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Short Circuit Current Gain is derived as:

Where

Therefore

7.3.24

In exactly the same manner short circuit current gain of NMOS is derived and set to unity.

7.3.25

Where

In Eq.7.3.25, ω 0 = 5 ω u therefore, in working range of frequencies, Equation 7.3.25 can be simplified to:

7.3.26.

If Equation 7.3.26 is equated to Unity then its corresponding Unity Gain Frequency is:

7.3.27

From Eq.7.3.27 it is evident that increase in transconductance gives a higher frequency range of opeartaion.

7.3.7. Theoretical Formulation of Output Conductance of (E)NMOS.

Theoretical expression of drain current in saturation region is given by Equation 7.3.16:

As is evident from the above Equation, I ds has no dependence on V ds and I ds -V ds family of curves are perfectly horizontal and parallel to one another. Horizontal I-V curve implies infinite output impedance of the active device. But in practice it is not so. Real MOS devices have slopes in their family of I-V curves and this slope becomes pronounced as we scale the devices for the different generation of Technology. This is known as Channel Length Modulation effect.

In BJT we have Base Width Modulation also known as Early Effect. This Early Effect is the cause of the slope in output family of curves of CB BJT and CE BJT. Due to these slopes we have h ob and h oe parameters in the two circuit configurations. Since Early Effect is more pronounced in CE BJT hence h oe = 1/40kΩ is greater than h ob = 1/2MΩ. Channel Length Modulation is analogous to Early Effect and its degradation of family of output curves of NMOS is clealrly brought out in Figure 7.3.2. The physics of this degradation is that we have assumed that after saturation, I ds (sat) becomes constant at:

7.3.2

In Equation 7.3.2 it is assumed that with increase in V DS , the voltage drop across the conical channel is constant at V DS * and excess voltage drops across the pinched off region. The second assumption is that the resistance of the conical section is constant at :

R 0 /3 where R 0 is the resistance of the parallelopied channel.

This assumption does not remain valid with the scaling of devices. As the the device is scaled, the variation in V ds leads to significant change in the resistance of the conical channel because as pinched off region increases the axial length of the conical channel reduces and hence resistance offered decreases and I DS(sat) increases with the increase in V DS .

Channel Length Modulation is included in the saturated drain current in the following manner:

7.3.28

Where λ = channel length modulation parameter which is dependent on channel length L and its typical values are:

.

Therefore the partial derivative of I ds with respect to V ds with gate voltage constant gives the the reciprocal of the incremental output resistance of (E)NMOS:

7.3.29

The overall dependence of 1/r ds is :

7.3.30.

The incremental model of MOSFET incorporating transconductance and channel length modulation is given in Figure 7.3.1.

7.3.8. Figure of Merit of MOSFET.

The Unity Gain Bandwidth of MOSFET defines the Figure of Merit of MOSFET. Using Equation 7.3.27:

7.3.31

Transconductance is given as:

Or

7.3.23

Where

Gate Capacitance is given as:

Substituting Eq.7.3.23 and 7.3.13 in Eq.7.3.31 we get:

From Equation 7.3.7

Therefore Figure of Merit is the reciprocal of the transit time across the channel.

Larger is the electron mobility, better will be the Figure of Merit. Hence<100>orientation Si Substrate is chosen for fabrication of CMOS circuis. The mobility of electron and hole is always much larger in<100>orientation substrate than that in<111>orientation substrate. In Table 7.3.2 a comparative study of the electron mobility in<111>and<100>substrate is given.

Table 7.3.2. Comparative study of mobilities in<100>and<111>orientation substrate in thin channel and in bulk.

Bulk mobility<100> 2D channel mobility<100> 2D Channel mobility<111>
µ n 1250cm 2 /(V-sec) 650 cm 2 /(V-sec) 500 cm 2 /(V-sec)
µ p 480 cm 2 /(V-sec) 240 cm 2 /(V-sec) 216 cm 2 /(V-sec)

For fast CMOS circuits fabrications,<100>Si Substrate is the choice of material in Industries.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Solid state physics and devices-the harbinger of third wave of civilization. OpenStax CNX. Sep 15, 2014 Download for free at http://legacy.cnx.org/content/col11170/1.89
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