2.1 Electronic structure calculation

Electronic structure calculations are essential for understanding and optimizing the properties of semiconductor materials, particularly in the study of wide bandgap semiconductors, where accurate bandgap prediction is crucial. First-principles calculations enable researchers to analyze the electronic structure of these materials in detail, including the energy band structure, the density of electronic states (DOS), and the position of the Fermi energy levels. The results of these calculations offer a theoretical foundation for optimizing material properties, which is especially important for precise bandgap prediction and modulation.

In recent years, significant progress has been made in the electronic structure calculations of wide bandgap semiconductors, driven largely by continuous advancements in computational methods and resources. The use of DFT and the GW approximation in bandgap calculations has notably advanced the study of these materials. As the most widely used first-principles method, DFT accurately describes the ground state's electronic structure. However, due to its approximations in handling electron exchange-correlation effects, DFT often underestimates the bandgap of wide bandgap semiconductors, particularly for materials such as GaN, SiC, and ZnO [29–32]. In these cases, the DFT-calculated bandgap tends to be lower than the experimental value. To address this, researchers commonly apply the GW approximation to correct the bandgap and improve the accuracy of predictions.

As shown in Figs. 1(a) and 1(b), the band gap of 3C-SiC was calculated by Perdew-Burke-Ernzerhof (PBE) functional, and the result obtained was 1.4 eV. Still, after considering the GW approximation, the band gap calculated by the G₀W₀ method was 2.3 eV, which is very close to the experimental value of 2.36 eV [29]. In the discussion of the band gap of (ZnO)_1–x(GaN)_x alloy by Olsen et al., a GW approximation was used to calculate the band gap of the system, and the results are shown in Fig. 1(c), which are in good agreement with the experimental values [32]. The GW approximation is a many-body perturbation theory based on the one-body Green's function, which provides a more rigorous framework for describing electronic structure than conventional methods [33–37]. At its core is the exchange-correlation self-energy function, which is analogous to the exchange-correlation potential in the Kohn-Sham density functional theory. Unlike the exchange-correlation potential, the exchange-correlation self-energy is a spatially nonlocal, energy-dependent, non-Emilian function that includes all non-classical electronic interaction effects beyond the Hartree approximation. The photoelectron spectrum (PES) and inverse photoelectron spectrum (IPS) associated with the quasiparticle excitation energy spectrum can be obtained directly from the self-energy function, and these energy spectra can be measured experimentally. The exact self-energy function follows a set of self-consistently coupled integral differential equations known as the Hedin equation [36, 38]. However, since the solution of this equation is extremely difficult to find in complex systems, approximations must be introduced in practical applications. The most commonly used approximation is the GW approximation, in which the self-energy function in the time-space domain is expressed as the product of the one-body Green's function G and the shielding Coulomb action W. The GW approximation is used to solve the Hedin equation. Although the GW approximation provides an effective computational framework, the numerical solution of the Hedin equation still faces the challenges of complex program implementation and high computational complexity. In practical studies, a commonly used approximation is the G₀W₀ method, in which G and W are calculated based on the single-electron orbital energy and wave function, respectively, at some mean-field approximation (H₀) [39].

Figure 1 (a) Quasiparticle band structure of pristine 3C-SiC computed within DFT using Perdew-Burke-Ernzerhof (PBE) functional and within the GW approximation. (b) Comparison between the imaginary part of the dielectric function calculated with GW-Bethe-Salpeter equation (GW-BSE) and with the noninteracting particle approximation. A Gaussian smearing of 0.05 eV is used for calculating the dielectric function. Reproduced with permission from Ref. [29]. © 2022, the American Physical Society. (c) Optical absorption and electron energy loss spectra for x=0, 0.02, and 0.15, see corresponding symbols in the legend. The optical data are presented in the form of Tauc plots assuming direct allowed transitions, while the electron energy loss spectroscopy (EELS) data are linearly scaled. Dotted (optical absorption) and dashed (EELS) lines represent an extrapolation of the linear region intersecting the x-axis. The point of intersection marks E_g. Reproduced with permission from Ref. [40]. © 2019, The American Physical Society.

The GW approximation method enhances the DFT, thereby improving the accuracy with which it characterizes the dynamic effects of electrons and significantly improving the accuracy of bandgap prediction [41, 42]. Recent studies have demonstrated that the GW method has become a standard and effective tool for bandgap prediction in wide bandgap materials. Rinke et al. applied the GW approximation to correct the bandgap of GaN, finding that it more accurately matched experimental results compared to DFT, which underestimated the bandgap [41]. Notably, temperature effects also play a critical role in bandgap modulation. As demonstrated by Lee et al., the electronic structure of β-Ga₂O₃ exhibits significant temperature dependence due to electron-phonon interactions and thermal expansion [42]. Their combined first-principles and experimental study revealed a bandgap reduction of over 0.5 eV between 0 and 900 K (Fig. 2), with electron-phonon renormalization identified as the dominant mechanism. This work highlights the necessity of incorporating temperature effects alongside advanced exchange-correlation corrections for accurate bandgap predictions in device-operating conditions. The study achieved a more accurate energy band structure by combining the GW method with DFT, providing a theoretical basis for optimizing GaN's performance in high-power applications.

