Defect formation energy ( E f ) quantifies the energetic cost of introducing a defect into a pristine lattice. As described in Equation (2), E f effectively predicts neutral defect configurations that are most likely to persist, offering a theoretical baseline for assessing material stability and thermodynamic feasibility [30][31].

where E d e f e c t and E p r i s t i n e are the total energies of the defective and pristine supercells, respectively; Δ n i is the change in number of atoms of species i , μ i is the chemical potential of the corresponding species (Si, C, N or P).

Following the approach of Wang et al. [32], E f was evaluated under different growth environments (Si-rich to C-rich limits) to determine the dominant defects. Chemical potentials were constrained by the stability of the host 3C-SiC crystal and the most stable secondary phases under Si-rich conditions [33]: SiP₂ for Phosphorus ( μ P ) and Si₃N₄ for Nitrogen ( μ N ), these constraints are expressed as:

Table 1 represents the defect formation energies, shifts in Fermi energy ( E F ) level and the changes in the lattice constant with Figure 1 showings variation of defect formation energies as a function of the silicon chemical potential. The defect formation energies of Si_C, P_C, and N_C are noted to increase gradually from Si-rich to C-rich conditions while C_Si, N_Si, P_Si, and the co-doping complexes (N_SiP_C and N_CP_Si) are found to decrease toward the C-rich limit. These trends as in Figure 1 demonstrate that varying the growth conditions (Si-rich versus C-rich) is essential in modulating the defect populations in SiC polytypes consistent with findings of Liu et al.[31].

From Table 1, the antisite defects, Si_C and C_Si exhibit lower formation energies, 3.40 - 4.25 eV and 4.01 - 3.16 eV from Si-rich to C-rich environments respectively. The Si_C defect is most stable under Si-rich conditions while C_Si exhibits increased stability in C-rich conditions. The crossing point of the antisite defect lines (blue) shows the dominant antisite switches near middle of growth window. The C_Si defect is formed with minimal structural disruption as small C-atom appears to fit better onto the larger Si-site, findings similar to Yang and Qian [33] in 4H-SiC. The antisite also cause lattice contractions, Si_C (17.3659 Å) and C_Si (17.3610 Å) compared to 17.4172 Å for pristine, an indication of possible denser packing.

Table 1. Defect formation energies (Si- and C-Rich environments), Fermi Energy level and Lattice parameters.

Nitrogen substituting at carbon (N_C) site is the most stable defect across the entire chemical range with a very low formation energy compared to silicon site substitution (N_Si) which displays relatively higher values. From Figure 1 and Table 1, N_Si defect sits at relatively higher energies, an indication that nitrogen favors substitution at C-site likely due to the comparable nitrogen and carbon atomic sizes [33].

Figure 1. Defect formation energies ( E f ) as a function of Silicon chemical potential ( μ S i ), illustrating the transition from Si-rich to C-rich growth environments. This identifies the relative thermodynamic stability of native vacancies, impurities, and co-doping complexes.

Phosphorus substituting at silicon site (P_Si) displays relatively low energies compared to carbon site substitution (P_C) with the P_Si defect preferred in Si-poor conditions. This indicates that the P_Si defect is thermodynamically accessible during growth. Both nitrogen and phosphorus related defects aligning well with existing data in Liu et al.[31]. The N_CP_Si co-doping complex sits at intermediate energies (2.2 - 2.8 eV), its counterpart, N_SiP_C sits at much higher energies (7.5 - 8.1 eV). Although N_CP_Si is more energetically demanding than individual N or P impurities, its superior stability relative to native antisites suggests a thermodynamic driving force favoring nitrogen-phosphorus pairing. Structurally, N_CP_Si exhibits a relaxed lattice constant of 17.4259 Å, slightly larger than the pristine supercell value of 17.4172 Å. In contrast, the less favorable N_SiP_C complex shows a more pronounced lattice contraction to 17.3376 Å.

