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Zero Bias Junction Capacitance Formula

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Zero Bias Junction Capacitance refers to the built-in potential of a semiconductor junction when no external voltage (bias) is applied to it. Check FAQs

C j0 = \sqrt{\frac{ε si \cdot [Charge-e]}{2} \cdot (\frac{N A \cdot N D}{N A + N D}) \cdot \frac{1}{Φ o}}

C_j0 - Zero Bias Junction Capacitance?ε_si - Permitivity of Silicon?N_A - Doping Concentration of Acceptor?N_D - Doping Concentration of Donor?Φ_o - Built in Junction Potential?[Charge-e] - Charge of electron?

Zero Bias Junction Capacitance Example

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Here is how the Zero Bias Junction Capacitance equation looks like with Values.

Here is how the Zero Bias Junction Capacitance equation looks like with Units.

Here is how the Zero Bias Junction Capacitance equation looks like.

6.6E-7 = \sqrt{\frac{11.7 \cdot 1.6E-19}{2} \cdot (\frac{1.32 \cdot 3.01}{1.32 + 3.01}) \cdot \frac{1}{2}}

6.6E-7F = \sqrt{\frac{11.7F/m \cdot 1.6E-19C}{2} \cdot (\frac{1.32electrons/cm³ \cdot 3.01electrons/cm³}{1.32electrons/cm³ + 3.01electrons/cm³}) \cdot \frac{1}{2V}}

6.6E-7 = \sqrt{\frac{11.7 \cdot 1.6E-19}{2} \cdot (\frac{1.32 \cdot 3.01}{1.32 + 3.01}) \cdot \frac{1}{2}}

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Zero Bias Junction Capacitance Solution

Follow our step by step solution on how to calculate Zero Bias Junction Capacitance?

FIRST Step Consider the formula

C j0 = \sqrt{\frac{ε si \cdot [Charge-e]}{2} \cdot (\frac{N A \cdot N D}{N A + N D}) \cdot \frac{1}{Φ o}}

Next Step Substitute values of Variables

∴

C j0 = \sqrt{\frac{11.7F/m \cdot [Charge-e]}{2} \cdot (\frac{1.32electrons/cm³ \cdot 3.01electrons/cm³}{1.32electrons/cm³ + 3.01electrons/cm³}) \cdot \frac{1}{2V}}

Next Step Substitute values of Constants

∴

C j0 = \sqrt{\frac{11.7F/m \cdot 1.6E-19C}{2} \cdot (\frac{1.32electrons/cm³ \cdot 3.01electrons/cm³}{1.32electrons/cm³ + 3.01electrons/cm³}) \cdot \frac{1}{2V}}

Next Step Convert Units

∴

C j0 = \sqrt{\frac{11.7F/m \cdot 1.6E-19C}{2} \cdot (\frac{1.3E+6electrons/m³ \cdot 3E+6electrons/m³}{1.3E+6electrons/m³ + 3E+6electrons/m³}) \cdot \frac{1}{2V}}

Next Step Prepare to Evaluate

∴

C j0 = \sqrt{\frac{11.7 \cdot 1.6E-19}{2} \cdot (\frac{1.3E+6 \cdot 3E+6}{1.3E+6 + 3E+6}) \cdot \frac{1}{2}}

Next Step Evaluate

∴

C j0 = 6.55759204749238E-07F

LAST Step Rounding Answer

∴

C j0 = 6.6E-7F

Zero Bias Junction Capacitance Formula Elements

Variables

Constants

Functions

Zero Bias Junction Capacitance

Zero Bias Junction Capacitance refers to the built-in potential of a semiconductor junction when no external voltage (bias) is applied to it.

Symbol: C_j0

Measurement: CapacitanceUnit: F

Note: Value should be greater than 0.

Formulas to find Zero Bias Junction Capacitance

Permitivity of Silicon

Permitivity of Silicon is a material property that describes how a material responds to an electric field.

