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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

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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
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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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