Donor Dopant Concentration Calculator

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MOS IC Fabrication

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✖Saturation Current refers to the maximum current that can flow through the transistor when it is fully turned on.ⓘ Saturation Current [I_sat]			+10% -10%
✖Transistor's Length refers to the length of the channel region in a MOSFET. This dimension plays a crucial role in determining the electrical characteristics and performance of the transistor.ⓘ Transistor's Length [L_t]			+10% -10%
✖Transistor's Width refers to the width of the channel region in a MOSFET. This dimension plays a crucial role in determining the electrical characteristics and performance of the transistor.ⓘ Transistor's Width [W_t]			+10% -10%
✖Electron Mobility describes how quickly electrons can move through the material in response to an electric field.ⓘ Electron Mobility [μ_n]			+10% -10%
✖Depletion Layer Capacitance per Unit Area is the capacitance of depletion layer per unit area.ⓘ Depletion Layer Capacitance [C_dep]			+10% -10%

✖Donor Dopant Concentration is the concentration of donor atoms per unit volume.ⓘ Donor Dopant Concentration [N_d]

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Formula

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Donor Dopant Concentration

Formula

`"N"_{"d"} = ("I"_{"sat"}*"L"_{"t"})/("[Charge-e]"*"W"_{"t"}*"μ"_{"n"}*"C"_{"dep"})`

Example

`"1.7E^23electrons/m³"=("2.015A"*"3.2μm")/("[Charge-e]"*"5.5μm"*"30m²/V*s"*"1.4μF")`

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Donor Dopant Concentration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Donor Dopant Concentration = (Saturation Current*Transistor's Length)/([Charge-e]*Transistor's Width*Electron Mobility*Depletion Layer Capacitance)
N_d = (I_sat*L_t)/([Charge-e]*W_t*μ_n*C_dep)
This formula uses 1 Constants, 6 Variables

Constants Used

[Charge-e] - Charge of electron Value Taken As 1.60217662E-19

Variables Used

Donor Dopant Concentration - (Measured in Electrons per Cubic Meter) - Donor Dopant Concentration is the concentration of donor atoms per unit volume.
Saturation Current - (Measured in Ampere) - Saturation Current refers to the maximum current that can flow through the transistor when it is fully turned on.
Transistor's Length - (Measured in Meter) - Transistor's Length refers to the length of the channel region in a MOSFET. This dimension plays a crucial role in determining the electrical characteristics and performance of the transistor.
Transistor's Width - (Measured in Meter) - Transistor's Width refers to the width of the channel region in a MOSFET. This dimension plays a crucial role in determining the electrical characteristics and performance of the transistor.
Electron Mobility - (Measured in Square Meter per Volt per Second) - Electron Mobility describes how quickly electrons can move through the material in response to an electric field.
Depletion Layer Capacitance - (Measured in Farad) - Depletion Layer Capacitance per Unit Area is the capacitance of depletion layer per unit area.

STEP 1: Convert Input(s) to Base Unit

Saturation Current: 2.015 Ampere --> 2.015 Ampere No Conversion Required
Transistor's Length: 3.2 Micrometer --> 3.2E-06 Meter (Check conversion here)
Transistor's Width: 5.5 Micrometer --> 5.5E-06 Meter (Check conversion here)
Electron Mobility: 30 Square Meter per Volt per Second --> 30 Square Meter per Volt per Second No Conversion Required
Depletion Layer Capacitance: 1.4 Microfarad --> 1.4E-06 Farad (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_d = (I_sat*L_t)/([Charge-e]*W_t*μ_n*C_dep) --> (2.015*3.2E-06)/([Charge-e]*5.5E-06*30*1.4E-06)

Evaluating ... ...

N_d = 1.74221865211214E+23

STEP 3: Convert Result to Output's Unit

1.74221865211214E+23 Electrons per Cubic Meter --> No Conversion Required

FINAL ANSWER

1.74221865211214E+23 ≈ 1.7E+23 Electrons per Cubic Meter <-- Donor Dopant Concentration

(Calculation completed in 00.004 seconds)

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Dayananda Sagar College of Engineering (DSCE), Bangalore

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< 15 MOS IC Fabrication Calculators

Switching Point Voltage

Go Switching Point Voltage = (Supply Voltage+PMOS Threshold Voltage+NMOS Threshold Voltage*sqrt(NMOS Transistor Gain/PMOS Transistor Gain))/(1+sqrt(NMOS Transistor Gain/PMOS Transistor Gain))

Body Effect in MOSFET

Go Threshold Voltage with Substrate = Threshold Voltage with Zero Body Bias+Body Effect Parameter*(sqrt(2*Bulk Fermi Potential+Voltage Applied to Body)-sqrt(2*Bulk Fermi Potential))

Donor Dopant Concentration

Go Donor Dopant Concentration = (Saturation Current*Transistor's Length)/([Charge-e]*Transistor's Width*Electron Mobility*Depletion Layer Capacitance)

Acceptor Dopant Concentration

Go Acceptor Dopant Concentration = 1/(2*pi*Transistor's Length*Transistor's Width*[Charge-e]*Hole Mobility*Depletion Layer Capacitance)

