CBSE Class 12 Physics: Semiconductor Electronics Marking Scheme

(a) A doped semiconductor is electrically neutral.

• Step 1 (Governing Principle): [0.5 Mark] The process of doping involves adding impurity atoms (pentavalent or trivalent) to a pure intrinsic semiconductor crystal lattice.
• Step 2 (Logical Deduction): [0.5 Mark] The impurity atoms are electrically neutral before they are incorporated into the lattice. Upon doping, the total number of protons in the nuclei of the impurity atoms is exactly equal to the total number of electrons in their shells.
• Step 3 (Final Conclusion): [0.0 Mark] Since the crystal as a whole remains a closed system with no net gain or loss of charge, the total positive charge equals the total negative charge, maintaining overall electrical neutrality.

💡 EL10 Concept Insight: Think of it like adding a pinch of salt to a glass of water; even though the salt is made of charged ions, the salt crystal itself is neutral, so the water remains neutral after you stir it in.

(b) In a p-n junction under equilibrium, there is no net current.

• Step 1 (Governing Law): [0.5 Mark] At equilibrium, the diffusion current ($I_{diff}$) due to the concentration gradient of charge carriers and the drift current ($I_{drift}$) due to the internal electric field ($E$) exist simultaneously.
• Step 2 (Mathematical Working): [0.5 Mark] The diffusion current flows from p-side to n-side, while the drift current flows from n-side to p-side. At equilibrium: $$I_{net} = I_{diff} + I_{drift} = 0$$
• Step 3 (Final Conclusion): [0.0 Mark] Because the magnitude of the diffusion current exactly equals the magnitude of the drift current in the opposite direction, the net current across the junction is zero.

💡 EL10 Concept Insight: It’s like a revolving door where people are walking in and out at the exact same speed; even though people are moving, the total number of people inside the room doesn't change.

(c) In a diode, the reverse current is practically not dependent on the applied voltage.

• Step 1 (Governing Law): [0.5 Mark] Reverse current is caused by the drift of minority charge carriers (electrons in p-region, holes in n-region) across the junction.
• Step 2 (Logical Deduction): [0.5 Mark] The number of minority carriers available is determined solely by the thermal generation rate at a given temperature ($T$), not by the external bias voltage ($V$).
• Step 3 (Final Conclusion): [0.0 Mark] Once the reverse bias voltage is sufficient to sweep all available minority carriers across the junction (saturation), increasing the voltage further does not increase the current, as no additional carriers are generated.

💡 EL10 Concept Insight: Imagine a bucket brigade passing water; the speed of the current is limited by how many people are in the line, not by how fast you shout at them to work harder.