## Narrow Channel Additional Threshold Voltage VLSI Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
ΔVT0(nc) = ((k*xdm)/(Wc*Coxide))*(sqrt(2*[Charge-e]*NA*[Permitivity-vacuum]*[Permitivity-silicon]*abs(2*Φs)))
This formula uses 3 Constants, 2 Functions, 7 Variables
Constants Used
[Permitivity-silicon] - Permittivity of silicon Value Taken As 11.7
[Permitivity-vacuum] - Permittivity of vacuum Value Taken As 8.85E-12 Farad / Meter
[Charge-e] - Charge of electron Value Taken As 1.60217662E-19 Coulomb
Functions Used
sqrt - Square root function, sqrt(Number)
abs - Absolut value function, abs(Number)
Variables Used
Narrow Channel Additional Threshold Voltage - (Measured in Volt) - Narrow Channel Additional Threshold Voltage is defined as a additional contribution to the threshold voltage due to narrow-channel effects in MOSFET.
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.
Vertical Extent Bulk Depletion in Substrate - (Measured in Meter) - Vertical Extent Bulk Depletion in Substrate refers to the depth of the depletion region into the substrate (bulk) of the MOSFET.
Channel Width - (Measured in Meter) - Channel Width is defined as the physical width of the semiconductor channel between the source and drain terminals within the transistor structure.
Oxide Capacitance per Unit Area - (Measured in Farad per Square Meter) - 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.
Acceptor Concentration - (Measured in 1 per Cubic Meter) - Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material.
Surface Potential - (Measured in Volt) - Surface Potential is a key parameter in evaluating the DC property of thin-film transistors.
STEP 1: Convert Input(s) to Base Unit
Empirical Parameter: 1.57 --> No Conversion Required
Vertical Extent Bulk Depletion in Substrate: 1.25 Micrometer --> 1.25E-06 Meter (Check conversion here)
Channel Width: 2.5 Micrometer --> 2.5E-06 Meter (Check conversion here)
Oxide Capacitance per Unit Area: 0.0703 Microfarad per Square Centimeter --> 0.000703 Farad per Square Meter (Check conversion here)
Acceptor Concentration: 1E+16 1 per Cubic Centimeter --> 1E+22 1 per Cubic Meter (Check conversion here)
Surface Potential: 6.86 Volt --> 6.86 Volt No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ΔVT0(nc) = ((k*xdm)/(Wc*Coxide))*(sqrt(2*[Charge-e]*NA*[Permitivity-vacuum]*[Permitivity-silicon]*abs(2*Φs))) --> ((1.57*1.25E-06)/(2.5E-06*0.000703))*(sqrt(2*[Charge-e]*1E+22*[Permitivity-vacuum]*[Permitivity-silicon]*abs(2*6.86)))
Evaluating ... ...
ΔVT0(nc) = 2.38246289976913
STEP 3: Convert Result to Output's Unit
2.38246289976913 Volt --> No Conversion Required
2.38246289976913 2.382463 Volt <-- Narrow Channel Additional Threshold Voltage
(Calculation completed in 00.004 seconds)
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## Credits

Created by Priyanka Patel
Lalbhai Dalpatbhai College of engineering (LDCE), Ahmedabad
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## < 25 VLSI Material Optimization Calculators

