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Short Channel Threshold Voltage Reduction VLSI Formula

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Short Channel Threshold Voltage Reduction is defined as a reduction in threshold voltage of MOSFET due to short channel effect. Check FAQs

ΔV T0 = \frac{\sqrt{2 \cdot [Charge-e] \cdot [Permitivity-silicon] \cdot [Permitivity-vacuum] \cdot N A \cdot | 2 \cdot Φ s |} \cdot x j}{C oxide \cdot 2 \cdot L} \cdot ((\sqrt{1 + \frac{2 \cdot x dS}{x j}} - 1) + (\sqrt{1 + \frac{2 \cdot x dD}{x j}} - 1))

ΔV_T0 - Short Channel Threshold Voltage Reduction?N_A - Acceptor Concentration?Φ_s - Surface Potential?x_j - Junction Depth?C_oxide - Oxide Capacitance per Unit Area?L - Channel Length?x_dS - P-n Junction Depletion Depth with Source?x_dD - P-n Junction Depletion Depth with Drain?[Charge-e] - Charge of electron?[Permitivity-silicon] - Permittivity of silicon?[Permitivity-vacuum] - Permittivity of vacuum?

Short Channel Threshold Voltage Reduction VLSI Example

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Here is how the Short Channel Threshold Voltage Reduction VLSI equation looks like with Values.

Here is how the Short Channel Threshold Voltage Reduction VLSI equation looks like with Units.

Here is how the Short Channel Threshold Voltage Reduction VLSI equation looks like.

0.4672 = \frac{\sqrt{2 \cdot 1.6E-19 \cdot 11.7 \cdot 8.9E-12 \cdot 1E+16 \cdot | 2 \cdot 6.86 |} \cdot 2}{0.0703 \cdot 2 \cdot 2.5} \cdot ((\sqrt{1 + \frac{2 \cdot 0.314}{2}} - 1) + (\sqrt{1 + \frac{2 \cdot 0.534}{2}} - 1))

0.4672V = \frac{\sqrt{2 \cdot 1.6E-19C \cdot 11.7 \cdot 8.9E-12F/m \cdot 1E+161/cm³ \cdot | 2 \cdot 6.86V |} \cdot 2μm}{0.0703μF/cm² \cdot 2 \cdot 2.5μm} \cdot ((\sqrt{1 + \frac{2 \cdot 0.314μm}{2μm}} - 1) + (\sqrt{1 + \frac{2 \cdot 0.534μm}{2μm}} - 1))

0.4672 = \frac{\sqrt{2 \cdot 1.6E-19 \cdot 11.7 \cdot 8.9E-12 \cdot 1E+16 \cdot | 2 \cdot 6.86 |} \cdot 2}{0.0703 \cdot 2 \cdot 2.5} \cdot ((\sqrt{1 + \frac{2 \cdot 0.314}{2}} - 1) + (\sqrt{1 + \frac{2 \cdot 0.534}{2}} - 1))

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Short Channel Threshold Voltage Reduction VLSI Solution

Follow our step by step solution on how to calculate Short Channel Threshold Voltage Reduction VLSI?

FIRST Step Consider the formula

ΔV T0 = \frac{\sqrt{2 \cdot [Charge-e] \cdot [Permitivity-silicon] \cdot [Permitivity-vacuum] \cdot N A \cdot | 2 \cdot Φ s |} \cdot x j}{C oxide \cdot 2 \cdot L} \cdot ((\sqrt{1 + \frac{2 \cdot x dS}{x j}} - 1) + (\sqrt{1 + \frac{2 \cdot x dD}{x j}} - 1))

Next Step Substitute values of Variables

∴

ΔV T0 = \frac{\sqrt{2 \cdot [Charge-e] \cdot [Permitivity-silicon] \cdot [Permitivity-vacuum] \cdot 1E+161/cm³ \cdot | 2 \cdot 6.86V |} \cdot 2μm}{0.0703μF/cm² \cdot 2 \cdot 2.5μm} \cdot ((\sqrt{1 + \frac{2 \cdot 0.314μm}{2μm}} - 1) + (\sqrt{1 + \frac{2 \cdot 0.534μm}{2μm}} - 1))

Next Step Substitute values of Constants

∴

ΔV T0 = \frac{\sqrt{2 \cdot 1.6E-19C \cdot 11.7 \cdot 8.9E-12F/m \cdot 1E+161/cm³ \cdot | 2 \cdot 6.86V |} \cdot 2μm}{0.0703μF/cm² \cdot 2 \cdot 2.5μm} \cdot ((\sqrt{1 + \frac{2 \cdot 0.314μm}{2μm}} - 1) + (\sqrt{1 + \frac{2 \cdot 0.534μm}{2μm}} - 1))

Next Step Convert Units

∴

ΔV T0 = \frac{\sqrt{2 \cdot 1.6E-19C \cdot 11.7 \cdot 8.9E-12F/m \cdot 1E+221/m³ \cdot | 2 \cdot 6.86V |} \cdot 2E-6m}{0.0007F/m² \cdot 2 \cdot 2.5E-6m} \cdot ((\sqrt{1 + \frac{2 \cdot 3.1E-7m}{2E-6m}} - 1) + (\sqrt{1 + \frac{2 \cdot 5.3E-7m}{2E-6m}} - 1))

Next Step Prepare to Evaluate

∴

ΔV T0 = \frac{\sqrt{2 \cdot 1.6E-19 \cdot 11.7 \cdot 8.9E-12 \cdot 1E+22 \cdot | 2 \cdot 6.86 |} \cdot 2E-6}{0.0007 \cdot 2 \cdot 2.5E-6} \cdot ((\sqrt{1 + \frac{2 \cdot 3.1E-7}{2E-6}} - 1) + (\sqrt{1 + \frac{2 \cdot 5.3E-7}{2E-6}} - 1))

Next Step Evaluate

∴

ΔV T0 = 0.467200582407994V

LAST Step Rounding Answer

∴

ΔV T0 = 0.4672V

Short Channel Threshold Voltage Reduction VLSI Formula Elements

Variables

Constants

Functions

Short Channel Threshold Voltage Reduction

Short Channel Threshold Voltage Reduction is defined as a reduction in threshold voltage of MOSFET due to short channel effect.