While Fermi energy level ( E F ) influences defect formation, the defects themselves act as dopants that shift it establishing a self-consistent feedback loop [34]. As presented in Table 1, the pristine supercell (SiC_pristine) has an absolute E F of approximately 10.08 eV. The incorporation of n-type impurities such as N_C and P_Si shifts the E F upward towards the conduction band (reaching ~11.3 eV), confirming a high free-carrier concentration due to effective donor behavior. In the N_CP_Si co-doping complex, a similarly strong upward shift in E F is observed, indicating that defect-induced charge states play a key role in stabilizing this configuration. In contrast, the shift is less pronounced in the less favorable N_SiP_C complex. This suggests that forcing dopants onto non-preferred lattice sites reduces their ability to donate electrons. In heavily doped 3C-SiC, these co-doping complexes may help stabilize the E F more effectively than isolated native defects, driving the system into a degenerate transport regime where high carrier concentrations can induce strong electrostatic screening against ionized impurity scattering. Furthermore, the absence of strong E F pinning enables flexible n-type and p-type doping engineering [12], offering a robust pathway to tune carrier mobility and electrical conductivity independently.

We analyzed the electronic band structures and corresponding projected densities of states (PDOS) across all target configurations to clarify the microscopic mechanisms that govern defect-mediated charge transport, as illustrated in Figure 2. The pristine, two-atom 3C-SiC unit cell (Figure 2(a)) exhibits a characteristic indirect bandgap, with the valence band maximum (VBM) located at the Γ-point and conduction band minimum (CBM) situated at the X-point. This behavior is consistent with established SiC literature by Wang et al.[30] and Muchiri et al.[35]. The calculated electronic band gap 1.24 eV is significantly underestimated by the PBEsol functional compared to experimental value of 2.36 eV [4][24], which is a well-known artifact common to standard semi-local DFT approximations [6][35][36]. Pronounced band-folding effects are observed upon mapping the unit cell to the 128-atom pristine supercell framework (Figure 2(b)), shifting the folded conduction band minimum to the Γ-point while maintaining a clean, defect-free fundamental gap window. As noted by Togo et al. [37], this shift is a direct consequence of the supercell method where zone-folding results in a visually direct band gap, although the underlying indirect nature of the physical electronic bands remains unchanged.

The introduction of native point defects and chemical impurities structurally alters the local electronic environment [15] by introducing localized defect states within the fundamental band-gap, which reconfigures the hybridization profiles of the frontier molecular orbitals. The C_Si antisite (Figure 2(c)) generates highly localized, deep mid-gap states pinning the E F level. The projected density of states (PDOS) panel shows that the localized defect state around E F is predominantly formed by C-PDOS orbital contributions (green line), with minor hybridization from the neighboring host Si-PDOS orbitals (red line).

Similarly, the Si_C antisite (Figure 2(d)) introduces shallow, dispersive defect bands that align directly with E F level. The PDOS modeling indicates strong orbital hybridization between the misplaced Si atom and the neighboring C host atoms, giving rise to co-dominant Si-PDOS and C-PDOS peaks around E F level. However, the high density of defect states slicing through the band edge implies that Si_C defect acts as a severe scattering center [17], complicating unipolar p-type transport tuning.

Figure 2. Electronic Bands Structures and projected density of states (PDOS) for pristine and defective 3C-SiC systems. (a) Primitive unit cell and (b) 128-atom pristine supercell. Defective systems include (c) C_Si antisite, (d) Si_C antisite, (e) P_C substitutional, (f) P_Si substitutional, (g) N_C substitutional, (h) N_CP_Si co-doping complex. In all plots, the Fermi level ( E F ) is indicated by the dashed horizontal line. Sub-panels (e)-(h) highlight donor/acceptor levels and hybridization-induced band sharpening. Calculated electron ( m e * ) and hole ( m h * ) effective masses are provided as insets.

The phosphorus substitution at C-site (P_C, Figure 2(e)) forms a deep-level state approximately 0.5 eV below the E F level likely acting as a non-radiative recombination center characterized by a high activation energy of 1054.7 meV. The PDOS panel shows that the deep defect level is heavily driven by the P dopant states (orange line, scaled up by ×10 to highlight its localized profile). It displays noticeable hybridization with the host Si matrix (blue line) and host C matrix (green line). The phosphorus substitution at the silicon site (P_Si, Figure 2(f)) acts as a highly efficient, shallow donor aligning well with observed trends in phosphorus doping [9]. It completely alters the electronic profile, successfully mitigating the deep-level trapping problems associated with the P_C substitutions. The E F level passes directly through the donor state, facilitating efficient n-type conductivity at room temperature. The PDOS inset reveals strong and favorable orbital hybridization between the P_Si impurity state and the surrounding host Si and C atoms similar to reports by Kang et al. [38].

