EE466: VLSI Design
Lecture 02
Non Ideal Effects in MOSFETs
Outline
• Junction Capacitances
– Parasitic capacitances
• Velocity Saturation
• Channel length modulation
• Threshold Voltage
– Body effect
– Subthreshold conduction
Junction Capacitances
• The n+ regions forms a number of
planar pn-junctions with the
surrounding p-type substrate
numbered 1-5 on the diagram.
• Planar junctions 2, 3 and 4 are
surrounded by the p+ channel stop
implant.
• Planar junction 1 is facing the
channel while the bottom planar
junction 5 is facing the p-type
substrate with doping NA.
• The junction types will be n+/p,
n+/p+, n+/p+ n+/p+ and n+/p.
Junction Capacitances
• The voltage dependent
source-substrate and drainsubstrate junction
capacitances are due to
depletion charge
surrounding the source or
drain diffusion regions
embedded in the substrate.
• The source-substrate and
drain-substrate junctions are
reverse biased under normal
operating conditions.
• The amount of junction
capacitance is a function of
applied terminal voltages
Vgs = 0
+
-
g
+
-
s
d
n+
n+
p-type body
b
Vgd
Junction Capacitances
• All junctions are assumed to
be abrupt.
• Given that the depletion
thickness is xd we can
compute the depletion
capacitance of a reverse
biased abrupt pn-junction.
• Where NA and ND are the ntype and p-type doping
densities respectively, V is the
negative reverse bias voltage.
• The built-in junction potential
is:
xd 
2 Si N A  N D
0  V 
q NAND
kT  N A N D
0 
ln 
q  ni2




Junction Capacitances
• The junction is forward biased for
a positive voltage V and reverse
biased for a negative voltage V.
• The depletion region charge
stored in this area in terms of xd is
• A stands for the junction area.
• The junction capacitance
associated with the depletion
region is defined as:
 N N 
 N N 
Q j  Aq A D  xd  A 2 Si q A D 0  V 
 NA  ND 
 NA  ND 
Cj 
• If we differentiate the equation
describing Qj with respect to the
bias voltage we get Cj.
dQ j
dV
Junction Capacitances
• We can write the junction
capacitance
 Si q  N A N D  


C j V   A



2  N A  N D   0  V 
• If the zero bias capacitance is:
• in a more general form as
• m is the gradient coefficient
and is 0.5 for abrupt junctions
and 1/3 for linearly graded
junction profiles
• The value of the junction
capacitance ultimately
depends on the external bias
voltage applied across the pnjunction.
C j0 
1
 Si q  N A N D  1 

