Question

For intrinsic semiconductor, if \(n_h\) and \(n_e\) represent the number of holes per unit volume and the number of free electrons per unit volume respectively then

• A. \(n_h < n_e\)
• B. \(n_h > n_e\)
• C. \(n_h = n_e\)
• D. \(n_h\neq n_e\)

Hint:

In a pure semiconductor each electron that leaves its bond leaves behind one hole, so the two numbers are equal.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
An intrinsic semiconductor is a pure crystal with no doping. At temperatures above absolute zero, thermal energy breaks some covalent bonds.

Step 2: Key Formula or Approach:
Every broken bond frees one electron into the conduction band and leaves one vacancy, a hole, in the valence band. Electrons and holes are created in pairs.

Step 3: Detailed Explanation:
Since the electrons and holes are made in equal numbers, the number of free electrons per unit volume equals the number of holes per unit volume:
\[ n_e = n_h \]
This equality is lost only after doping. In an n-type semiconductor \(n_e > n_h\), and in a p-type semiconductor \(n_h > n_e\). Options (A), (B) and (D) describe those doped cases or a general inequality, none of which holds for a pure crystal.

Final Answer:
For an intrinsic semiconductor \(n_h = n_e\), option (C). \[ \boxed{n_h=n_e \text{ (C)}} \]