Symbol: ε_si

Measurement: PermittivityUnit: F/m

Note: Value should be greater than 0.

Formulas to find Permitivity of Silicon

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

Doping Concentration of Donor

Doping Concentration of Donor refers to the concentration of donor atoms intentionally added to a semiconductor material.

Symbol: N_D

Measurement: Electron DensityUnit: electrons/cm³

Note: Value should be greater than 0.

Formulas to find Doping Concentration of Donor

Built in Junction Potential

Built in Junction Potential refers to the potential difference or voltage that exists across a semiconductor junction when it is not connected to an external voltage source.

Symbol: Φ_o

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Built in Junction 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

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)

Other formulas in MOSFET Amplifiers category

Go Zero Bias Sidewall Junction Capacitance

C j0sw = \sqrt{\frac{[Permitivity-silicon] \cdot [Charge-e]}{2} \cdot (\frac{N A(sw) \cdot N D}{N A(sw) + N D}) \cdot \frac{1}{Φ osw}}

How to Evaluate Zero Bias Junction Capacitance?

Zero Bias Junction Capacitance evaluator uses Zero Bias Junction Capacitance = sqrt((Permitivity of Silicon*[Charge-e])/2*((Doping Concentration of Acceptor*Doping Concentration of Donor)/(Doping Concentration of Acceptor+Doping Concentration of Donor))*1/Built in Junction Potential) to evaluate the Zero Bias Junction Capacitance, The Zero Bias Junction Capacitance formula is defined as the built-in potential of a semiconductor junction when no external voltage (bias) is applied to it. Zero Bias Junction Capacitance is denoted by C_j0 symbol.

How to evaluate Zero Bias Junction Capacitance using this online evaluator? To use this online evaluator for Zero Bias Junction Capacitance, enter Permitivity of Silicon (ε_si), Doping Concentration of Acceptor (N_A), Doping Concentration of Donor (N_D) & Built in Junction Potential (Φ_o) and hit the calculate button.

FAQs on Zero Bias Junction Capacitance

What is the formula to find Zero Bias Junction Capacitance?

The formula of Zero Bias Junction Capacitance is expressed as Zero Bias Junction Capacitance = sqrt((Permitivity of Silicon*[Charge-e])/2*((Doping Concentration of Acceptor*Doping Concentration of Donor)/(Doping Concentration of Acceptor+Doping Concentration of Donor))*1/Built in Junction Potential). Here is an example- 6.6E-7 = sqrt((11.7*[Charge-e])/2*((1320000*3010000)/(1320000+3010000))*1/2).

How to calculate Zero Bias Junction Capacitance?

With Permitivity of Silicon (ε_si), Doping Concentration of Acceptor (N_A), Doping Concentration of Donor (N_D) & Built in Junction Potential (Φ_o) we can find Zero Bias Junction Capacitance using the formula - Zero Bias Junction Capacitance = sqrt((Permitivity of Silicon*[Charge-e])/2*((Doping Concentration of Acceptor*Doping Concentration of Donor)/(Doping Concentration of Acceptor+Doping Concentration of Donor))*1/Built in Junction Potential). This formula also uses Charge of electron constant(s) and Square Root (sqrt) function(s).

Can the Zero Bias Junction Capacitance be negative?

No, the Zero Bias Junction Capacitance, measured in Capacitance cannot be negative.

Which unit is used to measure Zero Bias Junction Capacitance?

Zero Bias Junction Capacitance is usually measured using the Farad[F] for Capacitance. Kilofarad[F], Millifarad[F], Microfarad[F] are the few other units in which Zero Bias Junction Capacitance can be measured.

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Zero Bias Junction Capacitance Formula

Zero Bias Junction Capacitance Example

Zero Bias Junction Capacitance Solution

Zero Bias Junction Capacitance Formula Elements

Other formulas in MOSFET Amplifiers category

How to Evaluate Zero Bias Junction Capacitance?

FAQs on Zero Bias Junction Capacitance

Variable Name