Bulk Depletion Region Charge Density VLSI
Bulk Depletion Region Charge Density = -(1-((Lateral Extent of Depletion Region with Source+Lateral Extent of Depletion Region with Drain)/(2*Channel Length)))*sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*Acceptor Concentration*abs(2*Surface Potential))
Body Effect Coefficient
Body Effect Coefficient = modulus((Threshold Voltage-Threshold Voltage DIBL)/(sqrt(Surface Potential+(Source Body Potential Difference))-sqrt(Surface Potential)))
Junction Built-in Voltage VLSI
Junction Built-in Voltage = ([BoltZ]*Temperature/[Charge-e])*ln(Acceptor Concentration*Donor concentration/(Intrinsic Concentration)^2)
PN Junction Depletion Depth with Source VLSI
P-n Junction Depletion Depth with Source = sqrt((2*[Permitivity-silicon]*[Permitivity-vacuum]*Junction Built-in Voltage)/([Charge-e]*Acceptor Concentration))
Total Source Parasitic Capacitance
Source Parasitic Capacitance = (Capacitance between Junction of Body and Source*Area of Source Diffusion)+(Capacitance between Junction of Body and Side wall*Sidewall Perimeter of Source Diffusion)
Short Channel Saturation Current VLSI
Short Channel Saturation Current = Channel Width*Saturation Electron Drift Velocity*Oxide Capacitance per Unit Area*Saturation Drain Source Voltage
Junction Current
Junction Current = (Static Power/Base Collector Voltage)-(Sub Threshold Current+Contention Current+Gate Current)
Surface Potential
Surface Potential = 2*Source Body Potential Difference*ln(Acceptor Concentration/Intrinsic Concentration)
Threshold Voltage when Source is at Body Potential
Threshold Voltage DIBL = DIBL Coefficient*Drain to Source Potential+Threshold Voltage
DIBL Coefficient
DIBL Coefficient = (Threshold Voltage DIBL-Threshold Voltage)/Drain to Source Potential
Threshold Voltage
Threshold Voltage = Gate to Channel Voltage-(Channel Charge/Gate Capacitance)
Gate Capacitance
Gate Capacitance = Channel Charge/(Gate to Channel Voltage-Threshold Voltage)
Subthreshold Slope
Sub Threshold Slope = Source Body Potential Difference*DIBL Coefficient*ln(10)
Channel Charge
Channel Charge = Gate Capacitance*(Gate to Channel Voltage-Threshold Voltage)
Gate Length using Gate Oxide Capacitance
Gate Length = Gate Capacitance/(Capacitance of Gate Oxide Layer*Gate Width)
Gate Oxide Capacitance
Capacitance of Gate Oxide Layer = Gate Capacitance/(Gate Width*Gate Length)
Oxide Capacitance after Full Scaling VLSI
Oxide Capacitance after Full Scaling = Oxide Capacitance per Unit Area*Scaling Factor
Critical Voltage
Critical Voltage = Critical Electric Field*Electric Field Across Channel Length
Gate Oxide Thickness after Full Scaling VLSI
Gate Oxide Thickness after Full Scaling = Gate Oxide Thickness/Scaling Factor
Intrinsic Gate Capacitance
MOS Gate Overlap Capacitance = MOS Gate Capacitance*Transition Width
Channel Length after Full Scaling VLSI
Channel Length after Full Scaling = Channel Length/Scaling Factor
Junction Depth after Full Scaling VLSI
Junction Depth after Full Scaling = Junction Depth/Scaling Factor
Channel Width after Full Scaling VLSI
Channel Width after Full Scaling = Channel Width/Scaling Factor
Mobility in Mosfet
Mobility in MOSFET = K Prime/Capacitance of Gate Oxide Layer
K-Prime
K Prime = Mobility in MOSFET*Capacitance of Gate Oxide Layer

## Narrow Channel Additional Threshold Voltage VLSI 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)))
ΔVT0(nc) = ((k*xdm)/(Wc*Coxide))*(sqrt(2*[Charge-e]*NA*[Permitivity-vacuum]*[Permitivity-silicon]*abs(2*Φs)))

## What is the effect of narrow-channel on a MOS transistor?

The most significant narrow-channel effect is that the actual threshold voltage of such a device is larger than that predicted by the conventional threshold voltage formula.

## How to Calculate Narrow Channel Additional Threshold Voltage VLSI?

Narrow Channel Additional Threshold Voltage VLSI calculator 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 calculate 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 ΔVT0(nc) symbol.

How to calculate Narrow Channel Additional Threshold Voltage VLSI using this online calculator? To use this online calculator for Narrow Channel Additional Threshold Voltage VLSI, enter Empirical Parameter (k), Vertical Extent Bulk Depletion in Substrate (xdm), Channel Width (Wc), Oxide Capacitance per Unit Area (Coxide), Acceptor Concentration (NA) & Surface Potential s) and hit the calculate button. Here is how the Narrow Channel Additional Threshold Voltage VLSI calculation can be explained with given input values -> 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))).

### FAQ

What is Narrow Channel Additional Threshold Voltage VLSI?
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 and is represented as ΔVT0(nc) = ((k*xdm)/(Wc*Coxide))*(sqrt(2*[Charge-e]*NA*[Permitivity-vacuum]*[Permitivity-silicon]*abs(2*Φs))) or 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))). 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, Vertical Extent Bulk Depletion in Substrate refers to the depth of the depletion region into the substrate (bulk) of the MOSFET, Channel Width is defined as the physical width of the semiconductor channel between the source and drain terminals within the transistor structure, 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, Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material & Surface Potential is a key parameter in evaluating the DC property of thin-film transistors.
How to calculate Narrow Channel Additional Threshold Voltage VLSI?
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 is calculated using 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 calculate Narrow Channel Additional Threshold Voltage VLSI, you need Empirical Parameter (k), Vertical Extent Bulk Depletion in Substrate (xdm), Channel Width (Wc), Oxide Capacitance per Unit Area (Coxide), Acceptor Concentration (NA) & Surface Potential s). With our tool, you need to enter the respective value for Empirical Parameter, Vertical Extent Bulk Depletion in Substrate, Channel Width, Oxide Capacitance per Unit Area, Acceptor Concentration & Surface Potential and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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