Symbol: ΔV_T0

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Short Channel Threshold Voltage Reduction

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

Junction Depth

Junction Depth is defined as the distance from the surface of a semiconductor material to the point where a significant change in the concentration of dopant atoms occurs.

Symbol: x_j

Measurement: LengthUnit: μm

Note: Value should be greater than 0.

Formulas to find Junction Depth

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

Channel Length

Channel Length refers to the physical length of the semiconductor material between the source and drain terminals within the transistor structure.

Symbol: L

Measurement: LengthUnit: μm

Note: Value should be greater than 0.

Formulas to find Channel Length

P-n Junction Depletion Depth with Source

P-n Junction Depletion Depth with Source is defined as the region around a p-n junction where charge carriers have been depleted due to the formation of an electric field.

Symbol: x_dS

Measurement: LengthUnit: μm

Note: Value should be greater than 0.

Formulas to find P-n Junction Depletion Depth with Source

P-n Junction Depletion Depth with Drain

P-n Junction Depletion Depth with Drain is defined as the extension of the depletion region into the semiconductor material near the drain terminal.

Symbol: x_dD

Measurement: LengthUnit: μm

Note: Value should be greater than 0.

Formulas to find P-n Junction Depletion Depth with Drain

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 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

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

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 Short Channel Threshold Voltage Reduction VLSI?

Short Channel Threshold Voltage Reduction VLSI evaluator uses Short Channel Threshold Voltage Reduction = (sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*Acceptor Concentration*abs(2*Surface Potential))*Junction Depth)/(Oxide Capacitance per Unit Area*2*Channel Length)*((sqrt(1+(2*P-n Junction Depletion Depth with Source)/Junction Depth)-1)+(sqrt(1+(2*P-n Junction Depletion Depth with Drain)/Junction Depth)-1)) to evaluate the Short Channel Threshold Voltage Reduction, The Short Channel Threshold Voltage Reduction VLSI formula is defined as a reduction in threshold voltage of MOSFET due to short channel effect. Short Channel Threshold Voltage Reduction is denoted by ΔV_T0 symbol.

How to evaluate Short Channel Threshold Voltage Reduction VLSI using this online evaluator? To use this online evaluator for Short Channel Threshold Voltage Reduction VLSI, enter Acceptor Concentration (N_A), Surface Potential (Φ_s), Junction Depth (x_j), Oxide Capacitance per Unit Area (C_oxide), Channel Length (L), P-n Junction Depletion Depth with Source (x_dS) & P-n Junction Depletion Depth with Drain (x_dD) and hit the calculate button.

FAQs on Short Channel Threshold Voltage Reduction VLSI

What is the formula to find Short Channel Threshold Voltage Reduction VLSI?

The formula of Short Channel Threshold Voltage Reduction VLSI is expressed as Short Channel Threshold Voltage Reduction = (sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*Acceptor Concentration*abs(2*Surface Potential))*Junction Depth)/(Oxide Capacitance per Unit Area*2*Channel Length)*((sqrt(1+(2*P-n Junction Depletion Depth with Source)/Junction Depth)-1)+(sqrt(1+(2*P-n Junction Depletion Depth with Drain)/Junction Depth)-1)). Here is an example- 0.467201 = (sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*1E+22*abs(2*6.86))*2E-06)/(0.000703*2*2.5E-06)*((sqrt(1+(2*3.14E-07)/2E-06)-1)+(sqrt(1+(2*5.34E-07)/2E-06)-1)).

How to calculate Short Channel Threshold Voltage Reduction VLSI?

With Acceptor Concentration (N_A), Surface Potential (Φ_s), Junction Depth (x_j), Oxide Capacitance per Unit Area (C_oxide), Channel Length (L), P-n Junction Depletion Depth with Source (x_dS) & P-n Junction Depletion Depth with Drain (x_dD) we can find Short Channel Threshold Voltage Reduction VLSI using the formula - Short Channel Threshold Voltage Reduction = (sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*Acceptor Concentration*abs(2*Surface Potential))*Junction Depth)/(Oxide Capacitance per Unit Area*2*Channel Length)*((sqrt(1+(2*P-n Junction Depletion Depth with Source)/Junction Depth)-1)+(sqrt(1+(2*P-n Junction Depletion Depth with Drain)/Junction Depth)-1)). This formula also uses Charge of electron, Permittivity of silicon, Permittivity of vacuum constant(s) and , Square Root (sqrt), Absolute (abs) function(s).

Can the Short Channel Threshold Voltage Reduction VLSI be negative?

No, the Short Channel Threshold Voltage Reduction VLSI, measured in Electric Potential cannot be negative.

Which unit is used to measure Short Channel Threshold Voltage Reduction VLSI?

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

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Short Channel Threshold Voltage Reduction VLSI Formula

Short Channel Threshold Voltage Reduction VLSI Example

Short Channel Threshold Voltage Reduction VLSI Solution

Short Channel Threshold Voltage Reduction VLSI Formula Elements

Other formulas in VLSI Material Optimization category

How to Evaluate Short Channel Threshold Voltage Reduction VLSI?

FAQs on Short Channel Threshold Voltage Reduction VLSI

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