Relation Between Doping and Capacitance
In semiconductors, doping affects capacitance mainly by changing the width of the depletion region. This is especially important in PN junctions and MOS capacitors.
1. Capacitance of a PN Junction
For a reverse-biased PN junction:
C = ÎľA / W
Where:
- C = junction capacitance
- Îľ = permittivity of semiconductor
- A = junction area
- W = depletion width
Relation with Doping
W ∝ √(1 / N)
where N is the doping concentration.
Substituting into capacitance:
C ∝ √N
Therefore:
- Higher doping concentration → smaller depletion width → larger capacitance
- Lower doping concentration → wider depletion width → smaller capacitance
2. Physical Explanation
Doping adds charge carriers:
- More doping means more ions near the junction.
- The electric field balances over a shorter distance.
- Hence the depletion region becomes thinner.
- Since capacitance increases when plate separation decreases, capacitance rises.
3. In MOS Capacitors
Doping of the substrate changes:
- depletion capacitance,
- threshold voltage,
- and overall C–V characteristics.
For substrate doping NA:
Cdep ∝ √NA
Again, heavier substrate doping leads to higher depletion capacitance.
4. Summary
| Doping Level | Depletion Width | Capacitance |
|---|---|---|
| High | Small | High |
| Low | Large | Low |
Key Relation: C ∝ √(doping concentration)