Constructal design of comb-shaped high thermal conductivity channel in a stacked chip

Abstract

A model of stacked chip with comb-shaped high thermal conductivity channel (HTCC) is established. With fixed number of through‑silicon vias (TSVs), constructal designs of comb-shaped HTCC are performed with single-degree-of-freedom (DOF), two-DOF and three-DOF optimizations, and effects of heat generation rate per volume (HGRPV) of device layer, HGRPV of TSV and filling materials of HTCC on its optimal construct and maximum temperature difference (MTD) in stacked chip are analyzed. Furtherly, constructal design of two-stage branched comb-shaped HTCC is studied. The optimal constructs of comb-shaped HTCC are obtained under single-DOF, two-DOF and three-DOF optimizations, which make the MTD of stacked chip reach the minimum. The minimum MTD obtained by three-DOF optimization is 43.74 K, which is 1.21 K and 0.45 K lower than that obtained by single-DOF and two-DOF optimizations, respectively. Compared with the initial design, the MTD under optimizations of single-, two- and three-DOFs decreased by 2.8%, 4.5% and 5.5%, respectively. Filling materials of HTCC have effect on optimal constructs of comb-shaped HTCC, however, the HGRPVs of device layer and TSV have not. The first-stage branches of two-stage branch comb-shaped HTCC are close together by constructal design, so embedding single-stage branch comb-shaped HTCC is more beneficial to heat dissipation of stacked chip.