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Contact Potential Difference Formula

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

V 0 = \frac{[BoltZ] \cdot T}{[Charge-e]} \cdot \ln (\frac{N A \cdot N D}{{(n1 i)}^{2}})

V₀ - Voltage Across PN Junction?T - Absolute Temperature?N_A - Acceptor Concentration?N_D - Donor Concentration?n1_i - Intrinsic Carrier Concentration?[BoltZ] - Boltzmann constant?[Charge-e] - Charge of electron?

Contact Potential Difference Example

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Here is how the Contact Potential Difference equation looks like with Values.

Here is how the Contact Potential Difference equation looks like with Units.

Here is how the Contact Potential Difference equation looks like.

0.6238 = \frac{1.4E-23 \cdot 393}{1.6E-19} \cdot \ln (\frac{1E+22 \cdot 1E+24}{{(1E+19)}^{2}})

0.6238V = \frac{1.4E-23J/K \cdot 393K}{1.6E-19C} \cdot \ln (\frac{1E+221/m³ \cdot 1E+241/m³}{{(1E+191/m³)}^{2}})

0.6238 = \frac{1.4E-23 \cdot 393}{1.6E-19} \cdot \ln (\frac{1E+22 \cdot 1E+24}{{(1E+19)}^{2}})

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Contact Potential Difference Solution

Follow our step by step solution on how to calculate Contact Potential Difference?

FIRST Step Consider the formula

V 0 = \frac{[BoltZ] \cdot T}{[Charge-e]} \cdot \ln (\frac{N A \cdot N D}{{(n1 i)}^{2}})

Next Step Substitute values of Variables

∴

V 0 = \frac{[BoltZ] \cdot 393K}{[Charge-e]} \cdot \ln (\frac{1E+221/m³ \cdot 1E+241/m³}{{(1E+191/m³)}^{2}})

Next Step Substitute values of Constants

∴

V 0 = \frac{1.4E-23J/K \cdot 393K}{1.6E-19C} \cdot \ln (\frac{1E+221/m³ \cdot 1E+241/m³}{{(1E+191/m³)}^{2}})

Next Step Prepare to Evaluate

∴

V 0 = \frac{1.4E-23 \cdot 393}{1.6E-19} \cdot \ln (\frac{1E+22 \cdot 1E+24}{{(1E+19)}^{2}})

Next Step Evaluate

∴

V 0 = 0.623836767969216V

LAST Step Rounding Answer

∴

V 0 = 0.6238V

Contact Potential Difference Formula Elements

Variables

Constants

Functions

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

Absolute Temperature

Absolute Temperature represents the temperature of the system.

Symbol: T

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Absolute Temperature

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

Intrinsic Carrier Concentration

Intrinsic Carrier Concentration refers to the concentration of charge carriers, both majority and minority, of an intrinsic semiconductor at thermal equilibrium.

Symbol: n1_i

Measurement: Carrier ConcentrationUnit: 1/m³

Note: Value should be greater than 0.

Formulas to find Intrinsic Carrier Concentration

Boltzmann constant

Boltzmann constant relates the average kinetic energy of particles in a gas with the temperature of the gas and is a fundamental constant in statistical mechanics and thermodynamics.

Symbol: [BoltZ]

Value: 1.38064852E-23 J/K

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

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other formulas in Photonics Devices category

Go Optical Power Radiated

P opt = ε opto \cdot [Stefan-BoltZ] \cdot A s \cdot {T o}^{4}

Go Net Phase Shift

ΔΦ = \frac{π}{λ o} \cdot {(n ri)}^{3} \cdot r \cdot V cc

Go Length of Cavity

L c = \frac{λ \cdot m}{2}

Go Mode Number

m = \frac{2 \cdot L c \cdot n ri}{λ}

How to Evaluate Contact Potential Difference?

Contact Potential Difference evaluator uses Voltage Across PN Junction = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Carrier Concentration)^2) to evaluate the Voltage Across PN Junction, The Contact Potential Difference formula is defined as the voltage that exists across an unbiased pn junction. The contact potential is established across the space charge region, which is also referred to as the transition or depletion region. It is also called as diffusion potential or built-in junction potential. Voltage Across PN Junction is denoted by V₀ symbol.

How to evaluate Contact Potential Difference using this online evaluator? To use this online evaluator for Contact Potential Difference, enter Absolute Temperature (T), Acceptor Concentration (N_A), Donor Concentration (N_D) & Intrinsic Carrier Concentration (n1_i) and hit the calculate button.

FAQs on Contact Potential Difference

What is the formula to find Contact Potential Difference?

The formula of Contact Potential Difference is expressed as Voltage Across PN Junction = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Carrier Concentration)^2). Here is an example- 0.623837 = ([BoltZ]*393)/[Charge-e]*ln((1E+22*1E+24)/(1E+19)^2).

How to calculate Contact Potential Difference?

With Absolute Temperature (T), Acceptor Concentration (N_A), Donor Concentration (N_D) & Intrinsic Carrier Concentration (n1_i) we can find Contact Potential Difference using the formula - Voltage Across PN Junction = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Carrier Concentration)^2). This formula also uses Boltzmann constant, Charge of electron constant(s) and Natural Logarithm (ln) function(s).

Can the Contact Potential Difference be negative?

Yes, the Contact Potential Difference, measured in Electric Potential can be negative.

Which unit is used to measure Contact Potential Difference?

Contact Potential Difference is usually measured using the Volt[V] for Electric Potential. Millivolt[V], Microvolt[V], Nanovolt[V] are the few other units in which Contact Potential Difference can be measured.

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Contact Potential Difference Formula

Contact Potential Difference Example

Contact Potential Difference Solution

Contact Potential Difference Formula Elements

Other formulas in Photonics Devices category

How to Evaluate Contact Potential Difference?

FAQs on Contact Potential Difference

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