Drain Current of MOSFET at Saturation Region

Go Drain Current = Transconductance Parameter/2*(Gate Source Voltage-Threshold Voltage with Zero Body Bias)^2*(1+Channel Length Modulation Factor*Drain Source Voltage)

Maximum Dopant Concentration

Go Maximum Dopant Concentration = Reference Concentration*exp(-Activation Energy for Solid Solubility/([BoltZ]*Absolute Temperature))

Propagation Time

Go Propagation Time = 0.7*Number of Pass Transistors*((Number of Pass Transistors+1)/2)*Resistance in MOSFET*Load Capacitance

Drift Current Density due to Free Electrons

Go Drift Current Density due to Electrons = [Charge-e]*Electron Concentration*Electron Mobility*Electric Field Intensity

Drift Current Density due to Holes

Go Drift Current Density due to Holes = [Charge-e]*Hole Concentration*Hole Mobility*Electric Field Intensity

Channel Resistance

Go Channel Resistance = Transistor's Length/Transistor's Width*1/(Electron Mobility*Carrier Density)

MOSFET Unity-Gain Frequency

Go Unity Gain Frequency in MOSFET = Transconductance in MOSFET/(Gate Source Capacitance+Gate Drain Capacitance)

Critical Dimension

Go Critical Dimension = Process Dependent Constant*Wavelength in Photolithography/Numerical Aperture

Depth of Focus

Go Depth of Focus = Proportionality Factor*Wavelength in Photolithography/(Numerical Aperture^2)

Die Per Wafer

Go Die Per Wafer = (pi*Wafer Diameter^2)/(4*Size of Each Die)

Equivalent Oxide Thickness

Go Equivalent Oxide Thickness = Thickness of Material*(3.9/Dielectric Constant of Material)

Donor Dopant Concentration Formula

Donor Dopant Concentration = (Saturation Current*Transistor's Length)/([Charge-e]*Transistor's Width*Electron Mobility*Depletion Layer Capacitance)
N_d = (I_sat*L_t)/([Charge-e]*W_t*μ_n*C_dep)

What role do donor atoms play in a semiconductor?

Donor atoms introduce extra electrons into the semiconductor, creating a population of free electrons that contribute to the electrical conductivity of the material.

How to Calculate Donor Dopant Concentration?

Donor Dopant Concentration calculator uses Donor Dopant Concentration = (Saturation Current*Transistor's Length)/([Charge-e]*Transistor's Width*Electron Mobility*Depletion Layer Capacitance) to calculate the Donor Dopant Concentration, The Donor Dopant Concentration formula is defined as the concentration of donor atoms intentionally introduced into a semiconductor material to increase the number of free charge carriers (electrons) available for conduction. Donor Dopant Concentration is denoted by N_d symbol.

How to calculate Donor Dopant Concentration using this online calculator? To use this online calculator for Donor Dopant Concentration, enter Saturation Current (I_sat), Transistor's Length (L_t), Transistor's Width (W_t), Electron Mobility (μ_n) & Depletion Layer Capacitance (C_dep) and hit the calculate button. Here is how the Donor Dopant Concentration calculation can be explained with given input values -> 1.7E+23 = (2.015*3.2E-06)/([Charge-e]*5.5E-06*30*1.4E-06).

FAQ

What is Donor Dopant Concentration?

The Donor Dopant Concentration formula is defined as the concentration of donor atoms intentionally introduced into a semiconductor material to increase the number of free charge carriers (electrons) available for conduction and is represented as N_d = (I_sat*L_t)/([Charge-e]*W_t*μ_n*C_dep) or Donor Dopant Concentration = (Saturation Current*Transistor's Length)/([Charge-e]*Transistor's Width*Electron Mobility*Depletion Layer Capacitance). Saturation Current refers to the maximum current that can flow through the transistor when it is fully turned on, Transistor's Length refers to the length of the channel region in a MOSFET. This dimension plays a crucial role in determining the electrical characteristics and performance of the transistor, Transistor's Width refers to the width of the channel region in a MOSFET. This dimension plays a crucial role in determining the electrical characteristics and performance of the transistor, Electron Mobility describes how quickly electrons can move through the material in response to an electric field & Depletion Layer Capacitance per Unit Area is the capacitance of depletion layer per unit area.

How to calculate Donor Dopant Concentration?

The Donor Dopant Concentration formula is defined as the concentration of donor atoms intentionally introduced into a semiconductor material to increase the number of free charge carriers (electrons) available for conduction is calculated using Donor Dopant Concentration = (Saturation Current*Transistor's Length)/([Charge-e]*Transistor's Width*Electron Mobility*Depletion Layer Capacitance). To calculate Donor Dopant Concentration, you need Saturation Current (I_sat), Transistor's Length (L_t), Transistor's Width (W_t), Electron Mobility (μ_n) & Depletion Layer Capacitance (C_dep). With our tool, you need to enter the respective value for Saturation Current, Transistor's Length, Transistor's Width, Electron Mobility & Depletion Layer Capacitance 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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