Post on 31-Mar-2015
IL 2222 - MOSFETProfessor Ahmed Hemani
Dept. Of ES, School of ICT, KTH KistaEmail: hemani@kth.se
Website: www.it.kth.se/~hemani
MOS Capacitor, MOSFET
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
MOS: Metal-Oxide-Semiconductor
SiO2
metal
gate
Si body
Vg
gate
P-body
N+
MOS capacitor MOS transistor
Vg
SiO2
N+
~1.5nm thickFew oxide molecules
Usually made of Poly Silicon
Energy Diagram at Vg= 0
Flat-band Condition and Flat-band Voltage
Surface Accumulation
oxsfbg VVV Make Vg < Vfb fs : surface potential, band bendingVox: voltage across the oxide
Fs is neglible in accumulation
ox
ssa
ox
depa
ox
dep
ox
sox C
qN
C
WqN
C
Q
C
QV
2
Surface Depletion ( vg > vfb )
Surface Depletion
Slide 5-7
ox
ssasfboxsfbg C
qNVVVV
2
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Threshold Condition and Threshold Voltage
Threshold (of inversion):ns = Na , or
(Ec–Ef)surface= (Ef – Ev)bulk , or
A = B, and C = D
i
aBst n
N
q
kTln22
i
a
a
v
i
vbulkvf
gB n
N
q
kT
N
N
q
kT
n
N
q
kTEE
Eq lnlnln|)(
2
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Threshold Voltage
ox
BsaBfbgt C
qNVthresholdatVV
222
At threshold,
i
aBst n
N
q
kTln22
ox
Bsaox C
qNV
22
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
oxsfbg VVV
Threshold Voltage
ox
BssubBfbt C
qNVV
222
+ for P-body,– for N-body
Strong Inversion–Beyond Threshold
a
Bsdmaxdep qN
WW 22
Vg > Vt
Inversion Layer Charge, Qinv (C/cm2)
ox
invt
ox
inv
ox
BsaBfb
ox
inv
ox
depBfbg
C
QV
C
Q
C
qNV
C
Q
C
QVV
2222
)( tgoxinv VVCQ
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Choice of Vt and Gate Doping Type
Vt is generally set at a small positive value
So that, at Vg = 0,
the transistor does not have an inversion layer and current does not flow between the two N+ regions. Enhancement type device
• P-body is normally paired with N+-gate to achieve a small positive threshold voltage.• N-body is normally paired with P+-gate to achieve a small negative threshold voltage.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Review : Basic MOS Capacitor Theory
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Revi
ew :
Basi
c M
OS
Capa
cito
r The
ory
total substrate charge, Qs
invdepaccs QQQQ
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
MOS CV Characteristics
g
s
g
g
dV
dQ
dV
dQC
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
MOS CV Characteristics
g
s
g
g
dV
dQ
dV
dQC
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
The quasi-static CV is obtained by the application of a slow linear-ramp voltage (< 0.1V/s) to the gate, while measuring Ig with a very sensitive DC ammeter. C is calculated from Ig = C·dVg/dt. This allows sufficient time for Qinv to respond to the slow-changing Vg .
Cpoly
Cox
Cdep Cin v
Cox
Cdep
Cpoly
Cox
Cdep, min CinvCinv
Cox
(a) (b) (c) (d)
General case for both depletion and inversion regions.
In the depletion regions Vg Vt Strong inversion
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Equivalent circuit in the depletion and the inversion regimes
MOSFET
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
The MOSFET (MOS Field-Effect Transistor) is the building block of Gb memory chips, GHz microprocessors, analog, and RF circuits.
MOSFET the following characteristics:• small size• high speed• low power• high gain
Introduction to the MOSFET
Basic MOSFET structure and IV characteristics
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Introduction to the MOSFET
Two ways of representing a MOSFET:
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Complementary MOSFETs Technology
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
CMOS (Complementary MOS) Inverter
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
MOSFET Vt and the Body Effect
maxd
sdep W
C
sbdeptgsoxeinv VCVVCQ )(
))(( sboxe
deptgsoxe V
C
CVVC
sbtsboxe
deptsbt VVV
C
CVVV 00)(
• Redefine Vt as
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Two capacitors => two charge components
MOSFET Vt and the Body Effect
Body effect slows down circuits? How can it be reduced?
data model
-2 -1 0 1 2 Vsb (V)
NFET
PFET
Vt 0
Vt0
0.6
-0.2
-0.6
0.4
-0.4
Vt (V)
0.2
• Body effect: Vt is a function of Vsb. When the source-body junction is reverse-biased, Vt increases.