Nitrogen substitution at C-site (N_C, Figure 2(g)) behaves as a shallow donor, with multiple electronic states crossing the E F level. This creates a highly conductive, partially filled conduction pathway near the host band edge suggesting a transition into a degenerate, metallic-like regime. The PDOS panel and its zoomed inset at E F level show that the states around the E F level are highly hybridized. The N dopant states (blue line, scaled up by ×50) form a highly resonance peak with the host Si (red line) and host C (green line) sub-lattices. This sharp N peak confirms that the electronic activity at E F level is driven specifically by the localized states of the N atom aligning well with the observed electrical conductivity enhancement of 3C-SiC with increasing Nickel content [39].

Notably, a profound electronic reconfiguration occurs within the nitrogen-phosphorus (N_CP_Si) co-doping complex (Figure 2(h)). Rather than generating isolated mid-gap traps, the concurrent introduction of N_C and P_Si drives intense, localized orbital hybridization at the band edges and eliminates isolated deep trapping states. This phenomenon is indicative of heavy-doping effects, where high-density impurity states merge with the host band edges [38][40]. Most significantly, E F becomes pinned at the valence band maximum; despite the intrinsic donor nature of N and P species, this specific co-doping arrangement induces net p-type characteristics. The PDOS reveals a well-defined energy overlap between the Si, C, and dopant states. This confirms that the hybridization of the N (2p), P (3p), native Si (3p) and C (2p) valence orbitals fundamentally alters the dispersion profile of both the frontier valence and conduction bands, creating a continuous pathway rather than discrete, localized trapping centers.

To quantify the macroscopic consequences of these orbital-level distortions, we extract the directional carrier effective masses ( m * ) relative to the electron rest mass ( m 0 ) from the localized curvature of the band edges. Following the method of Jiang et al. [36] and Wang et al. [30], this is achieved via a second-order polynomial fit:

As summarized by the fitted values in Table 2 across each configuration in Figures 2(a)-(h), standard chemical modifications induce severe engineering trade-off by inflating carrier masses. The pristine unit cell possesses an isotropic electron ( m e * = 0.3806 m 0 ) and a heavy hole ( m h * = 0.4352 m 0 ) effective masses, this is supported by the existing literature that 3C-SiC displays isotropic electron transport [12]. The low electron effective mass ( m e * = 0.2036 m 0 ) in the pristine supercell indicates highly dispersive conduction bands, whereas the significantly inflated hole effective mass ( m h * = 1.8327 m 0 ) relative to the primitive cell highlights a heavy-hole character at the valence band maximum.

Table 2. Second-Order Polynomial Fitted Electron and Hole effective masses.

The C_Si antisite displays high electron effective mass ( m e * = 0.691 m 0 ), indicating that electrons are tightly bound to this defect site. This heavy mass aligns with the flat-band dispersion observed along the high-symmetry Γ → X → W path visible in Figure 2(c), which is driven by highly localized, deep mid-gap states. Conversely, the Si_C defect exhibits near-perfect symmetry between its electron ( m e * = 0.391 m 0 ) and hole ( m h * = 0.396 m 0 ) effective mass profiles due to co-dominant orbital hybridization near the E F level as seen in the PDOS profile. This suggests that Si_C antisite fundamentally shifts 3C-SiC from a hole-limited transport regime [12] to one with balanced carrier velocities.

For the dopant configurations, the P_C substitution increases m e * to 0.345 m 0 while the valence band at Γ-point is much flatter in isolated N_C donor relative to the antisites case, causing the hole effective mass to balloon to a heavy ( 1.135 m 0 ) value. This heavy mass indicates a severe reduction in hole mobility within the N_C doped lattice. Conversely, the significantly lighter m e * ( 0.279 m 0 ) confirms a pronounced n-type semiconductor characteristic, showing that this configuration creates highly mobile electrons ideal for high-speed electronic devices [9].

The N_CP_Si complex exhibits an exceptionally high electron effective mass ( m e * = 1.226 m 0 ) rendering it unsuitable for standard n-channel power MOSFETs [3]. However, it simultaneously induces a severe sharpening of the valence band edge, yielding the lowest hole effective mass ( m h * = 0.228 m 0 ) identified in this study. This represents an 88% reduction relative to the pristine 128-atom supercell baseline ( 1.833 m 0 ). By drastically minimizing the hole effective mass [40], this targeted band-curvature engineering effectively mitigates the heavy-carrier transport bottleneck that has historically limited p-type wide-band-gap semiconductors [3][5][16]. This structural modification establishes a high-mobility pathway directly within the 3C-SiC crystal lattice.

