Every chip gets hot where it works hardest. Heat has to escape through the material to the cold plate at the bottom. Diamond lets heat through about 15 times more easily than silicon, so the same chip stays much cooler.

∂T/∂t = α∇²T + q/(ρc) with α = κ/(ρc). At steady state κ∇²T = −q, so for identical geometry and power the peak temperature rise scales exactly as 1/κ: silicon 1.5, gallium nitride 2.3, silicon carbide 4.9, diamond 22 W/(cm·K). Diamond also reaches steady state fastest because its diffusivity is highest.

Explicit finite differences on a 48 × 48 cross-section, insulated sides and top, isothermal sink at the bottom, stability-limited sub-stepping per material. The steady-state peak ratio Si/diamond equals κ_diamond/κ_Si to 1% (unit test). Temperature-dependent κ and the thermal boundary resistance of real interfaces [cho2014] [yates2018] are not modeled; chapter E9 adds the junction-temperature ceilings.