Silicon carbide (SiC) has been a focal point in high-temperature and high-pressure wide-bandgap semiconductor research for the past few decades^{[1, 2]}. SiC can form various polytypes depending on the stacking sequence of Si−C atomic layers, with 3C, 4H, and 6H being the primary focus of current studies^[3]. Among these polytypes, 3C-SiC exhibits the lowest band gap energy (2.3 eV) while offering the highest electron mobility and saturation velocity^[4]. The cubic crystal structure provides higher symmetry, which reduces phonon scattering^[5]. Furthermore, 3C-SiC has a lower surface state density and improved carrier mobility in electronic applications^[6]. Additionally, 3C-SiC can be directly grown on silicon substrates, providing a significant advantage for integration into existing silicon semiconductor manufacturing processes. As a result, compared to other polytypes, 3C-SiC is better suited for electronic applications.

Despite extensive research on the growth, properties, and applications of single crystal SiC, the strict preparation conditions and high costs have remained barriers to its widespread use, even with substantial improvements in crystal and epitaxial quality^[7−9]. In contrast, polycrystalline SiC (poly-SiC) offers a simpler fabrication process and allows for a wider range of compositions and doping levels, resulting in diverse physical and electrical properties^[10]. Certain poly-SiC ceramics exhibit high thermal conductivity, mechanical strength, and oxidation resistance, making them suitable for applications in fusion reactors, gas turbines, filters, optical mirrors, and structural components^[11]. Furthermore, 3C-SiC is the most thermodynamically stable polytype, allowing it to be synthesized at lower temperatures. This also makes chemical vapor deposition (CVD) one of the key methods for producing high-quality 3C-SiC.

However, the doping mechanisms and carrier transport properties in polycrystalline SiC differ from those in single crystal SiC. While extensive research has been conducted on its structural and electrical properties^{[12, 13]}, the correlation between these properties in polycrystalline SiC has not been sufficiently explored. The most significant factor influencing electrical properties is doping concentration, similar to single-crystal SiC^[14]. Additionally, Lu et al.^[15] and Xiong et al.^[16] have reported that particle size affects the properties of SiC. However, no studies have yet evaluated the relationship between grain size and electrical characteristics. Understanding this relationship in polycrystalline 3C-SiC is crucial for advancing theoretical studies on carrier transport and defect states, ultimately facilitating the development and application of polycrystalline 3C-SiC ceramics in electronic devices and structural components.

This paper investigates the effect of grain size on polycrystalline 3C-SiC. The findings lay the foundation for future research on how crystal structure influences electrical properties. Finally, the relationship between grain size and resistivity is established, providing a basis for optimizing SiC material properties and expanding its applications. Especially in the field of power electronics, the performance of MEMS and diode devices can be adjusted by controlling the grain size^{[16, 17]}.

In this study, a series of poly 3C-SiC samples prepared by chemical vapor deposition (CVD) were selected for testing and characterization. The samples were primarily divided into two categories: unintentionally doped and nitrogen-doped. The electrical properties were first characterized using the Hall effect probe measurement. For the Hall effect measurements, a 100 nm layer of Ni was deposited on the surface of the samples by magnetron sputtering to form an electrode^[18]. Secondary ion mass spectrometry (SIMS) was utilized to determine the samples' doping and depth information, as well as to examine and verify their impact on resistivity. Transmission electron microscopy (TEM) was used to investigate the distribution of grains in the sample's cross section. This helps us understand how the grains change in thickness during the sample growing process. Crystallinity and orientation were analyzed using a high-resolution X-ray diffractometer, the Bruker-axs model D8-Discover. Raman spectroscopy was employed to analyze the composition. Electron back scatter diffraction (EBSD) was used to analyze the grain size manufactured by Oxford, the test area is 100 × 80 μm². This method not only gives a direct view of the presence of grains with different orientations, but it also allows for quantitative statistical analysis of the average grain size. The combination of these tests allowed us to determine the relationship between resistivity and grain size. These two tests give us an initial understanding of the differences between samples when the samples are inadvertently doped.

As is well known, doping concentration directly impacts the carrier concentration in SiC materials. Additionally, factors such as temperature, doping concentration, and dopant type influence their interactions^[19]. SMIS results indicate that the tested samples contain C, Si, N, B, and trace amounts of Al and Fe, shown in Fig. 1. The results include unintentionally doped and nitrogen-doped samples, with dopant N concentrations of 5 × 10¹⁷ and 8 × 10¹⁹ cm⁻³, respectively. Particular attention is given to the nitrogen (N) doping levels, as this was the primary parameter varied in the experiment. It does not vary significantly with depth apart from the surface.