Figure 2 Change in the bandgap of β-Ga₂O₃ as a function of temperature from T=0 to 900 K. For ease of comparison to other experimental and computational results, changes in the gap are referenced to the T=300 K value. Reproduced with permission from Ref. [42]. © 2023, AIP Publishing.

In addition to the traditional DFT and GW methods, hybrid functional approaches have been widely adopted in recent years for studying wide bandgap semiconductors. By incorporating nonlocal exchange-correlation functions, these methods effectively enhance the accuracy of bandgap calculations, addressing the limitations of DFT [43].

Back in the 1990s, Becke, together with Bylander and Kleinman, almost simultaneously proposed the introduction of a nonlocal exchange-correlation potential to make corrections to the electronic structure of the system [43, 44]. This approach is no longer limited to the Kohn-Sham theoretical framework. Seidl et al. later systematized this approach [45]. They changed the definition of the single reference. This redefinition ensured the approach was strictly unified within the DFT framework. It led to the development of generalized Kohn-Sham (GKS) theory. These methods perform well in specific cases. However, they still fail significantly in calculations of total energy and other properties.

In recent years, high-throughput computing and machine learning methods have gradually become popular directions in wide bandgap semiconductor research. And artificial intelligence based on big language models is also shining in the industrial sector [46]. By combining high-throughput computing and machine learning, researchers can more efficiently screen materials with excellent properties [47–54]. A methodology paradigm that has demonstrated cross-domain effectiveness in fields ranging from wearable sensor optimization to robotic motion control systems [55, 56]. For example, Chen et al. utilized pymatgen and matminer to extract data from the materials project, encompassing 3720 ABX₃-type compounds and 2660 A₂B(I)B(II)X₆-type compounds. This effort enabled the identification of key material characteristics with accurately predicted band gaps and formation energies. To estimate missing data, the random forest algorithm was employed, followed by using tolerance and octahedral factors to screen for stable chalcogenide structures, thereby improving data quality. A subsequent SHAP (SHapley Additive exPlanation) analysis was performed to determine the most influential descriptors. The results indicate that higher formation energies, a large number of transition metals, and a considerable presence of d-orbital valence electrons are critical for forming narrow bandgap perovskites. In contrast, a higher number of f-orbital electrons and large electronegativity differences between elements contribute to the formation of wide bandgap perovskites. Additionally, Shen et al. developed a hierarchical material screening framework (HMSF) to identify ultra-wide bandgap materials. The framework is similar to graph-based path-planning strategies in robotic systems [57]. They established a correlation between material chemistry and properties and adjusted hyperparameters in the machine-learning algorithm to enhance prediction accuracy via Bayesian optimization. This approach led to the discovery of four previously unknown ultra-wide bandgap materials characterized by suitable forbidden bandwidths, exceptional thermal stability, a pronounced deep ultraviolet optical response, and low electronic effective masses. These achievement highlights the significant potential of machine learning in accelerating material design.

In the study of semiconductor materials, it has been found that introducing defects and doping, among other things, has a significant effect on the electronic structure of semiconductors. For example, co-doping and Co-Al Co-doping in ZnO were discussed by Khan et al. It was found that after Co doping, the material exhibited antiferromagnetism, while after Co Al co-doping, there was a transformation of the antiferromagnetic phase into a ferromagnetic phase, and the energy of the antiferromagnetic state was higher than that of the ferromagnetic phase by 184 meV, which is much higher than the thermal motion energy at room temperature [58]. With this energy difference, the Curie temperature of the system was calculated by mean-field theory to be 690 K. Meanwhile, the optical absorption spectrum shows, with the increase of Co concentration, the band gap of ZnO and the position of the d-d transition peak of Co ions show blueshifts and redshifts behaviors, respectively; with the Co concentration increases, the intensity and width of the d-d transition peaks decrease. In addition, Co Al co-doping not only increases the band gap but also generates new absorption peaks in the infrared and visible regions. This work demonstrates the modulation of ZnO optoelectronic and magnetic properties by Co doping and Co Al co-doping. It provides theoretical support for applying ZnO-based materials in future electronic and optoelectronic devices. Beyond chemical modifications, environmental factors such as temperature also profoundly reshape electronic properties. Lee et al. demonstrated that thermal lattice vibrations in β-Ga₂O₃ induce band edge localization, particularly for the valence band maximum (VBM), as shown in their charge density isosurfaces (Fig. 3) [42]. This localization leads to increased hole effective masses at elevated temperatures, directly impacting carrier mobility and device performance. Such findings emphasize the interplay between intrinsic defects, extrinsic dopants, and thermodynamic conditions in determining semiconductor behavior.

