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

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).

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