gm= -2 IDSS/VP(1- VGS/VP) (2)

From eqn (1)

(1-VGS/VP)= (IDS/IDSS)1/2 (3)
Suppose gm=gm0 when vGS=0
gmo=-2IDSS/VP (4)
Therefore from eqn (2) and (4)
gm=gm0(1-VGS/VP)

MOSFET
MOSFET stands for metal oxide semiconductor field effect transistor. It is capable of
voltage gain and signal power gain. The MOSFET is the core of integrated circuit
designed as thousands of these can be fabricated in a single chip because of its very
small size. Every modern electronic system consists of VLST technology and without
MOSFET, large scale integration is impossible.
It is a four terminals device. The drain and source terminals are connected to the
heavily doped regions. The gate terminal is connected top on the oxide layer and the
substrate or body terminal is connected to the intrinsic semiconductor.
MOSFET has four terminals which is already stated above, they are gate, source drain
and substrate or body. MOS capacity present in the device is the main part. The
conduction and valance bands are position relative to the Fermi level at the surface is a
function of MOS capacitor voltage. The metal of the gate terminal and the sc acts the
parallel and the oxide layer acts as insulator of the state MOS capacitor. Between the
drain and source terminal inversion layer is formed and due to the flow of carriers in it,
the current flows in MOSFET the inversion layer is properties are controlled by gate
voltage. Thus it is a voltage controlled device.
Two basic types of MOSFET are n channel and p channel MOSFETs. In n channel
MOSFET is current is due to the flow of electrons in inversion layer and in p channel
current is due to the flow of holes. Another type of characteristics of clarification can be
made of those are enhancement type and depletion type MOSFETs. In enhancement
mode, these are normally off and turned on by applying gate voltage. The opposite
phenomenon happens in depletion type MOSFETs.
Working Principle of MOSFET
The working principle of MOSFET depends up on the MOS capacitor. The MOS
capacitor is the main part. The semiconductor surface at below the oxide layer and
between the drain and source terminal can be inverted from p-type to n-type by applying
a positive or negative gate voltages respectively. When we apply positive gate voltage
the holes present beneath the oxide layer experience repulsive force and the holes are
pushed downward with the substrate. The depletion region is populated by the bound
negative charges, which are associated with the acceptor atoms. The positive voltage
also attracts electrons from the n+ source and drain regions in to the channel. The
electron reach channel is formed. Now, if a voltage is applied between the source and
the drain, current flows freely between the source and drain gate voltage controls the
electrons concentration the channel. Instead of positive if apply negative voltage a hole
channel will be formed beneath the oxide layer.
Now, the controlling of source to gate voltage is responsible for the conduction of
current between source and the drain. If the gate voltage exceeds a given value, called
the three voltage only then the conduction begins.
The current equation of MOSFET in triode region is –

Where, un = Mobility of the electrons Cox = Capacitance of the oxide layer W = Width of
the gate area L = Length of the channel VGS = Gate to Source voltage VTH = Threshold
voltage VDS = Drain to Source voltage.
P-Channel MOSFET
MOSFET which has p - channel region between source any gate is known as p -
channel MOSFET. It is a four terminal devices, the terminals are gate, drain, source
and substrate or body. The drain and source are heavily doped p+ region and the
substrate is in n-type. The current flows due to the flow of positively charged holes that’s
why it is known as p-channel MOSFET. When we apply negative gate voltage, the
electrons present beneath the oxide layer, experiences repulsive force and they are
pushed downward in to the substrate, the depletion region is populated by the bound
positive charges which are associated with the donor atoms. The negative gate voltage
also attracts holes from p+ source and drain region in to the channel region. Thus hole
which channel is formed now if a voltage between the source and the drain is applied
current flows. The gate voltage controls the hole concentration of the channel. The
diagram of p- channel enhancement and depletion MOSFET are given below.

