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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Formula

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Maximum Depletion Depth

Formula

`"x"_{"dm"} = sqrt((2*"[Permitivity-silicon]"*"modulus"(2*"Φ"_{"f"}))/("[Charge-e]"*"N"_{"A"}))`

Example

`"7.4E^6m"=sqrt((2*"[Permitivity-silicon]"*"modulus"(2*"0.25V"))/("[Charge-e]"*"1.32electrons/cm³"))`

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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 00.004 seconds)

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Created by banuprakash

Dayananda Sagar College of Engineering (DSCE), Bangalore

banuprakash has created this Calculator and 50+ more calculators!

Verified by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

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< 21 MOS Transistor Calculators

Sidewall Voltage Equivalence Factor

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)))

Pull down Current in Linear Region

Go Linear Region Pull Down Current = sum(x,0,Number of Parallel Driver Transistors,(Electron Mobility*Oxide Capacitance/2)*(Channel Width/Channel Length)*(2*(Gate Source Voltage-Threshold Voltage)*Output Voltage-Output Voltage^2))

Node Voltage at Given Instance

Go Node Voltage at Given Instance = (Transconductance Factor/Node Capacitance)*int(exp(-(1/(Node Resistance*Node Capacitance))*(Time Period-x))*Current Flowing into Node*x,x,0,Time Period)

Pull down Current in Saturation Region

Go Saturation Region Pull Down Current = sum(x,0,Number of Parallel Driver Transistors,(Electron Mobility*Oxide Capacitance/2)*(Channel Width/Channel Length)*(Gate Source Voltage-Threshold Voltage)^2)

Saturation Time

Go Saturation Time = -2*Load Capacitance/(Transconductance Process Parameter*(High Output Voltage-Threshold Voltage)^2)*int(1,x,High Output Voltage,High Output Voltage-Threshold Voltage)

Drain Current Flowing through MOS Transistor

Go Drain Current = (Channel Width/Channel Length)*Electron Mobility*Oxide Capacitance*int((Gate Source Voltage-x-Threshold Voltage),x,0,Drain Source Voltage)

Time Delay when NMOS Operates in Linear Region

Go Linear Region in Time Delay = -2*Junction Capacitance*int(1/(Transconductance Process Parameter*(2*(Input Voltage-Threshold Voltage)*x-x^2)),x,Initial Voltage,Final Voltage)

Depletion Region Charge Density

Go Density of Depletion Layer Charge = (sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(Surface Potential-Bulk Fermi Potential)))

Depth of Depletion Region Associated with Drain

Go Drain's Depth of Depletion Region = sqrt((2*[Permitivity-silicon]*(Built in Junction Potential+Drain Source Voltage))/([Charge-e]*Doping Concentration of Acceptor))

Drain Current in Saturation Region in MOS Transistor

Go Saturation Region Drain Current = Channel Width*Saturation Electron Drift Velocity*int(Charge*Short Channel Parameter,x,0,Effective Channel Length)

Fermi Potential for P Type

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

Maximum Depletion Depth

Go Maximum Depletion Depth = sqrt((2*[Permitivity-silicon]*modulus(2*Bulk Fermi Potential))/([Charge-e]*Doping Concentration of Acceptor))

Fermi Potential for N Type

Go Fermi Potential for N Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Donor Dopant Concentration/Intrinsic Carrier Concentration)

Equivalent Large Signal Capacitance

Go Equivalent Large Signal Capacitance = (1/(Final Voltage-Initial Voltage))*int(Junction Capacitance*x,x,Initial Voltage,Final Voltage)

Built in Potential at Depletion Region

Go Built in Voltage = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(-2*Bulk Fermi Potential)))

Depth of Depletion Region Associated with Source

Go Source's Depth of Depletion Region = sqrt((2*[Permitivity-silicon]*Built in Junction Potential)/([Charge-e]*Doping Concentration of Acceptor))

Substrate Bias Coefficient

Go Substrate Bias Coefficient = sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor)/Oxide Capacitance

Average Power Dissipated over Period of Time

Go Average Power = (1/Total Time Taken)*int(Voltage*Current,x,0,Total Time Taken)

Equivalent Large Signal Junction Capacitance

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

Work Function in MOSFET

Go Work Function = Vaccum Level+(Conduction Band Energy Level-Fermi Level)

Zero Bias Sidewall Junction Capacitance per Unit Length

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

Maximum Depletion Depth Formula

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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