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SSPD_Chapter 7_Part 3 is the continuation of the Electrical Properties of MOS. In this module theoretical formulation of threshold voltage, transconductance, unity gain BW, output incremental conductance and figure of merit of NMOS is derived.

SSPD_Chapter 7_Part3_Electrical properties of MOS continued2

7.3.4. Theoretical Formulation of Threshold Voltage in (E)NMOS.

In SSPD_Chapter 6_Part 4_concluded_MOS and its Physics we have dealt with the theoretical formulation of the Threshold Voltage. The expression comes as follows:

7.3.18

Where The Flat Band Voltage is = V FB = ϕm – ϕs = ϕm – [χ + E g /(2q) + ψ B ]

χ = electron affinity in semi-conductor, E g = energy band-gap of Silicon and ψ B = potemtial diiference between Fermi-level(Ef) and intrinsic level(Ei) in Si-Bulk.

Therefore qV FB = qϕm – qϕs = qϕm – [qχ + E g /(2) + qψ B ];

If source to bulk voltage (V SB ) is not zero then this also has to be accounted. This is called Body Effect.

Q SS = Q it (interface trapped charges) + Q ot (oxide trapped charges) + Q m (mobile charges in the oxide) + Q f (fixed oxide charges).

Generally substrate and source are connected together and threshold voltage is at the minimum.

But in certain applications, substrate is kept at reverse bias with respect to source. NMOS is built in P tub and PMOS is built in N tub.

Hence in NMOS, substrate is at negative bias with respect to source and in PMOS, substrate is at positive bias with respect to source.

Substrate bias gives rise to increase in threshold voltage. Hence Body-effect is represented by the following empirical expression:

7.3.17

V TO = Threshold voltage with zero substrate bias;

And γ = body effect parameter (√V);

B = surface potential parameter.

Lower is the substrate doping, lower will be body effect.

The Typical values of Body effect is given in Table 7.3.1.

Table 7.3.1. Body effect in (E)NMOS and (D)NMOS

Device Substrate biasV SB ThresholdV Th
(E)NMOS 0V 0.2V DD 1V for V DD = +5V
5V 0.3V DD 1.5V for V DD = +5V
(D)NMOS 0V -0.7V DD -3.5V for V DD = +5V
5V -0.6V DD -3V for V DD = +5V

7.3.5. Theoretical formulation of Transconductance (g m )

Transconductance is the partial derivative of output current (I ds ) with respect to input voltage (V gs ) with output voltage constant i.e. V DS is held constant.

7.3.18

From Eq.7.3.3,

And Transit Time is given by equation 7.3.7,

Using these two equations incremental change in output current:

7.3.19

But channel charge induced depends on gate capacitance and gate voltage:

Therefore

Hence

7.3.21

In saturation from Eq.7.3.15,

.

is the actual drop across the conical channel no matter what V ds is.

Hence in saturatin region:

(
7.3.22

From Eq.7.3.13 ,

Substituting this in Eq.7.3.22:

(
=
(

Or

Or

7.3.23

Where

From Eq.7.3.23 it is evident that transconductance can be improved by reducing Channel Length.

Transconductance can be improved by increasing Channel Width. But both these methods have their drawbacks.

7.3.6. Theoretical Formulation of unity current gain band-width.

In BJT unity current gain band-width is defined as transit frequency ω T . It is derived by determining the Current Gain Band Width Product.

Questions & Answers

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RAW Reply
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Damian
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Professor
I think
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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
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What is meant by 'nano scale'?
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LITNING
scanning tunneling microscope
Sahil
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
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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
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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?
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?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
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Kyle
biomolecules are e building blocks of every organics and inorganic materials.
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research.net
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sciencedirect big data base
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Introduction about quantum dots in nanotechnology
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what does nano mean?
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nano basically means 10^(-9). nanometer is a unit to measure length.
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absolutely yes
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how did you get the value of 2000N.What calculations are needed to arrive at it
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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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