Concurrent high thermal conductivity and high carrier mobility in tetragonal tantalum nitride Open Access

High carrier mobility (⁠ $μ$⁠) is essential for achieving rapid switching speeds and minimizing power dissipation in electronic and optoelectronic devices. This necessity has spurred significant interest in identifying semiconductor materials with exceptionally high $μ$⁠. Simultaneously, the ongoing miniaturization and rising power density of modern devices have made efficient heat dissipation a critical challenge.^1,2 Addressing this challenge requires materials with high thermal conductivity (⁠ $κ$⁠), making the pursuit of materials that combine both high $κ$ and $μ$ an urgent priority for advancing device performance. However, bulk semiconductor materials that exhibit these dual properties remain rare, with most candidates excelling in either $κ$ or $μ$⁠, but not both.^3–8 

Diamond exemplifies a bulk material with exceptional thermal conductivity, achieving the highest known $κ$ among solids,^9–11 and a remarkable $μ$ of approximately 3500 cm² V⁻¹ s⁻¹ at room temperature (RT).^7,12 However, its ultrawide bandgap (>5 eV)¹³ and high synthesis costs^14,15 severely restrict its application in the semiconductor industry. Recent theoretical and experimental studies have highlighted cubic boron arsenide (BAs) as a compelling alternative. BAs boasts an extraordinary RT $κ$ exceeding 1000 W m⁻¹ K^−16,8,16 and an ambipolar $μ$ above 1500 cm² V⁻¹ s⁻¹,^17,18 making it a promising candidate for electronics and integrated circuits.

The exceptional transport properties of BAs arise from its unique phononic and electronic structures.^19–21 The large mass ratio between arsenic and boron, coupled with strong interatomic bonding, creates a phonon spectrum characterized by a significant acoustic–optical (a–o) gap and tightly bunched acoustic branches. These features suppress phonon–phonon scattering, yielding ultrahigh $κ$⁠.^19,20 Additionally, high optical phonon frequencies, weak polar electron–phonon scattering, and suppressed intervalley transitions, combined with a low effective mass, contribute to its high $μ$⁠.²¹ Inspired by BAs, $θ$-phase tantalum nitride (⁠ $θ$-TaN) has recently garnered attention for its remarkable RT $κ$ approaching 1000 W m⁻¹ K⁻¹.^22,23 This is attributed to mechanisms similar to those in BAs, with an additional factor of weak phonon–electron (ph–el) scattering. However, the semimetallic nature of $θ$-TaN limits its application in semiconductor devices. This raises a critical question: can alternative phases of tantalum nitride achieve semiconducting behavior while preserving high $κ$?

Among the known stoichiometric phases of tantalum nitride, $ϵ$-TaN (CoSn structure type) and $δ$-TaN (NaCl structure type) are either metallic or semimetallic,²⁴ rendering them unsuitable for semiconducting applications. To address this limitation, we extend our investigation to other tantalum-V compounds. Notably, tantalum arsenide (TaAs) and tantalum phosphide (TaP), known Weyl semimetals with body-centered tetragonal structures and nonsymmorphic space group $I41md$ (No. 109),^25,26 exhibit frequency-gapped phonon spectra.²⁷ As the anion changes from As to P to N, the frequency gap broadens, and the overall frequency distribution scales upward due to increased mass differences and stiffer bonding. This trend, confirmed by our phonon spectrum calculations [Figs. 1(c)–1(e)], reveals a corresponding increase in thermal conductivity with lighter anions. Surprisingly, when the anion is substituted with nitrogen, the resulting tetragonal tantalum nitride (t-TaN) displays semiconducting behavior with a bandgap of approximately 0.6 eV. Furthermore, t-TaN exhibits unique phononic properties, including a large frequency gap and phonon bunching, similar to $θ$-TaN. These attributes suppress phonon–isotope (ph–iso) and phonon–phonon (ph–ph) scattering, while the vanishing DOS near the Fermi level minimizes ph–el scattering.^23,28–30 Collectively, these features position t-TaN as a promising high- $κ$ semiconductor material.

