Body Effect Coefficient Solution

STEP 0: Pre-Calculation Summary
Formula Used
Body Effect Coefficient = modulus((Threshold Voltage-Threshold Voltage DIBL)/(sqrt(Surface Potential+(Source Body Potential Difference))-sqrt(Surface Potential)))
γ = modulus((Vt-Vt0)/(sqrt(Φs+(Vsb))-sqrt(Φs)))
This formula uses 2 Functions, 5 Variables
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
Body Effect Coefficient - Body Effect Coefficient is the influence of source-bulk voltage in the current due to the change of the threshold voltage.
Threshold Voltage - (Measured in Volt) - Threshold voltage of transistor is the minimum gate to source voltage required to create conducting path between the source and drain terminals.
Threshold Voltage DIBL - (Measured in Volt) - Threshold Voltage dibl is defined as the minimum voltage required by the source junction of the body potential, when source is at body potential.
Surface Potential - (Measured in Volt) - Surface Potential is a key parameter in evaluating the DC property of thin-film transistors.
Source Body Potential Difference - (Measured in Volt) - Source Body Potential Difference is calculated when an externally applied potential is equal to the sum of voltage drop across the oxide layer and the voltage drop across the semiconductor.
STEP 1: Convert Input(s) to Base Unit
Threshold Voltage: 0.3 Volt --> 0.3 Volt No Conversion Required
Threshold Voltage DIBL: 0.59 Volt --> 0.59 Volt No Conversion Required
Surface Potential: 6.86 Volt --> 6.86 Volt No Conversion Required
Source Body Potential Difference: 1.36 Volt --> 1.36 Volt No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
γ = modulus((Vt-Vt0)/(sqrt(Φs+(Vsb))-sqrt(Φs))) --> modulus((0.3-0.59)/(sqrt(6.86+(1.36))-sqrt(6.86)))
Evaluating ... ...
γ = 1.16985454290539
STEP 3: Convert Result to Output's Unit
1.16985454290539 --> No Conversion Required
FINAL ANSWER
1.16985454290539 1.169855 <-- Body Effect Coefficient
(Calculation completed in 00.020 seconds)

Credits

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Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat
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25 VLSI Material Optimization Calculators

Bulk Depletion Region Charge Density VLSI
Go Bulk Depletion Region Charge Density = -(1-((Lateral Extent of Depletion Region with Source+Lateral Extent of Depletion Region with Drain)/(2*Channel Length)))*sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*Acceptor Concentration*abs(2*Surface Potential))
Body Effect Coefficient
Go Body Effect Coefficient = modulus((Threshold Voltage-Threshold Voltage DIBL)/(sqrt(Surface Potential+(Source Body Potential Difference))-sqrt(Surface Potential)))
Junction Built-in Voltage VLSI
Go Junction Built-in Voltage = ([BoltZ]*Temperature/[Charge-e])*ln(Acceptor Concentration*Donor concentration/(Intrinsic Concentration)^2)
PN Junction Depletion Depth with Source VLSI
Go P-n Junction Depletion Depth with Source = sqrt((2*[Permitivity-silicon]*[Permitivity-vacuum]*Junction Built-in Voltage)/([Charge-e]*Acceptor Concentration))
Total Source Parasitic Capacitance
Go Source Parasitic Capacitance = (Capacitance between Junction of Body and Source*Area of Source Diffusion)+(Capacitance between Junction of Body and Side wall*Sidewall Perimeter of Source Diffusion)
Short Channel Saturation Current VLSI
Go Short Channel Saturation Current = Channel Width*Saturation Electron Drift Velocity*Oxide Capacitance per Unit Area*Saturation Drain Source Voltage
Junction Current
Go Junction Current = (Static Power/Base Collector Voltage)-(Sub Threshold Current+Contention Current+Gate Current)
Surface Potential
Go Surface Potential = 2*Source Body Potential Difference*ln(Acceptor Concentration/Intrinsic Concentration)
Threshold Voltage when Source is at Body Potential
Go Threshold Voltage DIBL = DIBL Coefficient*Drain to Source Potential+Threshold Voltage
DIBL Coefficient
Go DIBL Coefficient = (Threshold Voltage DIBL-Threshold Voltage)/Drain to Source Potential
Threshold Voltage
Go Threshold Voltage = Gate to Channel Voltage-(Channel Charge/Gate Capacitance)
Gate Capacitance
Go Gate Capacitance = Channel Charge/(Gate to Channel Voltage-Threshold Voltage)
Subthreshold Slope
Go Sub Threshold Slope = Source Body Potential Difference*DIBL Coefficient*ln(10)
Channel Charge
Go Channel Charge = Gate Capacitance*(Gate to Channel Voltage-Threshold Voltage)
Gate Length using Gate Oxide Capacitance
Go Gate Length = Gate Capacitance/(Capacitance of Gate Oxide Layer*Gate Width)
Gate Oxide Capacitance
Go Capacitance of Gate Oxide Layer = Gate Capacitance/(Gate Width*Gate Length)
Oxide Capacitance after Full Scaling VLSI
Go Oxide Capacitance after Full Scaling = Oxide Capacitance per Unit Area*Scaling Factor
Critical Voltage
Go Critical Voltage = Critical Electric Field*Electric Field Across Channel Length
Gate Oxide Thickness after Full Scaling VLSI
Go Gate Oxide Thickness after Full Scaling = Gate Oxide Thickness/Scaling Factor
Intrinsic Gate Capacitance
Go MOS Gate Overlap Capacitance = MOS Gate Capacitance*Transition Width
Channel Length after Full Scaling VLSI
Go Channel Length after Full Scaling = Channel Length/Scaling Factor
Junction Depth after Full Scaling VLSI
Go Junction Depth after Full Scaling = Junction Depth/Scaling Factor
Channel Width after Full Scaling VLSI
Go Channel Width after Full Scaling = Channel Width/Scaling Factor
Mobility in Mosfet
Go Mobility in MOSFET = K Prime/Capacitance of Gate Oxide Layer
K-Prime
Go K Prime = Mobility in MOSFET*Capacitance of Gate Oxide Layer

