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PN Junction Depletion Depth with Drain VLSI Calculator

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✖Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material.ⓘ Acceptor Concentration [N_A]			+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 [Ø₀]			+10% -10%
✖Drain to source Potential is potential between drain and source.ⓘ Drain to Source Potential [V_ds]			+10% -10%

✖P-n Junction Depletion Depth with Drain is defined as the extension of the depletion region into the semiconductor material near the drain terminal.ⓘ PN Junction Depletion Depth with Drain VLSI [x_dD]

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Formula

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PN Junction Depletion Depth with Drain VLSI

Formula

x dD = \sqrt{(\frac{2 \cdot [Permitivity-silicon] \cdot [Permitivity-vacuum]}{[Charge-e] \cdot N A}) \cdot (Ø 0 + V ds)}

Example

0.534467 μm = \sqrt{(\frac{2 \cdot [Permitivity-silicon] \cdot [Permitivity-vacuum]}{[Charge-e] \cdot 1e+16 /cm³}) \cdot (0.76 V + 1.45 V)}

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PN Junction Depletion Depth with Drain VLSI Solution

STEP 0: Pre-Calculation Summary

Formula Used

P-n Junction Depletion Depth with Drain = sqrt(((2*[Permitivity-silicon]*[Permitivity-vacuum])/([Charge-e]*Acceptor Concentration))*(Junction Built-in Voltage+Drain to Source Potential))
x_dD = sqrt(((2*[Permitivity-silicon]*[Permitivity-vacuum])/([Charge-e]*N_A))*(Ø₀+V_ds))
This formula uses 3 Constants, 1 Functions, 4 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 Drain - (Measured in Meter) - P-n Junction Depletion Depth with Drain is defined as the extension of the depletion region into the semiconductor material near the drain terminal.
Acceptor Concentration - (Measured in 1 per Cubic Meter) - Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material.
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.
Drain to Source Potential - (Measured in Volt) - Drain to source Potential is potential between drain and source.

STEP 1: Convert Input(s) to Base Unit

Acceptor Concentration: 1E+16 1 per Cubic Centimeter --> 1E+22 1 per Cubic Meter (Check conversion here)
Junction Built-in Voltage: 0.76 Volt --> 0.76 Volt No Conversion Required
Drain to Source Potential: 1.45 Volt --> 1.45 Volt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x_dD = sqrt(((2*[Permitivity-silicon]*[Permitivity-vacuum])/([Charge-e]*N_A))*(Ø₀+V_ds)) --> sqrt(((2*[Permitivity-silicon]*[Permitivity-vacuum])/([Charge-e]*1E+22))*(0.76+1.45))

Evaluating ... ...

x_dD = 5.34466520692296E-07

STEP 3: Convert Result to Output's Unit

5.34466520692296E-07 Meter -->0.534466520692296 Micrometer (Check conversion here)

FINAL ANSWER

0.534466520692296 ≈ 0.534467 Micrometer <-- P-n Junction Depletion Depth with Drain

(Calculation completed in 00.020 seconds)

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Body Effect Coefficient

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

DIBL Coefficient

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

Channel Charge

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

Critical Voltage

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

PN Junction Depletion Depth with Drain VLSI Formula

How does the widening of the PN Junction Depletion Depth impact MOSFET performance in VLSI?

As the depletion region widens, it introduces additional resistance to the flow of charge carriers in the channel between the source and drain. This increased resistance affects the overall performance of the MOSFET, influencing parameters such as drain current, transconductance, and threshold voltage. Understanding and controlling the PN Junction Depletion Depth is crucial for optimizing MOSFET behavior in VLSI designs.

How to Calculate PN Junction Depletion Depth with Drain VLSI?

PN Junction Depletion Depth with Drain VLSI calculator uses P-n Junction Depletion Depth with Drain = sqrt(((2*[Permitivity-silicon]*[Permitivity-vacuum])/([Charge-e]*Acceptor Concentration))*(Junction Built-in Voltage+Drain to Source Potential)) to calculate the P-n Junction Depletion Depth with Drain, The PN Junction Depletion Depth with Drain VLSI formula is defined as the extension of the depletion region into the semiconductor material near the drain terminal. P-n Junction Depletion Depth with Drain is denoted by x_dD symbol.

How to calculate PN Junction Depletion Depth with Drain VLSI using this online calculator? To use this online calculator for PN Junction Depletion Depth with Drain VLSI, enter Acceptor Concentration (N_A), Junction Built-in Voltage (Ø₀) & Drain to Source Potential (V_ds) and hit the calculate button. Here is how the PN Junction Depletion Depth with Drain VLSI calculation can be explained with given input values -> 534466.5 = sqrt(((2*[Permitivity-silicon]*[Permitivity-vacuum])/([Charge-e]*1E+22))*(0.76+1.45)).

FAQ

What is PN Junction Depletion Depth with Drain VLSI?

The PN Junction Depletion Depth with Drain VLSI formula is defined as the extension of the depletion region into the semiconductor material near the drain terminal and is represented as x_dD = sqrt(((2*[Permitivity-silicon]*[Permitivity-vacuum])/([Charge-e]*N_A))*(Ø₀+V_ds)) or P-n Junction Depletion Depth with Drain = sqrt(((2*[Permitivity-silicon]*[Permitivity-vacuum])/([Charge-e]*Acceptor Concentration))*(Junction Built-in Voltage+Drain to Source Potential)). Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material, Junction Built-in Voltage is defined as the voltage that exists across a semiconductor junction in thermal equilibrium, where no external voltage is applied & Drain to source Potential is potential between drain and source.

How to calculate PN Junction Depletion Depth with Drain VLSI?

The PN Junction Depletion Depth with Drain VLSI formula is defined as the extension of the depletion region into the semiconductor material near the drain terminal is calculated using P-n Junction Depletion Depth with Drain = sqrt(((2*[Permitivity-silicon]*[Permitivity-vacuum])/([Charge-e]*Acceptor Concentration))*(Junction Built-in Voltage+Drain to Source Potential)). To calculate PN Junction Depletion Depth with Drain VLSI, you need Acceptor Concentration (N_A), Junction Built-in Voltage (Ø₀) & Drain to Source Potential (V_ds). With our tool, you need to enter the respective value for Acceptor Concentration, Junction Built-in Voltage & Drain to Source 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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