In this study, we employ ab initio calculations to investigate the intrinsic thermal conductivity and carrier mobility of t-TaN. By accounting for three-phonon (3 ph) and four-phonon (4ph) scattering as well as ph–iso scattering, we predict an extraordinary RT $κ$ of 677 W m⁻¹ K⁻¹ along the a-axis and 273 W m⁻¹ K⁻¹ along the c-axis. Additionally, t-TaN achieves exceptional hole mobility, reaching up to 4700 cm² V⁻¹ s⁻¹ along the a-axis and 2034 cm² V⁻¹ s⁻¹ along the c-axis at RT. The coexistence of high thermal conductivity and high carrier mobility makes t-TaN a compelling candidate for the next-generation electronic and optoelectronic devices.

Tantalum-X (X=As, P, and N) compounds adopt a body-center tetragonal structure (space group $I41md$⁠), as illustrated in Fig. 1(a). In this structure, Ta and X atoms occupy the Wyckoff position of 4a (0, 0, u) with u = 0.626 196 10 and 0.207 693 85. For t-TaN, the optimized lattice parameters are a = b = 2.9145  $Å$⁠, and c = 10.2868  $Å$⁠. In this configuration, each Ta atom is coordinated with six nearest-neighbor X atoms via covalent bonds (⁠ $d1$ and $d2$⁠), where nearest Ta atoms are connected through nonbonding interaction (⁠ $d3$ and $d4$⁠). Integrated crystal orbital Hamilton population (ICOHP) calculation reveals that as the anion changes from As and P to N, the electronic bonding between Ta-X pairs (⁠ $d1$ and $d2$⁠) and between Ta–Ta pairs (⁠ $d3$ and $d4$⁠) becomes significantly stronger. This is evidenced by the larger absolute values of ICOHP in Fig. 1(b). Complementary analyses of the electron localization function and bond lengths further corroborate this trend (Table S1 and Fig. S3, supplementary material).

From Figs. 1(c)–1(e), it is apparent that the stronger $d1$ and $d2$ bonding, together with the reduced anion mass, shifts the overall phonon spectrum toward higher frequencies. Additionally, the increasing anion–cation mass ratio progressively widens the phonon frequency gap between acoustic and high-frequency optical branches. Based on the established criteria for high- $κ$ crystals,^19,31 this trend in the phonon spectrum suggests that t-TaN should exhibit a higher lattice thermal conductivity. Our calculations confirm this: as the anion transitions from As to P to N, RT $κph$ increases monotonically from 32 (27) to 155 (91) to 677 (273) $W m−1 K−1$ along the a (c) axis.

The electronic band structures [Figs. 1(f)–1(h)] reveal that as the anion changes from As to P to N, Ta atoms increasingly dominate the bands near the Fermi level. Remarkably, the stronger $d3$ and $d4$ bonding in t-TaN results in semiconducting behavior, with a bandgap exceeding 0.6 eV. These band characteristics indicate that t-TaN shows promise as a semiconductor material with superior thermal transport performance. Moreover, we compare the stability of t-TaN with other experimentally synthesized phases of TaN by calculating the formation energy (Table S2, supplementary material). The results indicate that the stability is in the order of $ε$-TaN $>θ$-TaN $>t$-TaN $>δ′$-TaN $>δ$-TaN. While this shows that t-TaN is slightly higher in energy than the experimentally synthesized $θ$-TaN, it exhibits considerably a lower energy than the likewise experimentally observed $δ$-TaN, suggesting favorable synthesis prospects for t-TaN.

Key results are summarized in Fig. 2, revealing that t-TaN exhibits an extraordinary thermal conductivity and hole mobility. The thermal conductivity of naturally occurring t-TaN is compared to high- $κ$ materials including diamond,²² BAs,²² c-BN,⁵ and $θ$-TaN²² [Fig. 2(a)]. Due to bonding heterogeneity, t-TaN displays a marked anisotropy in thermal conductivity, with the RT values of 677 W/m⁻¹ K⁻¹ along the a axis and 273 W/m⁻¹ K⁻¹ along the c axis. The $κ$ along the a axis, while lower than that of diamond, BAs, and $θ$-TaN, is comparable to cubic BN and surpasses most bulk materials. Note also that owing to the semiconducting nature of t-TaN, its intrinsic $κ$ is almost entirely dominated by the phonon contribution (⁠ $κph$⁠), whereas the electronic contribution to thermal conductivity (⁠ $κe$⁠) remains negligible even at high carrier concentrations (Sec. F, supplementary material).

