Thermal rectification (TR) has garnered significant attention in the field of thermal management and thermal circuits, similar to the pivotal role played by electric diodes in controlling electron flow in electronic devices [1], [2], [3], [4], [5], [6]. Controlling the flow of heat in a thermal diode is crucial for applications such as on-chip cooling and energy conversion in thermal management systems. The concept of thermal rectification, initially proposed theoretically and supported by early experimental results, has piqued the interest of scientists and engineers [7], [8]. Thermal rectification refers to the phenomenon where heat is transferred asymmetrically, favoring specific directions. The development of efficient thermal rectifiers, which can efficiently transfer high thermal energy in one direction while impeding heat flow in the opposite direction, holds great potential for cooling applications in electronics, particularly at the nanoscale. Integrating thermal rectifiers into electronic component designs could provide substantial advantages. There are various approaches to achieve thermal rectification. One common strategy is to utilize hybrid systems comprising two or more materials with temperature-dependent thermal conductivities. Additionally, mass-graded materials can be employed [4], [9]. Asymmetric structures [10], [11], [12], [13], [14], [15], inhomogeneous interfaces [16], [17], and specific arrangements of atomic defects [18], [19] can also lead to direction-dependent thermal transport and enable thermal rectification.

To the best of our knowledge, both experimental measurements and theoretical calculations indicate that the achieved TR ratio remains notably small, far from practical utility. Enhancing the TR ratio of nanostructures presents a multifaceted challenge, yet numerous strategies can be pursued to elevate their TR performance. Notably, a synergistic approach involving innovative material design, modifying the geometry and structure of nanostructures [13], interface optimization [17], advanced nanofabrication techniques, and hybrid methodologies holds promise for significant TR ratio enhancements in nanostructures. Exploring novel materials exhibiting tailored thermal properties could yield higher TR ratios. Among these materials, graphene-like BCN monolayers, with various atomic configurations [20], represent a promising class of semiconductors worthy of consideration for achieving elevated TR ratios, particularly in conjunction with graphene.

Graphene, a two-dimensional (2D) allotrope of carbon with sp2 hybridization, possesses remarkable mechanical [21], [22], [23], thermal [24], [25], [26], [27], and electrical properties [22], [23]. Researchers have extensively explored graphene in various thermal studies, including numerical investigations [16], [18], [28], [29], [30], experimental and theoretical analyses [31], [32]. Additionally, hybrid structures combining graphene with other 2D nanomaterials, such as carbon nitride, have been investigated as potential platforms for thermal rectification [16], [17]. One particularly intriguing area of research is the exploration of hybrid graphene heterostructures, which incorporate hexagonal boron nitride (h-BN) nanostructures [33], [34]. Although h-BN possesses a similar atomic structure to graphene (albeit with a larger lattice constant), it differs in electrical properties as it acts as an insulator. This distinction sets h-BN apart from graphene. Consequently, hexagonal structures composed of carbon, boron, and nitrogen atoms (h-BxCyNz) offer the potential to exhibit properties that span the spectrum from the zero-bandgap nature of graphene to the insulating characteristics of h-BxCyNz. The narrow electronic band gaps exhibited by h-BxCyNz 2D lattices, such as BC6N and BC2N, offer significant advantages for various state-of-the-art technologies where neither graphene nor h-BN are suitable. This claim has been supported by practical experiments where these h-BxCyNz lattices were fabricated, and their electrical, thermal, and mechanical properties were investigated [35], [36], [37]. In addition, Mortazavi et al. [20] conducted a study exploring the physical properties of different atomic configurations of BCN monolayers. According to their findings, all the BCN monolayers considered in the study exhibited semiconductor behavior, with electronic band gaps ranging from 0.05 to 2.46 eV. However, one exception was observed for the BCN-5 lattice, which displayed a semi-metallic character with a Dirac cone. These results highlight the potential of h-BxCyNz lattices and BCN monolayers as versatile materials for various applications that require specific electronic properties. Their narrow band gaps make them suitable for technologies where precise control of electronic states is necessary. The ability to engineer the band gaps and electronic properties of these materials opens up possibilities for designing and fabricating novel electronic devices with tailored functionalities. Further investigations and research on h-BxCyNz lattices and BCN monolayers will contribute to a better understanding of their properties, enabling the development of advanced technologies and devices in areas such as electronics, optoelectronics, and energy conversion.

The focus of our investigation is thermal rectification in hybrid graphene/2D BCN nanostructures due to the significant difference in their thermal conductivities, which makes them ideal candidates for thermal rectifiers. To begin, we examine the stability of various atomic configurations of BCN monolayers when combined with graphene. We find that there are only three stable configurations – BCN-2, BCN-3, and BCN-5 – when considering combinations with pure graphene. For reasons of simplicity we henceforth assume the following naming convention: BCN-5 → BCN-1; see also Fig. 1. Subsequently, NEMD simulations are employed to investigate thermal rectification in the corresponding samples. This study explores various temperature differences applied at the ends of the samples, as well as the potential impact of different levels of strain applied to the hybrid structures. Additionally, the interface between the two components of the hybrid structure is studied in terms of two types of grain boundaries: armchair and zigzag.

Section 2 discusses the problem formulation and briefly describes the employed computational approach. Our simulation results are presented and analyzed in Section 3. Specifically, a series of graphs depicting thermal rectification’s correlation to baths’ temperature differences and strain levels are included therein. Furthermore, since Kapitza resistance plays a significant role in thermal rectification and is interface dependent, we perform its calculation for the employed interface types in an attempt to further quantify their effects. Our concluding remarks along with potential future research directions are finally presented in Section 4.