Q.In the depletion region of a diode
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🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — P-N Junction Formation
P-N Junction Formation: From Intuition to Precision
Imagine two rooms connected by a door. One room is filled with people who have extra energy (they want to give it away), and the other room is filled with people who are missing energy (they want to take it). The moment you open the door, what happens? People rush from the high-energy room to the low-energy room until both rooms reach a balance. That rush, and the final balanced state, is the essence of a P-N junction.
In a semiconductor, the "people" are charge carriers: electrons (negative charge) and holes (the absence of an electron, which behaves like a positive charge). A P-type semiconductor has an excess of holes (positive carriers), and an N-type semiconductor has an excess of electrons (negative carriers). When you bring them together, they don't just sit still — they interact.
The Intuitive Picture
Take a P-type crystal and an N-type crystal. At the instant they touch, there is a huge concentration difference: lots of holes on the P-side, lots of electrons on the N-side. Nature hates steep gradients, so carriers begin to diffuse — they move from where they are abundant to where they are scarce.
- Electrons from the N-side cross into the P-side.
- Holes from the P-side cross into the N-side.
But here's the catch: when an electron from the N-side meets a hole on the P-side, they recombine — the electron fills the hole, and both disappear as free carriers. This recombination doesn't happen everywhere; it happens in a narrow region near the interface, called the depletion region (or space-charge region).
Why "depletion"? Because in that region, free electrons and free holes have been used up. All that remains are the fixed, immovable ions: positive donor ions on the N-side (which lost their electron) and negative acceptor ions on the P-side (which gained an electron). These fixed charges create an electric field that points from the N-side (positive ions) to the P-side (negative ions).
This electric field is crucial. It acts like a bouncer: it pushes electrons back toward the N-side and holes back toward the P-side. This drift motion opposes the initial diffusion. Eventually, the diffusion current (driven by concentration difference) exactly balances the drift current (driven by the electric field). The system reaches thermal equilibrium — no net current flows.
The Precise Statement
A P-N junction is formed by bringing P-type and N-type semiconductors into intimate contact. At equilibrium, a depletion region of fixed ions creates a built-in electric field that prevents further net diffusion of carriers.
More formally:
- Diffusion: Majority carriers (electrons from N-side, holes from P-side) diffuse across the junction due to the concentration gradient.
- Recombination: These carriers recombine near the interface, leaving behind fixed ionized impurities (donors on N-side, acceptors on P-side).
- Depletion region: A region devoid of free carriers, containing only fixed charges, forms at the junction.
- Built-in electric field: The fixed charges create an electric field (E) pointing from N to P.
- Equilibrium: The drift current due to E exactly cancels the diffusion current. The net current is zero.
The width of the depletion region (W) depends on the doping concentrations. For a one-sided junction (heavily doped on one side), the depletion region extends mostly into the lightly doped side. …
Why this formula?
Why the P-N Junction Forms: The Physics Behind the Barrier
A p-n junction isn't just two pieces of semiconductor stuck together. The key to understanding it is this: nature hates sharp gradients in carrier concentration. When you bring p-type (excess holes) and n-type (excess electrons) material into contact, carriers immediately begin to diffuse across the junction — holes from p to n, electrons from n to p.
This diffusion is the engine that drives everything else.
Step 1: Diffusion Creates a Depletion Region
As holes leave the p-side, they leave behind fixed, negatively charged acceptor ions (A−). As electrons leave the n-side, they leave behind fixed, positively charged donor ions (D+). These ions are immobile — they're locked in the crystal lattice.
The region near the junction that gets stripped of mobile carriers is called the depletion region (or space-charge region). It contains only fixed ions, creating an electric field that points from the n-side (positive ions) toward the p-side (negative ions).
Do not confuse "depletion" with "no charge." The depletion region is highly charged — it's just that the charge is from fixed ions, not mobile carriers.
Step 2: The Electric Field Opposes Diffusion
The built-in electric field E exerts a force on any mobile carrier that tries to cross:
- Holes (positive) feel a force pushing them back toward the p-side.
- Electrons (negative) feel a force pushing them back toward the n-side.
This field grows stronger as more carriers diffuse and more ions are uncovered. Eventually, the field becomes strong enough that the drift current (carriers swept by the field) exactly balances the diffusion current (carriers moving due to concentration gradient). At this point, the net current is zero — thermal equilibrium is reached.
