Built-in Potential Calculator

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✖Thermal Voltage is the voltage produced within the p-n junction.ⓘ Thermal Voltage [V_t]			+10% -10%
✖Acceptor concentration is the concentration of holes in acceptor state.ⓘ Acceptor Concentration [N_a]			+10% -10%
✖Donor concentration is the concentration of electrons in the donor state.ⓘ Donor Concentration [N_d]			+10% -10%
✖Intrinsic Electron Concentration is defined as the number of electrons in the conduction band or the number of holes in the valence band in intrinsic material.ⓘ Intrinsic Electron Concentration [n_i]			+10% -10%

✖Built-in Potential is potential inside the MOSFET.ⓘ Built-in Potential [ψ_o]

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Formula

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Built-in Potential

Formula

`"ψ"_{"o"} = "V"_{"t"}*ln(("N"_{"a"}*"N"_{"d"})/("n"_{"i"}^2))`

Example

`"18.81808V"="0.55V"*ln(("1100/m³"*"1.9e14/m³")/(("17")^2))`

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Built-in Potential Solution

STEP 0: Pre-Calculation Summary

Formula Used

Built-in Potential = Thermal Voltage*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Electron Concentration^2))
ψ_o = V_t*ln((N_a*N_d)/(n_i^2))
This formula uses 1 Functions, 5 Variables

Functions Used

ln - Natural logarithm function (base e), ln(Number)

Variables Used

Built-in Potential - (Measured in Volt) - Built-in Potential is potential inside the MOSFET.
Thermal Voltage - (Measured in Volt) - Thermal Voltage is the voltage produced within the p-n junction.
Acceptor Concentration - (Measured in 1 per Cubic Meter) - Acceptor concentration is the concentration of holes in acceptor state.
Donor Concentration - (Measured in 1 per Cubic Meter) - Donor concentration is the concentration of electrons in the donor state.
Intrinsic Electron Concentration - Intrinsic Electron Concentration is defined as the number of electrons in the conduction band or the number of holes in the valence band in intrinsic material.

STEP 1: Convert Input(s) to Base Unit

Thermal Voltage: 0.55 Volt --> 0.55 Volt No Conversion Required
Acceptor Concentration: 1100 1 per Cubic Meter --> 1100 1 per Cubic Meter No Conversion Required
Donor Concentration: 190000000000000 1 per Cubic Meter --> 190000000000000 1 per Cubic Meter No Conversion Required
Intrinsic Electron Concentration: 17 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ψ_o = V_t*ln((N_a*N_d)/(n_i^2)) --> 0.55*ln((1100*190000000000000)/(17^2))

Evaluating ... ...

ψ_o = 18.8180761773197

STEP 3: Convert Result to Output's Unit

18.8180761773197 Volt --> No Conversion Required

FINAL ANSWER

18.8180761773197 ≈ 18.81808 Volt <-- Built-in Potential

(Calculation completed in 00.004 seconds)

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Credits

Created by Shobhit Dimri

Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat

Shobhit Dimri has created this Calculator and 900+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< 24 CMOS Characteristics Calculators

Ground to Agression Capacitance

Go Adjacent Capacitance = ((Victim Driver*Time Constant Ratio of Agression to Victim*Ground V Capacitance)-(Agression Driver*Ground A Capacitance))/(Agression Driver-Victim Driver*Time Constant Ratio of Agression to Victim)

Victim Driver

Go Victim Driver = (Agression Driver*(Ground A Capacitance+Adjacent Capacitance))/(Time Constant Ratio of Agression to Victim*(Adjacent Capacitance+Ground V Capacitance))

Agression Driver

Go Agression Driver = (Victim Driver*Time Constant Ratio of Agression to Victim*(Adjacent Capacitance+Ground V Capacitance))/(Ground A Capacitance+Adjacent Capacitance)

Built-in Potential

Go Built-in Potential = Thermal Voltage*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Electron Concentration^2))

Agressor Voltage

Go Agressor Voltage = (Victim Voltage*(Ground V Capacitance+Adjacent Capacitance))/Adjacent Capacitance

Victim Voltage

Go Victim Voltage = (Agressor Voltage*Adjacent Capacitance)/(Ground V Capacitance+Adjacent Capacitance)

Adjacent Capacitance

Go Adjacent Capacitance = (Victim Voltage*Ground V Capacitance)/ (Agressor Voltage-Victim Voltage)

Branching Effort

Go Branching Effort = (Capacitance Onpath+Capacitance Offpath)/Capacitance Onpath