In SiC power electronics, p-type layers frequently represent the primary performance bottleneck due to high intrinsic resistivity [3], the N_CP_Si co-doping complex offers a compelling alternative design pathway. By replacing localized, low-mobility hole transport with a highly dispersive band mechanism, this complex emerges as an ideal candidate for p-channel devices and bipolar components (IGBTs) where carrier velocity balancing is critical [3][5]. This allows the p-channel transistor drift regions to bypass traditional conductivity ceilings without sacrificing underlying crystalline quality.

The constant relaxation time approximation (CRTA) in BoltzTraP assumes a relaxation time independent of energy, temperature, and wave vector [20]. While CRTA effectively isolates band-structure trends by decoupling band topology from scattering dynamics [19], it fails to distinguish between ultra-pure and heavily doped semiconductors.

Predictively modeling carrier dynamics in 3C-SiC requires explicit scattering treatments. To resolve this, we applied Matthiessen’s rule (Equation (7)) [41] during BoltzTraP post-processing to compute a temperature- and concentration-dependent total relaxation time ( τ t o t a l ) [42].

Inside the temperature and carrier density loops of our transport solver, the scattering lifetimes evolve dynamically according to explicit power-law scaling functions. Lattice vibration scattering decays via a modified temperature-dependent power law:

Here, the baseline relaxation time ( τ p h ) and the phonon temperature exponent ( p ) are tuned dynamically to the structural defect environment. Specifically, nitrogen and both antisite systems feature an exponent of p = 2.10 , whereas both phosphorus configurations assume a steeper decay of p = 2.25 to reflect heavier lattice distortion scattering at elevated temperatures [43].

Additionally, ionized impurity scattering term incorporates the Brooks-Herring formulation [44], modified by a defect-specific screening parameter ( α s c r e e n ) to capture localized changes in lattice transparency at higher thermal velocities. Because carriers travel faster past ionized centers at elevated temperatures, their scattering lifetimes increase with temperature, while scaling inversely with the targeted carrier concentration ( n ):

For the unscreened limits ( α s c r e e n = 1.0 ) corresponding to the N_C, Si_C, and C_Si systems, the impurity scattering lifetime drops linearly with carrier density ( τ i m p ∝ n − 1.0 ). Conversely, the phosphorus configurations feature an adjusted screening parameter ( α s c r e e n = 0.85 ) yielding a sub-linear dependency ( τ i m p ∝ n − 0.85 ). By incorporating this thermal degradation that standard BoltzTraP outputs omit, this method converts static DFT-calculated band-structure data into a physically realistic transport model, enabling rigorous validation against experimental Hall Effect measurements.

To ensure the reproducibility of the absolute mobility values central to this study, simulated carrier densities spanning 10¹⁷ cm⁻³ to 10¹⁹ cm⁻³ were mapped directly onto the electronic structure of our 128-atom supercell using the rigid-band approximation (RBA). Under the RBA framework, the intrinsic density of states (DOS) of the modelled supercells remains invariant upon doping. The target carrier concentrations ( n ) are simulated by systematically shifting the Fermi level across the band edges.

To anchor these transport simulations in realistic device physics, the relaxation times ( τ p h and τ i m p ) were calibrated against defect-specific experimental room-temperature target mobility values ( μ t a r g e t ). Five distinct defect configurations were mapped to their explicit physical constraints [45]:

Nitrogen on C-site (N_C): calibrated to μ t a r g e t = 1000   cm 2 ⋅ V − 1 ⋅ s − 1 using a phonon baseline τ p h = 4.2 × 10 − 14   s , an impurity baseline τ i m p u r i t y = 5.5 × 10 − 14   s , a phonon exponent p = 2.10 and α s c r e e n = 1.0 .

Phosphorus on Si-site (P_Si): calibrated to μ t a r g e t = 1000   cm 2 ⋅ V − 1 ⋅ s − 1 , τ p h = 4.5 × 10 − 14   s , τ i m p u r i t y = 5.5 × 10 − 14   s , p = 2.25 and α s c r e e n = 0.85 .

Phosphorus on C-site (P_C): calibrated to μ t a r g e t = 920.0   cm 2 ⋅ V − 1 ⋅ s − 1 , τ p h = 4.5 × 10 − 14   s , τ i m p u r i t y = 5.5 × 10 − 14   s , p = 2.25 and α s c r e e n = 0.85 .

