Junction Built-in Voltage VLSI Calculator

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VLSI Material Optimization

Analog VLSI Design

✖Temperature reflects how hot or cold an object or environment is.ⓘ Temperature [T]			+10% -10%
✖Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material.ⓘ Acceptor Concentration [N_A]			+10% -10%
✖Donor concentration refers to the concentration of donor dopant atoms introduced into a semiconductor material to increase the number of free electrons.ⓘ Donor concentration [N_D]			+10% -10%
✖Intrinsic Concentration refers to the concentration of charge carriers (electrons and holes) in an intrinsic semiconductor at thermal equilibrium.ⓘ Intrinsic Concentration [N_i]			+10% -10%

✖Junction Built-in Voltage is defined as the voltage that exists across a semiconductor junction in thermal equilibrium, where no external voltage is applied.ⓘ Junction Built-in Voltage VLSI [Ø₀]

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Formula

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Junction Built-in Voltage VLSI

Formula

`"Ø"_{"0"} = ("[BoltZ]"*"T"/"[Charge-e]")*ln("N"_{"A"}*"N"_{"D"}/("N"_{"i"})^2)`

Example

`"0.754632V"=("[BoltZ]"*"300K"/"[Charge-e]")*ln("1e+16/cm³"*"1e+17/cm³"/("1.45e+10/cm³")^2)`

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Junction Built-in Voltage VLSI Solution

STEP 0: Pre-Calculation Summary

Formula Used

Junction Built-in Voltage = ([BoltZ]*Temperature/[Charge-e])*ln(Acceptor Concentration*Donor concentration/(Intrinsic Concentration)^2)
Ø₀ = ([BoltZ]*T/[Charge-e])*ln(N_A*N_D/(N_i)^2)
This formula uses 2 Constants, 1 Functions, 5 Variables

Constants Used

[Charge-e] - Charge of electron Value Taken As 1.60217662E-19
[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Junction Built-in Voltage - (Measured in Volt) - Junction Built-in Voltage is defined as the voltage that exists across a semiconductor junction in thermal equilibrium, where no external voltage is applied.
Temperature - (Measured in Kelvin) - Temperature reflects how hot or cold an object or environment is.
Acceptor Concentration - (Measured in 1 per Cubic Meter) - Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material.
Donor concentration - (Measured in 1 per Cubic Meter) - Donor concentration refers to the concentration of donor dopant atoms introduced into a semiconductor material to increase the number of free electrons.
Intrinsic Concentration - (Measured in 1 per Cubic Meter) - Intrinsic Concentration refers to the concentration of charge carriers (electrons and holes) in an intrinsic semiconductor at thermal equilibrium.

STEP 1: Convert Input(s) to Base Unit

Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
Acceptor Concentration: 1E+16 1 per Cubic Centimeter --> 1E+22 1 per Cubic Meter (Check conversion here)
Donor concentration: 1E+17 1 per Cubic Centimeter --> 1E+23 1 per Cubic Meter (Check conversion here)
Intrinsic Concentration: 14500000000 1 per Cubic Centimeter --> 1.45E+16 1 per Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Ø₀ = ([BoltZ]*T/[Charge-e])*ln(N_A*N_D/(N_i)^2) --> ([BoltZ]*300/[Charge-e])*ln(1E+22*1E+23/(1.45E+16)^2)

Evaluating ... ...

Ø₀ = 0.75463200359389

STEP 3: Convert Result to Output's Unit

0.75463200359389 Volt --> No Conversion Required

FINAL ANSWER

0.75463200359389 ≈ 0.754632 Volt <-- Junction Built-in Voltage

(Calculation completed in 00.004 seconds)

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Credits

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!

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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

Junction Built-in Voltage VLSI Formula

Junction Built-in Voltage = ([BoltZ]*Temperature/[Charge-e])*ln(Acceptor Concentration*Donor concentration/(Intrinsic Concentration)^2)
Ø₀ = ([BoltZ]*T/[Charge-e])*ln(N_A*N_D/(N_i)^2)

How is the Junction Built-In Voltage created in a semiconductor device used in VLSI?

The Junction Built-In Voltage is created by the diffusion of charge carriers across a semiconductor junction, such as a p-n junction, resulting in a potential difference due to the difference in concentration of carriers on either side of the junction. This voltage is established at thermal equilibrium.

How to Calculate Junction Built-in Voltage VLSI?

Junction Built-in Voltage VLSI calculator uses Junction Built-in Voltage = ([BoltZ]*Temperature/[Charge-e])*ln(Acceptor Concentration*Donor concentration/(Intrinsic Concentration)^2) to calculate the Junction Built-in Voltage, The Junction Built-in Voltage VLSI formula is defined as the voltage that exists across a semiconductor junction in thermal equilibrium, where no external voltage is applied. Junction Built-in Voltage is denoted by Ø₀ symbol.

How to calculate Junction Built-in Voltage VLSI using this online calculator? To use this online calculator for Junction Built-in Voltage VLSI, enter Temperature (T), Acceptor Concentration (N_A), Donor concentration (N_D) & Intrinsic Concentration (N_i) and hit the calculate button. Here is how the Junction Built-in Voltage VLSI calculation can be explained with given input values -> 0.754632 = ([BoltZ]*300/[Charge-e])*ln(1E+22*1E+23/(1.45E+16)^2).

FAQ

What is Junction Built-in Voltage VLSI?

The Junction Built-in Voltage VLSI formula is defined as the voltage that exists across a semiconductor junction in thermal equilibrium, where no external voltage is applied and is represented as Ø₀ = ([BoltZ]*T/[Charge-e])*ln(N_A*N_D/(N_i)^2) or Junction Built-in Voltage = ([BoltZ]*Temperature/[Charge-e])*ln(Acceptor Concentration*Donor concentration/(Intrinsic Concentration)^2). Temperature reflects how hot or cold an object or environment is, Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material, Donor concentration refers to the concentration of donor dopant atoms introduced into a semiconductor material to increase the number of free electrons & Intrinsic Concentration refers to the concentration of charge carriers (electrons and holes) in an intrinsic semiconductor at thermal equilibrium.

How to calculate Junction Built-in Voltage VLSI?

The Junction Built-in Voltage VLSI formula is defined as the voltage that exists across a semiconductor junction in thermal equilibrium, where no external voltage is applied is calculated using Junction Built-in Voltage = ([BoltZ]*Temperature/[Charge-e])*ln(Acceptor Concentration*Donor concentration/(Intrinsic Concentration)^2). To calculate Junction Built-in Voltage VLSI, you need Temperature (T), Acceptor Concentration (N_A), Donor concentration (N_D) & Intrinsic Concentration (N_i). With our tool, you need to enter the respective value for Temperature, Acceptor Concentration, Donor concentration & Intrinsic Concentration 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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