 
2  N A  N D  0 
C j (V ) 
AC j 0
 V 
1  
 0 
m
Junction Capacitances
• The sidewalls of a typical
MOSFET source or drain
diffusion region are surrounded
by a p+ channel stop implant
having a higher doping density
than the substrate doping density
NA.
• The sidewall zero bias
capacitance is Cj0sw and will be
different from the previously
discussed junction capacitance.
• The zero-bias capacitance per unit
area can be found as follows:
C j 0 sw 
 Si q  N A( sw) N D  1
2  N A( sw)  N D  0( sw)
• Where NA(sw) is the sidewall
doping density, 0(sw) is the builtin potential of the sidewall
junctions.
• All sidewalls in a typical diffusion
structure have approximately the
same junction depth xj.
• The zero bias sidewall junction
capacitance per unit length is:
C jsw  C j 0 sw x j
MOS Capcitances
• Beyond the steady state behavior
of the MOS transistor.
• In order to examine the transient
(AC) response of MOSFETs the
digital circuits consisting of
MOSFETs we have to determine
the nature and amount of parasitic
capacitances associated with the
MOS transistor.
• On chip capacitances found on
MOS circuits are in general
complicated functions of the
layout geometries and the
manufacturing processes.
• Most of these capacitances are not
lumped but distributed and their
exact calculations would usually
require complex three
dimensional nonlinear chargevoltage models.
• A lumped representation of the
capacitance can be used to
analyze the dynamic transient
behavior of the device.
• The capacitances can be classified
as oxide related or junction
capacitances and we will start the
analysis with the oxide related
capacitances.
MOS Capacitances
Cgb D
Cdb
Cgd
G
B
Csb
Cgs
S
• Masks result in some
regions having overlaps,
for example the gate
electrode overlaps both the
source and drain regions at
the edges.
• Two overlap capacitances
arise as a result.
• These are Cgs and Cgd
respectively.
• If both the source and drain
regions have the same width (W),
the overlap capacitance becomes:
Cgs=CoxWLD and Cgd=CoxWLD.
• These overlap capacitances are
voltage dependent.
• Cgs, Cgd and Cgb are voltage
dependent and distributed
• They result from the interaction
between the gate voltage and the
channel charge.
MOS Capacitance Model
• Simply viewed as parallel plate
capacitor
• Gate-Oxide-Channel
• C = Cg = oxWL/tox = CoxWL
• Define
– Cpermicron = CoxL = oxL/tox
MOS Oxide Capacitances
• The gate-to-source capacitance is
actually the gate-to-channel
capacitance seen between the gate
and the source terminals.
• The gate-to-drain capacitance is
actually the gate-to-channel
capacitance seen between the gate
and the drain terminals.
• In Cut-off mode the surface is not
inverted and there is no
conducting channel linking the
surface to the source and to the
drain.
• The gate-to-source and gate-todrain capacitances are both equal
to zero (Cgs=Cgd=0).
• The gate-to-substrate capacitance
can be approximated by:
Cgb=CoxWL
• In linear mode the inverted
channel extends across the
MOSFET between the source and
drain. This conducting inversion
layer on the surface effectively
shields the substrate from the gate
electric field making it Cgb=0.
MOSFET Oxide Capacitance
• In linear mode the distributed
gate-to-channel capacitance
maybe viewed as being shared
equally between the source and
the drain leading to:
Cgs=Cgd=0.5CoxWL
• If the MOSFET is operating in
saturation mode the inversion
layer on the surface does not
extend to the drain, but is pinched
off.
• The gate-to-drain capacitance in
therefore zero (Cgd=0).
• The source is however still linked
to the conducting channel. It
shields the gate from the channel
leading to Cgb of zero.
• The distributed gate-to-channel
capacitance as seen between the
gate and the source is
approximated by: Cgs2/3CoxWL.
MOS Gate Capacitances
Cap
Cutoff Linear
Saturation
Cgb
C0
0
0
Cgs
0
C0/2
2/3C0
Cgd
0
C0/2
0
Cg=Cgs+Cgd+Cgb
C0
C0
2/3C0
Velocity Saturation
• Ideal carrier velocity relation:
– v = mE
– E = Vds/L
• In reality velocity does not increase forever
with applied field
• For high values of Applied field, E ~
10000V/cm
– v= mE/(1+E/Esat)
Velocity Saturation and Mobility
Degradation
• Recall ideal current equation
V
I ds   Vgs  Vt  dsat
2



2
Vgs  Vt 
V
 dsat

2
• With velocity saturated at v=vsat
I ds  C oxW (V gs  Vt )v sat
Velocity Saturated Current
Modeling
• Cutoff
– Ids = 0: Vgs<Vt
• Linear
– Ids = IdsatVds/Vdsat:
Vds<Vdsat
• Saturation
– Ids = Idsat: Vds>Vdsat
• Modeling with empirical
parameters
– α between 2(ideal) to
1(compeletely velocity
saturated
I dsat  Pc

2
(V gs  Vt ) 
Vdsat  Pv (Vgs  Vt ) / 2
Velocity Saturation
•
•
•
•
•
The critical E-field at which
scattering effects occur depends on
the doping levels and the vertical
electric field applied.
Velocity saturation effects are less
pronounced in pMOS devices.
By increasing VDS the electrical field
in the channel ultimately reaches the
critical value and the carriers at the
drain become velocity saturated.
Further increasing VDS does not result
in increased ID. The current saturates
at IDSAT
The behavior of the MOS transistor is
better understood by analysis of the IV curves.