A significant difference in nitrogen doping concentration is observed, as shown in Fig. 2(a). The doping concentration of samples grown under a nitrogen gas atmosphere is approximately 10²⁰ cm⁻³, demonstrating the strong effect of nitrogen doping. In contrast, the doping concentration in unintentionally doped samples was below 10¹⁸ cm⁻³. These variations in doping concentration may be attributed to background doping and inconsistencies between furnace runs. To further analyze the electrical properties of the samples, we characterized them using Hall effect measurements^[20].

The doping concentration results and resistivity are summarized and displayed in Fig. 2(a). As the doping concentration gradually increases, the sample's resistivity decreases. When the doping concentration is at the 10¹⁶ cm⁻³ level, the resistivity exceeds 10³ Ω·cm. As the doping concentration increases by four orders of magnitude, the resistivity decreases by five orders of magnitude. Overall, the data reveal an approximately linear relationship, demonstrating that doping significantly reduces the material's resistivity^[14]. However, at a doping level of 10¹⁷ cm⁻³, the resistivity of the samples varies by more than three orders of magnitude. This suggests that while doping concentration is a crucial factor, other factors also have a significant impact on resistivity. Resistivity fundamentally reflects variations in carrier concentration and mobility, and the observed differences may be attributed to distinct electron scattering mechanisms in the samples^[21].

To investigate structural features that could contribute to electron scattering, we performed TEM measurements on a typical unintentionally doped high-resistivity sample. As shown in Fig. 2(b), the sample exhibits a polycrystalline 3C-SiC structure. During the growth process, grains are not confined to the surface region but extend from the bottom to the surface, resulting in smaller grains at the surface. As the sample grows, the intersection of multiple grains leads to significant grain distortion and the formation of small grains, which obstruct electron transport within the sample. However, with continued growth, subsequent grains become slightly larger, and when growth ceases, a rough surface is formed. Details regarding surface grain characteristics will be further discussed in the EBSD results presented below.

To further investigate the impactors of resistivity, particularly the orientation and structural information of various grains as demonstrated in the TEM data. Samples with identical doping concentrations of around 10¹⁸ cm⁻³ are chosen for comparison and termed doping 18-1 to 18-4. And carried out XRD and Raman spectroscopy tests to examine the composition^[22]. All of the samples are tested, four typical samples are shown in Fig. 3. All the peaks observed in Fig. 3(a) correspond to the PDF card #73-1665 of 3C-SiC. Grains of crystal orientations (111), (200), (220), and (311) can be identified from the sample 18-1 and 18-4. And the preferred orientation of crystals in samples 18-2 and 18-3 has been reduced. The results indicate that samples exhibiting the same carrier mobility actually have different lattice orientations, which could be the cause of the observed variations in carrier mobility.

However, considering the testing accuracy, further Raman spectroscopy tests are performed as a comparison. The test findings in Fig. 3(b) show that the first-order TO and LO Raman peaks^[23] of 3C-SiC are around 797 and 970 cm⁻¹, respectively. In sample 18-2, the LO peak is significantly attenuated, which could be related to material problems. Other peaks demonstrate varied degrees of shift, indicating the presence of stress or contaminants in all samples^[24]. This is also one of the variables that affect electrical characteristics. The stress between these lattices is also corresponds to the TEM results in Fig. 2(b). Combining the results of XRD and Raman spectroscopy, we can observe that, in addition to doping concentration, the grain orientation and stress in polycrystalline 3C-SiC also vary, and these factors significantly influence the resistivity of the sample. We will delve into a more detailed analysis below.

