Concept:Controlled doping adds small, precise amounts of impurity atoms (typically 1 part in \( 10^6 \) to \( 10^8 \)) to dramatically increase conductivity without disrupting the host crystal lattice.
Formula:$$\text{Doping Ratio} = \frac{N_{\text{dopant}}}{N_{\text{host}}} \approx 10^{-6} \text{ to } 10^{-8}$$
Solution:- Silicon has an atomic density of \( \approx 5 \times 10^{22}\text{ atoms/cm}^3 \).
- Doping with 1 impurity atom per \( 10^6 \) to \( 10^8 \) host atoms introduces \( 10^{14} \) to \( 10^{16}\text{ dopants/cm}^3 \).
- This increases electrical conductivity by several orders of magnitude while preserving the structural integrity of the crystal.
Why other options are incorrect:- Option A: 1:10 is an alloy concentration that disrupts the semiconductor crystal lattice.
- Option C: 1:10^15 is too dilute to significantly alter conductivity beyond intrinsic levels.
- Option D: 1:2 represents an intermetallic compound, not a doped semiconductor.
Quality & Fidelity Assurance:
Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.