*3.9. Defects in 3C-SiC: Kinetic Monte Carlo Super Lattice Simulations*

The study of the kinetic evolution of a defective system is a difficult task as it requires both atomistic accuracies typical for the molecular dynamics approach and large spacetime scales typical for the experimental systems. Within the CHALLENGE project, we developed an ab-initio calibrated kinetic Monte Carlo super lattice (KMCsL) code, [62] offering a good compromise between accuracy and efficiency, which can simulate the results of the growth processes in non-polar SiC as a function of the growth parameters also in terms of defectivity and surface morphologies. Hence, the KMCsL simulations allowed for the investigation of the formation and development of extended as well as point defects over a realistic growth [62]. As an example of a simulation application strongly relevant to the experimental studies, we considered the evolution of anti-phase boundaries (APBs) in 3C-SiC and their interaction with stacking faults (SFs), which is discussed in detail in Reference [57].

Due to the comparable energetics of polytypes, SFs are a frequent and wide-spread extended defect in SiC, with respect to the polytype. They are classified as incorrect

atoms sequences in comparison with theoretical polytype stacking arrangements. In the purely hexagonal close-packed (hcp) representation, the polytype sequence is defined as a repeating series of layers made up of Si-C dimers aligned on the hexagonal axis. Dimers in every layer take one of three extremely symmetric locations (often denoted as A, B, and C). If the recurring arrangement is ABC ABC ABC . . . , etc., extending along the crystal <111> axes, the cubic 3C-SiC (zinc-blend) configuration is produced. As a result, the existence of {111} planes on the surface depletion allows for an increase in SF production. The formation of a pair of triple SFs (SF <3>: three bilayers not in the correct crystalline structure) from the surface depletion caused by an APB is shown in Figure 15. A series of pictures of the under-coordinated atoms obtained at various KMC intervals are displayed. The existence of three-fold coordinated Monte Carlo particles at its border leads to the generation of the triple SF in this depiction (i.e., at the corresponding partial dislocation). We note that the stacking sequence of the triple SF (sometimes termed micro-twin, i.e., ABC ABC ACB ABC ABC ABC) divides two crystal areas in pristine epitaxial order. The only atoms out of the right crystal locations are those within the extended defect. The APBs' localized asymmetry as well as the existence of the {111} faceted surface result in the development of a triple SF (due to polytype instability) (see Figure 15a,b). When the APB generates the SF, the two extended defects (SF and APB) maintain separate kinetics: the APB proceeds to move through the [110] plane, while the SF expands on the (111) plane (snapshots b, c, and d of Figure 15). A TEM picture of an SF generated by an APB along the epitaxial growth of a 3C-SiC (001) substrate is shown in Figure 15e. It expands autonomously from the APB kinetics along the {111} planes. Moreover, surface depletion can be seen in the correspondence of the (001) surface. These composed structures of proximal APB and SF-type defects have been also evidenced by the conductance maps in this paper.

**Figure 15.** *Cont.*

**Figure 15.** A pair of triple SFs are generated as a result of the surface depletion caused by an APB during 3C-SiC epitaxy along the [001] z-direction. Under-coordinated atoms from several KMC moments: (**a**) triple SFs created by an APB; (**b**–**d**) three consecutive images illustrating the autonomous kinetics of the APB traveling towards the [110] axis; and two formed triple SFs expanding along the (111) planes. (**e**) TEM picture of an SF caused by an APB along the epitaxial growth (001) of a 3C-SiC. It expands on the {111} planes autonomously from the APB kinetics. Moreover, the surface depletion is evident at the (001) surface (adapted from Reference [57]).

## *3.10. Defects in 3C-SiC: Electrical Effects*

Nanoscale-resolution current mapping of 3C-SiC by conductive atomic force microscopy (CAFM) provided a direct demonstration of APBs as the main extended defects responsible for the enhanced leakage under reverse-bias, whereas both APBs and SFs were shown to act as current paths under forward polarization. Figure 16a illustrates the experimental configuration used for CAFM measurements on the cubic silicon carbide surface. A typical topographic image collected on a 20 µm × 20 µm scan area is shown in Figure 16b, from which a surface root mean square (RMS) roughness of 3.2 nm was calculated. The nanometer deep "V-shape" depression in the morphology and in the height line-scan (Figure 16b, right panel) were associated to an APB in accordance with the Monte Carlo simulations of Section 3.7. Figure 16c,d report the current maps measured simultaneously to the topography by applying a reverse-bias (Vtip = −0.5 V) and forward-bias (Vtip = 0.5 V) polarization to the Pt tip, respectively. This Schottky diode behavior of the Pt/3C-SiC contact was confirmed by the significantly lower current values measured under reverse polarization with respect to those measured under forward-bias. Using the same current range (from 0 to 50 pA) for the two current maps, APBs are the most evident conductive features under reverse-bias, whereas both APBs and SFs (indicated by blue arrows in Figure 16d) contribute to the conduction under forward polarization. Two representative scan lines across the APB for the two opposite tip biases are also shown in the right panels of Figure 16c,d, showing a higher current peak on the APB under forward-bias with respect to the reverse one. This suggests that APBs are mainly responsible for the enhanced reverse leakage current measured in macroscopic Pt/3C-SiC Schottky diodes. In particular, the

separation between these extended defects deduced from this microscopic analysis is in the order of tens of micrometers, in very close agreement with the value of L (≈20 µm) deduced from the statistical characterization of Schottky diodes with different areas for thin 3C-SiC layers [63].

**Figure 16.** (**a**) Schematic illustration of the CAFM setup. (**b**) Morphology and (**c**) current maps collected under reverse-bias polarization of the tip (Vtip = −0.5 V) and (**d**) forward-bias polarization (Vtip = 0.5 V). An APB is indicated by a red arrow and SFs by blue arrows. Representative linescans across a grain boundary extracted from the topography ((**b**), right panel), current maps under reverse-bias polarization ((**c**), right panel), and forward-bias polarization ((**d**), right panel) of the tip are shown (see Reference [63]).