N-Channel MOSFET
MOSFET having n-channel region between source and drain is known as n-channel
MOSFET . It is a four terminal device, the terminals are gate, drain and source and
substrate or body. The drain and source are heavily doped n+ region and the substrate
is p-type. The current flows due to flow of the negatively charged electrons, that’s why it
is known as n- channel MOSFET. When we apply the positive gate voltage the holes
present beneath the oxide layer experiences repulsive force and the holes are pushed
downwards in to the bound negative charges which are associated with the acceptor
atoms. The positive gate voltage also attracts electrons from n+ source and drain region
in to the channel thus an electron reach channel is formed, now if a voltage is applied
between the source and drain. The gate voltage controls the electron concentration in
the channel n-channel MOSFET is preferred over p-channel MOSFET as the mobility of
electrons are higher than holes. The diagrams of enhancements mode and depletion
mode are given below.
Enhancement and Depletion Mode MOSFET
EMOSFET
Symbol
Construction

Figure shows the construction of an N-channel E-MOSFET. The main difference

between the construction of DE-MOSFET and that of E-MOSFET, as we see from the
figures given below the E-MOSFET substrate extends all the way to the silicon dioxide
(SiO2) and no channels are doped between the source and the drain. Channels are
electrically induced in these MOSFETs, when a positive gate-source voltage VGS is
applied to it.
Operation

As its name indicates, this MOSFET operates only in the enhancement mode and
has no depletion mode. It operates with large positive gate voltage only. It does not
conduct when the gate-source voltage VGS = 0. This is the reason that it is called
normally-off MOSFET. In these MOSFET’s drain current ID flows only when
VGS exceeds VGST [gate-to-source threshold voltage].
When drain is applied with positive voltage with respect to source and no potential is
applied to the gate two N-regions and one P-substrate from two P-N junctions
connected back to back with a resistance of the P-substrate. So a very small drain
current that is, reverses leakage current flows. If the P-type substrate is now connected
to the source terminal, there is zero voltage across the source substrate junction, and
the–drain-substrate junction remains reverse biased.
When the gate is made positive with respect to the source and the substrate,
negative (i.e. minority) charge carriers within the substrate are attracted to the positive
gate and accumulate close to the-surface of the substrate. As the gate voltage is
increased, more and more electrons accumulate under the gate. Since these electrons
cannot flow across the insulated layer of silicon dioxide to the gate, so they accumulate
at the surface of the substrate just below the gate. These accumulated minority charge
carriers N -type channel stretching from drain to source. When this occurs, a channel is
induced by forming what is termed an inversion layer (N-type). Now a drain current
starts flowing. The strength of the drain current depends upon the channel resistance
which, in turn, depends upon the number of charge carriers attracted to the positive
gate. Thus drain current is controlled by the gate potential.
Since the conductivity of the channel is enhanced by the positive bias on the gate so
this device is also called the enhancement MOSFET or E- MOSFET.
The minimum value of gate-to-source voltage VGS that is required to form the inversion
layer (N-type) is termed the gate-to-source threshold voltage VGST. For VGS below VGST,
the drain current ID = 0. But for VGS exceeding VGST an N-type inversion layer connects
the source to drain and the drain current ID is large. Depending upon the device being
used, VGST may vary from less than 1 V to more than 5 V.
JFETs and DE-MOSFETs are classified as the depletion-mode devices because
their conductivity depends on the action of depletion layers. E-MOSFET is classified as
an enhancement-mode device because its conductivity depends on the action of the
inversion layer. Depletion-mode devices are normally ON when the gate-source voltage
VGS = 0, whereas the enhancement-mode devices are normally OFF when VGS = 0.
Characteristics
Drain Characteristics
Drain characteristics of an N-channel E-MOSFET are shown in figure. The lowest
curve is the VGST curve. When VGS is lesser than VGST, ID is approximately zero. When
VGS is greater than VGST, the device turns- on and the drain current ID is controlled by
the gate voltage. The characteristic curves have almost vertical and almost horizontal
parts.

