Fluctuation-dissipation in thermoelectric sensors

- Thermoelectric materials exhibit correlated transport of charge and heat. The Johnson-Nyquist noise formula 4kBTR for the spectral density of voltage fluctuations accounts for fluctuations associated solely with Ohmic dissipation. Applying the fluctuation-dissipation theorem, we generalize the Johnson-Nyquist formula for thermoelectrics, finding an enhanced voltage fluctuation spectral density 4kBTR(1 + ZDT ) at frequencies below a thermal cut-off fre-quency fT, where ZDT is the dimensionless thermoelectric device figure of merit. The origin of the enhancement in voltage noise is thermoelectric coupling of temperature fluctuations. We use a wideband (fT similar to 1 kHz), integrated thermoelectric micro-device to experimentally confirm our findings. Measuring the ZDT enhanced voltage noise, we experimentally resolve temperature fluc-tuations with a root mean square amplitude of 0.8 mu K Hz-1/2 at a mean temperature of 295 K. We find that thermoelectric devices can be used for thermometry with sufficient resolution to measure the fundamental temperature fluctuations described by the fluctuation-dissipation theorem.