<< Chapter < Page Chapter >> Page >

Short Circuit Current Gain is derived as:




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



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


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


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:


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:


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:


The overall dependence of 1/r ds is :


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:


Transconductance is given as:




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

how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!

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
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Solid state physics and devices-the harbinger of third wave of civilization' conversation and receive update notifications?