In addition to high $κ$⁠, t-TaN demonstrates ultrahigh intrinsic hole mobility. As shown in Fig. 2(b), the hole mobility along the a axis reaches 4700 cm² V⁻¹ s⁻¹ at RT, outperforming all known high- $κ$ semiconductors.^17,18,35 Along the c axis, the RT hole mobility is 2034 cm² V⁻¹ s⁻¹, comparable to that of BAs.^17,18 Notably, while materials like GaAs exhibit higher carrier mobility, their thermal conductivity is an order of magnitude lower than that of t-TaN.³⁶ Sections II C–II E explore the mechanisms underlying the high thermal conductivity and hole mobility in t-TaN.

As mentioned above, the thermal conductivity in t-TaN primarily arises from phonon contributions, which largely depend on the features of phonon dispersion. As seen in Fig. 1(e), the absence of imaginary modes in the phonon dispersion confirms its dynamic stability. It is noteworthy that the phonon spectrum of t-TaN shares similarities with BAs and $θ$-TaN, particularly the separation of high- and low-frequency branches by a significant frequency gap, which suppresses the acoustic-optical-acoustic (aao) scattering process. Furthermore, the bunching of phonon branches in the 2–8 THz range limits 3ph scattering processes involving acoustic modes (aaa), as evidenced by the dip in 3ph scattering rates within this frequency range [Fig. 3(a)]. This suppression results in ultrahigh $κph$ along the a axis, exceeding 1000 Wm⁻¹ K⁻¹ at RT when only 3ph processes are considered [Fig. 3(b)].

The unique phonon structure of $θ$-TaN, although suppressing the 3ph scattering, cannot restrict the 4ph processes. Hence, 4ph scattering processes play a significant role in limiting $κph$⁠, just like in BAs and $θ$-TaN.^20,22 Figure 3(a) shows that 4 ph scattering rates are comparable to 3 ph scattering rates in the 2–8 THz region, where most heat-carrying phonons reside as revealed in the spectral $κ$ in Fig. 2(c). The inclusion of 4ph processes reduces $κph$ by 37% at RT, similar to the reduction observed in BAs.^20,37 Additionally, t-TaN exhibits exceptionally weak ph–iso scattering, which is several orders of magnitude lower than the 3ph scattering rates. The dominance of normal 3ph processes over Umklapp processes (Fig. S9, supplementary material) further contributes to high $κph$⁠. As seen in Fig. 3(b), the $κph$ calculated within the relaxation time approximation (RTA) is significantly lower than the exact value from the iterative solution over the entire temperature range.

Despite these shared features in the phonon band structure, $κph$ of t-TaN is 30% lower than that of $θ$-TaN, primarily due to higher 3ph scattering rates stemming from increased phase space and stronger phonon anharmonicity associated with t-TaN's more complex crystal structure (Sec. I, supplementary material). Given that the synthesis of high-quality single crystals of TaN compounds is quite challenging,^38,39 understanding the effect of grain size on $κph$ is highly beneficial for guiding future experimental measurements. The phonon mean free path (MFP) spectrum [Fig. 3(d)] reveals that phonons with MFPs < 1  $μ$m account for over 80% of t-TaN's $κph$⁠, suggesting weaker size effects compared to $θ$-TaN and superior phonon thermal conductivity at the nanoscale.

Carrier mobility calculations [Figs. 4(a) and 4(b)] reveal strong anisotropy. At RT, hole mobilities along the a and c axes are 4700 and 2029 cm² V⁻¹ s⁻¹, respectively, and remain high until carrier concentrations exceed 10¹⁸ cm³. In contrast, electron mobilities are significantly lower, with values of 402 and 362 cm² V⁻¹ s⁻¹ at RT along the a and c axes, respectively, indicating that t-TaN is an exceptional p-type but poor n-type semiconductor.

The carrier mobility is closely connected to its electronic band structure. Figure 1(h) shows an indirect bandgap of $∼$ 0.6 eV, with a valence band maximum (VBM) near the $S$ point and a conduction band minimum (CBM) near $Γ$ point. The high dispersion of these bands results in low effective masses for electrons (⁠ $me∼$ 0.35) and holes (⁠ $mh∼$ 0.16), much smaller than those in BAs (⁠ $me∼$ 1.10 and $mh∼$ 0.56).²¹ The effective mass ratio (⁠ $me/mh∼$ 2.2) explains the stark difference between electron and hole mobilities.

