Intrinsic semiconductor drift current expression and intrinsic concentration formula (assertion–reason) Assertion (A): In an intrinsic semiconductor, the drift current density is J = (μn × μp) * e * ni. Reason (R): The intrinsic carrier concentration varies with temperature as ni^2 = A0 * T^3 * exp(−Eg0 / (k T)). Determine the correct relationship between A and R.

Difficulty: Easy

Correct Answer: A is false but R is true

Explanation:


Introduction / Context:
Two cornerstone relations in semiconductor physics are the drift current formula and the temperature dependence of intrinsic carrier concentration. Getting the exact forms right is essential for device modeling and for understanding how conductivity changes with electric field and temperature in intrinsic materials like ultrapure silicon and germanium.


Given Data / Assumptions:

  • Intrinsic semiconductor (n = p = ni).
  • Uniform electric field E is the driving force for drift current.
  • Mobility symbols: μn (electrons) and μp (holes); e is elementary charge.
  • Temperature dependence: bandgap Eg0, Boltzmann constant k, material constant A0.


Concept / Approach:

The correct drift current density in an intrinsic semiconductor is J = e * ni * (μn + μp) * E. It is additive in mobilities, not multiplicative, and it is proportional to E. Therefore, the assertion J = (μn × μp) e ni (with no E and product of mobilities) is dimensionally and physically incorrect. On the other hand, the relation ni^2 = A0 * T^3 * exp(−Eg0/(kT)) is the standard expression (up to material-specific constants) for intrinsic concentration in many semiconductors, capturing the strong exponential increase with temperature.


Step-by-Step Solution:

Write correct drift current: J = e ni (μn + μp) E.Compare with asserted form: product μn μp and no E are wrong → Assertion is false.Check Reason: ni^2 ∝ T^3 exp(−Eg0/(kT)) → widely accepted relation → Reason is true.


Verification / Alternative check:

Dimensional analysis confirms that without E, the asserted J cannot have units of A/m^2. Textbook derivations from band theory and effective density of states lead to the stated ni^2 expression.


Why Other Options Are Wrong:

Any option claiming Assertion true contradicts both physics and units; any option denying the standard ni relation is likewise incorrect.


Common Pitfalls:

Mixing drift with diffusion current or forgetting the additive contribution of electron and hole mobilities in intrinsic material.


Final Answer:

A is false but R is true

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