Body Effect Coefficient Formula

Body Effect Coefficient = modulus((Threshold Voltage-Threshold Voltage DIBL)/(sqrt(Surface Potential+(Source Body Potential Difference))-sqrt(Surface Potential)))
γ = modulus((Vt-Vt0)/(sqrt(Φs+(Vsb))-sqrt(Φs)))

How the body, the fourth terminal of a transistor affetcs the threshold voltage?

The body is an implicit fourth terminal of a transistor. When a voltage is applied between the source and body, it increases the amount of charge required to invert the channel, hence, it increases the threshold voltage. The body effect further degrades the performance of pass transistors trying to pass the weak value.

How to Calculate Body Effect Coefficient?

Body Effect Coefficient calculator uses Body Effect Coefficient = modulus((Threshold Voltage-Threshold Voltage DIBL)/(sqrt(Surface Potential+(Source Body Potential Difference))-sqrt(Surface Potential))) to calculate the Body Effect Coefficient, The Body effect coefficient formula is defined as the influence of source-bulk voltage in the current due to change of the threshold voltage by the source-bulk voltage. Body Effect Coefficient is denoted by γ symbol.

How to calculate Body Effect Coefficient using this online calculator? To use this online calculator for Body Effect Coefficient, enter Threshold Voltage (Vt), Threshold Voltage DIBL (Vt0), Surface Potential s) & Source Body Potential Difference (Vsb) and hit the calculate button. Here is how the Body Effect Coefficient calculation can be explained with given input values -> 1.169855 = modulus((0.3-0.59)/(sqrt(6.86+(1.36))-sqrt(6.86))).

FAQ

What is Body Effect Coefficient?
The Body effect coefficient formula is defined as the influence of source-bulk voltage in the current due to change of the threshold voltage by the source-bulk voltage and is represented as γ = modulus((Vt-Vt0)/(sqrt(Φs+(Vsb))-sqrt(Φs))) or Body Effect Coefficient = modulus((Threshold Voltage-Threshold Voltage DIBL)/(sqrt(Surface Potential+(Source Body Potential Difference))-sqrt(Surface Potential))). Threshold voltage of transistor is the minimum gate to source voltage required to create conducting path between the source and drain terminals, Threshold Voltage dibl is defined as the minimum voltage required by the source junction of the body potential, when source is at body potential, Surface Potential is a key parameter in evaluating the DC property of thin-film transistors & Source Body Potential Difference is calculated when an externally applied potential is equal to the sum of voltage drop across the oxide layer and the voltage drop across the semiconductor.
How to calculate Body Effect Coefficient?
The Body effect coefficient formula is defined as the influence of source-bulk voltage in the current due to change of the threshold voltage by the source-bulk voltage is calculated using Body Effect Coefficient = modulus((Threshold Voltage-Threshold Voltage DIBL)/(sqrt(Surface Potential+(Source Body Potential Difference))-sqrt(Surface Potential))). To calculate Body Effect Coefficient, you need Threshold Voltage (Vt), Threshold Voltage DIBL (Vt0), Surface Potential s) & Source Body Potential Difference (Vsb). With our tool, you need to enter the respective value for Threshold Voltage, Threshold Voltage DIBL, Surface Potential & Source Body Potential Difference 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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