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Chapter 2
MOS Transistors
2.1 Structure of MOS transistors
We will discuss the structure of two MOS
Field-Effect-Transistors(FETs) that are building blocks for all
digital devices.The nMOS transistor shown in Figure 2.1 (n-type,
n-channel,enhancement mode field-effect transistor) is built on the
p-typesemiconductor substrate, which is usually acceptor-doped
silicon.
21
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IC design 2.1. STRUCTURE OF MOS TRANSISTORS
source drain
substrate
gate
n+ n+
oxidepolysilicon
p-type semiconductor (Si) substrate
channel length(L)
Source Drain
Substrate
Gate
Figure 2.1: An internal structure of an nMOS transistor.
Two n+ diffusion regions (+ indicates the high degree ofdoping)
form the source and drain of the transistor. The area inbetween
forms a conducting channel. Potentially, electrons,negative
carriers, will form the current in the channel.
The gate, which is formed from a conductor,
typicallypolysilicon, is insulated from the source-channel-drain
structure(and from the substrate) by the layer of silicon
dioxide.
The voltage between the gate and the substrate induces
theelectric field which controls the flow of the carriers in the
channel.This gives the rise to the name: field-effect transistor
(FET).
Transistor structure is completely symmetrical with respect
tothe source and drain. The role is defined by terminal
voltageswhich establish the direction of the current (carriers)
flow.
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IC design 2.1. STRUCTURE OF MOS TRANSISTORS
The pMOS transistor (p-type, p-channel) is a
complementarystructure to the nMOS transistor as depicted in Figure
2.2.
source drain
substrate
gate
oxide
channel length(L)
Source Drain
Substrate
Gate
n-type semiconductor (Si) substrate
p+ p+
polysilicon
Figure 2.2: An internal structure of a pMOS transistor.
The pMOS transistor is built on the n-type substrate which
isdonor-doped silicon.
The source and drain of a pMOS transistor are now p+
diffusionregions.
The carriers in the channel are now positive holes. As
previously,their flow is controlled by the gate-substrate
voltage.
MOS transistors described above are referred to as
enhancementmode transistors.There are also depletion mode
transistors used mainly in the analogcircuitry.
July 25, 2002 23 A.P.Paplinski
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IC design 2.2. OPERATION OF MOS TRANSISTORS
2.2 Operation of MOS transistors
We will describe operation of an enhancement-mode n-channel
MOSfield effect transistor (nMOS) as illustrated in Figure 2.1. The
pMOSoperates in the dual way. The basic principle of operation can
be statedas follows.
The flow of the current between the source and the drain
iscontrolled by the electric field generated by thegate-substrate
voltage.
In order for the drain-source current to exist there must be
carriersexisting in the area between the source and drain referred
to as theconducting channel. We will examine first how the channel
is createdand then how the drain current depends on relevant
voltage. Note that aMOS transistor is a four terminal device. In
most cases, the substrateand the source of an nMOS are connected to
the ground potential(GND) as in Figure 2.3.
A.P.Paplinski 24 July 25, 2002
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IC design 2.2. OPERATION OF MOS TRANSISTORS
Step 1: (Figure 2.3) VGS < VT = ID = 0
DEPLETION REGION
SUBSTRATE: p-Si
SOURCE(n+)
DRAIN(n+)
oxideGATE
V = 0Vsub
V = 0VSV
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IC design 2.2. OPERATION OF MOS TRANSISTORS
Step 2: (Figure 2.4) VGS > VT and VDS = 0 = ID = 0In this
case (Figure 2.4), when the gate voltage VGS increases above
DEPLETION REGION
SUBSTRATE: p-Si
SOURCE(n+)
DRAIN(n+)
oxideGATE
V = 0Vsub
V = 0VSV >VGS T
V = 0VDS
inversion layer (source--drain channel)
Figure 2.4: Formation of the conducting channel (inversion
layer) in an enhancement-mode nMOS.
the threshold voltage VT , then the electric field repels more
holes fromthe channel area leaving an excess of electrons.The field
also pulls out electrons from the source and drain area which,by
virtue of being the n+ regions, have excess of electrons.
