Maximum Depletion Depth Calculator

✖Bulk Fermi Potential is a parameter that describes the electrostatic potential in the bulk (interior) of a semiconductor material.ⓘ Bulk Fermi Potential [Φ_f]			+10% -10%
✖Doping Concentration of Acceptor refers to the concentration of acceptor atoms intentionally added to a semiconductor material.ⓘ Doping Concentration of Acceptor [N_A]			+10% -10%

✖Maximum Depletion Depth refers to the maximum extent to which the depletion region extends into the semiconductor material of the device under certain operating conditions.ⓘ Maximum Depletion Depth [x_dm]

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Maximum Depletion Depth Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Depletion Depth = sqrt((2*[Permitivity-silicon]*modulus(2*Bulk Fermi Potential))/([Charge-e]*Doping Concentration of Acceptor))
x_dm = sqrt((2*[Permitivity-silicon]*modulus(2*Φ_f))/([Charge-e]*N_A))
This formula uses 2 Constants, 2 Functions, 3 Variables

Constants Used

[Permitivity-silicon] - Permittivity of silicon Value Taken As 11.7
[Charge-e] - Charge of electron Value Taken As 1.60217662E-19

Functions Used

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., sqrt(Number)
modulus - Modulus of a number is the remainder when that number is divided by another number., modulus

Variables Used

Maximum Depletion Depth - (Measured in Meter) - Maximum Depletion Depth refers to the maximum extent to which the depletion region extends into the semiconductor material of the device under certain operating conditions.
Bulk Fermi Potential - (Measured in Volt) - Bulk Fermi Potential is a parameter that describes the electrostatic potential in the bulk (interior) of a semiconductor material.
Doping Concentration of Acceptor - (Measured in Electrons per Cubic Meter) - Doping Concentration of Acceptor refers to the concentration of acceptor atoms intentionally added to a semiconductor material.

STEP 1: Convert Input(s) to Base Unit

Bulk Fermi Potential: 0.25 Volt --> 0.25 Volt No Conversion Required
Doping Concentration of Acceptor: 1.32 Electrons per Cubic Centimeter --> 1320000 Electrons per Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x_dm = sqrt((2*[Permitivity-silicon]*modulus(2*Φ_f))/([Charge-e]*N_A)) --> sqrt((2*[Permitivity-silicon]*modulus(2*0.25))/([Charge-e]*1320000))

Evaluating ... ...

x_dm = 7437907.45302539

STEP 3: Convert Result to Output's Unit

7437907.45302539 Meter --> No Conversion Required

FINAL ANSWER

7437907.45302539 ≈ 7.4E+6 Meter <-- Maximum Depletion Depth

(Calculation completed in 00.008 seconds)

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Created by banuprakash

Dayananda Sagar College of Engineering (DSCE), Bangalore

banuprakash has created this Calculator and 50+ more calculators!

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Heritage Insitute of technology (HITK), Kolkata

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< MOS Transistor Calculators

Sidewall Voltage Equivalence Factor

LaTeX Go Sidewall Voltage Equivalence Factor = -(2*sqrt(Built in Potential of Sidewall Junctions)/(Final Voltage-Initial Voltage)*(sqrt(Built in Potential of Sidewall Junctions-Final Voltage)-sqrt(Built in Potential of Sidewall Junctions-Initial Voltage)))

Fermi Potential for P Type

LaTeX Go Fermi Potential for P Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Intrinsic Carrier Concentration/Doping Concentration of Acceptor)

Equivalent Large Signal Junction Capacitance

LaTeX Go Equivalent Large Signal Junction Capacitance = Perimeter of Sidewall*Sidewall Junction Capacitance*Sidewall Voltage Equivalence Factor

Zero Bias Sidewall Junction Capacitance per Unit Length

LaTeX Go Sidewall Junction Capacitance = Zero Bias Sidewall Junction Potential*Depth of Sidewall

Maximum Depletion Depth Formula

LaTeX Go

How is the depletion region formed in a MOSFET?

The depletion region is formed when a voltage is applied to the gate terminal, creating an electric field that repels majority carriers (electrons or holes) away from the interface.

How to Calculate Maximum Depletion Depth?

Maximum Depletion Depth calculator uses Maximum Depletion Depth = sqrt((2*[Permitivity-silicon]*modulus(2*Bulk Fermi Potential))/([Charge-e]*Doping Concentration of Acceptor)) to calculate the Maximum Depletion Depth, The Maximum Depletion Depth formula is defined as the maximum extent to which the depletion region extends into the semiconductor material of the device under certain operating conditions. Maximum Depletion Depth is denoted by x_dm symbol.

How to calculate Maximum Depletion Depth using this online calculator? To use this online calculator for Maximum Depletion Depth, enter Bulk Fermi Potential (Φ_f) & Doping Concentration of Acceptor (N_A) and hit the calculate button. Here is how the Maximum Depletion Depth calculation can be explained with given input values -> 7.4E+6 = sqrt((2*[Permitivity-silicon]*modulus(2*0.25))/([Charge-e]*1320000)).

FAQ

What is Maximum Depletion Depth?

The Maximum Depletion Depth formula is defined as the maximum extent to which the depletion region extends into the semiconductor material of the device under certain operating conditions and is represented as x_dm = sqrt((2*[Permitivity-silicon]*modulus(2*Φ_f))/([Charge-e]*N_A)) or Maximum Depletion Depth = sqrt((2*[Permitivity-silicon]*modulus(2*Bulk Fermi Potential))/([Charge-e]*Doping Concentration of Acceptor)). Bulk Fermi Potential is a parameter that describes the electrostatic potential in the bulk (interior) of a semiconductor material & Doping Concentration of Acceptor refers to the concentration of acceptor atoms intentionally added to a semiconductor material.

How to calculate Maximum Depletion Depth?

The Maximum Depletion Depth formula is defined as the maximum extent to which the depletion region extends into the semiconductor material of the device under certain operating conditions is calculated using Maximum Depletion Depth = sqrt((2*[Permitivity-silicon]*modulus(2*Bulk Fermi Potential))/([Charge-e]*Doping Concentration of Acceptor)). To calculate Maximum Depletion Depth, you need Bulk Fermi Potential (Φ_f) & Doping Concentration of Acceptor (N_A). With our tool, you need to enter the respective value for Bulk Fermi Potential & Doping Concentration of Acceptor and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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