Width of Depletion Zone Calculator

✖Doping Density refers to the concentration of dopant atoms in a semiconductor material. Dopants are impurity atoms that are intentionally introduced into the semiconductor.ⓘ Doping Density [N_d]			+10% -10%
✖Schottky Potential Barrier acts as a barrier for electrons, and the height of the barrier depends on the work function difference between the two materials.ⓘ Schottky Potential Barrier [V_i]			+10% -10%
✖Gate Voltage is the voltage developed at the gate source junction of a JFET transistor.ⓘ Gate Voltage [V_g]			+10% -10%

✖Width of Depletion Region is a region in a semiconductor device where there are no free charge carriers.ⓘ Width of Depletion Zone [x_depl]

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Formula

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Width of Depletion Zone

Formula

`"x"_{"depl"} = sqrt((("[Permitivity-silicon]"*2)/("[Charge-e]"*"N"_{"d"}))*("V"_{"i"}-"V"_{"g"}))`

Example

`"0.000159m"=sqrt((("[Permitivity-silicon]"*2)/("[Charge-e]"*"9e22/cm³"))*("15.9V"-"0.25V"))`

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Width of Depletion Zone Solution

STEP 0: Pre-Calculation Summary

Formula Used

Width of Depletion Region = sqrt((([Permitivity-silicon]*2)/([Charge-e]*Doping Density))*(Schottky Potential Barrier-Gate Voltage))
x_depl = sqrt((([Permitivity-silicon]*2)/([Charge-e]*N_d))*(V_i-V_g))
This formula uses 2 Constants, 1 Functions, 4 Variables

Constants Used

[Permitivity-silicon] - Permittivity of silicon Value Taken As 11.7
[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)

Variables Used

Width of Depletion Region - (Measured in Meter) - Width of Depletion Region is a region in a semiconductor device where there are no free charge carriers.
Doping Density - (Measured in 1 per Cubic Meter) - Doping Density refers to the concentration of dopant atoms in a semiconductor material. Dopants are impurity atoms that are intentionally introduced into the semiconductor.
Schottky Potential Barrier - (Measured in Volt) - Schottky Potential Barrier acts as a barrier for electrons, and the height of the barrier depends on the work function difference between the two materials.
Gate Voltage - (Measured in Volt) - Gate Voltage is the voltage developed at the gate source junction of a JFET transistor.

STEP 1: Convert Input(s) to Base Unit

Doping Density: 9E+22 1 per Cubic Centimeter --> 9E+28 1 per Cubic Meter (Check conversion here)
Schottky Potential Barrier: 15.9 Volt --> 15.9 Volt No Conversion Required
Gate Voltage: 0.25 Volt --> 0.25 Volt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x_depl = sqrt((([Permitivity-silicon]*2)/([Charge-e]*N_d))*(V_i-V_g)) --> sqrt((([Permitivity-silicon]*2)/([Charge-e]*9E+28))*(15.9-0.25))

Evaluating ... ...

x_depl = 0.000159363423174517

STEP 3: Convert Result to Output's Unit

0.000159363423174517 Meter --> No Conversion Required

FINAL ANSWER

0.000159363423174517 ≈ 0.000159 Meter <-- Width of Depletion Region

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electronics » Microwave Theory » Microwave Tubes and Circuits » Klystron » Width of Depletion Zone

Credits

Created by Sonu Kumar Keshri

National Institute of Technology, Patna (NITP), Patna

Sonu Kumar Keshri has created this Calculator and 5 more calculators!

Verified by Parminder Singh

Chandigarh University (CU), Punjab

Parminder Singh has verified this Calculator and 600+ more calculators!