As a result in the area between source and drain an inversion
layer iscreated in which there is an excess of the negative
carriers, that is,electrons. In other words a conducting channel
has been formedbetween the source and drain.
Due to the fact that in this case we assume that the
drain-sourcevoltage VDS = 0, thermal equilibrium exists in the
channel region andthe drain current, ID = 0.
The threshold voltage VT depends on a specific
transistorconfiguration, that is, on a specific technology of
fabrication of MOStransistors and usually is in a range of
0.5V.
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IC design 2.2. OPERATION OF MOS TRANSISTORS
Step 3: Linear region (Figure 2.5)VGS > VT and 0 < VDS
< Vsat = ID > 0
DEPLETION REGION
SUBSTRATE: p-Si
SOURCE(n+)
DRAIN(n+)
oxideGATE
V = 0Vsub
V = 0VSV >VGS T
V > 0VDS
CHANNEL
Figure 2.5: An nMOS transistor operating in the linear
region
In this case, in the presence of free electrons in the
conducting channel,when the drain-source voltage increases above
zero, VDS > 0, thedrain-source current, ID starts to flow.
When the VDS voltage is relatively small, the transistor
operates in theso-called linear region. In this region of operation
the drain current IDis a quadratic function of the source-drain
voltage, VDS. Descriptivelyit means that the increase of the drain
current slows down when thesource-drain voltage increases.
The channel depth at the drain end decreases with the increase
of thesource-drain voltage as illustrated in Figure 2.5.
Equivalently we cansay that the channel region acts as a voltage
controlled resistor: theresistance increases when the source-drain
voltage increases.
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IC design 2.2. OPERATION OF MOS TRANSISTORS
Step 4: pinch-off point (Figure 2.6)VGS > VT , VDS = Vsat =
ID > Isat
DEPLETION REGIONSUBSTRATE: p-Si
SOURCE(n+)
DRAIN(n+)
oxideGATE
V = 0Vsub
V = 0VSV >VGS T V = VDS sat
CHANNELPINCH-OFF POINT
Figure 2.6: The pinch-off point for an nMOS transistor
When the source-drain voltage, VDS, reaches a certain value,
Vsat, thechannel depth at the drain end is reduced to zero. This is
called thepinch-off point. In other words, at the pinch-off point,
VDS = Vsat.
From now on, the further increase of the source-drain voltage
does notresult in an increase of the source-drain current. The
transistor nowoperates in the saturation mode.
A.P.Paplinski 28 July 25, 2002
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IC design 2.2. OPERATION OF MOS TRANSISTORS
Step 5: Saturation mode (Figure 2.7)VG > VT , VD > VDsat =
ID = IDsat
DEPLETION REGIONSUBSTRATE: p-Si
SOURCE(n+)
DRAIN(n+)
oxideGATE
V = 0Vsub
V = 0VSV >VGS T V > VDS sat
CHANNELPINCH-OFF POINT
Figure 2.7: The nMOS transistor operating in the saturation
mode
In the saturation mode, the depletion region adjacent to the
drain isenlarged. Note that in the depletion region there are no
free electriccarriers and the area acts as a dielectric.
The source-drain current, ID is now independent of the
source-drainvoltage, VDS.
Electrons arriving from the source to the channel are injected
into thedepleted part of the channel and are accelerated towards
the drain bythe high electric field induced by the source-drain
voltage.
Finally, it is important to remember that under no conditions
there is aconstant current flowing between the gate and other
transistorterminals because the gate is insulated by a layer of
SiO2.
July 25, 2002 29 A.P.Paplinski
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IC design 2.3. GEOMETRIC AND MATERIAL PROPERTIES OF A MOS
TRANSISTOR
2.3 Geometric and material properties of a MOStransistor
2.3.1 Geometric configuration of a MOS transistor
Three components of the MOS transistor structure, namely, the
gate,source and drain form a 3-D structure as illustrated in Figure
2.8.