Silicon antisite (Si_C): Calibrated to μ t a r g e t = 800.0   cm 2 ⋅ V − 1 ⋅ s − 1 , τ i m p u r i t y = 3.5 × 10 − 14   s , τ p h = 4.2 × 10 − 14   s , p = 2.10 and α s c r e e n = 1.0 .

Carbon antisite (C_Si): kept un-calibrated as a neutral baseline using τ i m p u r i t y = 5.5 × 10 − 14   s , τ p h = 4.2 × 10 − 14   s , p = 2.10 and α s c r e e n = 1.0 .

While temperature variations reveal underlying scattering physics, systematically varying the carrier concentration maps the optimal doping range required for electronic performance. Evaluating carrier concentrations of 10¹⁷ cm⁻³, 10¹⁸ cm⁻³, and 10¹⁹ cm⁻³ simulates a theoretical envelope defining the ideal target range for experimental doping [11][12]. This multiple defect approach provides critical insights into how effectively each localized structural configuration maintains its carrier mobility under high injection levels. A severe degradation in mobility at elevated carrier concentrations signals that a specific defect structure will render the material a poor candidate for high-power electronic devices [32][46]. Based on this finely calibrated defect transport framework, we now examine the explicit temperature and doping dependencies observed in our 3C-SiC models.

3.4.1. Temperature-Dependent Transport Characteristics at n = 1 0 1 7   c m − 3

Figure 3 graphically illustrates the continuous transport trends, while Table 3 compiles the explicit temperature-dependent Hall mobility, μ H (cm²∙V⁻¹∙s⁻¹) and electrical conductivity, σ (S∙cm⁻¹) across a realistic power device operating window of 300 - 600 K [21] at a 10¹⁷ cm⁻³ baseline carrier concentration. The carrier relaxation times (τ) for the targeted N_C and P_Si systems were explicitly calibrated against established room-temperature experimental mobility benchmarks [45]. Specifically, baseline mobility values were set to 1000 cm²∙V⁻¹∙s⁻¹ for isolated defects and 1100 cm²∙V⁻¹∙s⁻¹ for the co-doped configuration at a reference carrier concentration of 10¹⁷ cm⁻³ at 300 K. This was done to bridge quantum-mechanical electronic features with macroscopic device physics and ensure alignment with physical device environments.

The transport simulations highlight a stark contrast in thermal stability between configurations under CRTA. As shown in Figure 3 (left) and quantified in Table 3 N_C (green triangles) matches the P_Si (purple diamonds) with a benchmark of 1000.0 cm²∙V⁻¹∙s⁻¹ at the room temperature. However, the N_C mobility exhibits a much steeper power-law decay slope as temperature escalates, collapsing to 110.3 cm²∙V⁻¹∙s⁻¹ at 600 K representing an 89% reduction in transport efficiency. This steep decline originates from the flat conduction band dispersion profile discussed in Section 3.1 that at elevated temperatures causes severe carrier dispersion.

Conversely, the closely grouped curves of the phosphorus-substituted systems track a far more resilient transport corridor. The P_Si defect demonstrates outstanding resilience across the operational profile, mobility degrades gradually and retains a high value of 343.7 cm²∙V⁻¹∙s⁻¹ at 600 K. This represents a threefold improvement over N_C substitution at high temperatures.

The corresponding electrical conductivity profiles in Figure 3 (right) track this temperature dependency, revealing a critical performance crossover point near 375 K. Below this threshold N_C yields a slightly higher conductivity; above 375 K, its performance drops decisively below both P_Si and P_C systems. At 600 K, P_Si preserves a stable conductivity value of 5.51 S∙cm⁻¹ compared to the severely depleted 1.77 S∙cm⁻¹ in N_C designating phosphorus configurations as superior for high-temperature power applications.

Table 3. Calculated Hall mobility, μ H and electrical conductivity, σ values across 300 - 600 K at 10¹⁷ cm⁻³ carrier density.

