Effects of tumour heterogeneous properties on modelling the transport of radiative particles

Dose calculation plays a critical role in radiotherapy (RT) treatment planning, and there is a growing need to develop accurate dose deposition models that incorporate heterogeneous tumour properties. Deterministic models have demonstrated their capability in this regard, making them the focus of recent treatment planning studies as they serve as a basis for simplified models in RT treatment planning. In this study, we present a simplified deterministic model for photon transport based on the Boltzmann transport equation (BTE) as a proof-of-concept to illustrate the impact of heterogeneous tumour properties on RT treatment planning. We employ the finite element method (FEM) to simulate the photon flux and dose deposition in real cases of diffuse intrinsic pontine glioma (DIPG) and neuroblastoma (NB) tumours. Importantly, in light of the availability of pipelines capable of extracting tumour properties from magnetic resonance imaging (MRI) data, we highlight the significance of such data. Specifically, we utilise cellularity data extracted from DIPG and NB MRI images to demonstrate the importance of heterogeneity in dose calculation. Our model simplifies the process of simulating a RT treatment system and can serve as a useful starting point for further research. To simulate a full RT treatment system, one would need a comprehensive model that couples the transport of electrons and photons.

Insight into Scattering Mechanisms and Transport Properties of AgCuS for Flexible Thermoelectric Applications

The development of flexible thermoelectric devices requires materials possessing ductility and high thermoelectric performance at room temperature. However, only a few existing materials meet both criteria. In this study, the ductile properties, electronic structure, and transport properties of the low-temperature phase α-AgCuS were elucidated using first-principles calculations combined with Boltzmann transport theory. With a layered zigzag structure similar to the well-known ductile semiconductor Ag2S, AgCuS is determined to have good metal-like ductility. Through consideration of various intrinsic scattering mechanisms, we found that electron-polar optical phonon interactions have the most significant impact on the transport behavior of AgCuS. The predominance of this type of interaction is also disclosed by the covalent-ionic bonding nature of the Ag-S and Cu-S bonds. Therefore, weakening this interaction via doping or alloying could optimize the thermoelectric performance of the system. At room temperature, a maximum dimensionless figure of merit ZT of up to 0.592 could be achieved under a tuning of hole concentration to 2 × 1019 cm-3, suggesting that α-AgCuS could be a promising p-type candidate for flexible thermoelectric applications.

High Thermoelectric Performance of a Novel γ-PbSnX2 (X = S, Se, Te) Monolayer: Predicted Using First Principles

Two-dimensional (2D) group IV metal chalcogenides are potential candidates for thermoelectric (TE) applications due to their unique structural properties. In this paper, we predicted a 2D monolayer group IV metal chalcogenide semiconductor γ-PbSn₂ (X = S, Se, Te), and first-principles calculations and Boltzmann transport theory were used to study the thermoelectric performance. We found that γ-PbSnX₂ had an ultra-high carrier mobility of up to 4.04 × 10³ cm² V^-1 s^-1, which produced metal-like electrical conductivity. Moreover, γ-PbSn₂ not only has a very high Seebeck coefficient, which leads to a high power factor, but also shows an intrinsically low lattice thermal conductivity of 6-8 W/mK at room temperature. The lower lattice thermal conductivity and high power factors resulted in excellent thermoelectric performance. The ZT values of γ-PbSnS₂ and γ-PbSnSe₂ were as high as 2.65 and 2.96 at 900 K, respectively. The result suggests that the γ-PbSnX₂ monolayer is a better candidates for excellent thermoelectric performance.

Phonon Dominated Thermal Transport in Metallic Niobium Diselenide from First Principles Calculations

Niobium diselenide (NbSe₂) is a layered transition metal dichalcogenide material which possesses unique electrical and superconducting properties for future nanodevices. While the superconducting, electrical, and bulk thermal transport properties of NbSe₂ have been widely studied, the in-plane thermal transport property of NbSe₂, which is important for potential thermoelectric applications, has not been thoroughly investigated. In this report, we study the lattice in-plane thermal transport of 2D NbSe₂ by solving the phonon Boltzmann transport equation with the help of the first principles calculation. The thermal conductivity obtained at room temperature is 12.3 W/mK. A detailed analysis shows that the transverse acoustic phonon dominates the lattice thermal transport, and an anomalously small portion of electron contribution to the total thermal conductivity is observed for this metallic phase. The results agree well with experimental measurements and provide detailed mode-by-mode thermal conductivity contribution from different phonon modes. This study can provide useful information for integrating NbSe₂ in nanodevices where both electrical and thermal properties are critical, showing great potential for integrating monolayer NbSe₂ to thermoelectric devices.

