Topics

Derivation of transistor characteristics.
Modern VLSI Design 3e: Chapter 2
Copyright  1998, 2002 Prentice Hall PTR
MOSFET gate as capacitor

Basic structure of gate is parallel-plate capacitor: (A good reference on
this is www4.ncsu.edu:8030/~vmisra/MOS.ppt and physics of MOSFET is
http://ece-www.colorado.edu/~bart/book/book/chapter2/ch2_6.htm)
gate
+
+
+
+
+
+
+
+
+
+
+
+
xox
SiO2
Vg
-
+
-
-
-
-
-
-
-
-
substrate
Modern VLSI Design 3e: Chapter 2
-
-
-
-
inversion
Copyright  1998, 2002 Prentice Hall PTR
MOS as a parallel plate capacitance

Formula for parallel plate capacitance/unit area:

Cox = ox / xox,
where xox is the thickness of the SO2 in cm, and
ox is its permittivity:
ox = 3.46 x 10-13 F/cm
Gate to substrate capacitance helps determine the
characteristics of a channel which forms an inversion
region (region devoid of dopant carriers in the substrate)
between the source and drain of a MOS transistor. In
particular, it plays a critical role in the determination of the
threshold voltage of a MOS transistor.
Modern VLSI Design 3e: Chapter 2
Copyright  1998, 2002 Prentice Hall PTR
Threshold voltage
The threshold voltage, Vt0, when the source to substrate voltage is 0.
Vt0 = Vfb + s + Qb/Cox + VII
Components of Vt0 are:
 Vfb = flatband voltage between gate and substrate, i.e., the work function
difference between gate and substrate. The work function is the energy required to
remove an electron from the Fermi energy to the vacuum level.
2kT N a

ln
 s is the surface potential which is equal to twice the Fermi potential
q
ni
where ni is the intrinsic carrier (electron or hole) concentration of the substrate,
kT/q is the thermal voltage, and Na is the hole concentration in the substrate.
 Qb/Cox is the voltage across the capacitor, whereQ  2q N  , q is the charge
b
si a s
of an electron, si is the permittivity of silicon,

 VII is the voltage adjustment = qDI/Cox, where DI is the ion implantation
concentration (body effect)

Modern VLSI Design 3e: Chapter 2
Copyright  1998, 2002 Prentice Hall PTR
Threshold voltage


The flat-band voltage between gate and substrate depends on the difference in
the work function between gate and substrate (gs) and on fixed surface charge
(Qf):
Q
V fb   gs  f
Cox
kT N N
 gs   ln a 2 dp
q
ni
assuming that the gate is doped with n-type carriers with the concentration of Ndp


When the source to substrate voltage is not 0 then the threshold voltage is shifted
by a differential voltage, called the body effect:
Vt   n( s  Vsb  s )
n 
Modern VLSI Design 3e: Chapter 2
2q si N a
Cox
Copyright  1998, 2002 Prentice Hall PTR
Body effect
Reorganize threshold voltage equation:
Vt = Vt0 + Vt
 Threshold voltage is a function of
source/substrate voltage Vsb.
 Body effect  is the coefficient for the Vsb
dependence factor.
 (I am skipping this slide as it is replicated in
my changes)

Modern VLSI Design 3e: Chapter 2
Copyright  1998, 2002 Prentice Hall PTR
Example 2-3 (pp-56-57): Threshold voltage of a transistor
Vt0 = Vfb + s + Qb/Cox + VII
= -0.91 V + 0.58 V + (1.4E-8/1.73E-7) +
0.92 V
= 0.68 V
Body effect n = sqrt(2qSiNA/Cox) = 0.1
Vt = n[sqrt(s + Vsb) - sqrt(Vs)]
= 0.16 V
Modern VLSI Design 3e: Chapter 2
Copyright  1998, 2002 Prentice Hall PTR
Example 2-3 (pp-56-57): Threshold voltage of a transistor
x ox  200 A
ox  3.45 1013 F /cm
 s  0.6v
Q f  1.6 108 C /cm 2
si  1.0 1012
N a  1015 /cm 3
N ap  1019 /cm 3
DI  1.0 1012
Cox  ox / x ox  3.45 1013 /2 106  1.73 107 C /cm 2
kT N a N dp
10151019
gs   ln
 0.026ln
 0.82V
2
q
(1.45 1010 ) 2
ni
1.6 108
V fb  gs 
 0.82 
 0.91V
Cox
1.73 107
Qf
2kT N a
1015
s 
ln
 2  0.026  ln
 0.58V
q
ni
1.45 1010
Qb  Qb  2qsiN a  s  2 1.6 1019 1012 1015  0.58  1.4 108
VII  qDI /Cox  1.6 1019 1012 /1.73 107  0.92V
Q
Vt 0  V fb   s  b  VII
Cox
 0.91 0.58 
1.4 108
 0.92  0.68V
1.73 107
2qsiN a
2 1.6 1019 1012 1015
n 

 0.1
Cox
1.73 107
Vt   n (  s  Vsb   s )  0.1 ( 0.58  5  0.58)  0.16
Modern VLSI Design 3e: Chapter 2
Copyright  1998, 2002 Prentice Hall PTR
More device parameters
Process transconductance k’ = Cox.
( denotes the mobility of channel electrons
or holes)
 Device transconductance  = k’W/L.

