## Short Channel Threshold Voltage Reduction VLSI Solution

STEP 0: Pre-Calculation Summary
Formula Used
Short Channel Threshold Voltage Reduction = (sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*Acceptor Concentration*abs(2*Surface Potential))*Junction Depth)/(Oxide Capacitance per Unit Area*2*Channel Length)*((sqrt(1+(2*P-n Junction Depletion Depth with Source)/Junction Depth)-1)+(sqrt(1+(2*P-n Junction Depletion Depth with Drain)/Junction Depth)-1))
ΔVT0 = (sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*NA*abs(2*Φs))*xj)/(Coxide*2*L)*((sqrt(1+(2*xdS)/xj)-1)+(sqrt(1+(2*xdD)/xj)-1))
This formula uses 3 Constants, 2 Functions, 8 Variables
Constants Used
[Permitivity-silicon] - Permittivity of silicon Value Taken As 11.7
[Permitivity-vacuum] - Permittivity of vacuum Value Taken As 8.85E-12
[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)
abs - The absolute value of a number is its distance from zero on the number line. It's always a positive value, as it represents the magnitude of a number without considering its direction., abs(Number)
Variables Used
Short Channel Threshold Voltage Reduction - (Measured in Volt) - Short Channel Threshold Voltage Reduction is defined as a reduction in threshold voltage of MOSFET due to short channel effect.
Acceptor Concentration - (Measured in 1 per Cubic Meter) - Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material.
Surface Potential - (Measured in Volt) - Surface Potential is a key parameter in evaluating the DC property of thin-film transistors.
Junction Depth - (Measured in Meter) - Junction Depth is defined as the distance from the surface of a semiconductor material to the point where a significant change in the concentration of dopant atoms occurs.
Oxide Capacitance per Unit Area - (Measured in Farad per Square Meter) - Oxide Capacitance per Unit Area is defined as the capacitance per unit area of the insulating oxide layer that separates the metal gate from the semiconductor material.
Channel Length - (Measured in Meter) - Channel Length refers to the physical length of the semiconductor material between the source and drain terminals within the transistor structure.
P-n Junction Depletion Depth with Source - (Measured in Meter) - P-n Junction Depletion Depth with Source is defined as the region around a p-n junction where charge carriers have been depleted due to the formation of an electric field.
P-n Junction Depletion Depth with Drain - (Measured in Meter) - P-n Junction Depletion Depth with Drain is defined as the extension of the depletion region into the semiconductor material near the drain terminal.
STEP 1: Convert Input(s) to Base Unit
Acceptor Concentration: 1E+16 1 per Cubic Centimeter --> 1E+22 1 per Cubic Meter (Check conversion ​here)
Surface Potential: 6.86 Volt --> 6.86 Volt No Conversion Required
Junction Depth: 2 Micrometer --> 2E-06 Meter (Check conversion ​here)
Oxide Capacitance per Unit Area: 0.0703 Microfarad per Square Centimeter --> 0.000703 Farad per Square Meter (Check conversion ​here)
Channel Length: 2.5 Micrometer --> 2.5E-06 Meter (Check conversion ​here)
P-n Junction Depletion Depth with Source: 0.314 Micrometer --> 3.14E-07 Meter (Check conversion ​here)
P-n Junction Depletion Depth with Drain: 0.534 Micrometer --> 5.34E-07 Meter (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ΔVT0 = (sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*NA*abs(2*Φs))*xj)/(Coxide*2*L)*((sqrt(1+(2*xdS)/xj)-1)+(sqrt(1+(2*xdD)/xj)-1)) --> (sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*1E+22*abs(2*6.86))*2E-06)/(0.000703*2*2.5E-06)*((sqrt(1+(2*3.14E-07)/2E-06)-1)+(sqrt(1+(2*5.34E-07)/2E-06)-1))
Evaluating ... ...
ΔVT0 = 0.467200582407994
STEP 3: Convert Result to Output's Unit
0.467200582407994 Volt --> No Conversion Required
0.467200582407994 0.467201 Volt <-- Short Channel Threshold Voltage Reduction
(Calculation completed in 00.004 seconds)
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## Credits

Created by Priyanka Patel
Lalbhai Dalpatbhai College of engineering (LDCE), Ahmedabad
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## <VLSI Material Optimization Calculators

Body Effect Coefficient
​ Go Body Effect Coefficient = modulus((Threshold Voltage-Threshold Voltage DIBL)/(sqrt(Surface Potential+(Source Body Potential Difference))-sqrt(Surface Potential)))
DIBL Coefficient
​ Go DIBL Coefficient = (Threshold Voltage DIBL-Threshold Voltage)/Drain to Source Potential
Channel Charge
​ Go Channel Charge = Gate Capacitance*(Gate to Channel Voltage-Threshold Voltage)
Critical Voltage
​ Go Critical Voltage = Critical Electric Field*Electric Field Across Channel Length

