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
[Charge-e] - Charge of electron Value Taken As 1.60217662E-19
Functions Used
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., 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., 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
FINAL ANSWER
2.38246289976913 2.382463 Volt <-- Narrow Channel Additional Threshold Voltage
(Calculation completed in 00.020 seconds)

Credits

Creator Image
Created by Priyanka Patel
Lalbhai Dalpatbhai College of engineering (LDCE), Ahmedabad
Priyanka Patel has created this Calculator and 25+ more calculators!
Verifier Image
Verified by Santhosh Yadav
Dayananda Sagar College Of Engineering (DSCE), Banglore
Santhosh Yadav has verified this Calculator and 50+ more calculators!

VLSI Material Optimization Calculators

Body Effect Coefficient
​ LaTeX ​ Go Body Effect Coefficient = modulus((Threshold Voltage-Threshold Voltage DIBL)/(sqrt(Surface Potential+(Source Body Potential Difference))-sqrt(Surface Potential)))
DIBL Coefficient
​ LaTeX ​ Go DIBL Coefficient = (Threshold Voltage DIBL-Threshold Voltage)/Drain to Source Potential
Channel Charge
​ LaTeX ​ Go Channel Charge = Gate Capacitance*(Gate to Channel Voltage-Threshold Voltage)
Critical Voltage
​ LaTeX ​ Go Critical Voltage = Critical Electric Field*Electric Field Across Channel Length

Narrow Channel Additional Threshold Voltage VLSI Formula

​LaTeX ​Go
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.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!