• Body effect coefficient:
a = Cdep/Coxe = 3Toxe / Wdep
sbtt VVV 0
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Retrograde Body Doping Profiles
• Wdep does not vary with Vsb .• Retrograde doping is popular because it reduces off-state leakage and allows higher surface mobility.
data model
-2 -1 0 1 2 Vsb (V)
NFET
PFET
Vt 0
Vt0
0.6
-0.2
-0.6
0.4
-0.4
Vt (V)
0.2
Wdmax for uniform doping
Wdmax for retrograde doping
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Uniform Body Doping
When the source/body junction is reverse-biased, there are two quasi-Fermi levels (Efn and Efp) which are separated by qVsb. An NMOSFET reaches threshold of inversion when Ec is close to Efn , not Efp . This requires the band-bending to be 2fB + Vsb , not 2fB.
)22(
)22(2
0
0
BsbBt
BsbBoxe
satt
VV
VC
qNVV
g is the body-effect parameter.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Qin
v in
MO
SFET Channel voltage Vcs
(x)x = 0: Vcs = Vs x = L: Vcs = Vd
• Qinv = – Coxe(Vgs – Vcs – Vt0 – a (Vsb+Vcs) = – Coxe(Vgs – Vcs – (Vt0 + a Vsb) – a Vcs)
= – Coxe(Vgs – mVcs – Vt) • m º 1 + a = 1 + 3Toxe/Wdmax
m is called the bulk-charge factor Typically m is 1.2 but can be simplified to 1
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
sbtsboxe
deptsbt VVV
C
CVVV 00)(
How to Measure the Vt of a MOSFET ?
•Method A. Vt is measured by extrapolating the Ids versus Vgs curve to Ids = 0.•Method B. The Vg at which Ids =0.1mA W/L
A
B
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
tgsdsnstgsoxedsat VVVVVCL
WI )(
Basic MOSFET IV ModelIds= WQinvv= WQinvmnE = WCox(Vgs– mVcs –
Vt)mndVcs/dxcs
L V
tcsgsnoxds dVVmVVWCdxIds
)(0 0
IdsL = WCoxmn(Vgs – Vt – mVds/2)Vds
dsdstgsn
dsdstgsn
dsdstgsnoxds
VVm
VVk
VVm
VVkL
W
VVm
VVCL
WI
)2
(
)2
(
)2
(
'
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
ox
oxnnoxn
tCk
' Process Transconductance
nn kL
Wk ' Gain factor
m is typically 1.2 but can be simplified to 1
Vdsat : Drain Saturation Voltage
)(0 dstgsnds
ds mVVVkdV
dI
m
VVV tgs
dsat
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Saturation Current and Transconductance
Transconductance: gm= dIds/dVgs
2
2
1)V(Vk
mI tgsndsat
Drain current in saturation region
)( tgsnsoxemsat VVCmL
Wg
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Satu
ratio
n –
Pinc
h O
ff
n+n+
S
G
VGS
D
VDS > VGS - VT
VGS - VT+-
Channel Length Modulation
)λV()V(Vkm
I dstgsndsat 12
1 2
• Increasing the Vds has the effect of the reducing the channel length as the depletion region on the drain side increases.