Poly-silicon
L
Diffusion DiffusionW
Top view
Gate
Cross-Section
Diffusion Diffusion
toxn+n+
SUBSTRATE, p - Si (WELL)
Poly
Figure 2.8: Basic geometric parameters of a MOS transistor.
The gate of the MOS transistor is usually made of polysilicon,
which isformed from polycrystaline silicon and relatively good
conductance.
The gate is insulated by the layer of the silicon dioxide, SiO2,
from aconducting channel existing between two diffusion areas which
formthe drain and the source of the transistor.
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IC design 2.3. GEOMETRIC AND MATERIAL PROPERTIES OF A MOS
TRANSISTOR
Diffusion areas (source and drain) are created inside a
substrate (alsoknown in some technological context as the well) of
the opposite type,e.g. n+ diffusion inside the p substrate, where
n+ indicates siliconhighly doped with donors.
From the top and cross-sectional views of the MOS
transistorpresented in Figure 2.8 we note that three basic
geometrical parametersof the transistor are the following:
L and W the length and width of the conducting channelbetween
the source and drain,
tox thickness of the oxide layer between the gate and
thediffusion/substrate areas.
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IC design 2.3. GEOMETRIC AND MATERIAL PROPERTIES OF A MOS
TRANSISTOR
2.3.2 The gate capacitance
The gate-oxide-channel structure forms a capacitor. The
gate-oxidecapacitance per unit area can be approximately calculated
as:
Cox =oxtox
(2.1)where
ox = 0.351pF/cm
is the permittivity (a dielectric constant) of SiO2. Note that
thecapacitance is inversely proportional to the thickness of the
silicondioxide layer.
Example
Let the oxide thickness be: tox = 500A = 500 108cm =
0.05m.Then
Cox =0.351 10120.5 105 = 0.7 10
7F/cm2 = 70nF/cm2
Note that the oxide thickness and the resulting gate capacitance
perunit area are parameters specified by the technological process
offabrication of MOS transistors.
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IC design 2.3. GEOMETRIC AND MATERIAL PROPERTIES OF A MOS
TRANSISTOR
2.3.3 Mobility of carriers
Movement of carriers (electron and holes) can be characterised
by theirmobility. The mobility is a proportionality constant
between appliedelectric field (in V/cm) and resulting velocity of
the carriers (incm/sec). The intrinsic values (for pure silicon) of
the mobility forelectrons and holes in the room temperature are
n = 1350cm2/Vs , (electrons) p = 480cm2/Vs (holes) (2.2)
Values of the mobility in doped semiconductor are smaller, but
the rationp
2.5 (2.3)
is preserved. The fact that holes are more sluggish than
electron hassome influence on relative sizes of nMOS and pMOS
transistors.
July 25, 2002 213 A.P.Paplinski
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IC design 2.3. GEOMETRIC AND MATERIAL PROPERTIES OF A MOS
TRANSISTOR
2.3.4 Basic configurations of MOS transistors
The four terminals of MOS transistors, namely, the drain,
source, gateand substrate are usually connected to the ground (GND)
and supplyvoltages in the way as indicated in Figure 2.9.
GND (VSS)
g dsubs
VGS
VDS
DI
nMOSVDD
pMOS
VGSVDS
d
s
sub
DI
g
VGS, VDS = 0 . . . VDD VGS, VDS = VDD . . . 0
p-ty
pe S
i sub
stra
te
n di
ffso
urce
n di
ffdr
ain
elec
trons
gate
GND
d
g
s
n-ty
pe S
i sub
stra
te
p di
ffso
urce
p di
ffdr
ain
hole
s
gate
VDD
d
g
s
Figure 2.9: Basic configurations of MOS transistors
The nMOS transistor has its source and the p-type substrate
connectedto the ground terminal GND (VSS) = 0V, whereas the pMOS
transistorhas its source and the n-type substrate connected to VDD
= 25V.The VGS and VDS voltages are positive for the nMOS transistor
andnegative for the pMOS.
