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Maximum Depletion Depth Formula

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Maximum Depletion Depth refers to the maximum extent to which the depletion region extends into the semiconductor material of the device under certain operating conditions. Check FAQs

x dm = \sqrt{\frac{2 \cdot [Permitivity-silicon] \cdot mod \underset{̲}{u} s (2 \cdot Φ f)}{[Charge-e] \cdot N A}}

x_dm - Maximum Depletion Depth?Φ_f - Bulk Fermi Potential?N_A - Doping Concentration of Acceptor?[Permitivity-silicon] - Permittivity of silicon?[Charge-e] - Charge of electron?

Maximum Depletion Depth Example

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Here is how the Maximum Depletion Depth equation looks like with Values.

Here is how the Maximum Depletion Depth equation looks like with Units.

Here is how the Maximum Depletion Depth equation looks like.

7.4E+6 = \sqrt{\frac{2 \cdot 11.7 \cdot mod \underset{̲}{u} s (2 \cdot 0.25)}{1.6E-19 \cdot 1.32}}

7.4E+6m = \sqrt{\frac{2 \cdot 11.7 \cdot mod \underset{̲}{u} s (2 \cdot 0.25V)}{1.6E-19C \cdot 1.32electrons/cm³}}

7.4E+6 = \sqrt{\frac{2 \cdot 11.7 \cdot mod \underset{̲}{u} s (2 \cdot 0.25)}{1.6E-19 \cdot 1.32}}

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Maximum Depletion Depth Solution

Follow our step by step solution on how to calculate Maximum Depletion Depth?

FIRST Step Consider the formula

x dm = \sqrt{\frac{2 \cdot [Permitivity-silicon] \cdot mod \underset{̲}{u} s (2 \cdot Φ f)}{[Charge-e] \cdot N A}}

Next Step Substitute values of Variables

∴

x dm = \sqrt{\frac{2 \cdot [Permitivity-silicon] \cdot mod \underset{̲}{u} s (2 \cdot 0.25V)}{[Charge-e] \cdot 1.32electrons/cm³}}

Next Step Substitute values of Constants

∴

x dm = \sqrt{\frac{2 \cdot 11.7 \cdot mod \underset{̲}{u} s (2 \cdot 0.25V)}{1.6E-19C \cdot 1.32electrons/cm³}}

Next Step Convert Units

∴

x dm = \sqrt{\frac{2 \cdot 11.7 \cdot mod \underset{̲}{u} s (2 \cdot 0.25V)}{1.6E-19C \cdot 1.3E+6electrons/m³}}

Next Step Prepare to Evaluate

∴

x dm = \sqrt{\frac{2 \cdot 11.7 \cdot mod \underset{̲}{u} s (2 \cdot 0.25)}{1.6E-19 \cdot 1.3E+6}}

Next Step Evaluate

∴

x dm = 7437907.45302539m

LAST Step Rounding Answer

∴

x dm = 7.4E+6m

Maximum Depletion Depth Formula Elements

Variables

Constants

Functions

Maximum Depletion Depth

Maximum Depletion Depth refers to the maximum extent to which the depletion region extends into the semiconductor material of the device under certain operating conditions.

Symbol: x_dm

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Maximum Depletion Depth

Bulk Fermi Potential

Bulk Fermi Potential is a parameter that describes the electrostatic potential in the bulk (interior) of a semiconductor material.

Symbol: Φ_f

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Bulk Fermi Potential

Doping Concentration of Acceptor

Doping Concentration of Acceptor refers to the concentration of acceptor atoms intentionally added to a semiconductor material.

Symbol: N_A

Measurement: Electron DensityUnit: electrons/cm³

Note: Value should be greater than 0.

Formulas to find Doping Concentration of Acceptor

Permittivity of silicon

Permittivity of silicon measures its ability to store electrical energy in an electric field, vital in semiconductor technology.

Symbol: [Permitivity-silicon]

Value: 11.7

Charge of electron

Charge of electron is a fundamental physical constant, representing the electric charge carried by an electron, which is the elementary particle with a negative electric charge.

Symbol: [Charge-e]

Value: 1.60217662E-19 C

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.

Syntax: sqrt(Number)

modulus

Modulus of a number is the remainder when that number is divided by another number.

Syntax: modulus

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Go Fermi Potential for P Type

Φ Fp = \frac{[BoltZ] \cdot T a}{[Charge-e]} \cdot \ln (\frac{n i}{N A})

Go Sidewall Voltage Equivalence Factor

K eq(sw) = - (2 \cdot \frac{\sqrt{Φ osw}}{V 2 - V 1} \cdot (\sqrt{Φ osw - V 2} - \sqrt{Φ osw - V 1}))

How to Evaluate Maximum Depletion Depth?

Maximum Depletion Depth evaluator uses Maximum Depletion Depth = sqrt((2*[Permitivity-silicon]*modulus(2*Bulk Fermi Potential))/([Charge-e]*Doping Concentration of Acceptor)) to evaluate the Maximum Depletion Depth, The Maximum Depletion Depth formula is defined as the maximum extent to which the depletion region extends into the semiconductor material of the device under certain operating conditions. Maximum Depletion Depth is denoted by x_dm symbol.

How to evaluate Maximum Depletion Depth using this online evaluator? To use this online evaluator for Maximum Depletion Depth, enter Bulk Fermi Potential (Φ_f) & Doping Concentration of Acceptor (N_A) and hit the calculate button.

FAQs on Maximum Depletion Depth

What is the formula to find Maximum Depletion Depth?

The formula of Maximum Depletion Depth is expressed as Maximum Depletion Depth = sqrt((2*[Permitivity-silicon]*modulus(2*Bulk Fermi Potential))/([Charge-e]*Doping Concentration of Acceptor)). Here is an example- 7.4E+6 = sqrt((2*[Permitivity-silicon]*modulus(2*0.25))/([Charge-e]*1320000)).

How to calculate Maximum Depletion Depth?

With Bulk Fermi Potential (Φ_f) & Doping Concentration of Acceptor (N_A) we can find Maximum Depletion Depth using the formula - Maximum Depletion Depth = sqrt((2*[Permitivity-silicon]*modulus(2*Bulk Fermi Potential))/([Charge-e]*Doping Concentration of Acceptor)). This formula also uses Permittivity of silicon, Charge of electron constant(s) and , Square Root (sqrt), Modulus (modulus) function(s).

Can the Maximum Depletion Depth be negative?

No, the Maximum Depletion Depth, measured in Length cannot be negative.

Which unit is used to measure Maximum Depletion Depth?

Maximum Depletion Depth is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Maximum Depletion Depth can be measured.

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Maximum Depletion Depth Formula

Maximum Depletion Depth Example

Maximum Depletion Depth Solution

Maximum Depletion Depth Formula Elements

Other formulas in MOS Transistor category

How to Evaluate Maximum Depletion Depth?

FAQs on Maximum Depletion Depth

Variable Name