In semiconductor transport, the ratio of diffusion coefficient to mobility (D/μ) has what units?

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Solve this multiple-choice question and choose the correct option.

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Introduction / Context:The Einstein relation connects diffusion (a random, concentration-gradient-driven process) with drift (field-driven transport) through a fundamental thermal voltage. Recognizing the dimensions of the ratio D/μ is a quick diagnostic for comfort with semiconductor physics and device equations used in diodes, BJTs, and MOS capacitors. Given Data / Assumptions: D is the carrier diffusion coefficient with units m^2/s (or cm^2/s). μ is the carrier mobility with units m^2/(V·s) (or cm^2/(V·s)). Einstein relation: D/μ = kT/q, where k is Boltzmann constant, T is absolute temperature, and q is the magnitude of electron charge. Concept / Approach:Dimensionally, D/μ must match the units of kT/q. Since kT is energy (joule) and q is charge (coulomb), kT/q has units joule/coulomb, which equals volt. Thus, the ratio D/μ is a voltage called the thermal voltage (approximately 25.9 mV at 300 K). Step-by-Step Solution: Write the Einstein relation: D/μ = kT/q.Check units: D [m^2/s], μ [m^2/(V·s)] ⇒ (m^2/s) / (m^2/(V·s)) = V.Therefore, D/μ carries units of volts. Verification / Alternative check: At room temperature (300 K): kT/q ≈ 0.0259 V (often rounded to 26 mV). This numerical value confirms that D/μ behaves like a voltage scale, independent of geometry. Why Other Options Are Wrong: Ampere and ohm are not consistent with the diffusion–mobility relation.Volt–second arises in magnetic or impulse contexts, not here.Watt is power and unrelated dimensionally. Common Pitfalls: Mixing D/μ with μ/D; forgetting that μ includes volts in its denominator; confusing thermal voltage with thermal energy. Final Answer: volt (V)

In semiconductor transport, the ratio of diffusion coefficient to mobility (D/μ) has what units?

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