< 13 Klystron Calculators

Width of Depletion Zone

Go Width of Depletion Region = sqrt((([Permitivity-silicon]*2)/([Charge-e]*Doping Density))*(Schottky Potential Barrier-Gate Voltage))

Mutual Conductance of Klystron Amplifier

Go Mutual Conductance of Klystron Amplifier = (2*Cathode Buncher Current*Beam Coupling Coefficient*First Order Bessel Function)/Input Signal Amplitude

Klystron Efficiency

Go Klystron Efficiency = (Beam Complex Coefficient*First Order Bessel Function)*(Catcher Gap Voltage/Cathode Buncher Voltage)

Bunching Parameter of Klystron

Go Bunching Parameter = (Beam Coupling Coefficient*Input Signal Amplitude*Angular Variation)/(2*Cathode Buncher Voltage)

Beam Loading Conductance

Go Beam Loading Conductance = Conductance of Cavity-(Loaded Conductance+Copper Loss Conductance)

Copper Loss of Cavity

Go Copper Loss Conductance = Conductance of Cavity-(Beam Loading Conductance+Loaded Conductance)

Cavity Conductance

Go Conductance of Cavity = Loaded Conductance+Copper Loss Conductance+Beam Loading Conductance

Anode Voltage

Go Anode Voltage = Power Generated in Anode Circuit/(Anode Current*Electronic Efficiency)

Resonant Frequency of Cavity

Go Resonant Frequency = Q factor of Cavity Resonator*(Frequency 2-Frequency 1)

Input Power of Reflex Klystron

Go Reflex Klystron Input Power = Reflex Klystron Voltage*Reflex Klystron Beam Current

DC Transit Time

Go DC Transient Time = Gate Length/Saturation Drift Velocity

Power Loss in Anode Circuit

Go Power Loss = DC Power Supply*(1-Electronic Efficiency)

DC Power Supply

Go DC Power Supply = Power Loss/(1-Electronic Efficiency)

Width of Depletion Zone Formula

What does width of depletion region signifies?

This equation shows that the width of the depletion region is proportional to the square root of the gate voltage and the doping density of the semiconductor material. In general, the depletion region width decreases as the gate voltage increases and the doping density decreases.
The width of the depletion region in a MESFET is an important parameter that affects the device performance, such as the cutoff frequency and the noise figure. It is typically specified by the manufacturer and can be optimized through the device design to achieve desired device characteristics.

How to Calculate Width of Depletion Zone?

Width of Depletion Zone calculator uses Width of Depletion Region = sqrt((([Permitivity-silicon]*2)/([Charge-e]*Doping Density))*(Schottky Potential Barrier-Gate Voltage)) to calculate the Width of Depletion Region, The Width of Depletion Zone formula is defined as a region in a semiconductor device where there are no free charge carriers. It depends on the doping levels of the semiconductor material, the gate voltage, and the physical dimensions of the device. Width of Depletion Region is denoted by x_depl symbol.

How to calculate Width of Depletion Zone using this online calculator? To use this online calculator for Width of Depletion Zone, enter Doping Density (N_d), Schottky Potential Barrier (V_i) & Gate Voltage (V_g) and hit the calculate button. Here is how the Width of Depletion Zone calculation can be explained with given input values -> 0.000159 = sqrt((([Permitivity-silicon]*2)/([Charge-e]*9E+28))*(15.9-0.25)).

FAQ

What is Width of Depletion Zone?

The Width of Depletion Zone formula is defined as a region in a semiconductor device where there are no free charge carriers. It depends on the doping levels of the semiconductor material, the gate voltage, and the physical dimensions of the device and is represented as x_depl = sqrt((([Permitivity-silicon]*2)/([Charge-e]*N_d))*(V_i-V_g)) or Width of Depletion Region = sqrt((([Permitivity-silicon]*2)/([Charge-e]*Doping Density))*(Schottky Potential Barrier-Gate Voltage)). Doping Density refers to the concentration of dopant atoms in a semiconductor material. Dopants are impurity atoms that are intentionally introduced into the semiconductor, Schottky Potential Barrier acts as a barrier for electrons, and the height of the barrier depends on the work function difference between the two materials & Gate Voltage is the voltage developed at the gate source junction of a JFET transistor.

How to calculate Width of Depletion Zone?

The Width of Depletion Zone formula is defined as a region in a semiconductor device where there are no free charge carriers. It depends on the doping levels of the semiconductor material, the gate voltage, and the physical dimensions of the device is calculated using Width of Depletion Region = sqrt((([Permitivity-silicon]*2)/([Charge-e]*Doping Density))*(Schottky Potential Barrier-Gate Voltage)). To calculate Width of Depletion Zone, you need Doping Density (N_d), Schottky Potential Barrier (V_i) & Gate Voltage (V_g). With our tool, you need to enter the respective value for Doping Density, Schottky Potential Barrier & Gate Voltage 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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