Narrow Channel Additional Threshold Voltage VLSI Calculator

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VLSI Material Optimization

Analog VLSI Design

✖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.ⓘ Empirical Parameter [k]			+10% -10%
✖Vertical Extent Bulk Depletion in Substrate refers to the depth of the depletion region into the substrate (bulk) of the MOSFET.ⓘ Vertical Extent Bulk Depletion in Substrate [x_dm]			+10% -10%
✖Channel Width is defined as the physical width of the semiconductor channel between the source and drain terminals within the transistor structure.ⓘ Channel Width [W_c]			+10% -10%
✖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.ⓘ Oxide Capacitance per Unit Area [C_oxide]			+10% -10%
✖Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material.ⓘ Acceptor Concentration [N_A]			+10% -10%
✖Surface Potential is a key parameter in evaluating the DC property of thin-film transistors.ⓘ Surface Potential [Φ_s]			+10% -10%

✖Narrow Channel Additional Threshold Voltage is defined as a additional contribution to the threshold voltage due to narrow-channel effects in MOSFET.ⓘ Narrow Channel Additional Threshold Voltage VLSI [ΔV_T0(nc)]

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Narrow Channel Additional Threshold Voltage VLSI

Formula

`"ΔV"_{"T0(nc)"} = (("k"*"x"_{"dm"})/("W"_{"c"}*"C"_{"oxide"}))*(sqrt(2*"[Charge-e]"*"N"_{"A"}*"[Permitivity-vacuum]"*"[Permitivity-silicon]"*abs(2*"Φ"_{"s"})))`

Example

`"2.382463V"=(("1.57"*"1.25μm")/("2.5μm"*"0.0703μF/cm²"))*(sqrt(2*"[Charge-e]"*"1e+16/cm³"*"[Permitivity-vacuum]"*"[Permitivity-silicon]"*abs(2*"6.86V")))`

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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)))
ΔV_T0(nc) = ((k*x_dm)/(W_c*C_oxide))*(sqrt(2*[Charge-e]*N_A*[Permitivity-vacuum]*[Permitivity-silicon]*abs(2*Φ_s)))
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

ΔV_T0(nc) = ((k*x_dm)/(W_c*C_oxide))*(sqrt(2*[Charge-e]*N_A*[Permitivity-vacuum]*[Permitivity-silicon]*abs(2*Φ_s))) --> ((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 ... ...

ΔV_T0(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 00.004 seconds)

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Created by Priyanka Patel

Lalbhai Dalpatbhai College of engineering (LDCE), Ahmedabad

Priyanka Patel has created this Calculator and 25+ more calculators!

Verified by Santhosh Yadav

Dayananda Sagar College Of Engineering (DSCE), Banglore

Santhosh Yadav has verified this Calculator and 50+ more calculators!

< 25 VLSI Material Optimization Calculators

Bulk Depletion Region Charge Density VLSI

Go 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

Go Body Effect Coefficient = modulus((Threshold Voltage-Threshold Voltage DIBL)/(sqrt(Surface Potential+(Source Body Potential Difference))-sqrt(Surface Potential)))

Junction Built-in Voltage VLSI

Go Junction Built-in Voltage = ([BoltZ]*Temperature/[Charge-e])*ln(Acceptor Concentration*Donor concentration/(Intrinsic Concentration)^2)

PN Junction Depletion Depth with Source VLSI

Go 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

Go 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

Go Short Channel Saturation Current = Channel Width*Saturation Electron Drift Velocity*Oxide Capacitance per Unit Area*Saturation Drain Source Voltage

Junction Current

Go Junction Current = (Static Power/Base Collector Voltage)-(Sub Threshold Current+Contention Current+Gate Current)

Surface Potential

Go Surface Potential = 2*Source Body Potential Difference*ln(Acceptor Concentration/Intrinsic Concentration)

DIBL Coefficient

Go DIBL Coefficient = (Threshold Voltage DIBL-Threshold Voltage)/Drain to Source Potential

Threshold Voltage when Source is at Body Potential

Go Threshold Voltage DIBL = DIBL Coefficient*Drain to Source Potential+Threshold Voltage

Subthreshold Slope

Go Sub Threshold Slope = Source Body Potential Difference*DIBL Coefficient*ln(10)

Threshold Voltage

Go Threshold Voltage = Gate to Channel Voltage-(Channel Charge/Gate Capacitance)

Gate Capacitance

Go Gate Capacitance = Channel Charge/(Gate to Channel Voltage-Threshold Voltage)

Channel Charge

Go Channel Charge = Gate Capacitance*(Gate to Channel Voltage-Threshold Voltage)

Gate Length using Gate Oxide Capacitance

Go Gate Length = Gate Capacitance/(Capacitance of Gate Oxide Layer*Gate Width)

Gate Oxide Capacitance

Go Capacitance of Gate Oxide Layer = Gate Capacitance/(Gate Width*Gate Length)

Oxide Capacitance after Full Scaling VLSI

Go Oxide Capacitance after Full Scaling = Oxide Capacitance per Unit Area*Scaling Factor

Critical Voltage

Go Critical Voltage = Critical Electric Field*Electric Field Across Channel Length

Gate Oxide Thickness after Full Scaling VLSI

Go Gate Oxide Thickness after Full Scaling = Gate Oxide Thickness/Scaling Factor

Intrinsic Gate Capacitance

Go MOS Gate Overlap Capacitance = MOS Gate Capacitance*Transition Width

Channel Length after Full Scaling VLSI

Go Channel Length after Full Scaling = Channel Length/Scaling Factor

Junction Depth after Full Scaling VLSI

Go Junction Depth after Full Scaling = Junction Depth/Scaling Factor

Channel Width after Full Scaling VLSI

Go Channel Width after Full Scaling = Channel Width/Scaling Factor

Mobility in Mosfet

Go Mobility in MOSFET = K Prime/Capacitance of Gate Oxide Layer

K-Prime

Go K Prime = Mobility in MOSFET*Capacitance of Gate Oxide Layer

Narrow Channel Additional Threshold Voltage VLSI Formula

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 ΔV_T0(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 (x_dm), Channel Width (W_c), Oxide Capacitance per Unit Area (C_oxide), Acceptor Concentration (N_A) & Surface Potential (Φ_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 ΔV_T0(nc) = ((k*x_dm)/(W_c*C_oxide))*(sqrt(2*[Charge-e]*N_A*[Permitivity-vacuum]*[Permitivity-silicon]*abs(2*Φ_s))) 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 (x_dm), Channel Width (W_c), Oxide Capacitance per Unit Area (C_oxide), Acceptor Concentration (N_A) & Surface Potential (Φ_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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