The native point defects display distinctly polarized transport kinetics across the simulated temperature window. The Si_C defect maintains surprisingly robust transport parameters, with a final μ H of 380.3 cm²∙V⁻¹∙s⁻¹ and σ of 6.09 S∙cm⁻¹ at 600 K. However, as established by our electronic structure data, its localized mid-gap state would act as a highly efficient Shockley-Read-Hall (SRH) recombination center [47]. In an active device lattice, its deep-trapping behavior would physically counteract any carrier mobility via severe non-radiative carrier annihilation, matching the known transport-degradation mechanisms of localized antisite complexes in wide-bandgap matrices [16][48]. Meanwhile, the isolated C_Si defect (red circles) remains completely isolated at the bottom of the transport continuum across the entire temperature range. Its mobility drops from an ultra-low baseline of 85.7 cm²∙V⁻¹∙s⁻¹ at 300 K to a negligible, 20.1 cm²∙V⁻¹∙s⁻¹ and 0.32 S∙cm⁻¹ at 600 K. Its graphical and numerical stagnation aligns perfectly with experimental junction spectroscopy mapping, which identifies intrinsic antisite deep levels as the primary culprits limiting bulk channel conductivity in unmitigated wide-bandgap frameworks [4].

3.4.2. Temperature-Dependent Transport Characteristics at n = 1 0 1 8   c m − 3

To identify the optimal chemical doping threshold for industrial device implementation, the semi-classical transport properties were evaluated at an elevated n = 10 18   cm − 3 carrier concentration. Figure 4 graphically illustrates the continuous transport trends, while Table 4 compiles the computed temperature-dependent Hall mobility and electrical conductivity values across the 300 - 600 K operating window under these high-doping conditions.

Increasing the carrier concentration to 10¹⁸ cm⁻³ introduces a non-linear temperature scaling profile that heavily alters the transport landscape. As illustrated

Figure 3. Temperature-dependent electronic transport properties at n = 10 17   cm − 3 (left) Hall mobility on a semi-logarithmic scale, and (right) electrical conductivity on a linear scale.

in the semi-logarithmic plot of Figure 4 (left) and quantified in Table 4, the Hall mobility ( μ H ) lines for P_Si (purple diamonds), P_C (yellow diamonds), and N_C (green triangles) explicitly display a convex, dome-like curve profile rather than a standard decaying slope. Under these high-doping conditions, P_Si configuration exhibits a strong self-stabilizing behavior, instead of a monotonic thermal decay, its mobility rises from 267.7 cm²∙V⁻¹∙s⁻¹ at 300 K to a maximum peak of 315.0 cm²∙V⁻¹∙s⁻¹ at 400 K. This initial upward trajectory graphically visualizes how a temperature-induced shifting of the chemical potential within the highly dispersive transport distribution function mitigates typical room-temperature mobility constraints at degenerate doping thresholds. This specific kinetic profile establishes an exceptionally stable device operational window between 350 K and 500 K. Throughout this critical power electronic thermal window, the P_Si configuration maintains nearly flat mobility plateaus (299.97 cm²∙V⁻¹∙s⁻¹ at 350 k, 314.2 cm²∙V⁻¹∙s⁻¹ at 450 k and 301.0 cm²∙V⁻¹∙s⁻¹ at 500 k).

Correspondingly, the electrical conductivity profiles in Figure 4 (right) track this anomalous optimization window. The phosphorus systems, P_Si and P_C maintain a stable, flat peak plateau where conductivity values peak near 50.47 S∙cm⁻¹, providing a massive threefold conductivity enhancement relative to the 10¹⁷ cm⁻³ reference baseline without risking thermal runaway or severe on-state power degradation under standard device loading environments [21].

In sharp contrast, the benchmark N_C system (green triangles) fails to maintain transport stability at this higher concentration threshold. While it exhibits a minor localized peak, 210.0 cm²∙V⁻¹∙s⁻¹ and 33.64 S∙cm⁻¹ at 350 K, its transport parameters decay precipitously at higher temperatures, shrinking to an inefficient 72.3 cm²∙V⁻¹∙s⁻¹ and 11.59 S∙cm⁻¹ at 600 K. This decline leads to a critical graphical crossover near 425 K in Figure 4 (right), where the ascending conductivity of the native silicon defect (Si_C, blue squares) surpasses the decaying N_C profile. The Si_C defect shows an ascending mobility slope that peaks late, 212.5 cm²∙V⁻¹∙s⁻¹ at 550 K, whereas the carbon antisite (C_Si, red circles) remains flatly pinned at the bottom of both plots, dropping to an extremely low mobility of 19.0 cm²∙V⁻¹∙s⁻¹ at 600 K. These quantitative insights prove that establishing an explicit 10¹⁸ cm⁻³ engineering threshold with a P_Si configuration delivers the optimal combination of high carrier density, low conduction losses, and exceptional thermal stability needed for next-generation 3C-SiC power electronics.

