Lets `n_p`and `n_e` be the number of holes and conduction electrons in an extrinsic semiconductor.

Options

A. `n_pgtn_e`
B. `n_p=n_e`
C. `n_pltn_e`
D. `n_p!=n_e`

Answer

To solve the question regarding the relationship between the number of holes \( n_p \) and the number of conduction electrons \( n_e \) in an extrinsic semiconductor, we can follow these steps:

### Step 1: Understand the Definitions
- **Holes (\( n_p \))**: These are the absence of electrons in a semiconductor lattice, created when an electron is excited to the conduction band.
- **Conduction Electrons (\( n_e \))**: These are the electrons that are free to move and contribute to electrical conduction.

### Step 2: Identify the Types of Doping
- In extrinsic semiconductors, doping is used to introduce impurities into the intrinsic semiconductor.
- There are two types of doping:
- **Donor Impurities (Pentavalent)**: These introduce extra electrons into the semiconductor (e.g., phosphorus in silicon). Here, \( n_e \) will be greater than \( n_p \).
- **Acceptor Impurities (Trivalent)**: These create holes by accepting electrons (e.g., boron in silicon). Here, \( n_p \) will be greater than \( n_e \).

### Step 3: Analyze the Scenarios
- If the semiconductor is doped with donor impurities, then:
\[ n_e > n_p \]
- If the semiconductor is doped with acceptor impurities, then:
\[ n_p > n_e \]

### Step 4: Conclusion
- Since the question does not specify whether the doping is donor or acceptor, we cannot definitively say whether \( n_p \) is greater than, equal to, or less than \( n_e \).
- Therefore, the most appropriate option is:
\[ n_p \neq n_e \]

### Final Answer
The correct option is: **Option 4: \( n_p \) not equal to \( n_e \)**.

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