Why 5× spreader conductivity does not deliver 5× lower junction temperature

For a fixed geometry, the spreader's own resistances — spreading plus through-thickness — scale approximately as 1/k: five times the conductivity, one-fifth the spreader resistance. The complete stack does not follow, because die conduction, interfaces and the cooler stay fixed. Slide k from copper to diamond and watch which number moves and which barely does.

Model: a pedagogical circular-equivalent approximation inspired by classical spreading-resistance correlations (constriction/spreading closed forms of the Song–Lee–Au and Muzychka–Culham–Yovanovich family), combined with a fixed representative non-spreader resistance of 15 mK/W (die, interfaces, cooler). It is intended to illustrate 1/k scaling of the spreader’s own resistance and the system-level diminishing returns that follow — not to reproduce any specific package geometry, boundary condition or published equation set. Absolute values are representative for a 1 kW-class package; real interfaces, anisotropy and boundary conditions shift every number.