The almost vertical components of the curves correspond to the ohmic region, and
the horizontal components correspond to the constant current region. Thus E-MOSFET
can be operated in either of these regions i.e. it can be used as a variable-voltage
resistor (WR) or as a constant current source.
Transfer Characteristics
Figure shows a typical transconductance curve. The current IDSS at VGS <=0 is
very small, being of the order of a few nano-amperes. When the VGS is made positive,
the drain current ID increases slowly at first, and then much more rapidly with an
increase in VGS. The manufacturer sometimes indicates the gate-source threshold
voltage VGST at which the drain current ID attains some defined small value, say 10 u A.
A current ID (0N, corresponding approximately to the maximum value given on the drain
characteristics and the values of VGS required to give this current VGs QN are also usually
given on the manufacturers data sheet.
The equation for the transfer characteristic does not obey equation. However it does
follow a similar “square law type” of relationship. The equation for the transfer
characteristic of E-MOSFETs is given as:
ID=K(VGS-VGST)2

Depletion Mode MOSFET

Symbol
Construction

Fig 5.1 Depletion Mode N Channel MOSFET

The depletion mode MOSFET shown as a N channel device (P channel is also
available) in Fig 5.1 is more usually made as a discrete component, i.e. a single
transistor rather than IC form. In this device a thin layer of N type silicon is deposited
just below the gate−insulating layer, and forms a conducting channel between source
and drain.
Therefore when the gate source voltage VGS is zero, current (in the form of free
electrons) can flow between source and drain. Note that the gate is totally insulated
from the channel by the layer of silicon dioxide. Now that a conducting channel is
present the gate does not need to cover the full width between source and drain.
Because the gate is totally insulated from the rest of the transistor this device, like other
IGFETs, has a very high input resistance.
Operation
In the N channel device, shown in Fig. 5.2 the gate is made negative with respect to
the source, which has the effect of creating a depletion area, free from charge carriers,
beneath the gate. This restricts the depth of the conducting channel, so increasing
channel resistance and reducing current flow through the device. Depletion mode
MOSFETS are also available in which the gate extends the full width of the channel
(from source to drain). In this case it is also possible to operate the transistor in
enhancement mode. This is done by making the gate positive instead of negative.

