Two knobs, one curve: why TDTR must audit its own sensitivity

A TDTR trace is the picosecond-delayed thermoreflectance decay after a pump pulse. Two unknowns shape it — the film’s conductivity k and the film–substrate interface conductance G — and over wide ranges they bend the curve in partially interchangeable ways. Move one dial, then try to undo it with the other: where the gray reference and the blue curve nearly coincide at different settings, the parameters are correlated, and only a sensitivity analysis decides what the fit actually constrained.

Model: an ILLUSTRATIVE two-parameter decay S(t) = exp(−√(t/τ_k))/(1+t/τ_G) with τ_k ∝ 1/√k and τ_G ∝ 1/G, chosen to reproduce the qualitative k–G correlation of real TDTR analysis — NOT the layered-structure solution real reductions use. Deviation is the mean absolute gap over the highlighted window. Schematic teaching tool, not an instrument.