PN Junction Depletion Depth with Source VLSI Calculator

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VLSI Material Optimization

Analog VLSI Design

✖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 [Ø₀]			+10% -10%
✖Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material.ⓘ Acceptor Concentration [N_A]			+10% -10%

✖P-n Junction Depletion Depth with Source is defined as the region around a p-n junction where charge carriers have been depleted due to the formation of an electric field.ⓘ PN Junction Depletion Depth with Source VLSI [x_dS]

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Formula

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PN Junction Depletion Depth with Source VLSI

Formula

`"x"_{"dS"} = sqrt((2*"[Permitivity-silicon]"*"[Permitivity-vacuum]"*"Ø"_{"0"})/("[Charge-e]"*"N"_{"A"}))`

Example

`"0.313423μm"=sqrt((2*"[Permitivity-silicon]"*"[Permitivity-vacuum]"*"0.76V")/("[Charge-e]"*"1e+16/cm³"))`

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PN Junction Depletion Depth with Source VLSI Solution

STEP 0: Pre-Calculation Summary

Formula Used

P-n Junction Depletion Depth with Source = sqrt((2*[Permitivity-silicon]*[Permitivity-vacuum]*Junction Built-in Voltage)/([Charge-e]*Acceptor Concentration))
x_dS = sqrt((2*[Permitivity-silicon]*[Permitivity-vacuum]*Ø₀)/([Charge-e]*N_A))
This formula uses 3 Constants, 1 Functions, 3 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)

Variables Used

P-n Junction Depletion Depth with Source - (Measured in Meter) - P-n Junction Depletion Depth with Source is defined as the region around a p-n junction where charge carriers have been depleted due to the formation of an electric field.
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.
Acceptor Concentration - (Measured in 1 per Cubic Meter) - Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material.

STEP 1: Convert Input(s) to Base Unit

Junction Built-in Voltage: 0.76 Volt --> 0.76 Volt No Conversion Required
Acceptor Concentration: 1E+16 1 per Cubic Centimeter --> 1E+22 1 per Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x_dS = sqrt((2*[Permitivity-silicon]*[Permitivity-vacuum]*Ø₀)/([Charge-e]*N_A)) --> sqrt((2*[Permitivity-silicon]*[Permitivity-vacuum]*0.76)/([Charge-e]*1E+22))

Evaluating ... ...

x_dS = 3.13423217933622E-07

STEP 3: Convert Result to Output's Unit

3.13423217933622E-07 Meter -->0.313423217933622 Micrometer (Check conversion here)

FINAL ANSWER

0.313423217933622 ≈ 0.313423 Micrometer <-- P-n Junction Depletion Depth with Source

(Calculation completed in 00.020 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

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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

PN Junction Depletion Depth with Source VLSI Formula

How can VLSI designers control the p-n junction depletion depth?

VLSI designers can control the p-n junction depletion depth by adjusting the doping concentrations during the semiconductor fabrication process and by applying appropriate bias voltages across the junction.

How to Calculate PN Junction Depletion Depth with Source VLSI?

PN Junction Depletion Depth with Source VLSI calculator uses P-n Junction Depletion Depth with Source = sqrt((2*[Permitivity-silicon]*[Permitivity-vacuum]*Junction Built-in Voltage)/([Charge-e]*Acceptor Concentration)) to calculate the P-n Junction Depletion Depth with Source, The PN Junction Depletion Depth with Source VLSI formula is defined as the region around a p-n junction where charge carriers have been depleted due to the formation of an electric field. P-n Junction Depletion Depth with Source is denoted by x_dS symbol.

How to calculate PN Junction Depletion Depth with Source VLSI using this online calculator? To use this online calculator for PN Junction Depletion Depth with Source VLSI, enter Junction Built-in Voltage (Ø₀) & Acceptor Concentration (N_A) and hit the calculate button. Here is how the PN Junction Depletion Depth with Source VLSI calculation can be explained with given input values -> 313423.2 = sqrt((2*[Permitivity-silicon]*[Permitivity-vacuum]*0.76)/([Charge-e]*1E+22)).

FAQ

What is PN Junction Depletion Depth with Source VLSI?

The PN Junction Depletion Depth with Source VLSI formula is defined as the region around a p-n junction where charge carriers have been depleted due to the formation of an electric field and is represented as x_dS = sqrt((2*[Permitivity-silicon]*[Permitivity-vacuum]*Ø₀)/([Charge-e]*N_A)) or P-n Junction Depletion Depth with Source = sqrt((2*[Permitivity-silicon]*[Permitivity-vacuum]*Junction Built-in Voltage)/([Charge-e]*Acceptor Concentration)). Junction Built-in Voltage is defined as the voltage that exists across a semiconductor junction in thermal equilibrium, where no external voltage is applied & Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material.

How to calculate PN Junction Depletion Depth with Source VLSI?

The PN Junction Depletion Depth with Source VLSI formula is defined as the region around a p-n junction where charge carriers have been depleted due to the formation of an electric field is calculated using P-n Junction Depletion Depth with Source = sqrt((2*[Permitivity-silicon]*[Permitivity-vacuum]*Junction Built-in Voltage)/([Charge-e]*Acceptor Concentration)). To calculate PN Junction Depletion Depth with Source VLSI, you need Junction Built-in Voltage (Ø₀) & Acceptor Concentration (N_A). With our tool, you need to enter the respective value for Junction Built-in Voltage & Acceptor 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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