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Built-in Potential Formula

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Built-in Potential is potential inside the MOSFET. Check FAQs

ψ o = V t \cdot \ln (\frac{N a \cdot N d}{{n i}^{2}})

ψ_o - Built-in Potential?V_t - Thermal Voltage?N_a - Acceptor Concentration?N_d - Donor Concentration?n_i - Intrinsic Electron Concentration?

Built-in Potential Example

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Here is how the Built-in Potential equation looks like with Values.

Here is how the Built-in Potential equation looks like with Units.

Here is how the Built-in Potential equation looks like.

18.8181 = 0.55 \cdot \ln (\frac{1100 \cdot 1.9E+14}{17^{2}})

18.8181V = 0.55V \cdot \ln (\frac{11001/m³ \cdot 1.9E+141/m³}{17^{2}})

18.8181 = 0.55 \cdot \ln (\frac{1100 \cdot 1.9E+14}{17^{2}})

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Built-in Potential Solution

Follow our step by step solution on how to calculate Built-in Potential?

FIRST Step Consider the formula

ψ o = V t \cdot \ln (\frac{N a \cdot N d}{{n i}^{2}})

Next Step Substitute values of Variables

∴

ψ o = 0.55V \cdot \ln (\frac{11001/m³ \cdot 1.9E+141/m³}{17^{2}})

Next Step Prepare to Evaluate

∴

ψ o = 0.55 \cdot \ln (\frac{1100 \cdot 1.9E+14}{17^{2}})

Next Step Evaluate

∴

ψ o = 18.8180761773197V

LAST Step Rounding Answer

∴

ψ o = 18.8181V

Built-in Potential Formula Elements

Variables

Functions

Built-in Potential

Built-in Potential is potential inside the MOSFET.

Symbol: ψ_o

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Built-in Potential

Thermal Voltage

Thermal Voltage is the voltage produced within the p-n junction.

Symbol: V_t

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Thermal Voltage

Acceptor Concentration

Acceptor Concentration is the concentration of holes in acceptor state.

Symbol: N_a

Measurement: Carrier ConcentrationUnit: 1/m³

Note: Value should be greater than 0.

Formulas to find Acceptor Concentration

Donor Concentration

Donor concentration is the concentration of electrons in the donor state.

Symbol: N_d

Measurement: Carrier ConcentrationUnit: 1/m³

Note: Value should be greater than 0.

Formulas to find Donor Concentration

Intrinsic Electron Concentration

Intrinsic Electron Concentration is defined as the number of electrons in the conduction band or the number of holes in the valence band in intrinsic material.

Symbol: n_i

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Intrinsic Electron Concentration

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

Syntax: ln(Number)

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How to Evaluate Built-in Potential?

Built-in Potential evaluator uses Built-in Potential = Thermal Voltage*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Electron Concentration^2)) to evaluate the Built-in Potential, The Built-in potential formula is defined as the built-in potential in a semiconductor which equals the potential across the depletion region in thermal equilibrium. It also equals the sum of the bulk potentials of each region, since the bulk potential quantifies the distance between the fermi energy and the intrinsic energy. Built-in Potential is denoted by ψ_o symbol.

How to evaluate Built-in Potential using this online evaluator? To use this online evaluator for Built-in Potential, enter Thermal Voltage (V_t), Acceptor Concentration (N_a), Donor Concentration (N_d) & Intrinsic Electron Concentration (n_i) and hit the calculate button.

FAQs on Built-in Potential

What is the formula to find Built-in Potential?

The formula of Built-in Potential is expressed as Built-in Potential = Thermal Voltage*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Electron Concentration^2)). Here is an example- 18.81808 = 0.55*ln((1100*190000000000000)/(17^2)).

How to calculate Built-in Potential?

With Thermal Voltage (V_t), Acceptor Concentration (N_a), Donor Concentration (N_d) & Intrinsic Electron Concentration (n_i) we can find Built-in Potential using the formula - Built-in Potential = Thermal Voltage*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Electron Concentration^2)). This formula also uses Natural Logarithm Function function(s).

Can the Built-in Potential be negative?

Yes, the Built-in Potential, measured in Electric Potential can be negative.

Which unit is used to measure Built-in Potential?

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

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Built-in Potential Formula

Built-in Potential Example

Built-in Potential Solution

Built-in Potential Formula Elements

Other formulas in CMOS Design Characteristics category

How to Evaluate Built-in Potential?

FAQs on Built-in Potential

Variable Name