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Narrow Channel Additional Threshold Voltage VLSI Formula

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Narrow Channel Additional Threshold Voltage is defined as a additional contribution to the threshold voltage due to narrow-channel effects in MOSFET. Check FAQs

ΔV T0(nc) = (\frac{k \cdot x dm}{W c \cdot C oxide}) \cdot (\sqrt{2 \cdot [Charge-e] \cdot N A \cdot [Permitivity-vacuum] \cdot [Permitivity-silicon] \cdot | 2 \cdot Φ s |})

ΔV_T0(nc) - Narrow Channel Additional Threshold Voltage?k - Empirical Parameter?x_dm - Vertical Extent Bulk Depletion in Substrate?W_c - Channel Width?C_oxide - Oxide Capacitance per Unit Area?N_A - Acceptor Concentration?Φ_s - Surface Potential?[Charge-e] - Charge of electron?[Permitivity-vacuum] - Permittivity of vacuum?[Permitivity-silicon] - Permittivity of silicon?

Narrow Channel Additional Threshold Voltage VLSI Example

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Here is how the Narrow Channel Additional Threshold Voltage VLSI equation looks like with Values.

Here is how the Narrow Channel Additional Threshold Voltage VLSI equation looks like with Units.

Here is how the Narrow Channel Additional Threshold Voltage VLSI equation looks like.

2.3825 = (\frac{1.57 \cdot 1.25}{2.5 \cdot 0.0703}) \cdot (\sqrt{2 \cdot 1.6E-19 \cdot 1E+16 \cdot 8.9E-12 \cdot 11.7 \cdot | 2 \cdot 6.86 |})

2.3825V = (\frac{1.57 \cdot 1.25μm}{2.5μm \cdot 0.0703μF/cm²}) \cdot (\sqrt{2 \cdot 1.6E-19C \cdot 1E+161/cm³ \cdot 8.9E-12F/m \cdot 11.7 \cdot | 2 \cdot 6.86V |})

2.3825 = (\frac{1.57 \cdot 1.25}{2.5 \cdot 0.0703}) \cdot (\sqrt{2 \cdot 1.6E-19 \cdot 1E+16 \cdot 8.9E-12 \cdot 11.7 \cdot | 2 \cdot 6.86 |})

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Narrow Channel Additional Threshold Voltage VLSI Solution

Follow our step by step solution on how to calculate Narrow Channel Additional Threshold Voltage VLSI?

FIRST Step Consider the formula

ΔV T0(nc) = (\frac{k \cdot x dm}{W c \cdot C oxide}) \cdot (\sqrt{2 \cdot [Charge-e] \cdot N A \cdot [Permitivity-vacuum] \cdot [Permitivity-silicon] \cdot | 2 \cdot Φ s |})

Next Step Substitute values of Variables

∴

ΔV T0(nc) = (\frac{1.57 \cdot 1.25μm}{2.5μm \cdot 0.0703μF/cm²}) \cdot (\sqrt{2 \cdot [Charge-e] \cdot 1E+161/cm³ \cdot [Permitivity-vacuum] \cdot [Permitivity-silicon] \cdot | 2 \cdot 6.86V |})

Next Step Substitute values of Constants

∴

ΔV T0(nc) = (\frac{1.57 \cdot 1.25μm}{2.5μm \cdot 0.0703μF/cm²}) \cdot (\sqrt{2 \cdot 1.6E-19C \cdot 1E+161/cm³ \cdot 8.9E-12F/m \cdot 11.7 \cdot | 2 \cdot 6.86V |})

Next Step Convert Units

∴

ΔV T0(nc) = (\frac{1.57 \cdot 1.3E-6m}{2.5E-6m \cdot 0.0007F/m²}) \cdot (\sqrt{2 \cdot 1.6E-19C \cdot 1E+221/m³ \cdot 8.9E-12F/m \cdot 11.7 \cdot | 2 \cdot 6.86V |})

Next Step Prepare to Evaluate

∴

ΔV T0(nc) = (\frac{1.57 \cdot 1.3E-6}{2.5E-6 \cdot 0.0007}) \cdot (\sqrt{2 \cdot 1.6E-19 \cdot 1E+22 \cdot 8.9E-12 \cdot 11.7 \cdot | 2 \cdot 6.86 |})

Next Step Evaluate

∴

ΔV T0(nc) = 2.38246289976913V

LAST Step Rounding Answer

∴

ΔV T0(nc) = 2.3825V

Narrow Channel Additional Threshold Voltage VLSI Formula Elements

Variables

Constants

Functions

Narrow Channel Additional Threshold Voltage

Narrow Channel Additional Threshold Voltage is defined as a additional contribution to the threshold voltage due to narrow-channel effects in MOSFET.

Symbol: ΔV_T0(nc)

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Narrow Channel Additional Threshold Voltage

Empirical Parameter

Empirical Parameter is a constant or value used in a model, equation, or theory that is derived from experiment and observation rather than being theoretically deduced.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Empirical Parameter

Vertical Extent Bulk Depletion in Substrate

Vertical Extent Bulk Depletion in Substrate refers to the depth of the depletion region into the substrate (bulk) of the MOSFET.

Symbol: x_dm

Measurement: LengthUnit: μm

Note: Value should be greater than 0.

Formulas to find Vertical Extent Bulk Depletion in Substrate

Channel Width

Channel Width is defined as the physical width of the semiconductor channel between the source and drain terminals within the transistor structure.

Symbol: W_c

Measurement: LengthUnit: μm

Note: Value should be greater than 0.

Formulas to find Channel Width

Oxide Capacitance per Unit Area

Oxide Capacitance per Unit Area is defined as the capacitance per unit area of the insulating oxide layer that separates the metal gate from the semiconductor material.