Electron Heat Source Driven Heat Transport in GaN at Nanoscale: Electron-Phonon Monte Carlo Simulations and a Two Temperature Model

The thermal energy transport in semiconductors is mostly determined by phonon transport. However in polar semiconductors like GaN electronic contribution to the thermal transport is non-negligible. In this paper, we use an electron–phonon Monte Carlo (MC) method to study temperature distribution and thermal properties in a two-dimensional GaN computational domain with a localized, steady and continuous electron heat source at one end. Overall, the domain mimics the two-dimensional electron gas (2DEG) channel of a typical GaN high electron mobility transistor (HEMT). High energy electrons entering the domain from the source interact with the phonons, and drift under the influence of an external electric field. Cases of the electric field being uniform and non-uniform are investigated separately. A two step/temperature analytical model is proposed to describe the electron as well as phonon temperature profiles and solved using the finite difference method (FDM). The FDM results are compared with the MC results and found to be in good agreement.

Anharmonic lattice dynamics and thermal transport in type-I inorganic clathrates

The anharmonic phonon properties of type-I filled inorganic clathrates Ba₈Ga₁₆Ge₃₀and Sr₈Ga₁₆Ge₃₀are obtained from the first-principles calculations by considering the temperature-dependent sampling of the potential energy surface and quartic phonon renormalization. Owing to the weak binding of guest atoms with the host lattice, the obtained guest modes undergo strong renormalization with temperature and become stiffer by up to 50% at room temperature in Sr₈Ga₁₆Ge₃₀. The calculated phonon frequencies and associated thermal mean squared displacements are comparable with experiments despite the on-centering of guest atoms at cage centers in both clathrates. Lattice thermal conductivities are obtained in the temperature range of 50-300 K accounting for three-phonon scattering processes and multi-channel thermal transport. The contribution of coherent transport channel is significant at room temperature (13% and 22% in Ba₈Ga₁₆Ge₃₀and Sr₈Ga₁₆Ge₃₀) but is insufficient to explain the experimentally observed glass-like thermal transport in Sr₈Ga₁₆Ge₃₀.

High Thermoelectric Performance in Two-Dimensional Janus Monolayer Material WS-X (X = Se and Te)

In the present work, Janus monolayers WSSe and WSTe are investigated by combining first-principles calculations and semiclassical Boltzmann transport theory. Janus WSSe and WSTe monolayers show a direct band gap of 1.72 and 1.84 eV at K-points, respectively. These layered materials have an extraordinary Seebeck coefficient and electrical conductivity. This combination of high Seebeck coefficient and high electrical conductivity leads to a significantly large power factor. In addition, the lattice thermal conductivity in the Janus monolayer is found to be relatively very low as compared to the WS₂ monolayer. This leads to a high figure of merit (ZT) value of 2.56 at higher temperatures for the Janus WSTe monolayer. We propose that the Janus WSTe monolayer could be used as a potential thermoelectric material due to its high thermoelectric performance. The result suggests that the Janus monolayer is a better candidate for excellent thermoelectric conversion.

