In semiconductors, which one of the following relations is correct at thermal equilibrium?

Options

A. `n_(i) = n_(e) = n_(h)`
B. `n_(i)^(2) = n_(e)n_(h)`
C. `n_(i) = n_(e)/n_(h)`
D. `n_(i)= n_(e) + n_(h)`

Answer

To solve the question regarding the correct relation in semiconductors at thermal equilibrium, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Thermal Equilibrium**:
- In a semiconductor, thermal equilibrium refers to a state where the temperature is constant, and the generation and recombination of charge carriers (electrons and holes) occur at equal rates.

2. **Rate of Generation and Recombination**:
- At thermal equilibrium, the rate of generation of electrons and holes must equal the rate of recombination of electrons and holes. This can be expressed mathematically as:
\[ G = R \]
where \( G \) is the generation rate and \( R \) is the recombination rate.

3. **Carrier Concentration Relation**:
- The generation of electrons and holes leads to the relationship between their concentrations. The product of the electron concentration (\( n \)) and the hole concentration (\( p \)) is constant at thermal equilibrium:
\[ n \cdot p = \text{constant} \]

4. **Intrinsic Carrier Concentration**:
- In intrinsic semiconductors, this constant can be expressed in terms of the intrinsic carrier concentration (\( n_i \)):
\[ n \cdot p = n_i^2 \]
where \( n_i \) is the number density of carriers in the intrinsic semiconductor.

5. **Conclusion**:
- Therefore, the correct relation for semiconductors at thermal equilibrium is:
\[ n \cdot p = n_i^2 \]
Based on this analysis, if we look at the options provided in the question, the second option will be the correct answer.

### Final Answer:
The correct relation in semiconductors at thermal equilibrium is:
\[ n \cdot p = n_i^2 \]