The ratio of number of holes and number of conduction electrons in an intrinsic semiconductor is

Options

A. One
B. Greater than one
C. Less than one
D. Infinity

Answer

To solve the problem of finding the ratio of the number of holes to the number of conduction electrons in an intrinsic semiconductor, we can follow these steps:

### Step 1: Understand the Concept of Intrinsic Semiconductors
An intrinsic semiconductor is a pure semiconductor material without any significant dopant species present. In intrinsic semiconductors, the charge carriers (electrons and holes) are generated by the thermal excitation of electrons.

**Hint:** Recall that intrinsic semiconductors are pure materials without doping.

### Step 2: Identify Charge Carriers
In an intrinsic semiconductor, when thermal energy is provided, some electrons gain enough energy to break free from their covalent bonds. When an electron leaves its bond, it creates a vacancy or "hole" in the lattice structure.

**Hint:** Remember that each electron that becomes free creates one hole.

### Step 3: Establish the Relationship Between Holes and Electrons
For every electron that is excited to the conduction band, a corresponding hole is created in the valence band. Therefore, the number of conduction electrons (n) is equal to the number of holes (p).

**Hint:** Think about the conservation of charge carriers in the semiconductor.

### Step 4: Write the Ratio
Since the number of conduction electrons is equal to the number of holes in an intrinsic semiconductor, we can express this relationship mathematically:
\[ \text{Ratio of holes to conduction electrons} = \frac{p}{n} = \frac{n}{n} = 1 \]

**Hint:** Use the equality of the number of holes and conduction electrons to simplify the ratio.

### Conclusion
The ratio of the number of holes to the number of conduction electrons in an intrinsic semiconductor is 1.

**Final Answer:** The ratio of the number of holes to the number of conduction electrons in an intrinsic semiconductor is 1:1.

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