Symmetry Breaking Induced Anisotropic Carrier Transport and Remarkable Thermoelectric Performance in Mixed Halide Perovskites CsPb(I1-xBrx)3

We present a combination of first-principles calculations and the Boltzmann transport theory to understand the carrier transport and thermoelectric performance of mixed halide perovskite alloys CsPb(I_1-xBr_x)₃ with different Br compositions. Our computational results correlate the conduction band splitting in CsPb(I_1-xBr_x)₃ to the significant anisotropy in their carrier transport properties, such as effective masses and deformation potential constants. Such band splitting originates from the symmetry-broken crystal structures of CsPb(I_1-xBr_x)₃ polymorphs: with residue stresses/strains in asymmetric CsPb(I_1-xBr_x)₃, nondegenerate orbitals reconstruct the conduction band and reduce the Pb-halide antibonding character along certain directions. While the Seebeck coefficient (S) and the relaxation time-normalized electrical conductivity (σ/τ) show weak directional anisotropy, the carrier relaxation time (τ) is highly direction-dependent. The reconstruction of the conduction band finally leads to significantly anisotropic and enhanced thermoelectric power factors (PF = S²σ) in CsPb(I_1-xBr_x)₃ compared to those in pure CsPbI₃ and CsPbBr₃, showing anomalous nonlinear alloy behavior. A delicate balance between S²σ and combined measurement of the carrier effective mass and deformation potential constant, m*E_DP, is confirmed. The lattice thermal conductivities of CsPb(I_1-xBr_x)₃ are significantly suppressed compared to those of their pure counterparts due to strong mass disordering and strain fields upon halogen substitution. As a result, symmetry breaking in CsPb(I_1-xBr_x)₃ leads to anisotropy in carrier transport, high PF, and scattered phonon transport (ultralow thermal conductivity), concurrently contributing to their promising thermoelectric figures of merit (ZT) up to 1.7 at room temperature. The principles behind the asymmetry-induced factors would serve as new design concepts to tailor the thermoelectric properties of alloys, mixtures, superlattices, and low-dimensional materials.

Fractional-order heat conduction models from generalized Boltzmann transport equation

The relationship between fractional-order heat conduction models and Boltzmann transport equations (BTEs) lacks a detailed investigation. In this paper, the continuity, constitutive and governing equations of heat conduction are derived based on fractional-order phonon BTEs. The underlying microscopic regimes of the generalized Cattaneo equation are thereafter presented. The effective thermal conductivity κ_eff converges in the subdiffusive regime and diverges in the superdiffusive regime. A connection between the divergence and mean-square displacement 〈|Δx|²〉 ∼ t^γ is established, namely, κ_eff ∼ t^γ-1, which coincides with the linear response theory. Entropic concepts, including the entropy density, entropy flux and entropy production rate, are studied likewise. Two non-trivial behaviours are observed, including the fractional-order expression of entropy flux and initial effects on the entropy production rate. In contrast with the continuous time random walk model, the results involve the non-classical continuity equations and entropic concepts. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.

Achieving an Ultrahigh Power Factor in Sb2Te2Se Monolayers via Valence Band Convergence

An efficient approach to improve the thermoelectric performance of materials is to converge their electronic bands, which is known as band engineering. In this regard, lots of effort has been made to further improve the thermoelectric efficiency of bulk and exfoliated monolayers of Bi₂Te₃ and Sb₂Te₃. However, ultrahigh band degeneracy and thus significant improvement of the power factor have not yet been realized in these materials. Using first-principles methods, we demonstrate that the valley degeneracy of Bi₂Te₃ and Sb₂Te₃ can be largely improved upon substitution of the middle-layer Te atoms with the more electronegative S or Se atoms. Our detailed analysis reveals that in this family of materials, two out of four possible valence band valleys merely depend on the electronegativity of the middle-layer chalcogen atoms, which makes the independent modulation of the valleys' position feasible. As such, band alignment of Bi₂Te₃ and Sb₂Te₃ largely improves upon substitution of the middle-layer Te atoms with more electronegative, yet chemically similar, S and Se ones. A superior valence band alignment is attained in Sb₂Te₂Se monolayers where three out of four possible valleys are well aligned, resulting in a giant band degeneracy of 18 that holds the record among all thermoelectric materials. As a result, an outstanding power factor for the hole-doped monolayers is achieved, indicating a highly efficient p-type thermoelectric material.