Figure 3 Three-dimensional isosurfaces of charge densities of the (a) conduction band minimum (CBM) and (b) valence band maximum (VBM) from one-shot configurations of β-Ga₂O₃ at T= 0 K without zero-point renormalization (ZPR), 0 K with ZPR, and 900 K. All isosurfaces are shown at the value of 1.5 × 10⁻⁴ e·Å⁻³. Reproduced with permission from Ref. [42]. © 2023, AIP Publishing.

First-principles calculations have played a crucial role in the study of the electronic structure of wide bandgap semiconductors, and significant progress has been made in the prediction and optimization of the bandgap. By using advanced computational methods such as DFT, GW approximation, and hybrid functional methods, researchers can gain a deeper understanding of the electronic properties of wide bandgap semiconductors. In addition, emerging research methods such as high-throughput computing, machine learning, and defect engineering offer more opportunities for material design and performance optimization. With continued improvements in computational accuracy and the emergence of new methods, researchers are able to more precisely control the electronic properties of wide bandgap semiconductors, providing a solid theoretical foundation for their applications in fields such as high-power electronics, optoelectronics, and quantum computing.

2.2 Calculation of optical properties

Optical properties are one of the important characteristics of wide bandgap semiconductors, as they directly determine the potential applications of these materials in optoelectronic devices, including photodetectors, lasers, solar cells, and light-emitting diodes [59–61]. Through first-principles calculations, researchers can analyze the optical response of materials in detail, including absorption spectra, reflectance, and optical bandgap. This, in turn, provides theoretical support for the optimization of the materials' optoelectronic properties. The optical properties of wide bandgap semiconductors are closely related to their electronic structures; therefore, accurate prediction of optical properties is crucial for the design and application of the materials [62–64].

The accurate calculation of the optical properties of materials by DFT, especially the calculation and prediction of absorption spectra and optical bandgap, has gradually become a research hotspot. The GW-BSE method has an important position in this field and has become one of the standard methods for predicting optical properties. The GW-BSE method is a computational approach grounded in many-body perturbation theory, which is employed to investigate the quasiparticle and optical characteristics of materials [65–67]. It combines the GW approximation and the Bethe-Salpeter equation (BSE) to accurately calculate the bandgap and exciton properties of materials from first principles. The GW approximation, as previously mentioned, is a method used to calculate the quasiparticle properties of materials by approximating the electron self-energy to the quasiparticle energy and wave function. It is able to provide more accurate band gap values than conventional DFT. The BSE is mainly used to study the optical properties of materials, especially exciton effects. It has been demonstrated to be a highly effective tool for predicting the optical response of materials by considering the electron-hole interaction [68–70]. The BSE approach treats the electron-hole pair as a whole, known as an exciton, and calculates the energy and wave function of its excited state. The GW-BSE method integrates the GW approximation and BSE, enabling the simultaneous consideration of quasiparticle and exciton effects. It is widely regarded as one of the most precise methodologies for calculating quasiparticle and optical properties of condensed matter systems [65, 67, 71, 72]. Holzer et al. investigated how GW-BSE can be used to calculate molecular excitation energies in strong magnetic fields. They extend the application of these methods by introducing the Bethe-Salpeter equation with the GW approximation into calculations in strong magnetic fields. They also provide a new computational framework that can accurately describe molecular excitation energies and optical properties in the presence of strong magnetic fields [71]. In addition, the work is compared with reference data on the excited energies of the triplet states of 36 small to medium-sized molecules. The results verify the validity of the method under strong magnetic fields, demonstrating the significant effect of strong magnetic fields on the optical properties of molecules. Excitation energy calculations for different molecules under strong magnetic field conditions yielded significant changes in the optical properties. As demonstrated in Fig. 4, the color of tetracene undergoes a transition from orange to green as the magnetic field strength increases from 0 to 9000 T. This color change can be accurately predicted by the GW-BSE method. The calculation of the excitation energy of a strong magnetic field based on the GW-BSE method proposed by Holzer et al. establishes a novel theoretical framework for the study of the optical properties of molecules in extreme environments. This work not only expands the application of the GW-BSE method but also provides a powerful tool for the accurate characterization of the optical properties of molecules under strong magnetic fields. Future studies can build on this foundation to further explore the excitation energy spectra and optical behaviors of different types of molecules, especially complex molecular systems, in high-intensity magnetic fields. With the continuous development of computational methods, combined with more efficient many-body theories and modern computational techniques, it is expected to be able to deal with larger and more complex molecular systems and to reveal the far-reaching effects of magnetic fields on the excitation energies of molecules.

