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PN Junction Capacitance Formula

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Junction Capacitance refers to the capacitance associated with the p-n junction formed between two semiconductor regions in a semiconductor device, such as a diode or a transistor. Check FAQs

C j = \frac{A pn}{2} \cdot \sqrt{\frac{2 \cdot [Charge-e] \cdot ε r \cdot [Permitivity-silicon]}{V 0 - (V)} \cdot (\frac{N A \cdot N D}{N A + N D})}

C_j - Junction Capacitance?A_pn - PN Junction Area?ε_r - Relative Permittivity?V₀ - Voltage Across PN Junction?V - Reverse Bias Voltage?N_A - Acceptor Concentration?N_D - Donor Concentration?[Charge-e] - Charge of electron?[Permitivity-silicon] - Permittivity of silicon?

PN Junction Capacitance Example

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

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

Here is how the PN Junction Capacitance equation looks like.

1.9E+6 = \frac{4.8}{2} \cdot \sqrt{\frac{2 \cdot 1.6E-19 \cdot 78 \cdot 11.7}{0.6 - (-4)} \cdot (\frac{1E+22 \cdot 1E+24}{1E+22 + 1E+24})}

1.9E+6fF = \frac{4.8µm²}{2} \cdot \sqrt{\frac{2 \cdot 1.6E-19C \cdot 78F/m \cdot 11.7}{0.6V - (-4V)} \cdot (\frac{1E+221/m³ \cdot 1E+241/m³}{1E+221/m³ + 1E+241/m³})}

1.9E+6 = \frac{4.8}{2} \cdot \sqrt{\frac{2 \cdot 1.6E-19 \cdot 78 \cdot 11.7}{0.6 - (-4)} \cdot (\frac{1E+22 \cdot 1E+24}{1E+22 + 1E+24})}

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PN Junction Capacitance Solution

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

FIRST Step Consider the formula

C j = \frac{A pn}{2} \cdot \sqrt{\frac{2 \cdot [Charge-e] \cdot ε r \cdot [Permitivity-silicon]}{V 0 - (V)} \cdot (\frac{N A \cdot N D}{N A + N D})}

Next Step Substitute values of Variables

∴

C j = \frac{4.8µm²}{2} \cdot \sqrt{\frac{2 \cdot [Charge-e] \cdot 78F/m \cdot [Permitivity-silicon]}{0.6V - (-4V)} \cdot (\frac{1E+221/m³ \cdot 1E+241/m³}{1E+221/m³ + 1E+241/m³})}

Next Step Substitute values of Constants

∴

C j = \frac{4.8µm²}{2} \cdot \sqrt{\frac{2 \cdot 1.6E-19C \cdot 78F/m \cdot 11.7}{0.6V - (-4V)} \cdot (\frac{1E+221/m³ \cdot 1E+241/m³}{1E+221/m³ + 1E+241/m³})}

Next Step Convert Units

∴

C j = \frac{4.8E-12m²}{2} \cdot \sqrt{\frac{2 \cdot 1.6E-19C \cdot 78F/m \cdot 11.7}{0.6V - (-4V)} \cdot (\frac{1E+221/m³ \cdot 1E+241/m³}{1E+221/m³ + 1E+241/m³})}

Next Step Prepare to Evaluate

∴

C j = \frac{4.8E-12}{2} \cdot \sqrt{\frac{2 \cdot 1.6E-19 \cdot 78 \cdot 11.7}{0.6 - (-4)} \cdot (\frac{1E+22 \cdot 1E+24}{1E+22 + 1E+24})}

Next Step Evaluate

∴

C j = 1.9040662888657E-09F

Next Step Convert to Output's Unit

∴

C j = 1904066.2888657fF

LAST Step Rounding Answer

∴

C j = 1.9E+6fF

PN Junction Capacitance Formula Elements

Variables

Constants

Functions

Junction Capacitance

Junction Capacitance refers to the capacitance associated with the p-n junction formed between two semiconductor regions in a semiconductor device, such as a diode or a transistor.

Symbol: C_j

Measurement: CapacitanceUnit: fF

Note: Value should be greater than 0.

Formulas to find Junction Capacitance

PN Junction Area

The PN Junction Area is the boundary or interface area between two types of semiconductor materials in a pn diode.

Symbol: A_pn

Measurement: AreaUnit: µm²

Note: Value should be greater than 0.

