In a junction field effect transistor the depletion layer width at a distance x from the source is:

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UGC NET Paper 2: Electronic Science 29 Oct 2022 Shift 1
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  1. [2ϵS[V(x) + VG + Vbt]/qND]1/2
  2. (V(x) + Vbt)1/2
  3. [2ϵs[V(x) + Vbt]/qND]1/2

Answer (Detailed Solution Below)

Option 1 : [2ϵS[V(x) + VG + Vbt]/qND]1/2
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UGC NET Paper 1: Held on 21st August 2024 Shift 1
50 Qs. 100 Marks 60 Mins

Detailed Solution

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Concept:

The width of the depletion region for an abrupt p-n junction is given by

Vbt is the built-in voltage across the junction and Va is the magnitude of the applied reverse-bias voltage across the junction.

Junction Field Effect Transistor:

In a JFET, the p-n junction between the gate and source is always reverse-biased leading to the depletion region as shown in the figure below.

For a JFET, in general, Na >> Nd, hence the depletion region extends primarily into the substrate and hence, Na can be neglected in the expression for depletion width. 

The voltage between the channel and the gate, V(x) also varies along the channel due to the drain voltage. The voltage across the depletion region is higher near the drain than the source, hence the depletion region is wider near the drain.

If VG is the magnitude of the applied reverse bias gate voltage, the width of the depletion region at a distance x from the source is thus, given by

Additional Information

For n-channel JFET, VG is negative. Hence, considering the sign of the applied gate voltage, the expression for depletion width is sometimes also written as

 

 

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