## Short Channel Threshold Voltage Reduction VLSI Formula

Short Channel Threshold Voltage Reduction = (sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*Acceptor Concentration*abs(2*Surface Potential))*Junction Depth)/(Oxide Capacitance per Unit Area*2*Channel Length)*((sqrt(1+(2*P-n Junction Depletion Depth with Source)/Junction Depth)-1)+(sqrt(1+(2*P-n Junction Depletion Depth with Drain)/Junction Depth)-1))
ΔVT0 = (sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*NA*abs(2*Φs))*xj)/(Coxide*2*L)*((sqrt(1+(2*xdS)/xj)-1)+(sqrt(1+(2*xdD)/xj)-1))

## Why does Short Channel Threshold Voltage Reduction occur in VLSI?

The reduction in channel length increases the influence of the source and drain regions on the channel. This enhanced influence results in a reduced control of the gate over the channel, causing the threshold voltage to decrease. Short-channel effects, such as drain-induced barrier lowering (DIBL) and punch-through, become more prominent in smaller transistors, contributing to the reduction in the threshold voltage.

## How to Calculate Short Channel Threshold Voltage Reduction VLSI?

Short Channel Threshold Voltage Reduction VLSI calculator uses Short Channel Threshold Voltage Reduction = (sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*Acceptor Concentration*abs(2*Surface Potential))*Junction Depth)/(Oxide Capacitance per Unit Area*2*Channel Length)*((sqrt(1+(2*P-n Junction Depletion Depth with Source)/Junction Depth)-1)+(sqrt(1+(2*P-n Junction Depletion Depth with Drain)/Junction Depth)-1)) to calculate the Short Channel Threshold Voltage Reduction, The Short Channel Threshold Voltage Reduction VLSI formula is defined as a reduction in threshold voltage of MOSFET due to short channel effect. Short Channel Threshold Voltage Reduction is denoted by ΔVT0 symbol.

How to calculate Short Channel Threshold Voltage Reduction VLSI using this online calculator? To use this online calculator for Short Channel Threshold Voltage Reduction VLSI, enter Acceptor Concentration (NA), Surface Potential s), Junction Depth (xj), Oxide Capacitance per Unit Area (Coxide), Channel Length (L), P-n Junction Depletion Depth with Source (xdS) & P-n Junction Depletion Depth with Drain (xdD) and hit the calculate button. Here is how the Short Channel Threshold Voltage Reduction VLSI calculation can be explained with given input values -> 0.467201 = (sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*1E+22*abs(2*6.86))*2E-06)/(0.000703*2*2.5E-06)*((sqrt(1+(2*3.14E-07)/2E-06)-1)+(sqrt(1+(2*5.34E-07)/2E-06)-1)).

### FAQ

What is Short Channel Threshold Voltage Reduction VLSI?
The Short Channel Threshold Voltage Reduction VLSI formula is defined as a reduction in threshold voltage of MOSFET due to short channel effect and is represented as ΔVT0 = (sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*NA*abs(2*Φs))*xj)/(Coxide*2*L)*((sqrt(1+(2*xdS)/xj)-1)+(sqrt(1+(2*xdD)/xj)-1)) or Short Channel Threshold Voltage Reduction = (sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*Acceptor Concentration*abs(2*Surface Potential))*Junction Depth)/(Oxide Capacitance per Unit Area*2*Channel Length)*((sqrt(1+(2*P-n Junction Depletion Depth with Source)/Junction Depth)-1)+(sqrt(1+(2*P-n Junction Depletion Depth with Drain)/Junction Depth)-1)). Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material, Surface Potential is a key parameter in evaluating the DC property of thin-film transistors, Junction Depth is defined as the distance from the surface of a semiconductor material to the point where a significant change in the concentration of dopant atoms occurs, Oxide Capacitance per Unit Area is defined as the capacitance per unit area of the insulating oxide layer that separates the metal gate from the semiconductor material, Channel Length refers to the physical length of the semiconductor material between the source and drain terminals within the transistor structure, P-n Junction Depletion Depth with Source is defined as the region around a p-n junction where charge carriers have been depleted due to the formation of an electric field & P-n Junction Depletion Depth with Drain is defined as the extension of the depletion region into the semiconductor material near the drain terminal.
How to calculate Short Channel Threshold Voltage Reduction VLSI?
The Short Channel Threshold Voltage Reduction VLSI formula is defined as a reduction in threshold voltage of MOSFET due to short channel effect is calculated using Short Channel Threshold Voltage Reduction = (sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*Acceptor Concentration*abs(2*Surface Potential))*Junction Depth)/(Oxide Capacitance per Unit Area*2*Channel Length)*((sqrt(1+(2*P-n Junction Depletion Depth with Source)/Junction Depth)-1)+(sqrt(1+(2*P-n Junction Depletion Depth with Drain)/Junction Depth)-1)). To calculate Short Channel Threshold Voltage Reduction VLSI, you need Acceptor Concentration (NA), Surface Potential s), Junction Depth (xj), Oxide Capacitance per Unit Area (Coxide), Channel Length (L), P-n Junction Depletion Depth with Source (xdS) & P-n Junction Depletion Depth with Drain (xdD). With our tool, you need to enter the respective value for Acceptor Concentration, Surface Potential, Junction Depth, Oxide Capacitance per Unit Area, Channel Length, P-n Junction Depletion Depth with Source & P-n Junction Depletion Depth with Drain 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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