Interface thermal resistance induced by geometric shape mismatch: A multiparticle Lorentz gas model

Poor heat dissipation caused by interface thermal resistance (ITR, or Kapitza resistance) has long been the bottleneck that limits the further miniaturization of integrated circuit. In this paper, different from previous studies on ITR induced by conjunction of two different materials, the ITR of a homogeneous stepped system is studied through the multiparticle Lorentz gas model. It is found that ITR can be triggered by pure geometric shape mismatch, and decreases when the degree of mismatch decreases. The ITRs for forward and backward transport are asymmetrical; thus, thermal rectification effect is also obtained in this system. Moreover, the effects of absolute width, width ratio, mean temperature, and temperature difference on ITR and thermal rectification effect are discussed. The ITR induced by geometric shape mismatch provides physics for interfacial thermal transport.

Figure 1

(a) The modeled system with a stepped structure, which consists of two rectangles with different width. (b) Temperature distributions for systems with different width ratios ($d_2/d_1$). The linearly extrapolated temperature at each side of the interface is used to define the interface temperature difference ($\mathrm{\Delta }T$).

Figure 2

(a) The dependence of interface temperature difference ($\mathrm{\Delta }T$, black dot) and heat flux ($J$, red dot) on width ratio. (b) The dependence of ITR on absolute width ($d_1$, black dot) and width ratio ($d_2/d_1$, red dot).

Figure 3

(a) The dependence of ITR on temperature difference between heat source and heat sink at different width ratios ($d_2/d_1$). (b) The dependence of ITR on the mean temperature ($T_0$) of heat source and heat sink at different width ratios ($d_2/d_1$).

Figure 4

(a) The dependence of TRR (γ) on absolute width of left rectangle ($d_1$). (b) The dependence of TRR (γ) and heat flux on width ratio ($d_2/d_1$).

Figure 5

The dependence of TRR (γ) and heat flux on the (a) mean temperature ($T_0$) and (b) temperature difference ($\mathrm{\Delta }T$) of heat source and heat sink.