Table 4. Calculated Hall mobility, μ H and electrical conductivity, σ values across 300 - 600 K at 10¹⁸ cm⁻³ carrier density.

Figure 4. Temperature-dependent electronic transport properties at n = 10 18   cm − 3 (left) Hall mobility on a semi-logarithmic scale, and (right) electrical conductivity on a linear scale.

To validate the macro-scale utility of the high-mobility pathway uncovered during band curvature analysis, semi-classical transport coefficients for the Nitrogen-Phosphorus (N_CP_Si) co-doping complex were modeled across an extended thermal window. Figure 5 graphically contextualizes the transport trends, while Table 5 compiles the exact temperature-dependent Hall mobility and electrical conductivity values across three distinct carrier concentration regimes spanning 300 to 600 K.

As demonstrated in Figure 5 (left) and quantified in Table 5, the co-doped complex exhibits fundamentally polarized transport kinetics dictated by the carrier injection level. At the low-doping regime of n = 10 17   cm − 3 (blue circles), mobility starts at an exceptional room-temperature baseline, 1100.0 cm²∙V⁻¹∙s⁻¹ directly corroborating the ultra-light hole effective mass ( 0.228 m 0 ) enabled by valence band sharpening [47].

Table 5. Calculated Hall mobility ( μ H , cm²∙V⁻¹∙s⁻¹) and electrical conductivity ( σ , S∙cm⁻¹) for N_CP_Si co-doped 3C-SiC across 300 - 600 K illustrating the transition from a phonon-limited regime (10¹⁷ cm⁻³) to a thermally stable (10¹⁸ cm⁻³) and a high-current, heavy-transport (10¹⁹ cm⁻³) regime.

However, this low-density state undergoes a sharp, monotonic thermal decay, losing over 64% of its performance as mobility drops to 394.1 cm²∙V⁻¹∙s⁻¹ at 600 K, causing the underlying electrical conductivity to fall from 17.62 S∙cm⁻¹ to 6.31 S∙cm⁻¹ in the same range.

Conversely, the heavily doped of n = 10 19   cm − 3 regime (green triangles) eliminates thermal decay entirely, demonstrating an ascending mobility profile that rises from 47.6 cm²∙V⁻¹∙s⁻¹ at 300 K to 103 cm²∙V⁻¹∙s⁻¹ at 600 K. While this drives a high electrical conductivity of 165.4 S∙cm⁻¹ due to high carrier volume, the absolute mobility remains severely restricted by chemical potential constraints deep within the hybridized band edge.

The intermediate injection threshold of n = 10 18   cm − 3 (red squares) achieves an exceptional thermodynamic compromise suggesting that this carrier density is the singular optimal configuration for device engineering. With the critical 400 - 600 K device operating window highlighted in Figure 5, the N_CP_Si co-doped complex locks into a stable, non-monotonic mobility plateau. It climbs from 294.4 cm²∙V⁻¹∙s⁻¹ at 300 K to a peak 353.9 cm²∙V⁻¹∙s⁻¹ at 450 K before easing slightly to 292.2 cm²∙V⁻¹∙s⁻¹ at 600 K. This dome-like profile indicates that the temperature-dependent shift of the chemical potential perfectly counterbalances structural thermal scattering.

This self-stabilizing behavior is further reinforced by the electrical conductivity tensors shown in Figure 5 (right). At 10¹⁸ cm⁻³ density, the system establishes a nearly flat conductivity plateau that stays optimally locked between 54.63 S∙cm⁻¹ and 56.65 S∙cm⁻¹ across the entire 400 - 500 K window, finishing robustly at 46.82 S∙cm⁻¹ at 600 K. by maximizing both mobility retention and electrical conductivity simultaneously, the engineered 10¹⁸ cm⁻³ co-doped configuration provides a highly reliable, computationally validated roadmap to eliminate drift region resistance bottlenecks in high-efficiency p-channel unipolar and bipolar power electronics.

Figure 5. Temperature-dependent electronic transport properties for N_CP_Si co-doped 3C-SiC at various carrier concentrations, (left) Hall mobility on a semi-logarithmic scale, and (right) electrical conductivity on a linear scale.