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Q.Explain the formation of depletion region in a p-n junction.

CBSECBSE Class XII Board 2022Subjective· 2mImportance★★★★★
✓ Free question

The depletion region forms when p-type and n-type semiconductors are joined, causing majority carriers (holes from p-side, electrons from n-side) to diffuse across the junction, recombine, and leave behind immobile ionized dopant atoms. This creates a region devoid of free carriers, with an internal electric field that opposes further diffusion.

The Core Idea: Diffusion Meets a Barrier

A p-n junction isn't just two blocks pressed together — it's a single crystal with a sharp transition in doping. On the p-side, you have an abundance of holes (positive charge carriers) and negatively charged acceptor ions fixed in the lattice. On the n-side, you have an abundance of electrons and positively charged donor ions. The key is that these carriers are mobile, while the ions are fixed.

When the junction forms, the concentration gradient is enormous — trillions of carriers per cubic centimeter on one side, nearly zero on the other. Nature abhors such a gradient, so carriers begin to diffuse. But diffusion alone would lead to a short circuit if something didn't stop it. That "something" is the depletion region.

Step-by-Step Formation

  1. Initial contact and diffusion

    The moment p-type and n-type materials meet, holes from the p-side (high concentration) diffuse into the n-side. Electrons from the n-side diffuse into the p-side. This is pure random thermal motion — no external voltage needed.

  2. Recombination and ion exposure

    As holes enter the n-region, they encounter free electrons and recombine. Similarly, electrons entering the p-region recombine with holes. Each recombination event removes a mobile carrier. What's left behind? The immobile dopant ions:

    • On the n-side near the junction, electrons have left, exposing positively charged donor ions (ND+N_D^+).
    • On the p-side near the junction, holes have left, exposing negatively charged acceptor ions (NA−N_A^-).
  3. Creation of a space-charge region

    These exposed ions are fixed in the crystal lattice. They cannot move. So a thin layer on either side of the junction now contains net positive charge (n-side) and net negative charge (p-side). This layer is called the depletion region (or space-charge region) because it is depleted of free carriers.

  4. Internal electric field develops

    The separation of positive and negative charges creates an electric field E⃗\vec{E} directed from the n-side (positive ions) toward the p-side (negative ions). This field is the key — it acts as a barrier.

  5. Drift opposes diffusion

    The electric field exerts a force on any remaining mobile carriers:

    • Holes (positive) are pushed back toward the p-side.
    • Electrons (negative) are pushed back toward the n-side. This drift motion is opposite to the diffusion direction. As more carriers diffuse, the field grows stronger until the drift current exactly balances the diffusion current. This is dynamic equilibrium — no net current flows.
  6. Final steady state

    At equilibrium, the depletion region has a fixed width (typically 0.10.1 to 1 μm1\ \mu\text{m}, depending on doping). The potential difference across it is called the built-in potential V0V_0, typically about 0.7 V0.7\ \text{V} for silicon.

V0=kTqln⁡(NANDni2)V_0 = \frac{kT}{q} \ln\left(\frac{N_A N_D}{n_i^2}\right)

where kk is Boltzmann's constant, TT is temperature, qq is electron charge, NAN_A and NDN_D are acceptor and donor concentrations, and nin_i is intrinsic carrier concentration.

Watch out

A common mistake is to think the depletion region is empty of charge. It is not — it is full of fixed ionic charge. It is only depleted of mobile carriers. The net charge density is nonzero, which is why an electric field exists.

Tip

Think of the depletion region as a "no-man's land" between two armies. The soldiers (carriers) have retreated, leaving behind their fortifications (ions). The electric field is like a barbed wire fence — it prevents either side from crossing easily.

Key Properties at a Glance

PropertyDescription
WidthTypically 0.10.1–1 μm1\ \mu\text{m}; wider for lighter doping
ChargeNet positive on n-side, net negative on p-side
Field directionFrom n-side to p-side
Carrier concentrationNearly zero (depleted)
Built-in voltageV0≈0.7 VV_0 \approx 0.7\ \text{V} for Si, 0.3 V0.3\ \text{V} for Ge
✓Final answer

The depletion region forms when diffusion of majority carriers across a p-n junction leaves behind immobile ionized dopant atoms, creating a space-charge layer with an internal electric field that opposes further diffusion, reaching equilibrium with a built-in potential of about 0.7 V0.7\ \text{V} in silicon.

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