GATE EC 2021 Set 1 — Question 52
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Electronic Devices → P-N Junction & Diodes → Junction Formation & Depletion
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Question
A silicon P-N junction is shown in the figure. The doping in the P region is and doping in the N region is . The parameters given are
Built-in voltage () = 0.8 V
Electron charge (q) =
Vacuum permittivity () =
Relative permittivity of silicon () = 12
The magnitude of reverse bias voltage that would completely deplete one of the two regions (P or N) prior to the other (rounded off to one decimal place) is __________ V.
Built-in voltage () = 0.8 V
Electron charge (q) =
Vacuum permittivity () =
Relative permittivity of silicon () = 12
The magnitude of reverse bias voltage that would completely deplete one of the two regions (P or N) prior to the other (rounded off to one decimal place) is __________ V.
Correct answer
8.1 to 8.4
Solution
Given parameters:
.
Convert to F/cm: .The depletion region widths on the P-side () and N-side () under reverse bias are given by:
The question asks for the magnitude of reverse bias voltage that would completely deplete one of the two regions prior to the other. This means we need to find the required to deplete each region to its full physical length and then choose the smaller .Case 1: P-region is completely depleted ()
Set .
.Case 2: N-region is completely depleted ()
Set .
.Comparing the two values of :
- Doping in P region,
- Doping in N region,
- Built-in voltage,
- Electron charge,
- Vacuum permittivity,
- Relative permittivity of silicon,
- Length of P region,
- Length of N region,
.
Convert to F/cm: .The depletion region widths on the P-side () and N-side () under reverse bias are given by:
The question asks for the magnitude of reverse bias voltage that would completely deplete one of the two regions prior to the other. This means we need to find the required to deplete each region to its full physical length and then choose the smaller .Case 1: P-region is completely depleted ()
Set .
.Case 2: N-region is completely depleted ()
Set .
.Comparing the two values of :
- To deplete P-region:
- To deplete N-region:
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