Figure 4 Magnetic field modulation of tetracene's optical properties: Spectral shifts, excitation wavelengths, and color evolution. (a) UV/vis spectra of tetracene as predicted at different magnetic field strengths between 0 T and 9000 T. Solid lines denote calculations using the CD-evGW(10)/BSE@BHLYP method while dashed lines denote CD-evGW(10)/BSE@CAM-B3LYP calculations. (b) Wavelengths of the relevant lowest vertical excitations of tetracene at different magnetic field strengths between 0 T and 9000 T. The p-excitation, which is predominantly responsible for the color of tetracene, is most affected by the external field. Solid lines denote calculations using the CD-evGW(10)/BSE@BHLYP method, while dashed lines denote CD-evGW(10)/BSE@CAM B3LYP calculations. (c) Color of tetracene as predicted at the CD-evGW(10)/BSE@CAM-B3LYP level of theory at different magnetic field strengths between 0 T and 9000 T. To obtain the depicted colors, the vertical excitations of the optical spectrum were broadened by 0.15 eV and converted into an RGB color code while the intensity was scaled relative to the zero-field by integrating over the visible region of the spectrum. Reproduced with permission from Ref. [71]. © 2021, Frontiers.

The GW-BSE method has been successful in calculating the optical properties of materials. However, we should also pay attention to the selective modulation of optical properties by heterojunctions and strains, and so on [73–77]. Feng et al. found that the strain of the material can have an important effect on the optical properties. For example, Feng et al. studied the electronic and optical properties of van der Waals heterostructures stacked with g-ZnO and Janus-WSSe monolayers using VASP to calculate their properties [78]. They used the hybridized, generalized Heyd-Scuseria-Ernzerhof (HSE) method to obtain more accurate band gap values. The electronic structure and band alignment of AB-stacked g-ZnO/Janus-WSSe heterostructures are discussed in the work. It is found that the configuration has a typical type II band alignment, i.e., the conduction band minimum (CBM) and the valence band maximum (VBM) are in different materials. This band alignment facilitates the separation of photogenerated electrons and holes, thus improving the photocatalytic efficiency. In addition, due to the difference in the figure of merit between g-ZnO and Janus-WSSe (ΔΦ = 0.533 eV), electrons are transferred from the g-ZnO layer to the Janus-WSSe layer, forming an intrinsic built-in electric field. This built-in electric field promotes the separation of photogenerated electron-hole pairs, which enhances the photocatalytic efficiency. A similar enhancement mechanism was observed in the S-type heterojunction of amorphous/crystalline carbon nitride, where the optimized interfacial charge transfer led to a significant improvement in the reduction efficiency of CO₂ [79]. Interestingly, the optical absorption coefficients of the AA-stacked and AB-stacked heterostructures show unique characteristics under different strains. Negative stretching increases the ultraviolet (UV) absorption and decreases the visible absorption, while positive stretching decreases the UV absorption and increases the visible absorption. Furthermore, the AB-stacked g-ZnO/Janus-WSSe heterostructure exhibits excellent photocatalytic water decomposition. The photoexcited electrons were transferred to the conduction band of the Janus-WSSe layer, while the photoexcited holes were transferred to the valence band of the g-ZnO layer. In the Janus WSSe layer, the collected photoexcited holes can drive the generation of oxygen; in the g-ZnO layer, the collected photoexcited electrons can drive the generation of hydrogen.

van der Waals heterostructures can be formed by stacking different two-dimensional materials. The combination of two or more materials into a heterojunction can effectively modulate the electronic and optical properties of the material [80–83]. While heterostructure engineering focuses on interfacial effects, chemical doping provides an alternative pathway for optical tuning. He et al. systematically compared Cr doping positions (center, radius ½, surface) in ZnSe nanowires (NWs) (Fig. 5), revealing that mid-gap defect states from Cr(d)-Se(p) hybridization dominate absorption characteristics [84]. Their Bader charge analysis (Fig. 6) further shows localized charge redistribution around dopants, creating defect-induced absorption peaks distinct from heterojunction-mediated modifications. This approach often achieves a better result and is a hot research topic in the academic community. In 2023, Mustafa et al. investigated the electronic and optical properties of photodetectors based on multilayer graphene/MoS₂ heterostructures [85]. Their work systematically investigated the electronic and optical properties of multilayer graphene/MoS₂ heterostructures. The results show that the band gap of MoS₂ can be significantly tuned by introducing graphene layers, which can be reduced by up to 36.3 meV, making the heterostructures promising for applications in photodetectors. Meanwhile, the optical absorption coefficients of the graphene/MoS₂-based heterostructures are significantly enhanced in the visible to ultraviolet region, especially at 1551 nm (0.8 eV) and 1240 nm (1 eV), indicating an enhanced light absorption capability in these wavelength ranges. In addition, these heterostructures exhibit nonlinear optical behavior from the infrared to the visible region, which has important implications for photonic devices, especially photodetectors.

Figure 5 The cross-section of the optimized NW structure and all types of doping positions. The bule ball is Cr atoms. Reproduced with permission from Ref. [84]. © 2023, Elsevier.

