Bulk Depletion Region Charge Density VLSI Calculator

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VLSI Material Optimization

Analog VLSI Design

✖Lateral Extent of Depletion Region with Source the horizontal distance across which the depletion region extends laterally from the source terminal in a semiconductor device.ⓘ Lateral Extent of Depletion Region with Source [ΔL_s]			+10% -10%
✖Lateral Extent of Depletion Region with Drain the horizontal distance across which the depletion region extends laterally from the drain terminal in a semiconductor device.ⓘ Lateral Extent of Depletion Region with Drain [ΔL_D]			+10% -10%
✖Channel Length refers to the physical length of the semiconductor material between the source and drain terminals within the transistor structure.ⓘ Channel Length [L]			+10% -10%
✖Acceptor Concentration refers to the concentration of acceptor dopant atoms in a semiconductor material.ⓘ Acceptor Concentration [N_A]			+10% -10%
✖Surface Potential is a key parameter in evaluating the DC property of thin-film transistors.ⓘ Surface Potential [Φ_s]			+10% -10%

✖Bulk Depletion Region Charge Density is defined as electric charge per unit area associated with the depletion region in the bulk of a semiconductor device.ⓘ Bulk Depletion Region Charge Density VLSI [Q_B0]

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Formula

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Bulk Depletion Region Charge Density VLSI

Formula

`"Q"_{"B0"} = -(1-(("ΔL"_{"s"}+"ΔL"_{"D"})/(2*"L")))*sqrt(2*"[Charge-e]"*"[Permitivity-silicon]"*"[Permitivity-vacuum]"*"N"_{"A"}*abs(2*"Φ"_{"s"}))`

Example

`"-0.200558μC/cm²"=-(1-(("0.1μm"+"0.2μm")/(2*"2.5μm")))*sqrt(2*"[Charge-e]"*"[Permitivity-silicon]"*"[Permitivity-vacuum]"*"1e+16/cm³"*abs(2*"6.86V"))`

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Bulk Depletion Region Charge Density VLSI Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
Q_B0 = -(1-((ΔL_s+ΔL_D)/(2*L)))*sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*N_A*abs(2*Φ_s))
This formula uses 3 Constants, 2 Functions, 6 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

Bulk Depletion Region Charge Density - (Measured in Coulomb per Square Meter) - Bulk Depletion Region Charge Density is defined as electric charge per unit area associated with the depletion region in the bulk of a semiconductor device.
Lateral Extent of Depletion Region with Source - (Measured in Meter) - Lateral Extent of Depletion Region with Source the horizontal distance across which the depletion region extends laterally from the source terminal in a semiconductor device.
Lateral Extent of Depletion Region with Drain - (Measured in Meter) - Lateral Extent of Depletion Region with Drain the horizontal distance across which the depletion region extends laterally from the drain terminal in a semiconductor device.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Lateral Extent of Depletion Region with Source: 0.1 Micrometer --> 1E-07 Meter (Check conversion here)
Lateral Extent of Depletion Region with Drain: 0.2 Micrometer --> 2E-07 Meter (Check conversion here)
Channel Length: 2.5 Micrometer --> 2.5E-06 Meter (Check conversion here)
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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_B0 = -(1-((ΔL_s+ΔL_D)/(2*L)))*sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*N_A*abs(2*Φ_s)) --> -(1-((1E-07+2E-07)/(2*2.5E-06)))*sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*1E+22*abs(2*6.86))

Evaluating ... ...

Q_B0 = -0.00200557851391776

STEP 3: Convert Result to Output's Unit

-0.00200557851391776 Coulomb per Square Meter -->-0.200557851391776 Microcoulomb per Square Centimeter (Check conversion here)

FINAL ANSWER

-0.200557851391776 ≈ -0.200558 Microcoulomb per Square Centimeter <-- Bulk Depletion Region Charge Density

(Calculation completed in 00.004 seconds)

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Credits

Created by Priyanka Patel

Lalbhai Dalpatbhai College of engineering (LDCE), Ahmedabad

Priyanka Patel has created this Calculator and 25+ more calculators!

Verified by Santhosh Yadav

Dayananda Sagar College Of Engineering (DSCE), Banglore

Santhosh Yadav has verified this Calculator and 50+ more calculators!

< 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)

DIBL Coefficient

Go DIBL Coefficient = (Threshold Voltage DIBL-Threshold Voltage)/Drain to Source Potential

Threshold Voltage when Source is at Body Potential

Go Threshold Voltage DIBL = DIBL Coefficient*Drain to Source Potential+Threshold Voltage

Subthreshold Slope

Go Sub Threshold Slope = Source Body Potential Difference*DIBL Coefficient*ln(10)

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)

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

Bulk Depletion Region Charge Density VLSI Formula

How does Bulk Depletion Region Charge Density affect semiconductor devices in VLSI?

Bulk Depletion Region Charge Density influences the electrical characteristics of semiconductor devices, including capacitance, threshold voltage, and overall device performance.

How to Calculate Bulk Depletion Region Charge Density VLSI?

Bulk Depletion Region Charge Density VLSI calculator uses 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)) to calculate the Bulk Depletion Region Charge Density, The Bulk Depletion Region Charge Density VLSI formula is defined as electric charge per unit area associated with the depletion region in the bulk of a semiconductor device. Bulk Depletion Region Charge Density is denoted by Q_B0 symbol.

How to calculate Bulk Depletion Region Charge Density VLSI using this online calculator? To use this online calculator for Bulk Depletion Region Charge Density VLSI, enter Lateral Extent of Depletion Region with Source (ΔL_s), Lateral Extent of Depletion Region with Drain (ΔL_D), Channel Length (L), Acceptor Concentration (N_A) & Surface Potential (Φ_s) and hit the calculate button. Here is how the Bulk Depletion Region Charge Density VLSI calculation can be explained with given input values -> -20.055785 = -(1-((1E-07+2E-07)/(2*2.5E-06)))*sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*1E+22*abs(2*6.86)).

FAQ

What is Bulk Depletion Region Charge Density VLSI?

The Bulk Depletion Region Charge Density VLSI formula is defined as electric charge per unit area associated with the depletion region in the bulk of a semiconductor device and is represented as Q_B0 = -(1-((ΔL_s+ΔL_D)/(2*L)))*sqrt(2*[Charge-e]*[Permitivity-silicon]*[Permitivity-vacuum]*N_A*abs(2*Φ_s)) or 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)). Lateral Extent of Depletion Region with Source the horizontal distance across which the depletion region extends laterally from the source terminal in a semiconductor device, Lateral Extent of Depletion Region with Drain the horizontal distance across which the depletion region extends laterally from the drain terminal in a semiconductor device, Channel Length refers to the physical length of the semiconductor material between the source and drain terminals within the transistor structure, 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.

How to calculate Bulk Depletion Region Charge Density VLSI?

The Bulk Depletion Region Charge Density VLSI formula is defined as electric charge per unit area associated with the depletion region in the bulk of a semiconductor device is calculated using 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)). To calculate Bulk Depletion Region Charge Density VLSI, you need Lateral Extent of Depletion Region with Source (ΔL_s), Lateral Extent of Depletion Region with Drain (ΔL_D), Channel Length (L), Acceptor Concentration (N_A) & Surface Potential (Φ_s). With our tool, you need to enter the respective value for Lateral Extent of Depletion Region with Source, Lateral Extent of Depletion Region with Drain, Channel Length, Acceptor Concentration & Surface Potential 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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