Saturation Current:
Id = 0.5k’ (W/L)(Vgs - Vt) 2 = 0.5  (Vgs - Vt) 2
Modern VLSI Design 3e: Chapter 2
Copyright  1998, 2002 Prentice Hall PTR
Channel length modulation
length parameter



a describes small dependence of drain current on
Vds in saturation.
Factor is measured empirically.
New drain current equation:
– Id = 0.5k’ (W/L)(Vgs - Vt) 2(l - a Vds)


Equation has a discontinuity between linear and
saturation regions---small enough to be ignored.
Note: I use a instead of lto avoid confusion with
channel parameter l.
Modern VLSI Design 3e: Chapter 2
Copyright  1998, 2002 Prentice Hall PTR
Gate voltage and the channel
gate
current
source
drain
Linear region
Vds < Vgs - Vt
Id
Vgs > Vds + Vt
Inversion layer
gate
current
source
drain
Saturation region
Vds = Vgs - Vt
Id
Vgs = Vds + Vt
Inversion layer shrinks
source
gate
current
drain
Id
dId/dVds decreases
Modern VLSI Design 3e: Chapter 2
Pinch off
Channel transconductance decreases
Vds > Vgs - Vt
Vgs < Vds + Vt
Copyright  1998, 2002 Prentice Hall PTR
Leakage and subthreshold current
A variety of leakage currents draw current
away from the main logic path.
 The sub-threshold current is one particularly
important type of leakage current.
 (When the gate voltage is just below the
threshold voltage, the point of weakinversion)

Modern VLSI Design 3e: Chapter 2
Copyright  1998, 2002 Prentice Hall PTR
Types of leakage current.


Weak inversion current (sub-threshold current).
Punch-through currents. (When the drain to source voltage
gets to be too high, the source and drain regions may be shorted.)
 Gate oxide tunneling-- Hot carriers
(For short channels, electrons may accumulate into the gate oxide, leading
to changes in threshold conditions.)


Reverse-biased pn junctions
Drain-induced barrier lowering (Shift in threshold level to
increase in drain voltage-- higher current flow near cut-off when the
drain voltage increases)

Gate-induced drain leakage (As gate oxide layer becomes
very thin, channel current may leak into the gate-- non-ideal capacitor)
Modern VLSI Design 3e: Chapter 2
Copyright  1998, 2002 Prentice Hall PTR
Subthreshold current

Subthreshold current:
www4.ncsu.edu:8030/~vmisra/MOS.ppt and physics of MOSFET

IDS
I 
'
GS
T
L
2q S N A
2 2 F  VSB

2
t
W
log10 IDS  log 10
 L
1 1
q

S n kTln(10)


W q(VGS VT ) nkT
I e
1  e qVDS kT
L
W q(V V ) nk T
 I e
when Vds >> q/kT
IDS 
Modern VLSI Design 3e: Chapter 2
n  1

2 2 F  VSB
 q VGS VT
I 
 log 10 e
 kT
n
S is called the sub-threshhold swing;
smaller values of S are desirable
Copyright  1998, 2002 Prentice Hall PTR
The modern MOSFET
Features of deep submicron MOSFETs:
– epitaxial layer for heavily-doped channel;
– (both n and p wells over an epitaxial layer)
– reduced area source/drain contacts for lower
capacitance;
– lightly-doped drains to reduce hot electron
effects;
– silicided poly, diffusion to reduce resistance.
Modern VLSI Design 3e: Chapter 2
Copyright  1998, 2002 Prentice Hall PTR
Circuit simulation
Circuit simulators like Spice numerically
solve device models and Kirchoff’s laws to
determine time-domain circuit behavior.
 Numerical solution allows more
sophisticated models, non-functional (tabledriven) models, etc.

Modern VLSI Design 3e: Chapter 2
Copyright  1998, 2002 Prentice Hall PTR
Spice MOSFET models





Level 1: basic transistor equations of Section 2.2;
not very accurate.
Level 2: more accurate model (effective channel
length, etc.).
Level 3: empirical model.
Level 4 (BSIM): efficient empirical model.
New models: level 28 (BSIM2), level 47
(BSIM3). (BSIM4-July 2005- for submicron MOS
simulation--Level 54)
Modern VLSI Design 3e: Chapter 2
Copyright  1998, 2002 Prentice Hall PTR
Some (by no means all) Spice
model parameters
L, W: transistor length width.
 KP: transconductance.
 GAMMA: body bias factor.
 AS, AD: source/drain areas.
 CJSW: zero-bias sidewall capacitance.
 CGBO: zero-bias gate/bulk overlap
capacitance.

Modern VLSI Design 3e: Chapter 2
Copyright  1998, 2002 Prentice Hall PTR