Figure 6 Bader charge analysis: (a) ZnSe NWs and (b) Cr²⁺: ZnSe NWs. Reproduced with permission from Ref. [84]. © 2023, Elsevier.

From the above, we can realize that optical property calculations are the key to understanding and optimizing the optoelectronic performance of wide bandgap semiconductors. With the advancement of computational methods, especially the application of GW-BSE method, researchers are able to predict the optical response of wide bandgap semiconductors more accurately. In addition, the influence of factors such as heterojunction, stress modulation, and surface interfacial effects on the optical properties has become a hot topic of current research. Through these studies, more accurate theoretical support and design guidance can be provided for the application of wide-bandgap semiconductors in optoelectronic devices.

2.3 Calculation of thermal properties

As one of the core research areas in condensed matter physics and materials science, the thermal properties of materials are directly related to key engineering and technological issues such as energy conversion efficiency, reliability of electronic devices, and thermal protection systems in aerospace. Traditional experimental methods for measuring thermal conductivity, thermal expansion coefficient, and lattice vibrational properties face many challenges: the difficulty of in-situ characterization under extreme conditions (high temperature/high pressure), the bottleneck of accurate quantification of the interfacial thermal resistance of low-dimensional materials, and the limitations in analyzing the heat transport mechanism of new complex compounds. In this context, first-principle computational methods, with their unique advantages based on the fundamental principles of quantum mechanics, have gradually emerged as an important research paradigm for revealing the microscopic mechanisms of the thermal properties of materials. It is well known that thermal properties are key indicators of the stability and application performance of wide bandgap semiconductors in high-temperature environments [86–88]. Recent experimental breakthroughs in the thermal management of AlN further validate this thesis. Alvarez-Escalante et al. demonstrated that homoepitaxial AlN thin films achieve exceptional thermal conductivity up to 195.71 W·m^–1·K^–1 at 1 μm thickness (Fig. 7(a)), approaching 57% of the bulk theoretical value (340 W·m^–1·K^–1) [89]. Remarkably, their frequency domain thermoreflectance (FDTR) measurements revealed ultrahigh thermal boundary conductance (G) exceeding 2590 MW·m^–2·K^–1) for 3 μm films (Fig. 7(b)), attributed to atomic-level interface control via Al-assisted surface cleaning. This represents a 10-fold improvement over heteroepitaxial systems like GaN/SiC (G≈230 MW·m^–2·K^–1), effectively overcoming the interfacial resistance bottleneck in traditional low-dimensional materials. With the increasing application of semiconductor materials in high-power electronic devices, optoelectronic devices, and thermoelectric devices, it becomes particularly important to accurately calculate and optimize the thermal properties of materials, such as thermal conductivity, specific heat capacity, and thermal expansion [90–93]. Thermal properties are directly related to the thermal stability, thermal diffusivity, and energy conversion efficiency of materials at high temperatures [94, 95]. Therefore, first-principles calculations provide a powerful theoretical tool to study these properties and are especially indispensable in the design and performance optimization of wide bandgap semiconductor materials.

Figure 7 (a) Comparison between the calculated k based on first-principles calculations and measured k based on domain thermoreflectance (FDTR) (thickness dependence of AlN). The red square indicates homoepitaxially grown AlN samples impacted by surface pits (i.e., material defects), while the green square indicates homoepitaxially grown AlN samples with a negligible surface pit impact. (b) Comparison of thermal conductance among various WBG and ultra-wide bandgap (UWBG) thin films/substrate reports β-Ga₂O₃/diamond, GaN/SiC, GaN-AlN/SiC, GaN-AlN/Si, diamond-SiN/GaN, diamond-Si₃N₄/GaN, diamond/Si, and AlN/AlN (magenta squares, data by FDTR) from this work with respective error bars. The red square indicates homoepitaxially grown AlN samples impacted by surface pits (i.e., material defects). The green square indicates the ultrahigh G₂ of the 1 and 3 μm samples. Reproduced with permission from Ref. [89]. © 2022, AIP Publishing.

In 1996, Mahan and Sofo presented a study on maximizing the eutectic value of thermoelectric materials by optimizing the electronic structure [96]. They unified the electrical conductivity, thermal potential, and thermal conductivity as integrals of a transport distribution function and derived a mathematical function of the transport distribution that maximizes the optimum value. Specifically, they used the Boltzmann equation to describe the transport coefficients and introduced a transport distribution function related to the velocity, lifetime, and dispersion relations of the electron population. By using a transport distribution in the form of a delta function, the thermoelectric optimum can be maximized. This suggests that the electron energy distribution involved in the transport process should be as narrow as possible to achieve higher thermoelectric efficiency. This study provides a new theoretical perspective for the design of high-efficiency thermoelectric materials, which is of great significance for the subsequent improvement of the optimum value of thermoelectric materials.

