Depletion Region Charge Density Calculator

✖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%
✖Surface Potential is the electric potential at the surface of the semiconductor, specifically at the interface between the semiconductor and the insulator.ⓘ Surface Potential [Φ_s]			+10% -10%
✖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%

✖Density of Depletion Layer Charge is the amount of these fixed charges per unit area within the depletion region.ⓘ Depletion Region Charge Density [Q_d]

⎘ Copy

👎

Formula

✖

Depletion Region Charge Density

Formula

`"Q"_{"d"} = (sqrt(2*"[Charge-e]"*"[Permitivity-silicon]"*"N"_{"A"}*"modulus"("Φ"_{"s"}-"Φ"_{"f"})))`

Example

`"1.6E^-6electrons/m³"=(sqrt(2*"[Charge-e]"*"[Permitivity-silicon]"*"1.32electrons/cm³"*"modulus"("0.78V"-"0.25V")))`

Calculator

LaTeX

Reset

👍

Download MOSFET Formula PDF PDF Image

Depletion Region Charge Density Solution

STEP 0: Pre-Calculation Summary

Formula Used

Density of Depletion Layer Charge = (sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(Surface Potential-Bulk Fermi Potential)))
Q_d = (sqrt(2*[Charge-e]*[Permitivity-silicon]*N_A*modulus(Φ_s-Φ_f)))
This formula uses 2 Constants, 2 Functions, 4 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

Density of Depletion Layer Charge - (Measured in Electrons per Cubic Meter) - Density of Depletion Layer Charge is the amount of these fixed charges per unit area within the depletion region.
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.
Surface Potential - (Measured in Volt) - Surface Potential is the electric potential at the surface of the semiconductor, specifically at the interface between the semiconductor and the insulator.
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.

STEP 1: Convert Input(s) to Base Unit

Doping Concentration of Acceptor: 1.32 Electrons per Cubic Centimeter --> 1320000 Electrons per Cubic Meter (Check conversion here)
Surface Potential: 0.78 Volt --> 0.78 Volt No Conversion Required
Bulk Fermi Potential: 0.25 Volt --> 0.25 Volt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_d = (sqrt(2*[Charge-e]*[Permitivity-silicon]*N_A*modulus(Φ_s-Φ_f))) --> (sqrt(2*[Charge-e]*[Permitivity-silicon]*1320000*modulus(0.78-0.25)))

Evaluating ... ...

Q_d = 1.61952637096272E-06

STEP 3: Convert Result to Output's Unit

1.61952637096272E-06 Electrons per Cubic Meter --> No Conversion Required

FINAL ANSWER

1.61952637096272E-06 ≈ 1.6E-6 Electrons per Cubic Meter <-- Density of Depletion Layer Charge

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Electronics » MOSFET » Analog Electronics » MOS Transistor » Depletion Region Charge Density

Credits

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

Dipanjona Mallick has verified this Calculator and 50+ more calculators!

< 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

Depletion Region Charge Density Formula

Why does the depletion layer form in a p-n junction?

The depletion layer forms in a p-n junction due to the diffusion of majority charge carriers (holes and electrons) across the junction, resulting in the creation of a region depleted of these carriers.

How to Calculate Depletion Region Charge Density?

Depletion Region Charge Density calculator uses Density of Depletion Layer Charge = (sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(Surface Potential-Bulk Fermi Potential))) to calculate the Density of Depletion Layer Charge, The Depletion Region Charge Density formula is defined as the amount of the fixed charges per unit area within the depletion region. Density of Depletion Layer Charge is denoted by Q_d symbol.

How to calculate Depletion Region Charge Density using this online calculator? To use this online calculator for Depletion Region Charge Density, enter Doping Concentration of Acceptor (N_A), Surface Potential (Φ_s) & Bulk Fermi Potential (Φ_f) and hit the calculate button. Here is how the Depletion Region Charge Density calculation can be explained with given input values -> 1.6E-6 = (sqrt(2*[Charge-e]*[Permitivity-silicon]*1320000*modulus(0.78-0.25))).

FAQ

What is Depletion Region Charge Density?

The Depletion Region Charge Density formula is defined as the amount of the fixed charges per unit area within the depletion region and is represented as Q_d = (sqrt(2*[Charge-e]*[Permitivity-silicon]*N_A*modulus(Φ_s-Φ_f))) or Density of Depletion Layer Charge = (sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(Surface Potential-Bulk Fermi Potential))). Doping Concentration of Acceptor refers to the concentration of acceptor atoms intentionally added to a semiconductor material, Surface Potential is the electric potential at the surface of the semiconductor, specifically at the interface between the semiconductor and the insulator & Bulk Fermi Potential is a parameter that describes the electrostatic potential in the bulk (interior) of a semiconductor material.

How to calculate Depletion Region Charge Density?

The Depletion Region Charge Density formula is defined as the amount of the fixed charges per unit area within the depletion region is calculated using Density of Depletion Layer Charge = (sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(Surface Potential-Bulk Fermi Potential))). To calculate Depletion Region Charge Density, you need Doping Concentration of Acceptor (N_A), Surface Potential (Φ_s) & Bulk Fermi Potential (Φ_f). With our tool, you need to enter the respective value for Doping Concentration of Acceptor, Surface Potential & Bulk Fermi Potential and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search