Fig. 4: Signature for Te modulations in nonequilibrium TE effect.
From: Direct observation of hot-electron-enhanced thermoelectric effects in silicon nanodevices
a Schematic illustration of energy flow within/between electron (top panel) and lattice systems (bottom panel). b 1D profiles of experimental measured Te (dots) and simulated (solid lines) Te taken along the channel at various Vb of 4–10 V. The inset shows the voltage (current) dependent peak values of \(\Delta {T}_{{{{{{\rm{e}}}}}}}\) (\({T}_{{{{{{\rm{e}}}}}}}-{T}_{{{{{{\rm{Room}}}}}}}\)) extracted from experiments (blue dots) and simulations (red dots), which matched well with quadratic fitting (\(\propto {I}^{2}\)) as indicated by the light red line. Error bars in inset are 100-K of Te-fluctuation as extracted from the noise level of SNoiM measurement. c When a sinusoidal wave current I with a frequency of f is supplied to the device, the \(\Delta {T}_{{{{{{\rm{e}}}}}}}\) (\(\propto \nabla \varPi\)) is then oscillated by the frequency of 2f, hence owing to the correlation: \({\dot{Q}}_{{{{{{\rm{TE}}}}}}}\propto \nabla \varPi \cdot {{{{{\bf{J}}}}}}\propto {I}^{3}\), the total TE signals (\({\dot{Q}}_{{{{{{\rm{TE}}}}}}}\)) would be modulated by the admixture of first (\({\dot{Q}}_{1{{{{{\rm{f}}}}}}}\)) and third (\({\dot{Q}}_{3{{{{{\rm{f}}}}}}}\)) harmonic, which can be decoupled by flourier transform (FT). d Measured 1D profiles of \({\dot{Q}}_{1{{{{{\rm{f}}}}}}}({{{{{\rm{x}}}}}})\) (top panel) and \({\dot{Q}}_{3{{{{{\rm{f}}}}}}}({{{{{\rm{x}}}}}})\) (bottom panel) along the channel at \({V}_{{{{{{\rm{b}}}}}}}=10\,{{{{{\rm{V}}}}}}\), which are demodulated at the first and third harmonic by the lock-in technique.
