drain-Induced Barrier Lowering
► Channel length: Short Channel Effect
3.29
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Body Effect
■ Body is a fourth transistor terminal
■ Vsb affects the charge required to invert the channel
► Increasing Vs or decreasing Vb increases Vt
Vt  Vt 0  g

fs  Vsb  fs

■ fs = surface potential at threshold
fs  2vT ln
NA
ni
► Depends on doping level NA
► And intrinsic carrier concentration ni
■
g = body effect coefficient
g
3.30
tox
e ox
2qe si N A
2qe si N A 
Cox
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Short Channel Effect
■ In small transistors, source/drain depletion regions extend
into the channel
► Impacts the amount of charge required to invert the channel
► And thus makes Vt a function of channel length
■ Short channel effect: Vt increases with L
► Some processes exhibit a reverse short channel effect in which Vt
decreases with L
3.31
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Leakage
■ What about current in cutoff?
■ Simulated results
■ What differs?
► Current doesn’t
go to 0 in cutoff
3.32
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Leakage Sources
■ Subthreshold conduction
► Transistors can’t abruptly turn ON or OFF
► Dominant source in contemporary transistors
■ Gate leakage
► Tunneling through ultrathin gate dielectric
■ Junction leakage
► Reverse-biased PN junction diode current
3.33
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Subthreshold Leakage
■ Subthreshold leakage exponential with Vgs
Vgs Vt 0 Vds  kg Vsb
Vds


nvT
vT
I ds  I ds 0 e
1  e 




■ n is process dependent
► typically 1.3-1.7
■ Rewrite relative to Ioff on log scale
■ S ≈ 100 mV/decade @ room temperature
34
3.34
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Gate Leakage
■ Carriers tunnel thorough very thin gate oxides
■ Exponentially sensitive to tox and VDD
► A and B are tech constants
► Greater for electrons
▼ So nMOS gates leak more
■ Negligible for older processes (tox > 20 Å)
■ Critically important at 65 nm and below (tox ≈ 10.5 Å)
3.35
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
From
[Song01]
Junction Leakage
■ Reverse-biased p-n junctions have some leakage
 VvD

T
I D  I S  e  1




► Ordinary diode leakage
► Band-to-band tunneling (BTBT)
► Gate-induced drain leakage (GIDL)
■ Is depends on doping levels
► And area and perimeter of diffusion regions
► Typically < 1 fA/mm2 (negligible)
p+
n+
n+
p+
p+
n well
p substrate
3.36
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
n+
Temperature Sensitivity
■ Increasing temperature
► Reduces mobility
► Reduces Vt
■ ION decreases with temperature
■ IOFF increases with temperature
I ds
increasing
temperature
Vgs
3.37
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
So What?
■ So what if transistors are not ideal?
► They still behave like switches.
■ But these effects matter for…
► Supply voltage choice
► Logical effort
► Quiescent power consumption
► Pass transistors
► Temperature of operation
3.38
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Parameter Variation
■ Transistors have uncertainty in parameters
► Process: Leff, Vt, tox of nMOS and pMOS
► Vary around typical (T) values
► Leff: short
► Vt: low
fast
■ Fast (F)
FF
SF
■ Slow (S): opposite
■ Not all parameters are independent
pMOS
► tox: thin
TT
for nMOS and pMOS
FS
slow
SS
slow
3.39
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
nMOS
fast
Environmental Variation
■ VDD and T also vary in time and space
■ Fast:
► VDD: high
► T:
3.40
low
Corner
Voltage
Temperature
F
1.98
0C
T
1.8
70 C
S
1.62
125 C
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Process Corners
■ Process corners describe worst case variations
► If a design works in all corners, it will probably work for any
variation.
■ Describe corner with four letters (T, F, S)
► nMOS speed
► pMOS speed
► Voltage
► Temperature
3.41
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis
Important Corners
■ Some critical simulation corners include
Purpose
nMOS
pMOS
VDD
Temp
Cycle time
S
S
S
S
Power
F
F
F
F
Subthreshold
leakage
F
F
F
S
3.42
Z. Feng MTU EE4800 CMOS Digital IC Design & Analysis