Symbol: C_oxide

Measurement: Oxide Capacitance Per Unit AreaUnit: μF/cm²

Note: Value should be greater than 0.

Formulas to find Oxide Capacitance per Unit Area

Acceptor Concentration

Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material.

Symbol: N_A

Measurement: Carrier ConcentrationUnit: 1/cm³

Note: Value should be greater than 0.

Formulas to find Acceptor Concentration

Surface Potential

Surface Potential is a key parameter in evaluating the DC property of thin-film transistors.

Symbol: Φ_s

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Surface Potential

Charge of electron

Charge of electron is a fundamental physical constant, representing the electric charge carried by an electron, which is the elementary particle with a negative electric charge.

Symbol: [Charge-e]

Value: 1.60217662E-19 C

Permittivity of vacuum

Permittivity of vacuum is a fundamental physical constant that describes the ability of a vacuum to permit the transmission of electric field lines.

Symbol: [Permitivity-vacuum]

Value: 8.85E-12 F/m

Permittivity of silicon

Permittivity of silicon measures its ability to store electrical energy in an electric field, vital in semiconductor technology.

Symbol: [Permitivity-silicon]

Value: 11.7

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

abs

The absolute value of a number is its distance from zero on the number line. It's always a positive value, as it represents the magnitude of a number without considering its direction.

Syntax: abs(Number)

Other formulas in VLSI Material Optimization category

Go Body Effect Coefficient

γ = mod \underset{̲}{u} s (\frac{V t - V t0}{\sqrt{Φ s + (V sb)} - \sqrt{Φ s}})

Go Channel Charge

Q ch = C g \cdot (V gc - V t)

How to Evaluate Narrow Channel Additional Threshold Voltage VLSI?

Narrow Channel Additional Threshold Voltage VLSI evaluator uses Narrow Channel Additional Threshold Voltage = ((Empirical Parameter*Vertical Extent Bulk Depletion in Substrate)/(Channel Width*Oxide Capacitance per Unit Area))*(sqrt(2*[Charge-e]*Acceptor Concentration*[Permitivity-vacuum]*[Permitivity-silicon]*abs(2*Surface Potential))) to evaluate the Narrow Channel Additional Threshold Voltage, The Narrow Channel Additional Threshold Voltage VLSI formula is defined as a additional contribution to the threshold voltage due to narrow-channel effects in MOSFET. Narrow Channel Additional Threshold Voltage is denoted by ΔV_T0(nc) symbol.

How to evaluate Narrow Channel Additional Threshold Voltage VLSI using this online evaluator? To use this online evaluator for Narrow Channel Additional Threshold Voltage VLSI, enter Empirical Parameter (k), Vertical Extent Bulk Depletion in Substrate (x_dm), Channel Width (W_c), Oxide Capacitance per Unit Area (C_oxide), Acceptor Concentration (N_A) & Surface Potential (Φ_s) and hit the calculate button.

FAQs on Narrow Channel Additional Threshold Voltage VLSI

What is the formula to find Narrow Channel Additional Threshold Voltage VLSI?

The formula of Narrow Channel Additional Threshold Voltage VLSI is expressed as Narrow Channel Additional Threshold Voltage = ((Empirical Parameter*Vertical Extent Bulk Depletion in Substrate)/(Channel Width*Oxide Capacitance per Unit Area))*(sqrt(2*[Charge-e]*Acceptor Concentration*[Permitivity-vacuum]*[Permitivity-silicon]*abs(2*Surface Potential))). Here is an example- 2.382463 = ((1.57*1.25E-06)/(2.5E-06*0.000703))*(sqrt(2*[Charge-e]*1E+22*[Permitivity-vacuum]*[Permitivity-silicon]*abs(2*6.86))).

How to calculate Narrow Channel Additional Threshold Voltage VLSI?

With Empirical Parameter (k), Vertical Extent Bulk Depletion in Substrate (x_dm), Channel Width (W_c), Oxide Capacitance per Unit Area (C_oxide), Acceptor Concentration (N_A) & Surface Potential (Φ_s) we can find Narrow Channel Additional Threshold Voltage VLSI using the formula - Narrow Channel Additional Threshold Voltage = ((Empirical Parameter*Vertical Extent Bulk Depletion in Substrate)/(Channel Width*Oxide Capacitance per Unit Area))*(sqrt(2*[Charge-e]*Acceptor Concentration*[Permitivity-vacuum]*[Permitivity-silicon]*abs(2*Surface Potential))). This formula also uses Charge of electron, Permittivity of vacuum, Permittivity of silicon constant(s) and , Square Root (sqrt), Absolute (abs) function(s).

Can the Narrow Channel Additional Threshold Voltage VLSI be negative?

No, the Narrow Channel Additional Threshold Voltage VLSI, measured in Electric Potential cannot be negative.

Which unit is used to measure Narrow Channel Additional Threshold Voltage VLSI?

Narrow Channel Additional Threshold Voltage VLSI is usually measured using the Volt[V] for Electric Potential. Millivolt[V], Microvolt[V], Nanovolt[V] are the few other units in which Narrow Channel Additional Threshold Voltage VLSI can be measured.

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Narrow Channel Additional Threshold Voltage VLSI Formula

Narrow Channel Additional Threshold Voltage VLSI Example

Narrow Channel Additional Threshold Voltage VLSI Solution

Narrow Channel Additional Threshold Voltage VLSI Formula Elements

Other formulas in VLSI Material Optimization category

How to Evaluate Narrow Channel Additional Threshold Voltage VLSI?

FAQs on Narrow Channel Additional Threshold Voltage VLSI

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