In addition, DFT calculations show significant potential in the study of the thermal properties of two dimensional (2D) materials. Tang et al. found that nanohoneycomb-pleated PbTe monolayers have very low lattice thermal conductivity (0.75–0.79 W·m^–1·K^–1 at 900 K) and high electron mobility (499.552 cm²·V^–1·s^–1) through an in-depth study of PbTe [97]. They calculated the phonon dispersion relation using density functional perturbation theory (DFPT), confirmed the kinetic stability of the system, and quantified the phonon scattering effect. The folded structure induces strong phonon anharmonicity, which reduces the lattice thermal conductivity at 900 K to 0.75–0.79 W·m^–1·K^–1, which is two orders of magnitude lower than that of conventional bulk materials. Combined with Boltzmann transport theory calculations, the system exhibits a Seebeck coefficient of 1.574 mV·K^–1 and a thermoelectric figure of merit (ZT) of 1.55 in the 300–900 K range. The performance enhancement is mainly attributed to the optimization of carrier transport under electron-phonon coupling. This study has successfully established a theoretical correlation model from the atomic-scale electronic structure to the mesoscale thermal transport properties, which provides a quantitative research framework for the rational design of low-dimensional thermoelectric materials. Further, recent advances in structural design further demonstrate the versatility of 2D materials in thermal-electronic coupling. Zhao et al. systematically investigated strain-modulated anomalous thermal transport in porous buckled X-AlN (X=C, Si, TC) monolayers through evolutionary structural search and first-principles calculations [98]. As shown in Fig. 8(a) of their work, the lattice thermal conductivity of TC-AlN reached 123.75 W·m^–1·K^–1 at 300 K, 17 times higher than pristine AlN, due to strong covalent bonds suppressing out-of-plane phonon scattering. Remarkably, their Fig. 8(b) revealed a non-monotonic thermal conductivity response under biaxial strain: an initial increase peaking at 4% strain (165 W·m^–1·K^–1) followed by decline, arising from competition between enhanced N-N bond strength reducing anharmonicity and phonon mode softening at higher strains. This strain-engineered thermal switching mechanism provides new insights for dynamically controlling heat dissipation in semiconductor devices. Notably, reducing the dimensionality of the material to two dimensions has also been shown to be an effective way to improve the thermodynamic stability. Li et al. predicted two BeH₂ monolayer structures (α-BeH₂ and β-BeH₂) by performing a global search via a particle swarm optimization method and found that these two structures have high thermodynamic stability and mechanical strength [99]. The study also unexpectedly found that α-BeH₂ has a negative Poisson's ratio, which is rare in 2D materials. Since the beryllium hydride monolayer has the same number of electrons as graphene, its 2D structure is highly feasible in experiments, which provides a strong theoretical basis for the experimental preparation of monolayer BeH₂. The above studies have successfully revealed the microscopic mechanism of the material properties at the theoretical level, providing a new perspective for further understanding the physical connotation of the materials.

Figure 8 Strain modulates lattice thermal conductivity in holey crumpled AlN systems and reveals doping-dependent responses under varying strains. (a) Lattice thermal conductivity at 300 K of holey crumpled surface, AlN vs. X-AlN (X=C, Si, TC). (b) Lattice thermal conductivity of X-AlN (X=C, Si, TC) at 300 K at different strains. Reproduced with permission from Ref. [98]. © 2023, Science Press.

The thermal properties of materials are a key area of research in condensed matter physics and materials science, directly affecting the efficiency of energy conversion and a wide range of engineering applications. In polymer nanocomposites, morphologically tailored nanostructures have been shown to achieve exceptional breakdown field strength (>10 MV·cm^–1) alongside giant electrocaloric effects, illustrating the universal value of microstructure design in thermal-electrical property optimization [100]. Traditional experimental methods have significant limitations in in-situ characterization under extreme conditions of high temperature and pressure, in quantifying thermal resistance at low-dimensional material interfaces, and in resolving heat transport mechanisms in complex materials. First-principles calculation, with its essential advantages based on quantum mechanics, provides a powerful tool for revealing the microscopic mechanisms of the thermal properties of materials. It is particularly important for the systematic understanding of thermal properties such as thermal conductivity, specific heat capacity, and thermal expansion of materials. Through first-principles calculations, the thermal behavior of materials in complex environments can be accurately predicted, and on this basis, materials design and performance optimization can be carried out, providing theoretical basis and guidance for the research and development of high-efficiency thermoelectric materials, wide-bandgap semiconductors, and novel low-dimensional materials, and promoting the continuous development of the frontiers of materials science.

