Zero Bias Junction Capacitance Calculator

✖Permitivity of Silicon is a material property that describes how a material responds to an electric field.ⓘ Permitivity of Silicon [ε_si]			+10% -10%
✖Doping Concentration of Acceptor refers to the concentration of acceptor atoms intentionally added to a semiconductor material.ⓘ Doping Concentration of Acceptor [N_A]			+10% -10%
✖Doping Concentration of Donor refers to the concentration of donor atoms intentionally added to a semiconductor material.ⓘ Doping Concentration of Donor [N_D]			+10% -10%
✖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.ⓘ Built in Junction Potential [Φ_o]			+10% -10%

✖Zero Bias Junction Capacitance refers to the built-in potential of a semiconductor junction when no external voltage (bias) is applied to it.ⓘ Zero Bias Junction Capacitance [C_j0]

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Formula

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Zero Bias Junction Capacitance

Formula

`"C"_{"j0"} = sqrt(("ε"_{"si"}*"[Charge-e]")/2*(("N"_{"A"}*"N"_{"D"})/("N"_{"A"}+"N"_{"D"}))*1/"Φ"_{"o"})`

Example

`"6.6E^-7F"=sqrt(("11.7F/m"*"[Charge-e]")/2*(("1.32electrons/cm³"*"3.01electrons/cm³")/("1.32electrons/cm³"+"3.01electrons/cm³"))*1/"2V")`

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Zero Bias Junction Capacitance Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
C_j0 = sqrt((ε_si*[Charge-e])/2*((N_A*N_D)/(N_A+N_D))*1/Φ_o)
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

[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

Zero Bias Junction Capacitance - (Measured in Farad) - Zero Bias Junction Capacitance refers to the built-in potential of a semiconductor junction when no external voltage (bias) is applied to it.
Permitivity of Silicon - (Measured in Farad per Meter) - Permitivity of Silicon is a material property that describes how a material responds to an electric field.
Doping Concentration of Acceptor - (Measured in Electrons per Cubic Meter) - Doping Concentration of Acceptor refers to the concentration of acceptor atoms intentionally added to a semiconductor material.
Doping Concentration of Donor - (Measured in Electrons per Cubic Meter) - Doping Concentration of Donor refers to the concentration of donor atoms intentionally added to a semiconductor material.
Built in Junction Potential - (Measured in Volt) - 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.

STEP 1: Convert Input(s) to Base Unit

Permitivity of Silicon: 11.7 Farad per Meter --> 11.7 Farad per Meter No Conversion Required
Doping Concentration of Acceptor: 1.32 Electrons per Cubic Centimeter --> 1320000 Electrons per Cubic Meter (Check conversion here)
Doping Concentration of Donor: 3.01 Electrons per Cubic Centimeter --> 3010000 Electrons per Cubic Meter (Check conversion here)
Built in Junction Potential: 2 Volt --> 2 Volt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_j0 = sqrt((ε_si*[Charge-e])/2*((N_A*N_D)/(N_A+N_D))*1/Φ_o) --> sqrt((11.7*[Charge-e])/2*((1320000*3010000)/(1320000+3010000))*1/2)

Evaluating ... ...

C_j0 = 6.55759204749238E-07

STEP 3: Convert Result to Output's Unit

6.55759204749238E-07 Farad --> No Conversion Required

FINAL ANSWER

6.55759204749238E-07 ≈ 6.6E-7 Farad <-- Zero Bias Junction Capacitance

(Calculation completed in 00.021 seconds)

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< 2 MOSFET Amplifiers Calculators

Zero Bias Sidewall Junction Capacitance

Go Zero Bias Sidewall Junction Potential = sqrt(([Permitivity-silicon]*[Charge-e])/2*((Sidewall Doping Density*Doping Concentration of Donor)/(Sidewall Doping Density+Doping Concentration of Donor))*1/Built in Potential of Sidewall Junctions)

Zero Bias Junction Capacitance

Go 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)

Zero Bias Junction Capacitance Formula

Why is it called "zero bias"?

It is termed "zero bias" because there is no external voltage applied to the semiconductor junction. The potential that exists across the junction is a built-in potential arising from the inherent properties of the materials forming the junction.

How to Calculate Zero Bias Junction Capacitance?

Zero Bias Junction Capacitance calculator 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 calculate 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 calculate Zero Bias Junction Capacitance using this online calculator? To use this online calculator 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. Here is how the Zero Bias Junction Capacitance calculation can be explained with given input values -> 6.6E-7 = sqrt((11.7*[Charge-e])/2*((1320000*3010000)/(1320000+3010000))*1/2).

FAQ

What is 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 and is represented as C_j0 = sqrt((ε_si*[Charge-e])/2*((N_A*N_D)/(N_A+N_D))*1/Φ_o) or 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). Permitivity of Silicon is a material property that describes how a material responds to an electric field, Doping Concentration of Acceptor refers to the concentration of acceptor atoms intentionally added to a semiconductor material, Doping Concentration of Donor refers to the concentration of donor atoms intentionally added to a semiconductor material & 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.

How to calculate 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 is calculated using 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 calculate Zero Bias Junction Capacitance, you need Permitivity of Silicon (ε_si), Doping Concentration of Acceptor (N_A), Doping Concentration of Donor (N_D) & Built in Junction Potential (Φ_o). With our tool, you need to enter the respective value for Permitivity of Silicon, Doping Concentration of Acceptor, Doping Concentration of Donor & Built in Junction 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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