Beyond the State of the Art: Novel Approaches for Thermal and Electrical Transport in Nanoscale Devices

Almost any interaction between two physical entities can be described through the transfer of either charge, spin, momentum, or energy. Therefore, any theory able to describe these transport phenomena can shed light on a variety of physical, chemical, and biological effects, enriching our understanding of complex, yet fundamental, natural processes, e.g., catalysis or photosynthesis. In this review, we will discuss the standard workhorses for transport in nanoscale devices, namely Boltzmann's equation and Landauer's approach. We will emphasize their strengths, but also analyze their limits, proposing theories and models useful to go beyond the state of the art in the investigation of transport in nanoscale devices.

High Thermoelectric Performance Originating from the Grooved Bands in the ZrSe3 Monolayer

Low-dimensional layered materials have attracted tremendous attentions because of their wide range of physical and chemical properties and potential applications in electronic devices. Using first-principles method taking into account the quasi-particle self-energy correction and Boltzmann transport theory, the electronic transport properties of the ZrSe₃ monolayer are investigated, where the carrier relaxation time is accurately calculated within the framework of electron-phonon coupling. It is demonstrated that the high power factor of the monolayer can be attributed to the grooved bands near the conduction band minimum. Combined with the low lattice thermal conductivity obtained by solving the phonon Boltzmann transport equation, a considerable n-type ZT value of ∼2.4 can be achieved at 800 K in the ZrSe₃ monolayer.

Phonon Transport through Nanoscale Contact in Tip-Based Thermal Analysis of Nanomaterials

Nanomaterials have been actively employed in various applications for energy and sustainability, such as biosensing, gas sensing, solar thermal energy conversion, passive radiative cooling, etc. Understanding thermal transports inside such nanomaterials is crucial for optimizing their performance for different applications. In order to probe the thermal transport inside nanomaterials or nanostructures, tip-based nanoscale thermometry has often been employed. It has been well known that phonon transport in nanometer scale is fundamentally different from that occurred in macroscale. Therefore, Fourier’s law that relies on the diffusion approximation is not ideally suitable for describing the phonon transport occurred in nanostructures and/or through nanoscale contact. In the present study, the gray Boltzmann transport equation (BTE) is numerically solved using finite volume method. Based on the gray BTE, phonon transport through the constriction formed by a probe itself as well as the nanoscale contact between the probe tip and the specimen is investigated. The interaction of a probe and a specimen (i.e., treated as a substrate) is explored qualitatively by analyzing the temperature variation in the tip-substrate configuration. Besides, each contribution of a probe tip, tip-substrate interface, and a substrate to the thermal resistance are analyzed for wide ranges of the constriction ratio of the probe.

Titanium Trisulfide Monolayer as a Potential Thermoelectric Material: A First-Principles-Based Boltzmann Transport Study

Good electronic transport capacity and low lattice thermal conductivity are beneficial for thermoelectric applications. In this study, the potential use as a thermoelectric material for the recently synthesized two-dimensional TiS₃ monolayer is explored by applying first-principles method combined with Boltzmann transport theory. Our work demonstrates that carrier transport in the TiS₃ sheet is orientation-dependent, caused by the difference in charge density distribution at band edges. Due to a variety of Ti-S bonds with longer lengths, we find that the TiS₃ monolayer shows thermal conductivity much lower compared with that of transition-metal dichalcogenides such as MoS₂. Combined with a high power factor along the y-direction, a considerable n-type ZT value (3.1) can be achieved at moderate carrier concentration, suggesting that the TiS₃ monolayer is a good candidate for thermoelectric applications.

First-Principles Prediction of Ultralow Lattice Thermal Conductivity of Dumbbell Silicene: A Comparison with Low-Buckled Silicene

The dumbbell structure of two-dimensional group IV material offers alternatives to grow thin films for diverse applications. Thermal properties are important for these applications. We obtain the lattice thermal conductivity of low-buckled (LB) and dumbbell (DB) silicene by using first-principles calculations and the Boltzmann transport equation for phonons. For LB silicene, the calculated lattice thermal conductivity with naturally occurring isotope concentrations is 27.72 W/mK. For DB silicene, the calculated value is 2.86 W/mK. The thermal conductivity for DB silicene is much lower than LB silicene due to stronger phonon scattering. Our results will induce further theoretical and experimental investigations on the thermoelectric (TE) properties of DB silicene. The size-dependent thermal conductivity in both LB and DB silicene is investigated as well for designing TE devices. This work sheds light on the manipulation of phonon transport in two-dimensional group IV materials by dumbbell structure formed from the addition of adatoms.

