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

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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