Fig. 5.2 Operation of a Depletion Mode MOSFET

The positive voltage on the gate attracts more free electrons into the conducing
channel, while at the same time repelling holes down into the P type substrate. The
more positive the gate potential, the deeper, and lower resistance is the channel.
Increasing positive bias therefore increases current flow. This useful
depletion/enhancement version has the disadvantage that, as the gate area is
increased, the gate capacitance is also larger than true depletion types. This can
present difficulties at higher frequencies.
Handling Precautions for MOSFET
The MOSFET has the drawback of being very susceptible to overload voltage and
may require special handling during installation. The MOSFET gets damaged easily if it
is not properly handled. A very thin layer of SiO 2, between the gate and channel is
damaged due to high voltage and even by static electricity. The static electricity may
result from the sliding of a device in a plastic bag. If a person picks up the transistor by
its case and brushes the gate against some grounded objects, a large electrostatic
discharge may result.In a relatively dry atmosphere, a static potential of 300V is not
uncommon on a person who has high resistance soles on his footwear.
 MOSFETs are protected by a shorting ring that is wrapped around all four
terminals during shipping and must remain in place until after the devices soldered in
position. prior to soldering ,the technician should use a shorting strap to discharge his
static electricity and make sure that the tip of the soldering iron is grounded. Once in
circuit, there are usually low resistances present to prevent any excessive accumulation
of electro static charge .However, the MOSFET should never be inserted into or
removed from a circuit with the power ON.JFET is not subject to these restrictions, and
even some MOSFETs have a built in gate protection known as “integral gate
protection”, a system built into the device to get around the problem of high voltage on
the gate causing a puncturing of the oxide layer. The manner in which this is done is
shown in the cross sectional view of Fig.7.11.The symbol clearly shows that between
each and the sorce is placed a back-to-back (or front-to-front)pair of diodes, which are
built right into P type substrate.
FET as Voltage-Variable Resistor
FET is operated in the constant-current portion of its output characteristics for the
linear applications. In the region before pinch-off , where VDS is small , the drain to
source resistance rd can be controlled by the bias voltage V GS . The FET is useful as
a voltage variable resistor (VVR) or voltage dependent resistor (VDR) .
In JFET , the drain to source conductance gd =ID/VDS for small values of VDS , which
may also be expressed as
gd=g do [1-(VGS/VP)1/2]
where gdo is the value of drain conductance when the bias voltage V GS is zero. The
variation of the rd with VGS can be closely approximated by the empirical expression ,
rd =ro/(1-KVGS)
Where ro=drain resistance at zero gate bias, and K=a constant , dependent upon FET
type .
Comparison of MOSFET and JFET
1. In enhancement and depletion types of MOSFET, the transverse
electric field induced across an insulating layer deposited on the semiconductor
material controls the conductivity of the channel. In the JFET the transverse
electric field across the reverse biased PN junction controls the conductivity of
the channel.
2. The gate leakage current in a MOSFET is of the order of 10-12A.Hence the input
resistance of a MOSFET is very high in the order of 1010 to 1015 ohm. The gate
leakage current of a JFET is of the order of 10-9A and its input resistance is of the
order of 108 ohm.
3. The output characteristics of the JFET are flatter than those of the MOSFET and
hence, the drain resistance of a JFET(0.1 to 1Mohm) is much higher than that of
a MOSFET(1 to 50 K ohm)
4. JFETs are operated only in the depletion mode. The depletion type MOSFET
may be operated in both depletion and enhancement mode.
5. Comparing to JFET, MOSFETs are easier to fabricate.
 6. MOSFET is very susceptible to overload voltage and needs special handling
during installation. It gets damaged easily if it is not properly handled.
7. MOSFET has zero offset voltage. As it is a symmetrical device, the source and
drain can be interchanged. These two properties are very useful in analog signal
switching.
8. Special digital CMOS circuits are available which involves near –zero power
dissipation and very low voltage and current requirements. This makes them
most suitable for portable systems.
Comparison of JFET And BJT
1. FET operations depend only on the flow of majority carrier-holes for P-channel
FETs and electrons for N-channel FETs. Therefore, they are called Unipolar
devices. Bipolar transistor (BJT) operation depends on both minority and majority
current carrier.
2. As FET has no junctions and the conduction is through an N-type or P-type
semiconductor material, FET is less noisy than BJT.
3. As the input circuit of FET is reverse biased, FET exhibits as much higher input
impedance (in the order of 100MOHM) and lower output impedance and there
will be a high degree of isolation between input and output. So, FET can act as
excellent buffer amplifier but the BJT has low input impedance because its input
circuit is forward biased.
4. FET is a voltage control device, i.e. voltage at the input terminal controls the
output current, whereas BJT is a current control device, i.e. the input current
controls the output current.
5. FETs are much easier to fabricate and are particularly suitable for ICs because
they occupy less space than BJTs.
6. The performance of BJT is degraded by neutron radiations because of reduction
in minority carrier life time, whereas FET can tolerate a much higher level of
radiation since they do not rely on minority carrier for their operation.
7. The performance of FET is relatively unaffected by ambient temperature
changes. As it has a negative temperature coefficient at high current levels, it
 prevents the FET from thermal break down. The BJT has a positive temperature
coefficient at high current levels which leads to thermal break down.
8. Since FET does not suffer from minority carrier storage effects, it has a higher
switching speeds and cut off frequencies.BJT suffers a minority carrier storage
effects and therefore has lower switching speed and cut off frequencies.
9. FET amplifiers have low gain bandwidth product due to the junction capacitive
effects and produce more signal distortion except for small signal operation.
10. BJT are cheaper to produce than FETs.