Modeling the Frequency-Dependent Response of Heterojunction Thermal Diodes for AC-to-DC Thermal Rectification

Thermal diodes can rectify time-periodic temperature (Τ) fields present in applications such as waste heat scavenging, passive thermal regulation, and solid-state refrigeration cycles. However, the time-periodic response of thermal diodes at arbitrary heating frequencies is difficult to model because the governing heat conduction problem is nonlinear in Τ. Here, we use an analytical perturbation solution of the heat conduction equation to study time-periodic rectification in a one-dimensional heterojunction diode.¹ This diode consists of two materials with Τ-dependent thermal conductivity κ and heat capacity c that each scale linearly with Τ. Validation against finite-element method (FEM) calculations show that the perturbation solution is valid for small-to-moderate temperature rise amplitudes and arbitrary heating frequencies ω, and prior steady-state perturbation calculations are in good agreement with heterojunction diode experiments.<br/><br/>The primary output from the thermal modeling is a prediction of the direct current (dc) component of the heat flux that emerges from an ac thermal bias. This dc heat flux is independent of the heat capacity Τ dependence for all ω, but depends strongly on the thermal conductivity Τ coefficient γ≡1/κ(dκ/dΤ). Heterojunction diodes should be selected to maximize the difference in γ between the two materials in the diode. Near 300 K, an efficient material combination would involve a crystalline semiconductor with a large and negative γ (e.g. diamond, BAs, or BN), and a metallic alloy with a large and positive γ (e.g. Al-Re-Si or Al-Cu-Fe²). Larger dc heat fluxes could be achieved if material systems with extreme γ near 300 K could be identified and synthesized.<br/><br/>We introduce a figure-of-merit rectification asymmetry metric φ to compare the performance of different thermal diodes. φ is defined as the difference between the dc heat fluxes in the forward and reverse diode orientations, and naturally extends the typical steady-state rectification figure-of-merit into the transient regime. As an example of the utility of the figure-of-merit, consider the scenario of a thermal rectifier circuit that utilizes two thermal diodes and two thermal masses to convert an oscillating Τ profile from a fluctuating thermal source into a dc Τ difference between the thermal masses, as has been recently demonstrated.^3,4 We find that this desired dc Τ difference in the thermal rectifier circuit scales linearly with φ, indicating that φ is a rational figure-of-merit to compare thermal diode materials.<br/><br/>Our solution shows that φ can be enhanced at large ω by up to a factor of two compared to the maximum quasi-steady φ at small ω. For a given pair of materials, we also identify the optimal dimensionless parameters to maximize φ. In summary, our findings can guide the design of heterojunction thermal diodes used for thermal circuits in time-periodic applications such as temperature doubler circuits for energy harvesting or dynamic building insulation for climate control.<br/><br/>References:<br/>1. Shimokusu, T. J., Zhu, Q., Rivera, N. & Wehmeyer, G., <i>Int. J. Heat Mass Transf.</i> <b>182</b>, 122035 (2022).<br/>2. Nakayama, R. S. & Takeuchi, T. J., <i>J. Electron. Mater.</i> <b>44</b>, 356–361 (2015).<br/>3. Zhang, G. et al., <i>Appl. Energy</i> <b>280</b>, 115881 (2020).<br/>4. Westwood, M., Zhao, X., Chen, Z. & Dames, C., <i>Joule</i> <b>5</b>, 2223-2240 (2021).<br/><br/>Funding: This work was supported by an Early Career Faculty grant from NASA’s Space Technology Research Grants Program (Grant #80NSSC20K0066) and a NASA Space Technology Graduate Research Opportunities Award (80NSSC20K1220).