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IC design 2.4. DC ANALYSIS OF THE MOS TRANSISTORS
2.4 DC analysis of the MOS transistors
2.4.1 Transistor parameters
In this section we will discuss the relationship between
constant (DC)voltages at the transistor terminals and the resulting
drain current ID.Apart from the voltages, the ID current is also a
function of
the process parameters: VT the threshold voltages (VTn orVTp),
and a process transconductance, kc defined as follows
kc = c Cox (2.4)where c is an effective mobility of the carriers
(e or p ), andCox is the gate capacitance per unit area,
the width, W , and length, L, of the channel between the
sourceand the drain (see Figure 2.8).
The parameter which links the process transconductance, kc, with
thetransistor dimension is called the (non-linear)
transistortransconductance parameter, gc, and is defined in the
following way:
gc =c Cox
2 WL
(2.5)It is also convenient to use a gate voltage relative to the
thresholdvoltage defined as follows:
V = VGS VT (2.6)Note that all the above parameters, namely, kc,
gc, V can be referred toa specific type on MOS transistor as, kn,
kp, gn, gp, and Vn, Vp,respectively.
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IC design 2.4. DC ANALYSIS OF THE MOS TRANSISTORS
2.4.2 Current-Voltage relationships
With the above parameters, the relationships between the DC
IDcurrent and relevant voltages can be summarised as in Table
2.1.
nMOS | pMOS
Cut-off region:VGS < VTn | VGS > VTp
ID = 0
Linear region:VGS VTn, VDS < Vn | VGS VTp, VDS > Vp
ID = gc (2V VDS)VDS
Saturation region:VGS VTn, VDS Vn | VGS VTp, VDS Vp
ID = gc V 2
Table 2.1: Fundamental DC relationships for MOS transistors
Note that the drain current ID is proportional to the ratio W/L
of thetransistor channel size. For given process parameters and
voltages,
the wider the transistor channel, W , the larger ID current, and
the longer the transistor channel, L, the smaller ID current.
Note also that the saturation occurs when
VDS = VGS VT = V
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IC design 2.4. DC ANALYSIS OF THE MOS TRANSISTORS
At the saturation point the current expressions for the linear
andsaturation regions are identical what can be seen from the
followingderivation:
Isat = gc (2VV V 2) = gc V 2 (2.7)
Example
Consider an nMOS transistor with the following parameters:n =
600 cm
2/Vs ,Cox = 7 108 F/cm2,VTn = 1V,W = 20m, L = 2m.The
transconductance parameter can be calculated as (watch out to
usethe consistent units):
gc = 0.5 600 7 108 202
= 210 106A/V2 = 0.21mA/V2
July 25, 2002 217 A.P.Paplinski
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IC design 2.4. DC ANALYSIS OF THE MOS TRANSISTORS
2.4.3 Current-voltage characteristics of an nMOS transistor
Now we can use MATLAB (or similar package)to plot
thecurrent-voltage characteristics
ID = ID(VGS, VDS)
as presenter in Table 2.1. The drain current is a function of
twovoltages, namely, the gate-source and drain-source voltages,
therefore,could be represented as a surface in a three-dimensional
space,VDS, VGS, ID. Traditionally, however, this surface is
represented by thefamily of curves as in Figure 2.10.
0 2 4 60
1
2
3
4
VDS (V)
I D (m
A)
Drain current vs. drainsource voltage
VGS = 3 V
VGS = 4 V
VGS = 5 V
0 2 4 60
1
2
3
4
VGS (V)
I D (m
A)Drain current vs. gatesource voltage
VT|
Figure 2.10: An example of MATLAB generated current-voltage
characteristics of aMOS transistor. Left plot: the drain current ID
versus the drain-source voltage, VDSfor various values of the
gate-source voltage, VGS . Right plot: the drain current IDversus
the gain-source voltage, VGS , in saturation.