Step 3: The Built-in Potential Barrier
Because the electric field exists over a distance, there is a potential difference across the depletion region. This is the built-in potential V0 (also called Vbi). It represents the energy barrier that a majority carrier must overcome to cross to the other side.
V0=qkTln(ni2NAND)
Where:
- k = Boltzmann constant
- T = absolute temperature
- q = electron charge magnitude
- NA = acceptor doping concentration (p-side)
- ND = donor doping concentration (n-side)
- ni = intrinsic carrier concentration
Why This Formula Holds: The Derivation
The derivation comes from equating the Fermi levels on both sides. In equilibrium, the Fermi level must be constant throughout the entire structure.
On the p-side, the Fermi level EF lies close to the valence band. The position relative to the intrinsic Fermi level Ei is:
EF−Ei=kTln(niNA)(for p-type)
On the n-side, the Fermi level lies close to the conduction band:
EF−Ei=−kTln(niND)(for n-type)
The difference in Ei between the two sides (which is the same as the difference in EF between the two sides before contact) must be accommodated by the built-in potential. The total band bending qV0 equals this difference:
qV0=[kTln(niNA)]−[−kTln(niND)]
qV0=kT[ln(niNA)+ln(niND)] …
The depletion region forms when majority carriers diffuse across the junction and recombine, leaving the region stripped of mobile carriers but populated by the fixed dopant ions.
- (A) True — the free electrons and holes have been removed, so there are essentially no mobile charges.
- (B) False — the region is not neutral because of equal mobile electrons and holes; the charge that remains is that of fixed ions, and locally the two sides carry opposite net charge. …
The depletion region has no mobile carriers (A) because they recombined (C), leaving behind fixed charged ions (D). Correct options: (A), (C) and (D).
How the depletion region forms
When p-type and n-type materials meet, electrons from the n-side and holes from the p-side diffuse across the junction and recombine near the interface. This removes the free carriers from a thin region on either side of the junction, leaving only the fixed, ionised dopant atoms — positive donor ions on the n-side and negative acceptor ions on the p-side. This carrier-free region is the depletion (space-charge) region.
Checking each option
- (A) There are no mobile charges — TRUE. Recombination has swept out the free electrons and holes, so for a diode in equilibrium the region is essentially devoid of mobile carriers. …
Method: Tracing the Depletion Region Back to Its Formation Mechanism
Instead of memorising facts about the depletion region separately, derive each option from the single process that creates the region in the first place -- diffusion followed by recombination.
Step 1 -- Recall how the depletion region forms.
When p-type and n-type materials meet, majority carriers diffuse across the junction: electrons from the n-side, holes from the p-side. Near the interface, these diffusing carriers recombine with each other.
Step 2 -- Check option (C): "recombination has taken place."
This is exactly what Step 1 describes -- the depletion region's very existence is a direct consequence of this recombination. TRUE.
Step 3 -- Check option (A): "there are no mobile charges."
Since the free carriers that were near the junction have recombined away, essentially nothing mobile is left in this thin region. TRUE.
Step 4 -- Check option (D): "immobile charged ions exist." …
- JKBOSE Class 12 Annual Regular Examination 2025Set SZ3 marksQ.What is meant by depletion region in a junction diode ? Explain its formation.
›Reveal solutionSolution
The depletion region is a carrier-free layer at the p-n junction formed by diffusion of majority carriers across the junction and their recombination, leaving behind immobile ions and a built-in potential barrier.
When a p-type semiconductor (majority carriers: holes) is joined with an n-type semiconductor (majority carriers: free electrons) to form a p-n junction, a large concentration gradient exists across the junction for both types of carriers.
Formation process:
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Due to this concentration gradient, holes from the p-side diffuse across the junction into the n-side, and free electrons from the n-side diffuse across into the p-side (diffusion current).
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As electrons and holes cross into the opposite region, they recombine with the majority carriers there and are annihilated (e.g. an electron diffusing into the p-side recombines with a hole).
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This recombination removes free charge carriers from a thin layer on either side of the junction. What remains behind in this layer are the fixed, immobile ionized dopant atoms: uncompensated negative acceptor ions on the p-side (near the junction) and uncompensated positive donor ions on the n-side (near the junction), since these ions are bound in the crystal lattice and cannot move.
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This thin layer, now containing only these immobile ions and depleted of free charge carriers, is called the depletion region (or depletion layer / space-charge region), typically a fraction of a micrometre wide.
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