Question: Ge is doped with As. Due to doping,

Step 1 (Governing Principle & Doping Mechanism): [0.5 Mark]

Germanium (Ge) is a Group 14 element with 4 valence electrons. Arsenic (As) is a Group 15 pentavalent impurity. When Ge is doped with As, each As atom replaces a Ge atom in the crystal lattice. Four valence electrons of As form covalent bonds with the neighboring Ge atoms, while the fifth valence electron remains weakly bound to the As atom.

Step 2 (Step-by-Step Logical Deduction): [0.25 Mark]

The energy required to ionize this fifth electron is very small ($ \Delta E \approx 0.01 \, \text{eV} $ for Ge). At room temperature, this electron is easily excited into the conduction band. The governing relation for charge carrier concentration in an n-type semiconductor is:

Where $ n_e $ is the number density of conduction electrons and $ N_D $ is the donor impurity concentration. Since $ N_D > 0 $, the concentration of free electrons increases significantly compared to the intrinsic carrier concentration $ n_i $.

Step 3 (Final Concluded Answer): [0.25 Mark]

The correct option is (B) the number of conduction electrons increases.

💡 EL10 Concept Insight: Think of the Arsenic atom as a generous donor who brings an "extra" electron to the party that isn't needed for bonding; this extra electron is free to move around and conduct electricity, which is why the number of conduction electrons goes up!