• Channel length reduction lower resistance Increase in Drain Current
• More pronounced for short channels• One of the five short channel effects
Velocity Saturation
sat
nv
EEE
+=
1
m
• Velocity saturation has large and deleterious effect on the Ion of MOSFETS
E << Esat : v = m En
E >> Esat : v = m Esatn
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
x (V/µm)xc = 1.5
u n (m
/s)
usat = 105
Constant mobility (slope = µ)
Constant velocity
MOSFET IV Model with Velocity Saturation
invds vWQI =
satdsdsdsdstgsnsoxeds EVIVVm
VVWCLI /)2
( ---= m
cssat
L V
dstcsgsnsoxeds dVEIVmVVWCdxIds
]/)([0 0
---=ò ò m
satcs
csnstcsgsoxeds
Edx
dVdxdV
VmVVWCI/1
/)(
+--=
m
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Vcs /L– the average electric field is replaced by
MOSFET IV Model with Velocity Saturation
LE
V
VVm
VVCL
W
I
sat
ds
dsdstgsnsoxe
ds
+
--=
1
)2
(m
LEV
Ichannel-longI
satds
dsds /1
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
MOSFET IV Model with Velocity Saturation
LmEVV
mVVV
sattgs
tgsdsat
/)(211
/)(2-++
-=
dVdI
ds
ds ,0Solving =
LEVVm
V sattgsdsat
11 +-
=
ns
dsatsat
vE m
2º
A simpler and more accurate Vdsat is:
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
EXAMPLE: Drain Saturation Voltage
Question: At Vgs = 1.8 V, what is the Vdsat of an NFET with Toxe = 3 nm, Vt = 0.25 V, and Wdmax = 45 nm for (a) L =10 mm, (b) L = 1 um, (c) L = 0.1 mm, and (d) L = 0.05 mm?
Solution: From Vgs , Vt , and Toxe , mns is 200 cm2V-1s-1. Esat= 2vsat/ m ns = 8 104 V/cm m = 1 + 3Toxe/Wdmax = 1.2
11
-
| |ø
öççè
æ+
-=
LEVVm
Vsattgs
dsat
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
(a) L = 10 mm, Vdsat= (1/1.3V + 1/80V)-1 = 1.3 V
(b) L = 1 mm, Vdsat= (1/1.3V + 1/8V)-1 = 1.1 V
(c) L = 0.1 mm, Vdsat= (1/1.3V + 1/.8V)-1 = 0.5 V
(d) L = 0.05 mm, Vdsat= (1/1.3V + 1/.4V)-1 = 0.3 V
EXAMPLE: Drain Saturation Voltage
1ççè
æ+
-=
LEVVm
Vsattgs
dsat
1-
| |ø
ö
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Idsat with Velocity Saturation
Substituting Vdsat for Vds in Ids equation gives:
LmEVV
Ichannel-long
LmEVV
VVC
mLW
I
sat
tgs
dsat
sat
tgs
tgssoxdsat -
+=-
+
-=
11
)(2
2
m
Very short channel case: tgssat VVLE -<<
)( VVCWvI tgsoxsatdsat -=
Idsat is proportional to Vgs–Vt rather than (Vgs – Vt)2 , not as sensitive to L
)( LmEVVCWvI sattgsoxsatdsat --=
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Current-Voltage RelationsA good ol’ transistor
QuadraticRelationship
0 0.5 1 1.5 2 2.50
1
2
3
4
5
6x 10
-4
VDS (V)
I D (
A)
VGS= 2.5 V
VGS= 2.0 V
VGS= 1.5 V
VGS= 1.0 V
Resistive Saturation
VDS = VGS - VT
Velocity Saturation
Long-channel device
Short-channel device
ID
VDSV
DSAT VGS
- VT
VGS
= VDD
The Short Channel Device enters saturation before VDS > VGS - VT
The IDSAT in short Channel Device has linear dependence on VGS as opposed to square dependence thus significantly reducing the drain current delivered for a given voltage and thus slows down the device
Velocity Saturation
What is the main difference between the Vg dependence of the long- and short-channel length IV curves?
