To a germanium sample, traces of gallium are added as an impurity. The resultant sample would behave like

Options

A. A conductor
B. A p-type semiconductor
C. An n- type semiconductor
D. An insulator

Explanation

To solve the problem, we need to analyze the effect of adding gallium (a trivalent impurity) to germanium (a tetravalent semiconductor).

### Step-by-Step Solution:

1. **Identify the Nature of Germanium**:
- Germanium (Ge) is a tetravalent semiconductor, meaning each germanium atom has four valence electrons and forms four covalent bonds with neighboring atoms.

**Hint**: Remember that tetravalent elements can form four bonds due to having four electrons in their outer shell.

2. **Identify the Nature of Gallium**:
- Gallium (Ga) is a trivalent element, which means it has three valence electrons. When gallium is introduced into the germanium crystal lattice, it can only form three bonds with neighboring germanium atoms.

**Hint**: Trivalent elements can form three bonds and will leave one bond unfulfilled when incorporated into a tetravalent structure.

3. **Doping Process**:
- When gallium is added to germanium, it replaces some of the germanium atoms in the crystal lattice. Each gallium atom forms three covalent bonds with neighboring germanium atoms, leaving one bond unfulfilled. This creates a "hole" or vacancy in the lattice.

**Hint**: Visualize how the bonding works: gallium's inability to form a fourth bond creates a space (hole) in the structure.

4. **Understanding Holes as Charge Carriers**:
- The unfulfilled bond (hole) behaves as a positive charge carrier. In semiconductor physics, these holes are considered as positive carriers because they represent the absence of an electron.

**Hint**: Remember that in semiconductors, holes are treated as positive charge carriers, while electrons are negative charge carriers.

5. **Resulting Semiconductor Type**:
- Since the addition of gallium introduces more holes than electrons, the resultant semiconductor behaves like a p-type semiconductor. In p-type semiconductors, holes are the majority carriers.

**Hint**: P-type semiconductors are characterized by having more holes than electrons, leading to positive charge dominance.

### Final Conclusion:
The resultant sample of germanium doped with gallium will behave like a **p-type semiconductor**.