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MOS IC Fabrication

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✖Process Dependent Constant refers to a parameter or value that characterizes a specific aspect of the fabrication process and has a significant impact on the performance of semiconductor devices.ⓘ Process Dependent Constant [k₁]			+10% -10%
✖Wavelength in Photolithography refers to the specific range of electromagnetic radiation employed to pattern semiconductor wafers during the semiconductor fabrication process.ⓘ Wavelength in Photolithography [λ_l]			+10% -10%
✖Numerical Aperture of an Optical System is a parameter used in optics to describe the ability of an optical system. In the context of semiconductor manufacturing and photolithography.ⓘ Numerical Aperture [NA]			+10% -10%

✖Critical Dimension in semiconductor manufacturing refers to the smallest feature size or the smallest measurable size in a given process.ⓘ Critical Dimension [CD]

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Formula

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Critical Dimension

Formula

`"CD" = "k"_{"1"}*"λ"_{"l"}/"NA"`

Example

`"485.1883nm"="1.56"*"223nm"/"0.717"`

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Critical Dimension Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Dimension = Process Dependent Constant*Wavelength in Photolithography/Numerical Aperture
CD = k₁*λ_l/NA
This formula uses 4 Variables

Variables Used

Critical Dimension - (Measured in Meter) - Critical Dimension in semiconductor manufacturing refers to the smallest feature size or the smallest measurable size in a given process.
Process Dependent Constant - Process Dependent Constant refers to a parameter or value that characterizes a specific aspect of the fabrication process and has a significant impact on the performance of semiconductor devices.
Wavelength in Photolithography - (Measured in Meter) - Wavelength in Photolithography refers to the specific range of electromagnetic radiation employed to pattern semiconductor wafers during the semiconductor fabrication process.
Numerical Aperture - Numerical Aperture of an Optical System is a parameter used in optics to describe the ability of an optical system. In the context of semiconductor manufacturing and photolithography.

STEP 1: Convert Input(s) to Base Unit

Process Dependent Constant: 1.56 --> No Conversion Required
Wavelength in Photolithography: 223 Nanometer --> 2.23E-07 Meter (Check conversion here)
Numerical Aperture: 0.717 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

CD = k₁*λ_l/NA --> 1.56*2.23E-07/0.717

Evaluating ... ...

CD = 4.85188284518829E-07

STEP 3: Convert Result to Output's Unit

4.85188284518829E-07 Meter -->485.188284518829 Nanometer (Check conversion here)

FINAL ANSWER

485.188284518829 ≈ 485.1883 Nanometer <-- Critical Dimension

(Calculation completed in 00.004 seconds)

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Dayananda Sagar College of Engineering (DSCE), Bangalore

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< 15 MOS IC Fabrication Calculators

Switching Point Voltage

Go Switching Point Voltage = (Supply Voltage+PMOS Threshold Voltage+NMOS Threshold Voltage*sqrt(NMOS Transistor Gain/PMOS Transistor Gain))/(1+sqrt(NMOS Transistor Gain/PMOS Transistor Gain))

Body Effect in MOSFET

Go Threshold Voltage with Substrate = Threshold Voltage with Zero Body Bias+Body Effect Parameter*(sqrt(2*Bulk Fermi Potential+Voltage Applied to Body)-sqrt(2*Bulk Fermi Potential))

Donor Dopant Concentration

Go Donor Dopant Concentration = (Saturation Current*Transistor's Length)/([Charge-e]*Transistor's Width*Electron Mobility*Depletion Layer Capacitance)

Acceptor Dopant Concentration

Go Acceptor Dopant Concentration = 1/(2*pi*Transistor's Length*Transistor's Width*[Charge-e]*Hole Mobility*Depletion Layer Capacitance)

Drain Current of MOSFET at Saturation Region

Go Drain Current = Transconductance Parameter/2*(Gate Source Voltage-Threshold Voltage with Zero Body Bias)^2*(1+Channel Length Modulation Factor*Drain Source Voltage)