2.4 Doping and defect engineering

Doping and defect engineering is a fundamental strategy for optimizing the performance of wide bandgap semiconductors. This approach is achieved through precise control of energy band structures, effective modulation of carrier concentrations, and strategic management of surface states, etc., which collectively enhance material functionality [101–105]. By implementing elemental doping strategies (e.g., rare earth ion implantation or transition metal substitution) as well as controllable defect construction (including vacancy defects and dislocation modulation, etc.), researchers are able to achieve precise modulation of material properties [106–109]. Taking GaN-based compounds and wide bandgap oxide systems in third-generation semiconductor materials as an example, advanced defect engineering design not only significantly improves carrier mobility (1000–1500 cm²·V^–1·s^–1) and breakdown field strength (>3 MV·cm^–1), but also realizes linear enhancement of photoelectric response in the visible-ultraviolet region (about 40% increase in external quantum efficiency (EQE)) through defect energy level modulation [110–112]. Recent advances in defect stabilization mechanisms further expand the scope of defect engineering. Ivády et al. demonstrated that quantum wells formed by Frank-type stacking faults in 4H-SiC can stabilize divacancy spin qubits by locally lowering the conduction band minimum (~0.24 eV reduction) through polytypic 6H-SiC inclusions (Fig. 9). This quantum confinement effect enables selective ionization of divacancy dark states (VV⁻) under optical excitation, significantly enhancing charge state stability during room-temperature spin manipulation [113]. Such crystallographically engineered environments provide a materials-centric solution to persistent challenges in photoionization-induced charge fluctuations. In addition, recent advances in 2D van der Waals semiconductors, such as CrSCl with intrinsic p-type conductivity and multipolarity coexistence, further demonstrate the potential of defect engineering beyond conventional doping paradigms [114]. This micro-regulation technology has been successfully applied to high-power electronic devices, deep-ultraviolet LEDs, photovoltaic catalysis and other cutting-edge fields, and the industrialization conversion rate of relevant research results has been increased by nearly 70% compared with the traditional process, promoting the continuous development of wide bandgap semiconductor materials toward high integration and low energy consumption.

Figure 9 Comparison of light-state and dark-state dynamical mechanisms of quantum systems under optical excitation and energy band structure of defective 4H-SiC containing layer faults. (a) Mechanisms of light and dark state dynamics of quantum systems under optical excitation. a. A bright state of a color center under optical excitation. b. These incident photons may ionize the defect and turn it into a dark state, while. c. does not have sufficient energy to repopulate the bright state. d. In a quantum well, however, the excitation laser can successfully re-pump the bright state. (b) Band structure of a defective 4H-SiC including a stacking fault. Red curves depict bulk-like conduction and valence band states in the basal plane of the hexagonal Brillouin zone. Purple curves show the stacking fault states that localized in the c direction and are dispersive in the basal plane. Reproduced with permission from Ref. [113]. ©2019, Springer Nature.

Along this technological path, diamond, as a typical wide-band semiconductor material, shows significant advantages in the field of miniaturization of high-power electronic devices by virtue of its ultra-high breakdown field strength (>10 MV·cm^–1) and excellent carrier mobility (≥2000 cm²·V^–1·s^–1) [115]. Although significant progress has been made in boron-doped p-type diamond (BDD), efficient n-type doping is still a key technological bottleneck limiting the development of diamond devices due to the high dissociation energy property of the donor impurity. To address this challenge, Liu's research team successfully prepared boron-rich layers of 1–1.5 μm thickness on the (111) crystal surface of boron-doped diamond single crystals using the temperature gradient growth (TGG) method [116]. This study shows that by precisely tuning the experimental parameters during diamond crystallization, the controllable formation of B-O complexes can be achieved, which in turn induces the material to exhibit n-type conducting properties. Mechanistic analysis based on first-principles calculations indicates that the B₃O and B₄O complexes form shallow donor energy levels in the diamond lattice, which is essentially responsible for the n-type semiconductor behavior. It is particularly noteworthy that the formation energies of these two complexes are as low as – 4.27 eV and – 6.05 eV, respectively, indicating their significant thermodynamic formation advantage in the diamond system. Further comparative analysis confirms that the B₄O complexes have the lowest formation energies compared to other defect configurations, thus dominating the crystal growth process. This study successfully breaks the technical bottleneck of n-type diamond preparation by innovatively introducing the doping strategy of B-O complexes, which provides a new research direction for the development of diamond-based semiconductor devices. This work not only elucidates the electronic structure regulation mechanism of the compound defects but also lays an important theoretical foundation for the subsequent performance optimization of diamond electronic devices.

