K-Prime Calculator

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VLSI Material Optimization

Analog VLSI Design

✖Mobility in MOSFET is defined based on the ability of an electron to move quickly through a metal or semiconductor, when pulled by an electric field.ⓘ Mobility in MOSFET [μ_eff]			+10% -10%
✖Capacitance of Gate Oxide Layer is defined as the capacitance of the gate terminal of a field-effect transistor.ⓘ Capacitance of Gate Oxide Layer [C_ox]			+10% -10%

✖K Prime is the reverse rate constant of the reaction.ⓘ K-Prime [K_p]

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Formula

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K-Prime

Formula

`"K"_{"p"} = "μ"_{"eff"}*"C"_{"ox"}`

Example

`"4.4745cm²/V*s"="0.15cm²/V*s"*"29.83μF/mm²"`

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K-Prime Solution

STEP 0: Pre-Calculation Summary

Formula Used

K Prime = Mobility in MOSFET*Capacitance of Gate Oxide Layer
K_p = μ_eff*C_ox
This formula uses 3 Variables

Variables Used

K Prime - (Measured in Square Meter per Volt per Second) - K Prime is the reverse rate constant of the reaction.
Mobility in MOSFET - (Measured in Square Meter per Volt per Second) - Mobility in MOSFET is defined based on the ability of an electron to move quickly through a metal or semiconductor, when pulled by an electric field.
Capacitance of Gate Oxide Layer - (Measured in Farad per Square Meter) - Capacitance of Gate Oxide Layer is defined as the capacitance of the gate terminal of a field-effect transistor.

STEP 1: Convert Input(s) to Base Unit

Mobility in MOSFET: 0.15 Square Centimeter per Volt Second --> 1.5E-05 Square Meter per Volt per Second (Check conversion here)
Capacitance of Gate Oxide Layer: 29.83 Microfarad per Square Millimeter --> 29.83 Farad per Square Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_p = μ_eff*C_ox --> 1.5E-05*29.83

Evaluating ... ...

K_p = 0.00044745

STEP 3: Convert Result to Output's Unit

0.00044745 Square Meter per Volt per Second -->4.4745 Square Centimeter per Volt Second (Check conversion here)

FINAL ANSWER

4.4745 Square Centimeter per Volt Second <-- K Prime

(Calculation completed in 00.004 seconds)

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Created by Shobhit Dimri

Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat

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< 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

K-Prime Formula

K Prime = Mobility in MOSFET*Capacitance of Gate Oxide Layer
K_p = μ_eff*C_ox

What is transistor?

In electronics, a transistor is a semiconductor device commonly used to amplify or switch electronic signals. The transistor is the fundamental building block of computers, and all other modern electronic devices. Some transistors are packaged individually but most are found in integrated circuits.

How to Calculate K-Prime?

K-Prime calculator uses K Prime = Mobility in MOSFET*Capacitance of Gate Oxide Layer to calculate the K Prime, The K-Prime formula is calculated based on the need of finding the number of K-prime numbers in the range [A, B]. A number is called K-prime, if it has K distinct prime factors. K Prime is denoted by K_p symbol.

How to calculate K-Prime using this online calculator? To use this online calculator for K-Prime, enter Mobility in MOSFET (μ_eff) & Capacitance of Gate Oxide Layer (C_ox) and hit the calculate button. Here is how the K-Prime calculation can be explained with given input values -> 45015 = 1.5E-05*29.83.

FAQ

What is K-Prime?

The K-Prime formula is calculated based on the need of finding the number of K-prime numbers in the range [A, B]. A number is called K-prime, if it has K distinct prime factors and is represented as K_p = μ_eff*C_ox or K Prime = Mobility in MOSFET*Capacitance of Gate Oxide Layer. Mobility in MOSFET is defined based on the ability of an electron to move quickly through a metal or semiconductor, when pulled by an electric field & Capacitance of Gate Oxide Layer is defined as the capacitance of the gate terminal of a field-effect transistor.

How to calculate K-Prime?

The K-Prime formula is calculated based on the need of finding the number of K-prime numbers in the range [A, B]. A number is called K-prime, if it has K distinct prime factors is calculated using K Prime = Mobility in MOSFET*Capacitance of Gate Oxide Layer. To calculate K-Prime, you need Mobility in MOSFET (μ_eff) & Capacitance of Gate Oxide Layer (C_ox). With our tool, you need to enter the respective value for Mobility in MOSFET & Capacitance of Gate Oxide Layer 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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