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Effective Density of States in Conduction Band Formula

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Effective Density of States refers to the density of available electron states per unit volume within the energy band structure of a material. Check FAQs

N eff = 2 \cdot {(2 \cdot π \cdot m eff \cdot [BoltZ] \cdot \frac{T}{{[hP]}^{2}})}^{\frac{3}{2}}

N_eff - Effective Density of States?m_eff - Effective Mass of Electron?T - Absolute Temperature?[BoltZ] - Boltzmann constant?[hP] - Planck constant?π - Archimedes' constant?

Effective Density of States in Conduction Band Example

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Here is how the Effective Density of States in Conduction Band equation looks like with Values.

Here is how the Effective Density of States in Conduction Band equation looks like with Units.

Here is how the Effective Density of States in Conduction Band equation looks like.

3.9E+24 = 2 \cdot {(2 \cdot 3.1416 \cdot 2E-31 \cdot 1.4E-23 \cdot \frac{393}{{6.6E-34}^{2}})}^{\frac{3}{2}}

3.9E+24 = 2 \cdot {(2 \cdot 3.1416 \cdot 2E-31kg \cdot 1.4E-23J/K \cdot \frac{393K}{{6.6E-34}^{2}})}^{\frac{3}{2}}

3.9E+24 = 2 \cdot {(2 \cdot 3.1416 \cdot 2E-31 \cdot 1.4E-23 \cdot \frac{393}{{6.6E-34}^{2}})}^{\frac{3}{2}}

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Effective Density of States in Conduction Band Solution

Follow our step by step solution on how to calculate Effective Density of States in Conduction Band?

FIRST Step Consider the formula

N eff = 2 \cdot {(2 \cdot π \cdot m eff \cdot [BoltZ] \cdot \frac{T}{{[hP]}^{2}})}^{\frac{3}{2}}

Next Step Substitute values of Variables

∴

N eff = 2 \cdot {(2 \cdot π \cdot 2E-31kg \cdot [BoltZ] \cdot \frac{393K}{{[hP]}^{2}})}^{\frac{3}{2}}

Next Step Substitute values of Constants

∴

N eff = 2 \cdot {(2 \cdot 3.1416 \cdot 2E-31kg \cdot 1.4E-23J/K \cdot \frac{393K}{{6.6E-34}^{2}})}^{\frac{3}{2}}

Next Step Prepare to Evaluate

∴

N eff = 2 \cdot {(2 \cdot 3.1416 \cdot 2E-31 \cdot 1.4E-23 \cdot \frac{393}{{6.6E-34}^{2}})}^{\frac{3}{2}}

Next Step Evaluate

∴

N eff = 3.87070655661186E+24

LAST Step Rounding Answer

∴

N eff = 3.9E+24

Effective Density of States in Conduction Band Formula Elements

Variables

Constants

Effective Density of States

Effective Density of States refers to the density of available electron states per unit volume within the energy band structure of a material.

Symbol: N_eff

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Effective Density of States

Effective Mass of Electron

Effective Mass of Electron is a concept used in solid-state physics to describe the behavior of electrons in a crystal lattice or a semiconductor material.

Symbol: m_eff

Measurement: WeightUnit: kg

Note: Value should be less than 9.2E-31.

Formulas to find Effective Mass of Electron

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

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

Planck constant

Planck constant is a fundamental universal constant that defines the quantum nature of energy and relates the energy of a photon to its frequency.

Symbol: [hP]

Value: 6.626070040E-34

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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How to Evaluate Effective Density of States in Conduction Band?

Effective Density of States in Conduction Band evaluator uses Effective Density of States = 2*(2*pi*Effective Mass of Electron*[BoltZ]*Absolute Temperature/[hP]^2)^(3/2) to evaluate the Effective Density of States, The Effective Density of States in Conduction Band formula is defined as the density of states in the conduction band of a semiconductor, integrated over a range of energy and is a constant for a particular temperature. Effective Density of States is denoted by N_eff symbol.

How to evaluate Effective Density of States in Conduction Band using this online evaluator? To use this online evaluator for Effective Density of States in Conduction Band, enter Effective Mass of Electron (m_eff) & Absolute Temperature (T) and hit the calculate button.

FAQs on Effective Density of States in Conduction Band

What is the formula to find Effective Density of States in Conduction Band?

The formula of Effective Density of States in Conduction Band is expressed as Effective Density of States = 2*(2*pi*Effective Mass of Electron*[BoltZ]*Absolute Temperature/[hP]^2)^(3/2). Here is an example- 3.9E+24 = 2*(2*pi*2E-31*[BoltZ]*393/[hP]^2)^(3/2).

How to calculate Effective Density of States in Conduction Band?

With Effective Mass of Electron (m_eff) & Absolute Temperature (T) we can find Effective Density of States in Conduction Band using the formula - Effective Density of States = 2*(2*pi*Effective Mass of Electron*[BoltZ]*Absolute Temperature/[hP]^2)^(3/2). This formula also uses Boltzmann constant, Planck constant, Archimedes' constant .

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