Identify the correct expression for the Einstein relation :
\(\frac{D}{\mu} = \frac{KT}{q}\)
The Einstein relation links the diffusion constant D of a carrier to its mobility μ. It follows from setting the net current to zero in equilibrium: the drift current due to the built-in field must exactly cancel the diffusion current.
Balancing the two currents with a Boltzmann carrier distribution gives \(\frac{D}{\mu} = \frac{KT}{q} = V_T\), where \(V_T\) is the thermal voltage (about 25.9 mV at 300 K).
The relation is dimensionally consistent: D has units cm2/s and μ has units cm2/V·s, so D/μ has units of volts, exactly the units of KT/q. The forms with q/KT on the right, or with μ/D equated to KT/q, invert one side and give the wrong units.
Hence, the Einstein relation is \(\frac{D}{\mu} = \frac{KT}{q}\).
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