Formulas to find PN Junction Area

Relative Permittivity

Relative Permittivity is a measure of a material's ability to store electrical energy in an electric field.

Symbol: ε_r

Measurement: PermittivityUnit: F/m

Note: Value should be greater than 0.

Formulas to find Relative Permittivity

Voltage Across PN Junction

Voltage Across PN Junction is the built-in potential across the pn junction of a semiconductor without any external bias.

Symbol: V₀

Measurement: Electric PotentialUnit: V

Note: Value should be between 0.3 to 0.8.

Formulas to find Voltage Across PN Junction

Reverse Bias Voltage

Reverse Bias Voltage is the negative external voltage applied to the pn junction.

Symbol: V

Measurement: Electric PotentialUnit: V

Note: Value should be less than 0.

Formulas to find Reverse Bias Voltage

Acceptor Concentration

Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material.

Symbol: N_A

Measurement: Carrier ConcentrationUnit: 1/m³

Note: Value should be greater than 0.

Formulas to find Acceptor Concentration

Donor Concentration

Donor Concentration refers to the concentration of donor dopant atoms introduced into a semiconductor material to increase the number of free electrons.

Symbol: N_D

Measurement: Carrier ConcentrationUnit: 1/m³

Note: Value can be positive or negative.

Formulas to find Donor Concentration

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)

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How to Evaluate PN Junction Capacitance?

PN Junction Capacitance evaluator uses Junction Capacitance = PN Junction Area/2*sqrt((2*[Charge-e]*Relative Permittivity*[Permitivity-silicon])/(Voltage Across PN Junction-(Reverse Bias Voltage))*((Acceptor Concentration*Donor Concentration)/(Acceptor Concentration+Donor Concentration))) to evaluate the Junction Capacitance, The PN Junction Capacitance formula is defined as the capacitance associated with the depletion region of a pn junction due to charges accumulated. It is prominent in the reverse biased condition because, this condition increases the barrier potential and hence the capacitance across it. Junction Capacitance is denoted by C_j symbol.

How to evaluate PN Junction Capacitance using this online evaluator? To use this online evaluator for PN Junction Capacitance, enter PN Junction Area (A_pn), Relative Permittivity (ε_r), Voltage Across PN Junction (V₀), Reverse Bias Voltage (V), Acceptor Concentration (N_A) & Donor Concentration (N_D) and hit the calculate button.

FAQs on PN Junction Capacitance

What is the formula to find PN Junction Capacitance?

The formula of PN Junction Capacitance is expressed as Junction Capacitance = PN Junction Area/2*sqrt((2*[Charge-e]*Relative Permittivity*[Permitivity-silicon])/(Voltage Across PN Junction-(Reverse Bias Voltage))*((Acceptor Concentration*Donor Concentration)/(Acceptor Concentration+Donor Concentration))). Here is an example- 1.9E+21 = 4.8E-12/2*sqrt((2*[Charge-e]*78*[Permitivity-silicon])/(0.6-((-4)))*((1E+22*1E+24)/(1E+22+1E+24))).

How to calculate PN Junction Capacitance?

With PN Junction Area (A_pn), Relative Permittivity (ε_r), Voltage Across PN Junction (V₀), Reverse Bias Voltage (V), Acceptor Concentration (N_A) & Donor Concentration (N_D) we can find PN Junction Capacitance using the formula - Junction Capacitance = PN Junction Area/2*sqrt((2*[Charge-e]*Relative Permittivity*[Permitivity-silicon])/(Voltage Across PN Junction-(Reverse Bias Voltage))*((Acceptor Concentration*Donor Concentration)/(Acceptor Concentration+Donor Concentration))). This formula also uses Charge of electron, Permittivity of silicon constant(s) and Square Root (sqrt) function(s).

Can the PN Junction Capacitance be negative?

No, the PN Junction Capacitance, measured in Capacitance cannot be negative.

Which unit is used to measure PN Junction Capacitance?

PN Junction Capacitance is usually measured using the Femtofarad[fF] for Capacitance. Farad[fF], Kilofarad[fF], Millifarad[fF] are the few other units in which PN Junction Capacitance can be measured.

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PN Junction Capacitance Formula

PN Junction Capacitance Example

PN Junction Capacitance Solution

PN Junction Capacitance Formula Elements

Other formulas in Devices with Optical Components category

How to Evaluate PN Junction Capacitance?

FAQs on PN Junction Capacitance

Variable Name