## 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))
ψo = Vt*ln((Na*Nd)/(ni^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
ψo = Vt*ln((Na*Nd)/(ni^2)) --> 0.55*ln((1100*190000000000000)/(17^2))
Evaluating ... ...
ψo = 18.8180761773197
STEP 3: Convert Result to Output's Unit
18.8180761773197 Volt --> No Conversion Required
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
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## < 24 CMOS Characteristics Calculators

Ground to Agression Capacitance
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
Victim Driver = (Agression Driver*(Ground A Capacitance+Adjacent Capacitance))/(Time Constant Ratio of Agression to Victim*(Adjacent Capacitance+Ground V Capacitance))
Agression Driver
Agression Driver = (Victim Driver*Time Constant Ratio of Agression to Victim*(Adjacent Capacitance+Ground V Capacitance))/(Ground A Capacitance+Adjacent Capacitance)
Built-in Potential
Built-in Potential = Thermal Voltage*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Electron Concentration^2))
Agressor Voltage
Victim Voltage
Adjacent Capacitance = (Victim Voltage*Ground V Capacitance)/ (Agressor Voltage-Victim Voltage)
Branching Effort
Branching Effort = (Capacitance Onpath+Capacitance Offpath)/Capacitance Onpath
Agression Time Constant
Agression Time Constant = Time Constant Ratio of Agression to Victim*Victim Time Constant
Victim Time Constant
Victim Time Constant = Agression Time Constant/Time Constant Ratio of Agression to Victim
Time Constant Ratio of Agression to Victim
Time Constant Ratio of Agression to Victim = Agression Time Constant/Victim Time Constant
Capacitance Onpath
Capacitance Onpath = Total Capacitance Seen by a Stage-Capacitance Offpath
Total Capacitance Seen by Stage
Total Capacitance Seen by a Stage = Capacitance Onpath+Capacitance Offpath
Capacitance Offpath
Capacitance Offpath = Total Capacitance Seen by a Stage-Capacitance Onpath
Input Capacitance of Gate
Input Capacitance = Drive of Arbitrary Gate*Logical Effort
Logical Effort(G)
Logical Effort = Input Capacitance/Drive of Arbitrary Gate
VCO Single Gain Factor
VCO Gain = Change in Frequency of Clock/VCO Control Voltage
Drive of Arbitrary Gate
Drive of Arbitrary Gate = Input Capacitance/Logical Effort
Output Clock Phase
Output Clock Phase = 2*3.14*VCO Control Voltage*VCO Gain
VCO Control Voltage
VCO Control Voltage = Lock Voltage+VCO Offset Voltage
VCO Offset Voltage
VCO Offset Voltage = VCO Control Voltage-Lock Voltage
Lock Voltage
Lock Voltage = VCO Control Voltage-VCO Offset Voltage
Static Current
Static Current = Static Power/Drain Voltage
Static Power Dissipation
Static Power = Static Current*Drain Voltage

## Built-in Potential Formula

Built-in Potential = Thermal Voltage*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Electron Concentration^2))
ψo = Vt*ln((Na*Nd)/(ni^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 ψo symbol.

How to calculate Built-in Potential using this online calculator? To use this online calculator for Built-in Potential, enter Thermal Voltage (Vt), Acceptor Concentration (Na), Donor Concentration (Nd) & Intrinsic Electron Concentration (ni) 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 ψo = Vt*ln((Na*Nd)/(ni^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 (Vt), Acceptor Concentration (Na), Donor Concentration (Nd) & Intrinsic Electron Concentration (ni). 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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