Doping Profile from C–V Characteristics
In semiconductor junctions, capacitance-voltage (C–V) measurements are used to determine the doping profile.
If the graph of:
1 / C³ versus V
is a straight line, then the junction has a linearly graded doping profile.
1. Abrupt Junction
For a uniformly doped abrupt PN junction:
1 / C² ∝ V
Therefore:
- Linear (1/C²) vs V → Abrupt junction
- Doping concentration remains constant
2. Linearly Graded Junction
For a linearly varying doping concentration:
N(x) ∝ x
the capacitance relation becomes:
1 / C³ ∝ V
Therefore:
- Linear (1/C³) vs V → Linearly graded junction
- Doping concentration changes linearly with distance
3. Doping Profile
The doping profile is:
N(x) = ax
Where:
- N(x) = doping concentration
- a = doping gradient constant
- x = distance from the metallurgical junction
This means the doping concentration increases linearly across the junction.
4. Summary Table
| Linear Plot | Junction Type | Doping Profile |
|---|---|---|
| 1/C² vs V | Abrupt Junction | Constant Doping |
| 1/C³ vs V | Linearly Graded Junction | N(x) ∝ x |
Conclusion: Linear (1/C³) vs V indicates a linearly graded doping profile.