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Built in Potential at Depletion Region Formula

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Built in Voltage is a characteristic voltage that exists across a semiconductor device. Check FAQs

Φ B0 = - (\sqrt{2 \cdot [Charge-e] \cdot [Permitivity-silicon] \cdot N A \cdot mod \underset{̲}{u} s (- 2 \cdot Φ f)})

Φ_B0 - Built in Voltage?N_A - Doping Concentration of Acceptor?Φ_f - Bulk Fermi Potential?[Charge-e] - Charge of electron?[Permitivity-silicon] - Permittivity of silicon?

Built in Potential at Depletion Region Example

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With units

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Here is how the Built in Potential at Depletion Region equation looks like with Values.

Here is how the Built in Potential at Depletion Region equation looks like with Units.

Here is how the Built in Potential at Depletion Region equation looks like.

-1.6E-6 = - (\sqrt{2 \cdot 1.6E-19 \cdot 11.7 \cdot 1.32 \cdot mod \underset{̲}{u} s (- 2 \cdot 0.25)})

-1.6E-6V = - (\sqrt{2 \cdot 1.6E-19C \cdot 11.7 \cdot 1.32electrons/cm³ \cdot mod \underset{̲}{u} s (- 2 \cdot 0.25V)})

-1.6E-6 = - (\sqrt{2 \cdot 1.6E-19 \cdot 11.7 \cdot 1.32 \cdot mod \underset{̲}{u} s (- 2 \cdot 0.25)})

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Built in Potential at Depletion Region Solution

Follow our step by step solution on how to calculate Built in Potential at Depletion Region?

FIRST Step Consider the formula

Φ B0 = - (\sqrt{2 \cdot [Charge-e] \cdot [Permitivity-silicon] \cdot N A \cdot mod \underset{̲}{u} s (- 2 \cdot Φ f)})

Next Step Substitute values of Variables

∴

Φ B0 = - (\sqrt{2 \cdot [Charge-e] \cdot [Permitivity-silicon] \cdot 1.32electrons/cm³ \cdot mod \underset{̲}{u} s (- 2 \cdot 0.25V)})

Next Step Substitute values of Constants

∴

Φ B0 = - (\sqrt{2 \cdot 1.6E-19C \cdot 11.7 \cdot 1.32electrons/cm³ \cdot mod \underset{̲}{u} s (- 2 \cdot 0.25V)})

Next Step Convert Units

∴

Φ B0 = - (\sqrt{2 \cdot 1.6E-19C \cdot 11.7 \cdot 1.3E+6electrons/m³ \cdot mod \underset{̲}{u} s (- 2 \cdot 0.25V)})

Next Step Prepare to Evaluate

∴

Φ B0 = - (\sqrt{2 \cdot 1.6E-19 \cdot 11.7 \cdot 1.3E+6 \cdot mod \underset{̲}{u} s (- 2 \cdot 0.25)})

Next Step Evaluate

∴

Φ B0 = -1.57302306783086E-06V

LAST Step Rounding Answer

∴

Φ B0 = -1.6E-6V

Built in Potential at Depletion Region Formula Elements

Variables

Constants

Functions

Built in Voltage

Built in Voltage is a characteristic voltage that exists across a semiconductor device.

Symbol: Φ_B0

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Built in Voltage

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

Bulk Fermi Potential

Bulk Fermi Potential is a parameter that describes the electrostatic potential in the bulk (interior) of a semiconductor material.

Symbol: Φ_f

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Bulk Fermi 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

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)

modulus

Modulus of a number is the remainder when that number is divided by another number.

Syntax: modulus

Other formulas in MOS Transistor category

Go Zero Bias Sidewall Junction Capacitance per Unit Length

C jsw = C j0sw \cdot x j

Go Equivalent Large Signal Junction Capacitance

C eq(sw) = P \cdot C jsw \cdot K eq(sw)

Go Fermi Potential for P Type

Φ Fp = \frac{[BoltZ] \cdot T a}{[Charge-e]} \cdot \ln (\frac{n i}{N A})

Go Sidewall Voltage Equivalence Factor

K eq(sw) = - (2 \cdot \frac{\sqrt{Φ osw}}{V 2 - V 1} \cdot (\sqrt{Φ osw - V 2} - \sqrt{Φ osw - V 1}))

How to Evaluate Built in Potential at Depletion Region?

Built in Potential at Depletion Region evaluator uses Built in Voltage = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(-2*Bulk Fermi Potential))) to evaluate the Built in Voltage, The Built in Potential at Depletion Region formula is defined as the voltage established across this depleted region when the p-n junction is in thermal equilibrium. Built in Voltage is denoted by Φ_B0 symbol.

How to evaluate Built in Potential at Depletion Region using this online evaluator? To use this online evaluator for Built in Potential at Depletion Region, enter Doping Concentration of Acceptor (N_A) & Bulk Fermi Potential (Φ_f) and hit the calculate button.

FAQs on Built in Potential at Depletion Region

What is the formula to find Built in Potential at Depletion Region?

The formula of Built in Potential at Depletion Region is expressed as Built in Voltage = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(-2*Bulk Fermi Potential))). Here is an example- -1.6E-6 = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*1320000*modulus(-2*0.25))).

How to calculate Built in Potential at Depletion Region?

With Doping Concentration of Acceptor (N_A) & Bulk Fermi Potential (Φ_f) we can find Built in Potential at Depletion Region using the formula - Built in Voltage = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(-2*Bulk Fermi Potential))). This formula also uses Charge of electron, Permittivity of silicon constant(s) and , Square Root (sqrt), Modulus (modulus) function(s).

Can the Built in Potential at Depletion Region be negative?

Yes, the Built in Potential at Depletion Region, measured in Electric Potential can be negative.

Which unit is used to measure Built in Potential at Depletion Region?

Built in Potential at Depletion Region 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 at Depletion Region can be measured.

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