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NEET PHYSICSSEMICONDUCTOR ELECTRONICSMedium

Question

Pure Si\text{Si} at 500 K500\text{ K} has an equal number of electron (nen_e) and hole (nhn_h) concentration of 1.5×1016 m−31.5 \times 10^{16} \text{ m}^{-3}. Doping by indium increases the hole concentration nhn_h to 4.5×1022 m−34.5 \times 10^{22} \text{ m}^{-3}. The doped semiconductor is of:

A

n-type with electron concentration ne=5×1022 m−3n_e = 5 \times 10^{22} \text{ m}^{-3}

B

p-type with electron concentration ne=2.5×1023 m−3n_e = 2.5 \times 10^{23} \text{ m}^{-3}

C

n-type with electron concentration ne=2.5×1010 m−3n_e = 2.5 \times 10^{10} \text{ m}^{-3}

D

p-type with electron concentration ne=5×109 m−3n_e = 5 \times 10^9 \text{ m}^{-3}

Step-by-Step Solution

  1. Identify the Type of Semiconductor: Indium is a Group 13 (trivalent) impurity. Doping an intrinsic silicon crystal with a trivalent impurity creates excess holes, making it a p-type semiconductor.
  2. Apply Mass Action Law: For any semiconductor in thermal equilibrium, the product of majority and minority charge carrier concentrations is equal to the square of the intrinsic carrier concentration: nenh=ni2n_e n_h = n_i^2.
  3. Calculate Electron Concentration (nen_e): Given the intrinsic concentration ni=1.5×1016 m−3n_i = 1.5 \times 10^{16} \text{ m}^{-3} and the new hole concentration nh=4.5×1022 m−3n_h = 4.5 \times 10^{22} \text{ m}^{-3}, we can solve for nen_e: ne=ni2nhn_e = \frac{n_i^2}{n_h} ne=(1.5×1016)24.5×1022n_e = \frac{(1.5 \times 10^{16})^2}{4.5 \times 10^{22}} ne=2.25×10324.5×1022n_e = \frac{2.25 \times 10^{32}}{4.5 \times 10^{22}} ne=0.5×1010 m−3=5×109 m−3n_e = 0.5 \times 10^{10} \text{ m}^{-3} = 5 \times 10^9 \text{ m}^{-3}
  4. Conclusion: The semiconductor is p-type with an electron concentration of 5×109 m−35 \times 10^9 \text{ m}^{-3}.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from SEMICONDUCTOR ELECTRONICS. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSSEMICONDUCTOR ELECTRONICStextsinumberelectronconcentrationdoping

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