Disparate Strain Dependent Thermal Conductivity of Two-dimensional Penta-Structures

Two-dimensional (2D) carbon allotrope called penta-graphene was recently proposed from first-principles calculations and various similar penta-structures emerged. Despite significant effort having been dedicated to electronic structures and mechanical properties, little research has been focused on thermal transport in penta-structures. Motivated by this, we performed a comparative study of thermal transport properties of three representative pentagonal structures, namely penta-graphene, penta-SiC2, and penta-SiN2, by solving the phonon Boltzmann transport equation with interatomic force constants extracted from first-principles calculations. Unexpectedly, the thermal conductivity of the three penta-structures exhibits diverse strain dependence, despite their very similar geometry structures. While the thermal conductivity of penta-graphene exhibits standard monotonic reduction by stretching, penta-SiC2 possesses an unusual nonmonotonic up-and-down behavior. More interestingly, the thermal conductivity of penta-SiN2 has 1 order of magnitude enhancement due to the strain induced buckled to planar structure transition. The mechanism governing the diverse strain dependence is identified as the competition between the change of phonon group velocity and phonon lifetime of acoustic phonon modes with combined effect from the unique structure transition for penta-SiN2. The disparate thermal transport behavior is further correlated to the fundamentally different bonding nature in the atomic structures with solid evidence from the distribution of deformation charge density and more in-depth molecular orbital analysis. The reported giant and robust tunability of thermal conductivity may inspire intensive research on other derivatives of penta-structures as potential materials for emerging nanoelectronic devices. The fundamental physics understood from this study also solidifies the strategy to engineer thermal transport properties of broad 2D materials by simple mechanical strain.

A review of recent advances in the spherical harmonics expansion method for semiconductor device simulation

The Boltzmann transport equation is commonly considered to be the best semi-classical description of carrier transport in semiconductors, providing precise information about the distribution of carriers with respect to time (one dimension), location (three dimensions), and momentum (three dimensions). However, numerical solutions for the seven-dimensional carrier distribution functions are very demanding. The most common solution approach is the stochastic Monte Carlo method, because the gigabytes of memory requirements of deterministic direct solution approaches has not been available until recently. As a remedy, the higher accuracy provided by solutions of the Boltzmann transport equation is often exchanged for lower computational expense by using simpler models based on macroscopic quantities such as carrier density and mean carrier velocity. Recent developments for the deterministic spherical harmonics expansion method have reduced the computational cost for solving the Boltzmann transport equation, enabling the computation of carrier distribution functions even for spatially three-dimensional device simulations within minutes to hours. We summarize recent progress for the spherical harmonics expansion method and show that small currents, reasonable execution times, and rare events such as low-frequency noise, which are all hard or even impossible to simulate with the established Monte Carlo method, can be handled in a straight-forward manner. The applicability of the method for important practical applications is demonstrated for noise simulation, small-signal analysis, hot-carrier degradation, and avalanche breakdown.

First-Principles Prediction of the Charge Mobility in Black Phosphorus Semiconductor Nanoribbons

We have investigated the electronic structure and carrier mobility of monolayer black phosphorus nanoribbons (BPNRs) using density functional theory combined with Boltzmann transport method with relaxation time approximation. It is shown that the calculated ultrahigh electron mobility can even reach the order of 10(3) to 10(7) cm(2) V(-1) s(-1) at room temperature. Owing to the electron mobility being higher than the hole mobility, armchair and diagonal BPNRs behave like n-type semiconductors. Comparing with the bare BPNRs, the difference between the hole and electronic mobilities can be enhanced in ribbons with the edges terminated by H atoms. Moreover, because the hole mobility is about two orders of magnitude larger than the electron mobility, zigzag BPNRs with H termination behave like p-type semiconductors. Our results indicate that BPNRs can be considered as a new kind of nanomaterial for applications in optoelectronics, nanoelectronic devices owing to the intrinsic band gap and ultrahigh charge mobility.