To achieve a balance between high resolution and the number of grains analyzed, EBSD testing was used for characterization^{[25, 26]}. Several unintentionally doped samples were examined, and the findings are presented in Fig. 4. The colors represent relative crystal plane orientations, with the corresponding relationships illustrated in the inset of Fig. 4(a)^[27]. For ease of comparison, the samples are categorized by resistivity, ranging from high to low, as shown in Figs. 4(a)−4(h). Specifically, the samples in Figs. 4(a) and 4(b) exhibit high resistivity, those in Figs. 4(g) and 4(h) show low resistivity, and the remaining samples fall in between. Fig. 4 reveals that high-resistivity samples primarily consist of homogeneous, fine-grained structures. As grain size increases, homogeneity decreases. To better illustrate grain size variations, statistical data is compiled in Fig. 5, which will be discussed in detail in the following sections. Additionally, the grain orientation of the sample in Fig. 4(e) is relatively uniform, aligning with XRD data that indicate a single orientation in some samples. However, distinct grain boundaries remain visible, likely due to variations in the in-plane grain orientation. Furthermore, the consistency of grain information across different characterization methods confirms the reliability and reproducibility of the test results.

The grain size of samples with similar carrier concentrations, as determined from EBSD results, is summarized in Fig. 5. While some grains in the EBSD images of unintentionally doped samples are larger than 20 μm in size, their average grain size ranges from 1.44 to 4.04 μm due to their relatively low proportion. Overall, resistivity increases with grain size, corresponding to an increase in sample number. This clearly indicates that, for polycrystalline samples with similar carrier concentrations, grain boundaries have a significant scattering effect on electron conduction. As grain size increases, the number of grain boundaries decreases, reducing electron scattering during transport and thereby enhancing electrical conductivity^[28].

As a comparison, EBSD and grain size results of nitrogen doped sample are shown in Fig. 6. The average size is 3.03 μm, which is between the size of unintentionally doped sample f and g. Thus, nitrogen doping primarily alters carrier concentration, not grain structure.

To correlate the grain size of the samples with their resistivity, it is essential to understand the conduction mechanisms of the crystal. In single-crystal materials, there is a well-defined relationship between resistivity and carrier mobility, given by^{[21, 29]}:

1ρc=1qni(un+up),

2ni=2(2πkTh)32(me*mh*)34exp(−Eg2kT).

Here un and up are the electron and hole motilities, respectively, and E_g is the bandgap of the material. Based on the calculation models from Eqs. (1) and (2), it can be inferred that a larger bandgap results in a lower intrinsic carrier concentration (ni), leading to higher resistivity in the corresponding crystal structure. However, in polycrystalline samples, no clear trend is observed, likely due to the significant influence of grain boundaries on electron scattering.

Additionally, in polycrystalline material systems, the resistivity is proportional to the surface area of grain boundary per unit volume (S_GB/V)^[30]. The increase in resistivity due to the grain boundary surface area per unit volume, can be used to determine the specific grain boundary resistivity ρ_SGBR. The total resistivity of polycrystalline SiC can be defined as ρ, and the relationship can be expressed as follows:

3ρ=ρbulk+ρGB.

Here ρbulkis the bulk resistivity of the material in the absence of defects and grain effects, and ρGBis the grain boundary resistivity of the material. The grain boundary resistivity has the following relationship:

4ρGB=ρSGBR⋅(SGBV).

Here S_GB/V is inversely proportional to the average grain size d, i.e.

5SGBV=kGB(1d).

Here, kGB is a constant. Therefore, the relationship can be expressed as:

6ρGB=ρSGBR⋅kGB(1d)=Ad.

A is kGB⋅ρSGBR. Thus, the total resistivity can be written as:

7ρ=ρbulk+Ad.

Consequently, the particular experimental test data is fitted using this function, to derive an equation for the grain size-dependent resistivity of polycrystalline 3C-SiC. The link between the tested grain size and resistivity is depicted in Fig. 7. To better match the data, the resistivity test data were converted to logarithmic values and fitted with Eq. (8). The final result can be described as:

8log(ρ)=−1.93+8.67d.

The resistivity of a material is inversely proportional to its grain size, when the doping ranges from 10¹⁶ to 10²⁰ cm⁻³ and grain size is between 1.44 and 4.04 μm. Similar results in other materials, are discovered by researchers like Bakonyi et al.^[31] and Bishara et al.^[27]. This equation indicates that grain size in polycrystalline samples is one of the significant factors influencing electrical properties.

In this study, the electrical properties of various polycrystalline 3C-SiC samples were analyzed, and the influencing factors were investigated using multiple testing methods. When the doping concentration is similar, the scattering effects of grain size and grain boundaries play a significant role in the electron transport process. Additionally, a quantitative relationship between grain size and resistivity was established as: log(ρ) = −1.93 + 8.67/d. This finding provides a foundation for the future quantitative control and optimization of resistivity in polycrystalline 3C-SiC.