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