If `n_i,` `n_e` and `n_h` represents the number of intrinsic charge carrier, number of free electrons and number of holes respectively in semiconductor, then relation `n_h n_e=n_i^2` is true for

Options

A. intrinsic semiconductor
B. p type semiconductor
C. n-type semiconductor
D. all of these

Answer

To solve the question regarding the relationship \( n_h n_e = n_i^2 \) in semiconductors, we will break down the concepts involved step by step.

### Step 1: Understand the Terms
- **Intrinsic Charge Carrier (\( n_i \))**: This refers to the number of charge carriers (electrons and holes) in a pure semiconductor at thermal equilibrium.
- **Free Electrons (\( n_e \))**: This is the number of electrons that are available for conduction in the semiconductor.
- **Holes (\( n_h \))**: These are the absence of electrons in the valence band, which act as positive charge carriers.

### Step 2: Recognize the Relationship
In a semiconductor, the relationship between the number of free electrons, holes, and intrinsic charge carriers is given by the equation:
\[ n_h n_e = n_i^2 \]
This equation is derived from the principle of charge neutrality and the conservation of charge in thermal equilibrium.

### Step 3: Conditions for the Relation
This relationship holds true under two conditions:
1. **Intrinsic Semiconductors**: In pure semiconductors, the number of electrons equals the number of holes, hence \( n_e = n_h \) and \( n_i \) is simply the number of charge carriers.
2. **Extrinsic Semiconductors**: In doped semiconductors (either p-type or n-type), the relation still holds true because the charge neutrality condition remains valid.

### Step 4: Conclusion
Thus, the relation \( n_h n_e = n_i^2 \) is valid for both intrinsic and extrinsic semiconductors. Therefore, the correct answer to the question is:
**All of the above** (Option 4).