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Depletion Region Charge Density Formula

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Density of Depletion Layer Charge is the amount of these fixed charges per unit area within the depletion region. Check FAQs

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

Q_d - Density of Depletion Layer Charge?N_A - Doping Concentration of Acceptor?Φ_s - Surface Potential?Φ_f - Bulk Fermi Potential?[Charge-e] - Charge of electron?[Permitivity-silicon] - Permittivity of silicon?

Depletion Region Charge Density Example

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Here is how the Depletion Region Charge Density equation looks like with Values.

Here is how the Depletion Region Charge Density equation looks like with Units.

Here is how the Depletion Region Charge Density equation looks like.

1.6E-6 = (\sqrt{2 \cdot 1.6E-19 \cdot 11.7 \cdot 1.32 \cdot mod \underset{̲}{u} s (0.78 - 0.25)})

1.6E-6electrons/m³ = (\sqrt{2 \cdot 1.6E-19C \cdot 11.7 \cdot 1.32electrons/cm³ \cdot mod \underset{̲}{u} s (0.78V - 0.25V)})

1.6E-6 = (\sqrt{2 \cdot 1.6E-19 \cdot 11.7 \cdot 1.32 \cdot mod \underset{̲}{u} s (0.78 - 0.25)})

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Depletion Region Charge Density Solution

Follow our step by step solution on how to calculate Depletion Region Charge Density?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

Q d = (\sqrt{2 \cdot [Charge-e] \cdot [Permitivity-silicon] \cdot 1.32electrons/cm³ \cdot mod \underset{̲}{u} s (0.78V - 0.25V)})

Next Step Substitute values of Constants

∴

Q d = (\sqrt{2 \cdot 1.6E-19C \cdot 11.7 \cdot 1.32electrons/cm³ \cdot mod \underset{̲}{u} s (0.78V - 0.25V)})

Next Step Convert Units

∴

Q d = (\sqrt{2 \cdot 1.6E-19C \cdot 11.7 \cdot 1.3E+6electrons/m³ \cdot mod \underset{̲}{u} s (0.78V - 0.25V)})

Next Step Prepare to Evaluate

∴

Q d = (\sqrt{2 \cdot 1.6E-19 \cdot 11.7 \cdot 1.3E+6 \cdot mod \underset{̲}{u} s (0.78 - 0.25)})

Next Step Evaluate

∴

Q d = 1.61952637096272E-06electrons/m³

LAST Step Rounding Answer

∴

Q d = 1.6E-6electrons/m³

Depletion Region Charge Density Formula Elements

Variables

Constants

Functions

Density of Depletion Layer Charge

Density of Depletion Layer Charge is the amount of these fixed charges per unit area within the depletion region.

Symbol: Q_d

Measurement: Electron DensityUnit: electrons/m³

Note: Value can be positive or negative.

Formulas to find Density of Depletion Layer Charge

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

Surface Potential

Surface Potential is the electric potential at the surface of the semiconductor, specifically at the interface between the semiconductor and the insulator.

Symbol: Φ_s

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Surface Potential

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

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

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

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

Other formulas in MOS Transistor category

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Go Equivalent Large Signal Junction Capacitance

C eq(sw) = P \cdot C jsw \cdot K eq(sw)

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 Depletion Region Charge Density?

Depletion Region Charge Density evaluator uses Density of Depletion Layer Charge = (sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(Surface Potential-Bulk Fermi Potential))) to evaluate the Density of Depletion Layer Charge, The Depletion Region Charge Density formula is defined as the amount of the fixed charges per unit area within the depletion region. Density of Depletion Layer Charge is denoted by Q_d symbol.

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

FAQs on Depletion Region Charge Density

What is the formula to find Depletion Region Charge Density?

The formula of Depletion Region Charge Density is expressed as Density of Depletion Layer Charge = (sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(Surface Potential-Bulk Fermi Potential))). Here is an example- 1.6E-6 = (sqrt(2*[Charge-e]*[Permitivity-silicon]*1320000*modulus(0.78-0.25))).

How to calculate Depletion Region Charge Density?

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

Can the Depletion Region Charge Density be negative?

Yes, the Depletion Region Charge Density, measured in Electron Density can be negative.

Which unit is used to measure Depletion Region Charge Density?

Depletion Region Charge Density is usually measured using the Electrons per Cubic Meter[electrons/m³] for Electron Density. Electrons per Cubic Centimeter[electrons/m³] are the few other units in which Depletion Region Charge Density can be measured.

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Depletion Region Charge Density Formula

Depletion Region Charge Density Example

Depletion Region Charge Density Solution

Depletion Region Charge Density Formula Elements

Other formulas in MOS Transistor category

How to Evaluate Depletion Region Charge Density?

FAQs on Depletion Region Charge Density

Variable Name