Heat flux (W) through a material. k = thermal conductivity (W/m·K), A = area (m²), ΔT = temperature difference (K), L = thickness (m).
Each layer contributes series resistance. R_total = R_die + R_contact + R_tim + R_diamond + R_conv.
h = convective heat transfer coefficient. Base: ~25 W/m²K (air), ~5000 W/m²K (liquid). Microchannels enhance h.
h_eff includes microchannel enhancement. A_eff = spreader area × fin area multiplier.
Where ε = a/b (die-to-spreader ratio), φ(ε) = (1−ε)(1 + 0.68ε + 0.16ε²). Models heat spreading from a small die to a larger substrate.
R″_c ≈ 1×10⁻⁶ m²K/W (polished) or 8×10⁻⁶ (rough). Surface roughness directly impacts interface resistance.
Multiplicative factors: coverage (1+2.5c), aspect ratio (1+0.3·min(AR,10)), count, geometry (grid 1.8×, sinusoidal 2.0×, fractal 1.6+0.5n).
Impurities scatter phonons. Boron: −0.01%/ppm. Nitrogen: −0.025%/ppm. Hydrogen: +0.005%/ppm (defect passivation).
Fundamental equation. Junction temp = ambient + power × total thermal resistance. Hotspots add localized intensity.
1D thermal resistance network with 2D spreading approximations. Does not solve full 3D heat equation or Navier-Stokes. Qualitatively accurate for comparative analysis—not a replacement for CFD/FEA design validation.