The current-voltage characteristics were generated for the value
of thetransistor non-linear transconductance gc = 0.21mA/V2 and
thethreshold voltage VT = 1V.From the plots in Figure 2.10 and
Table 2.1 you can identify: thethreshold voltage, the linear
region, the saturation region, thesaturation voltage.
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IC design 2.4. DC ANALYSIS OF THE MOS TRANSISTORS
2.4.4 Switching model of MOS transistors
In digital circuits MOS transistors work in such a way that they
switchbetween the off-state and saturation.Therefore their
switching DC model can be approximated by acontrolled switch and a
controlled current source (sink) as presentedin Figure 2.11.
ON: if VGS > VT
SATURATION:if VDS > VGS VthID(VGS)
ID(VGS)
SATURATION:if VDS < VGS VTON: if VGS < VT < 0GND
g ds
VGS
nMOSVDD
gds
VGS
pMOS
Figure 2.11: A simplified switching model of MOS transistors
In other words, in digital circuits, a MOS transistor is either
in
off-state, VGS 0V: an open switch in the off-state, or in
saturation, VGS VDD: a current source generating currentID = gc
V 2
Note that the gate is always electrically insulated from the
source andthe drain.
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IC design2.5. MOS TRANSISTORS TOPOLOGY AND GEOMETRY OF THE
CIRCUIT
LAYOUT
2.5 MOS transistors topology and geometry of thecircuit
layout
From the designer view point we will be operating with
threerepresentations of MOS circuitry as presented in Figure 2.12.
Thesethree representations are:
Schematic diagrams. Stick diagrams representing topology of the
integrated circuit. Circuit layouts representing the exact geometry
of the integrated
circuit. The layouts are generalisation of the top view of a
MOStransistor as in Figure 2.8 with additional connections required
tobuild a complete circuit.The circuit geometry must have its
dimensions specified preciselyin micrometers (m) or in relative
units called units.Ultimately, from the circuit layouts we extract
photolithographicmasks used in fabrication of integrated
circuits.
Comparing three circuit representations from Figure 2.12 we note
that:
Transistors are represented by four-terminal symbols in
theschematics. In the stick diagram and the circuit layout
transistorsare identified by crossing of the red path representing
the gate,over the green (nMOS) or brown(pMOS) path representing
therelevant diffusion. The drain and source terminals exist on
bothsides of the gate.
Note that the sources of the transistors are connected to to
eitherVDD (pMOS), or GND (nMOS). These two power rails are madeof
metal and are represented by blue paths in the stick diagramsand
circuit layouts. A special contact must be made to connectdiffusion
to metal.
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IC design2.5. MOS TRANSISTORS TOPOLOGY AND GEOMETRY OF THE
CIRCUIT
LAYOUT
n substr tocontact:
metal
contact:p diff to
metal
VDDmetal
p diffusion
polysilicon
pMOS
VDD
G S
D
GS
Dsub
metal
polysilicon
nMOS n diffusion
GNDcontact:n diff to
metalp substr to
contact:
metal
GND
G
S
DG sub
CIRCUIT LAYOUTSTICK-DIAGRAMSCHEMATIC
nMOS
pMOS
S
D
Figure 2.12: Three representations of MOS circutry: schematics,
stick diagrams andcircuit layouts.
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IC design2.5. MOS TRANSISTORS TOPOLOGY AND GEOMETRY OF THE
CIRCUIT
LAYOUT
Finally, the forth terminal, namely the substrate must be
alsoconnected to the appropriate power rail, that is, to either
VDD(pMOS, n substrate), or GND (nMOS, p substrate). Rememberthat
pMOS transistors are created in the n-type substrate andnMOS
transistors in the p-type substrate. We have to rememberabout the
substrate contacts even if we use simplifiedthree-terminal symbols
of MOS transistors as in (Figure 2.13).
nMOS pMOS
Figure 2.13: Three-terminal symbols of MOS transistors.
In the example in Figure 2.12, transistors have the size:W = 4 ,
L = 2
The contacts usually have dimension 4 4 and they occupied
asignificant portion of the circuit layout.
A.P.Paplinski 222 July 25, 2002