Quantifying anisotropic thermal transport in two-dimensional perovskite $\left({\mathrm{PEA}}_2{\mathrm{PbI}}_4\right)$ through cross-sectional scanning thermal microscopy

In this paper, we investigated the anisotropic thermal transport in two-dimensional (2D) perovskite (phenethylammonium lead iodide) nanolayers through a measurement technique called cross-sectional scanning thermal microscopy. In this method, a target perovskite layer on a substrate was oblique polished with an Ar ion beam to create a low-angle wedge with nanoscale roughness that is followed by high-vacuum scanning thermal microscopy to obtain the thermal conductance map as a function of local thickness. The experimentally obtained data were processed with an analytical model and validated by the finite elemental analysis simulation to quantify the in-plane $\left(k_{l,xy}\right)$ and cross-plane thermal conductivities $\left(k_{l,z}\right)$ of the 2D perovskite from a single set of measurements with nanoscale resolution. We obtained ultralow thermal conductivity $\left(k_l=0.25\pm 0.05\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}\right)$ for the 2D perovskite along with an anisotropy $\left(k_{l,xy}=0.45\pm 0.05\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}\mathrm{and}{k}_{l,z}=0.13\pm 0.05\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}\right)$ linked to the unique structure of the perovskite and different phonon lifetimes and group velocities for in-plane and out-of-plane directions. The results that are available are essential for the thermal management of 2D perovskite-based optoelectronic devices and potential thermoelectric applications of these materials.

Figure 1

(a) Schematic representations of ${\left(\mathrm{PEA}\right)}_2{\mathrm{PbI}}_4$ crystal structure. The first one shows the ball-stick model of the crystal. In the second polyhedral model, the octahedra are presented. (b) and (c) X-ray diffraction (XRD) patterns, optical absorbance, and photoluminescence spectra of the ${\left(\mathrm{PEA}\right)}_2{\mathrm{PbI}}_4$ thin film.

Figure 2

(a) Topography, (b) deflection, (c) thermal signal image, (d) section analysis, (e) thermal voltage, and (f) variation of thermal resistance at different regions of the beam exit cross-sectional polishing (BEXP) cut sample as mentioned in the plots.

Figure 3

(a) The fitting plot for the $\mathrm{Si}/\mathrm{Si}{\mathrm{O}}_2$ heterojunction (analytical model). (b) Finite elemental analysis (FEA)-simulated results of thermal gradient and heat flow at a high thickness (the inset shows a zoomed-in view).

Figure 4

(a) and (b) Simulated thermal resistance dependence for different $k_{l,\mathrm{anis}}$ ($k_{\mathrm{avg}}$) and ${\mathrm{\Delta }}_{\mathrm{anis}}$ $\left(\frac{k_{l,xy}}{k_{l,z}}\right)$ and (c) the fitting plots for the $\mathrm{Si}/\mathrm{Si}{\mathrm{O}}_2$ heterojunction (analytical model). (d) and (e) Finite elemental analysis (FEA)-simulated forward plots for different $k_{l,\mathrm{anis}}$ ($k_{\mathrm{avg}}$) and ${\mathrm{\Delta }}_{\mathrm{anis}}.\left(\frac{k_{l,xy}}{k_{l,z}}\right)$. (f) FEA-simulated results of thermal gradient and heat flow (inset shows a zoomed-in view).

Figure 5

(a) Thermal signal image of the $\mathrm{Si}/\mathrm{Si}{\mathrm{O}}_2/\mathrm{SU}-8$ heterojunction as obtained from cross-sectional scanning thermal microscopy (xSThM). (b) and (c) The fitting plots for $\mathrm{Si}/\mathrm{Si}{\mathrm{O}}_2$ and $\mathrm{Si}{\mathrm{O}}_2/\mathrm{SU}-8$ heterojunctions, respectively, through the analytical model.

Figure 6

(a) Heat (phonon) conduction pathways in a general two-dimensional (2D) Ruddlesden-Popper (RP) perovskite along in-plane and out-of-plane directions. (b) Comparison of in-plane and out-of-plane thermal conductivity of ${\left(\mathrm{PEA}\right)}_2{\mathrm{PbI}}_4$ with respect to molecular dynamics (MD) simulation of similar 2D perovskite [20]. (c) Anisotropic ratio vs average thermal conductivity of 2D-RP perovskite compared with other layered compounds in which the other data points were adapted [20].