Maximum Dopant Concentration

Go Maximum Dopant Concentration = Reference Concentration*exp(-Activation Energy for Solid Solubility/([BoltZ]*Absolute Temperature))

Propagation Time

Go Propagation Time = 0.7*Number of Pass Transistors*((Number of Pass Transistors+1)/2)*Resistance in MOSFET*Load Capacitance

Drift Current Density due to Free Electrons

Go Drift Current Density due to Electrons = [Charge-e]*Electron Concentration*Electron Mobility*Electric Field Intensity

Drift Current Density due to Holes

Go Drift Current Density due to Holes = [Charge-e]*Hole Concentration*Hole Mobility*Electric Field Intensity

Channel Resistance

Go Channel Resistance = Transistor's Length/Transistor's Width*1/(Electron Mobility*Carrier Density)

MOSFET Unity-Gain Frequency

Go Unity Gain Frequency in MOSFET = Transconductance in MOSFET/(Gate Source Capacitance+Gate Drain Capacitance)

Critical Dimension

Go Critical Dimension = Process Dependent Constant*Wavelength in Photolithography/Numerical Aperture

Depth of Focus

Go Depth of Focus = Proportionality Factor*Wavelength in Photolithography/(Numerical Aperture^2)

Die Per Wafer

Go Die Per Wafer = (pi*Wafer Diameter^2)/(4*Size of Each Die)

Equivalent Oxide Thickness

Go Equivalent Oxide Thickness = Thickness of Material*(3.9/Dielectric Constant of Material)

Critical Dimension Formula

Critical Dimension = Process Dependent Constant*Wavelength in Photolithography/Numerical Aperture
CD = k₁*λ_l/NA

What factors influence CD in semiconductor fabrication?

CD is influenced by various factors, including the lithography process, photomask quality, exposure wavelength, numerical aperture, and the characteristics of the photoresist used.

How to Calculate Critical Dimension?

Critical Dimension calculator uses Critical Dimension = Process Dependent Constant*Wavelength in Photolithography/Numerical Aperture to calculate the Critical Dimension, The Critical Dimension refers to the smallest dimension or feature size that determines the performance and functionality of the circuit. It is crucial for defining the resolution and accuracy of the fabrication process. Critical Dimension is denoted by CD symbol.

How to calculate Critical Dimension using this online calculator? To use this online calculator for Critical Dimension, enter Process Dependent Constant (k₁), Wavelength in Photolithography (λ_l) & Numerical Aperture (NA) and hit the calculate button. Here is how the Critical Dimension calculation can be explained with given input values -> 4.9E+11 = 1.56*2.23E-07/0.717.

FAQ

What is Critical Dimension?

The Critical Dimension refers to the smallest dimension or feature size that determines the performance and functionality of the circuit. It is crucial for defining the resolution and accuracy of the fabrication process and is represented as CD = k₁*λ_l/NA or Critical Dimension = Process Dependent Constant*Wavelength in Photolithography/Numerical Aperture. Process Dependent Constant refers to a parameter or value that characterizes a specific aspect of the fabrication process and has a significant impact on the performance of semiconductor devices, Wavelength in Photolithography refers to the specific range of electromagnetic radiation employed to pattern semiconductor wafers during the semiconductor fabrication process & Numerical Aperture of an Optical System is a parameter used in optics to describe the ability of an optical system. In the context of semiconductor manufacturing and photolithography.

How to calculate Critical Dimension?

The Critical Dimension refers to the smallest dimension or feature size that determines the performance and functionality of the circuit. It is crucial for defining the resolution and accuracy of the fabrication process is calculated using Critical Dimension = Process Dependent Constant*Wavelength in Photolithography/Numerical Aperture. To calculate Critical Dimension, you need Process Dependent Constant (k₁), Wavelength in Photolithography (λ_l) & Numerical Aperture (NA). With our tool, you need to enter the respective value for Process Dependent Constant, Wavelength in Photolithography & Numerical Aperture 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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