Besides diamond, cubic boron nitride (c-BN) is another semiconductor material with great application potential. They serve as promising ultra-wideband semiconductors in the field of high-power, high-frequency electronics, and experimental measurements of their carrier mobility have long differed significantly. To elucidate the intrinsic physical mechanisms, Sanders's team systematically revealed the microscopic properties of carrier transport in these two types of materials and their governing laws for device performance through a first-principles approach [117]. In the study, density functional theory combined with many-body perturbation theory (G₀W₀ quasiparticle correction) was used to accurately calculate. It obtains the bandgap values of 5.66 eV and 6.80 eV for diamond and c-BN, respectively. It is found that the phonon-limited electron mobility at room temperature is similar for both materials (diamond: 1790 cm²·V^–1·s^–1, c-BN: 1610 cm²·V^–1·s^–1) by density functional perturbation theory using the maximally localized Wannier function method, but the hole mobility of c-BN (80.4 cm²·V^–1·s^–1) shows a two order of magnitude difference compared to that of diamond (1970 cm²·V^–1·s^–1). The phenomenon is attributed to the strong inelastic scattering effect induced by the significant increase in the effective mass of holes at the top of the c-BN valence band. The study also reveals the dynamic evolution properties of the carrier scattering mechanism: lattice scattering dominates in the low temperature region, while neutral impurity scattering becomes the main constraint at high doping concentrations. The theoretical model predicts the n-type c-BN and p-type diamond mobility with an error of less than 20%, verifying the reliability of the computational framework. This work not only elucidates the competition mechanism between intrinsic scattering and defect scattering in ultra-wide bandwidth semiconductors but also points out that the inherent hole mobility defect of c-BN will seriously limit its application prospects in bipolar devices, providing theoretical guidance for material performance optimization.

The above systematically discusses the intrinsic properties of two types of typical wide-band semiconductor materials and reveals the regulatory mechanisms of doping and defect engineering on their energy band structures and carrier transport properties. In-depth analysis reveals that the key scientific issues that constrain the performance enhancement of these semiconductor devices focus on the precise analysis of defect behavior and the effective suppression of their harmful effects. Using hybridization density functional theory calculations, Gao et al. systematically investigated the local structural relaxation properties, formation energy evolution laws, and their electron migration properties of neutral/charged intrinsic point defects (including vacancy, interstitial, and antisite defects) in GaN, AlN, and InN crystal systems [118]. By comparing the jump energy levels associated with the Fermi energy levels, it is found that Ga interstitial, nitrogen vacancy, N interstitial, In antisite, and In interstitial in the GaN system are stable only in the positive charge state with a donor energy level. While In vacancy are more stable in the neutral state, the other defects show both donor and acceptor behavior. Theoretical analysis of defect states shows that nitrogen vacancy in p-type nitrides and gallium/aluminum vacancy in n-type nitrides are the most stable defect configurations, a finding that provides a microscopic explanation for self-compensating effects in nitride materials and elucidates the physical cause of defect-induced n/p-type doping efficiency decay. It is also confirmed that the diffusion rate of nitrogen interstitials is significantly higher than that of vacancy defects, which directly leads to the low concentration characteristic of nitrogen interstitials and nitrogen-based defect complexes in nitrides. It is particularly noteworthy that the trends of formation energies, jump energy levels, and migration barriers of nitrides show significant correlations with their intrinsic atomic sizes and the width of the bandgap. The theoretical framework for defect identification and control established in this work is of great importance in guiding the performance optimization and reliability enhancement of nitride semiconductor devices.

Doping and defect engineering play a critical role in the performance modulation of broadband semiconductor materials, the core of which lies in the precise modulation of energy band structure, carrier dynamics and defect behavior through atomic-scale design. Using diamond and cubic boron nitride (c-BN) as examples, the study reveals the intrinsic constraints on carrier mobility in ultrawide-bandgap semiconductors: Although diamond has excellent carrier transport properties, its n-type doping has long been limited by the high dissociation energy of the sizing impurity, and innovative doping strategies based on the B-O complexes provide a new way to break the bottleneck by constructing a shallow sizing energy level; while in c-BN, the significant increase in the effective mass of the hole leads to a significant increase in the effective mass of the hole. The significant increase in effective mass leads to a sharp decrease in hole mobility, highlighting the inherent defects of its bipolar device applications. In nitride semiconductors, the defect-induced self-compensation effect and the dynamic evolution characteristics further reveal the microscopic roots of the doping efficiency decay. Complementary studies on GaN systems highlight the tunability of defect-mediated properties. Liao et al. systematically investigated C_N point defects in GaN NWs, revealing their dual role in enhancing electrical conductivity (1.15×10¹⁴ W·m^–1·K^–1 at 700 K) while suppressing Seebeck coefficients (0.0008 V·K⁻¹ at 700 K). As shown in Figs. 10(a) and 10(b), the increased density of states near the Fermi level from C(p)-N(p) orbital hybridization drives these effects, offering a trade-off strategy for optimizing thermoelectric performance [119]. Theoretical calculations based on the ab initio methods have deeply resolved the correlation mechanism between defect formation energy and electronic structure, providing an important theoretical basis for suppressing harmful defects and optimizing doping paths. Taken together, these studies show that the synergistic design of atomic-level defect engineering and energy-band engineering, which reconciles the contradiction between intrinsic material properties and doping regulation, is the key way to advance wide bandgap semiconductors toward high-performance and high-reliability devices.

Figure 10 Changes in electrical conductivity of GaN NWs: (a) Intrinsic GaN NWs and (b) GaN NWs containing C_N point defects. Reproduced with permission from Ref. [119]. © 2023, Elsevier.