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A potential barrier of 0.50 V exists across a p-n junction. If the depletion region is 5.0×10⁻⁷ m wide, the intensity of the electric field in this region is ________.

Asked in GSEB Board July 2016 · Depletion region and barrier potential

• (1) 1.0×10⁶ V m⁻¹
• (2) 1.0×10⁹ V m⁻¹
• (3) 2.0×10⁵ V m⁻¹
• (4) 2.0×10⁶ V m⁻¹

Step-by-step solution

Why the other options are wrong

• (2) 1.0×10⁹ is a thousand times too large: it divides by 5.0×10⁻¹⁰ m, that is, it takes the depletion region to be 5 A wide rather than 5.0×10⁻⁷ m.
• (3) No single slip produces 2.0×10⁵. Sanity check: dividing 5.0 into 0.50 gives 0.10, so the mantissa has to be 1.0, not 2.0, and 10⁻⁷ in the denominator makes the power 10⁶.
• (4) 2.0×10⁶ comes from dividing by 2.5×10⁻⁷ m, half the width, as though the field only spanned the p side of the junction. The barrier is built up across the whole depletion layer.

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