0 1 2 2.5Vds (V)
0.0
0.1
0.2
0.3
0.4
I ds
(mA
/m
)
L = 0.15 mV
gs = 2.5V
Vgs
= 2.0V
Vgs
= 1.5V
Vgs
= 1.0V
Vds (V)
I ds
(A
/m
)
L = 2.0 m Vgs = 2.5V
Vgs = 2.0V
Vgs = 1.5V
Vgs
= 1.0V
0.0
0.01
0.02
0.03
(a)
(b)
Vt = 0.7 V
Vt = 0.4 V
0 1 2 2.5Vds (V)
0.0
0.1
0.2
0.3
0.4
I ds
(mA
/m
)
L = 0.15 mV
gs = 2.5V
Vgs
= 2.0V
Vgs
= 1.5V
Vgs
= 1.0V
Vds (V)
I ds
(A
/m
)
L = 2.0 m Vgs = 2.5V
Vgs = 2.0V
Vgs = 1.5V
Vgs
= 1.0V
0.0
0.01
0.02
0.03
(a)
(b)
Vt = 0.7 V
Vt = 0.4 V
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Sub-Threshold Conduction
0 0.5 1 1.5 2 2.510
-12
10-10
10-8
10-6
10-4
10-2
VGS (V)
I D (
A)
VT
Linear
Exponential
Quadratic
Typical values for S:60 .. 100 mV/decade
The Slope Factor
ox
DnkT
qV
D C
CneII
GS
1 ,~ 0
S is DVGS for ID2/ID1 =10
kT
qV
nkT
qV
D
DSGS
eeII 10
A U
nifie
d M
odel
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5x 10
-4
VDS (V)
I D (
A)
VelocitySaturated
Linear
Saturated
VDSAT=VGT
VDS=VDSAT
VDS=VGT
S D
G
B
Transistor Model for Manual Analysis
The Transistor as a SwitchVGS VT
RonS D
ID
VDS
VGS = VD D
VDD/2 VDD
R0
Rmid
ID
VDS
VGS = VD D
VDD/2 VDD
R0
Rmid
0.5 1 1.5 2 2.50
1
2
3
4
5
6
7x 10
5
VDD
(V)
Req
(O
hm)
The Transistor as a Switch
Dynamic Behavior of MOS Transistor
DS
G
B
CGDCGS
CSB CDBCGB
The Gate Capacitance
tox
n+ n+
Cross section
L
Gate oxide
xd xd
L d
Polysilicon gate
Top view
Gate-bulkoverlap
Source
n+
Drain
n+W
Gate Capacitance
S D
G
CGC
S D
G
CGC
S D
G
CGC
Cut-off Resistive Saturation
Most important regions in digital design: saturation and cut-off
Gate Capacitance
WLCox
WLCox
2
2WLCox
3
CGC
CGCS
VDS /(VGS-VT)
CGCD
0 1
CGC
CGCS = CGCDCGC B
WLCox
WLCox
2
VGS
Capacitance as a function of VGS(with VDS = 0)
Capacitance as a function of the degree of saturation
Diffusion Capacitance
Bottom
Side wall
Side wallChannel
SourceND
Channel-stop implant N A1
Substrate NA
W
xj
LS
Capacitances in 0.25 mm CMOS process
MOSFET – Some Secondary Effects
VT
L
Long-channel threshold Low V DS threshold
Threshold as a function of the length (for low V DS )
Drain-induced barrier lowering (for low L)
VDS
VT
Parasitic Resistances
W
LD
Drain
Draincontact
Polysilicon gate
R GD
S D
VGS,eff
RS RD
RS,D = R LS,D/W + RC
• Three Levels– Level 1
• Long Channel, Channel Length Modulation
– Level 2• Geometry based that includes detailed device physics• Velocity saturation, mobility degradation, DIBL• Analytical physics based model makes it complex and
inaccurate
– Level 3• Semi-empirical model• Measured data to calibrate and decide the main parameters• Accurate and efficient. Widely used.
SPICE Models for the MOS Transistor
BSIM3-V3
Parameter Category Description
Control Selection of level and models for mobility, capacitance and noise
DC Parameters for threshold and current and calculations
AC & Capacitance Parameters for capacitance computations
dW and dL Derivation of effective channel length and width
Process Process parameters such as oxide thickness and doping concentrations TOX, XJ, GAMMA1, NCH, NSUB
Temperature Nominal temperature and temperature coefficients for various device parameters TNOM
Bin Bounds device dimensions for which the model is validLMIN, LMAX, WMIN, WMAX
Flicker Noise Noise model parameters
SPICE Transistor ParametersParameter Name Symbol SPICE
NameUnits Default
Value
Drawn Length L L m -
Effective Width W W m -
Source Area AREA AS m2 0
Drain Area AREA AD m2 0
Source Perimeter PERIM PS m 0
Drain Perimeter PERIM PD m 0
Squares of Source Diffusion NRS - 1
Squares of Drain Diffusion NRD - 1