mos field-effect transistors mos field-effect transistorsfor high-speed operation d.l. pulfrey...
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MOS Field-Effect TransistorsMOS Field-Effect Transistors
forfor
High-Speed OperationHigh-Speed Operation
D.L. Pulfrey
Department of Electrical and Computer EngineeringUniversity of British ColumbiaVancouver, B.C. V6T1Z4, Canada
pulfrey@ece.ubc.ca
http://nano.ece.ubc.ca
Day 4A, May 30, 2008, Pisa
Si MOSFET featuresSi MOSFET features
• 4 terminals
• 2D-device
• "The most abundant object made by mankind"
What happens ?
NP-junctions and transistor actionNP-junctions and transistor action
E
B G
S
RB
Rj
Cox
Cs=dQs/dVaj
HBT, BJT
MOSFET
)/exp(
and
)/exp()0(
kTqVI
kTqVQ
V
RR
RVV
BEC
BE
BE
jB
jBEaj
oxGSs
GSD
GS
GSaj
oxGSs
oxGSsGSaj
CVC
kTqVI
kTqVQ
VV
CVC
CVCVV
)( if
)/exp(
and
)/exp()0(
)( if
/)(1
1
x=0 x=0
DC
Transistor transfer characteristicsTransistor transfer characteristics
MOSFET:
S/B: 1E20/8E17
BJT:
E/B: 1E19/1E17
Vbi
ON Getting HOT
"OFF"
Sub-threshold
ON
Note: relative "linearities" and current ranges
SUB-THRESHOLD CONDITION (DEPLETION)
- --
- --
- --y
x
+ + +- --
VSB
VGS
-+
iB
+ + +iG
-++
VDS
t
Qi BB
t
Qi GG
G
BBG V
QC
G
GGG V
QC
• Depletion layer forms
ON CONDITION (Strong Inversion)
- --
- --
- --
VSB
VGS
- +
iB
iS iD
iG+ + + ++ + + + +
+-
y
t
Qi GG
t
Qi BB
t
Qi nSS
t
Qi nDD
• Inversion layer forms
G
nSSG V
QC
VDS
x
Decomposing the MOSFET Decomposing the MOSFET
Note:• n+ poly gate• work functions• oxide electron affinity and Eg
1. Ignore S and D
2. Take vertical section from G → B
y
x
y
EC
Equilibrating the MOSCAP Equilibrating the MOSCAP
Equilibration process:
- electrons transfer, driven by difference in EF
- electrons recombine in body at the interface- depletion layer forms- charge separation creates field in oxide
= -Vfb
Introducing the channel potential Introducing the channel potential
THE GRADUAL CHANNEL APPROXIMATION
The Drain CurrentThe Drain Current
Charge Sheet Approximation & Depletion Approximation
DDE
IEEE convention
Drain I-V characteristicsDrain I-V characteristics
• Diffusion in sub-threshold
• Drift in strongly ON
• Smooth curves !
In Saturation:
• Qn(L) becomes very small.
• Field lines from gate terminate on acceptors in body.
• Drain end of channel is NOT in strong inversion,
• but SPICE models assume that it is !
Saturation and loss of inversionSaturation and loss of inversion
Development of SPICE Level 1 modelDevelopment of SPICE Level 1 model
From PSP:
Make strong-inversion assumptions
Use Binomial Expansion
Threshold voltage
SPICE Level 49: allowing for vSPICE Level 49: allowing for vsat sat
v =E(x)
v=vsat
satvx
xv1
)(
11
)(
Combining the velocities:
Putting this together with :
GCA, CSM, dVCS(x)/dx
Subthreshold currentSubthreshold current
From PSP:
Weak inversion:
Expand Qn and substitute in PSP Diffusion Equation.
Convert s to VGS:
Subthreshold current:
Si CMOS: why is it dominant for Si CMOS: why is it dominant for digital?digital?
4 reasons:
1. "Low" OFF current.
2. Compact logic: few transistors and no level shifting.
3. Small footprint.
4. Industrial investment.
pFET nFET
VSSVDD
INOUT
Example of small footprint
CMOS: the Industrial driveCMOS: the Industrial drive
Nodes relate to the DRAM half pitch, i.e., the width, and space in between, metal lines connecting DRAM bit cells
Logic speed is about Q and ILogic speed is about Q and I
Need:
• high - certainly
• Low L - but it adversely affects VT
• High Cox - but low CoxZL
• Low VDD - but it adversely affects ION
• Low VT - but it adversely affects ISUBT
3 major concerns for digital CMOS3 major concerns for digital CMOS
1. Increasing ION via mobility improvement
2. Reducing gate leakage via thicker, high-k dielectrics
3. Controlling VT and Isubt via suppression of the short-channel effect
Improving Improving : direction-dependent : direction-dependent m*m*
• k1 is a <100> direction
• k2 and k3 are orthogonal at the point of the energy minimum EC
Which direction has the higher effective mass?
Conductivity effective mass mConductivity effective mass mCC**
Electron accelerates in field E and reaches vd on next collision after time
v =0 v =vd
**/
2
**/
2
*
2
*
21
3
1
42
6
t
t
C
C
d
d
mmnq
mm
nq
Em
nqEqnEJ
m
q
E
v
qEmv
maF
For unstrained <100> Si: mC* = 0.26m0
What happens when Si is biaxially tensioned?
Effect of biaxial tensile strain on EEffect of biaxial tensile strain on ECC
• 4 valleys raised in energy
• 2 valleys lowered in energy
*
**/
*
**/
2
2
2
1 to(ideally)
21
3
1
42
6
t
tC
t
m
mmm
mm
nq
Unstrained
High-k dielectrics
ox
oxox tC
• High COX needed for ID and S
• High tOX needed to reduce gate leakage
• Resolve conflict by increasing
Tunneling through the oxideTunneling through the oxide
y (10 nm)
Ele
ctro
n en
ergy
E
Simplify the U profile →
Solve SWE in each region:
022
2
ykdx
d write as:
Solutions for Solutions for **
What is * ?* ?
Why is it :
-oscillatory in the channel ?
- damped in the oxide ?
- constant in the gate ?
Physically what is the "D-wave" ?
y (m)
Transmission Probability: DefinitionTransmission Probability: Definition
1. For the channel:
2. Do the derivatives and the conjugates:
3. Define the Transmission Probability:
What do these mean ?
What is the interpretation of this ?
Tunneling currentTunneling current
)(
)4(
silicatunn
silicatunn
kI
kkI
)4( silicakk
100% improvement in Cox
50% improvement in Cox
The Short-Channel EffectThe Short-Channel Effect
s = f (L, VDS) VT = f (L, VDS)
s is determined by capacitive coupling via Cox and Cbody,
AND
by capacitive coupling
via CDS
Reduce CReduce CDSDS by shrinking y by shrinking yjj
new yj
It's like reducing the area of a parallel plate capacitor
yj
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