A Green’s-function method for vertical thermal boundary conductance in anisotropic multilayers

Vertical thermal interfaces occur in both engineered and natural materials. Their vertical thermal boundary conductance can differ from the horizontal counterpart, requiring dedicated characterization. Yet current thermal metrology resolves vertical thermal boundary conductance only in restricted geometries such as two bulk media, for lack of an efficient forward solution that admits anisotropy, multilayers, and depth-dependent vertical thermal boundary conductance together. We present a Green's-function boundary integral equation (GBIE) method that couples transfer-matrix Green's functions to an interface-only integral equation for depth-dependent Gᵥ(z), supporting dissimilar orthotropic multilayers (kₓ≠ ky≠ kz) on either side and horizontal conductance Gₕ. For anisotropic film-on-substrate multilayers with films from 1~μm to 100~nm, the GBIE agrees with three-dimensional finite element method (FEM) predictions to within one percent mean normalized phase and amplitude error, while running 29--210× faster and reducing peak memory by factors of 120--450 in single-core tests; a JIT-compiled JAX implementation reaches up to 4100× on a matched 16-core comparison. The GBIE further reproduces a continuous film over a buried interface, representative of a thermoreflectance measurement, and a finite-depth interface with depth-dependent Gᵥ(z). The GBIE accommodates lateral-to-film-thickness ratios above 10⁵, where volumetric FEM can become computationally prohibitive. These results establish an efficient forward solution for vertical-interface heat transport in systems ranging from microelectronic device sidewalls to grain boundaries in polycrystalline solids.