Agression Time Constant

Go Agression Time Constant = Time Constant Ratio of Agression to Victim*Victim Time Constant

Victim Time Constant

Go Victim Time Constant = Agression Time Constant/Time Constant Ratio of Agression to Victim

Time Constant Ratio of Agression to Victim

Go Time Constant Ratio of Agression to Victim = Agression Time Constant/Victim Time Constant

Capacitance Onpath

Go Capacitance Onpath = Total Capacitance Seen by a Stage-Capacitance Offpath

Total Capacitance Seen by Stage

Go Total Capacitance Seen by a Stage = Capacitance Onpath+Capacitance Offpath

Capacitance Offpath

Go Capacitance Offpath = Total Capacitance Seen by a Stage-Capacitance Onpath

Input Capacitance of Gate

Go Input Capacitance = Drive of Arbitrary Gate*Logical Effort

Logical Effort(G)

Go Logical Effort = Input Capacitance/Drive of Arbitrary Gate

VCO Single Gain Factor

Go VCO Gain = Change in Frequency of Clock/VCO Control Voltage

Drive of Arbitrary Gate

Go Drive of Arbitrary Gate = Input Capacitance/Logical Effort

Output Clock Phase

Go Output Clock Phase = 2*3.14*VCO Control Voltage*VCO Gain

VCO Control Voltage

Go VCO Control Voltage = Lock Voltage+VCO Offset Voltage

VCO Offset Voltage

Go VCO Offset Voltage = VCO Control Voltage-Lock Voltage

Lock Voltage

Go Lock Voltage = VCO Control Voltage-VCO Offset Voltage

Static Current

Go Static Current = Static Power/Drain Voltage

Static Power Dissipation

Go Static Power = Static Current*Drain Voltage

Built-in Potential Formula

Built-in Potential = Thermal Voltage*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Electron Concentration^2))
ψ_o = V_t*ln((N_a*N_d)/(n_i^2))

Brief notes on MOS diffusion capacitance model.

A MOS transistor can be viewed as a four-terminal device with capacitances between each terminal pair. The gate capacitance includes an intrinsic component (to the body, source and drain, or source alone, depending on operating regime) and overlap terms with the source and drain. The source and drain have parasitic diffusion capacitance to the body.

How to Calculate Built-in Potential?

Built-in Potential calculator uses Built-in Potential = Thermal Voltage*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Electron Concentration^2)) to calculate the Built-in Potential, The Built-in potential formula is defined as the built-in potential in a semiconductor which equals the potential across the depletion region in thermal equilibrium. It also equals the sum of the bulk potentials of each region, since the bulk potential quantifies the distance between the fermi energy and the intrinsic energy. Built-in Potential is denoted by ψ_o symbol.

How to calculate Built-in Potential using this online calculator? To use this online calculator for Built-in Potential, enter Thermal Voltage (V_t), Acceptor Concentration (N_a), Donor Concentration (N_d) & Intrinsic Electron Concentration (n_i) and hit the calculate button. Here is how the Built-in Potential calculation can be explained with given input values -> 18.81808 = 0.55*ln((1100*190000000000000)/(17^2)).

FAQ

What is Built-in Potential?

The Built-in potential formula is defined as the built-in potential in a semiconductor which equals the potential across the depletion region in thermal equilibrium. It also equals the sum of the bulk potentials of each region, since the bulk potential quantifies the distance between the fermi energy and the intrinsic energy and is represented as ψ_o = V_t*ln((N_a*N_d)/(n_i^2)) or Built-in Potential = Thermal Voltage*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Electron Concentration^2)). Thermal Voltage is the voltage produced within the p-n junction, Acceptor concentration is the concentration of holes in acceptor state, Donor concentration is the concentration of electrons in the donor state & Intrinsic Electron Concentration is defined as the number of electrons in the conduction band or the number of holes in the valence band in intrinsic material.

How to calculate Built-in Potential?

The Built-in potential formula is defined as the built-in potential in a semiconductor which equals the potential across the depletion region in thermal equilibrium. It also equals the sum of the bulk potentials of each region, since the bulk potential quantifies the distance between the fermi energy and the intrinsic energy is calculated using Built-in Potential = Thermal Voltage*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Electron Concentration^2)). To calculate Built-in Potential, you need Thermal Voltage (V_t), Acceptor Concentration (N_a), Donor Concentration (N_d) & Intrinsic Electron Concentration (n_i). With our tool, you need to enter the respective value for Thermal Voltage, Acceptor Concentration, Donor Concentration & Intrinsic Electron Concentration 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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