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))
xdepl = sqrt((([Permitivity-silicon]*2)/([Charge-e]*Nd))*(Vi-Vg))
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
xdepl = sqrt((([Permitivity-silicon]*2)/([Charge-e]*Nd))*(Vi-Vg)) --> sqrt((([Permitivity-silicon]*2)/([Charge-e]*9E+28))*(15.9-0.25))
Evaluating ... ...
xdepl = 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)

Credits

Created by Sonu Kumar Keshri
National Institute of Technology, Patna (NITP), Patna
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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

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

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 xdepl 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 (Nd), Schottky Potential Barrier (Vi) & Gate Voltage (Vg) 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 xdepl = sqrt((([Permitivity-silicon]*2)/([Charge-e]*Nd))*(Vi-Vg)) 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 (Nd), Schottky Potential Barrier (Vi) & Gate Voltage (Vg). 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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