High hole mobility benefits from high Fermi velocities and long carrier lifetimes. Figure 4(c) shows the calculated Fermi velocities projected onto Fermi pockets for electrons and holes when the carrier concentration is $1017$ cm³. At this concentration, hole pockets exhibit an average Fermi velocity of 2.9  $×$ 10⁵ m/s, surpassing those of electrons (1.3  $×$ 10⁵ m/s) and high- $μ$ semiconductors such as diamond (1.1  $×$ 10⁵ m/s)⁴⁰ and GaAs (2.1  $×$ 10⁵ m/s).^41, Figure 4(d) reveals that the phonon-limited hole lifetimes at RT are well above 100 fs for energies within the 0.2 eV range around the corresponding Fermi levels, three times longer than electron lifetimes. The long carrier lifetimes are derived from the weak electron–phonon (el–ph) scattering, as reflected in the el–ph coupling strength $λ$⁠. From Fig. 4(e), it is evident that the saturated $λ$ is exceptionally low, with values of 0.058 for electrons and 0.031 for holes, even lower than highly conducting metals such as $PdCoO2$ (⁠ $λ$ = 0.057).⁴² This is also reflected in the Eliashberg spectral function $α2F(ω)$⁠, whose value is rather low in the whole frequency range. We note that the carrier lifetime can be approximated as $τ=ℏ(2πkBTλ)−1$⁠.⁴³ Using the computed $λ$ values, the carrier lifetime of t-TaN at 300 K is estimated to be $∼$ 70 fs for electrons and $∼$131 fs for holes, comparable to that of BAs.⁴⁴ 

The exceptionally small $λ$ stems from a combination of factors. The highly dispersive band structure reduces the density of states near the VBM. As illustrated in Fig. 4(f), the electronic DOS near the Fermi level is predominantly contributed by the 5d orbitals of Ta atoms, and their contribution to the states near the VBM rises more slowly with energy compared to that near the CBM. Consequently, the minimal DOS near the VBM results in a very limited number of carriers participating in el–ph scattering processes. Meanwhile, high-frequency optical phonon scattering, which contributes primarily to $α2F(ω)$ [Fig. 4(e)], is rather weak, due to small Born effective charges (⁠ $Z*$⁠) and a large high-frequency dielectric constant (⁠ $ϵ∞$⁠). In polar semiconductors, the polar-optical-phonon scattering usually contributes substantially to the el–ph scattering, particularly in strongly polar materials like GaAs.⁴⁵ The intensity of this scattering is proportional to $Z*/ϵ∞$⁠.⁴⁶ Notably, the $Z*/ϵ∞$ ratio in t-TaN (⁠ $∼$ 0.1) is only half that of GaAs,²¹ further mitigating polar-optical-phonon scattering and thereby contributing to the material's exceptional hole mobility.

In summary, we identify t-TaN as a narrow-bandgap semiconductor with outstanding thermal conductivity and hole mobility, based on first-principles calculations. At RT, t-TaN achieves thermal conductivities of 677 and 273 W m⁻¹ K⁻¹ along the a- and c-axes, respectively, surpassing $θ$-TaN at the nanoscale. These exceptional values are attributed to strong interatomic bonding, a pronounced frequency gap between acoustic and optical phonon branches, phonon bunching, and minimal phonon-isotope scattering.

Additionally, t-TaN exhibits ultrahigh hole mobilities of 4700 and 2034 cm² V⁻¹ s⁻¹ along the a- and c-axes, respectively, outperforming all known high- $κ$ semiconductors. This performance stems from a unique combination of high Fermi velocity—driven by highly dispersive valence band states—and exceptionally weak electron–phonon coupling, facilitated by low electronic density of states near the valence band maximum and high optical phonon frequencies that suppress polar scattering.

Notably, the tetragonal phase of TaN shares its crystal structure with well-studied Weyl semimetals, such as TaAs and TaP, simplifying experimental synthesis and characterization. These findings position t-TaN as a groundbreaking candidate for the next-generation microelectronic and optoelectronic devices, offering an unparalleled combination of high thermal conductivity and carrier mobility.

The phonon MFP (F $λβ$⁠) is iteratively solved using the linearized BTE starting from the RTA. Detailed expressions for $Δλ$⁠, $1/τiso,λ$⁠, $1/τ3,λ$⁠, and $1/τ4,λ$ can be found in Refs. 20 and 49–52.

To solve the phonon BTE, we computed harmonic and anharmonic (third- and fourth-order) interatomic force constants (IFCs) using density functional theory (DFT) calculations performed with the VASP package,^55,56 within the generalized gradient approximation.⁵⁷ Temperature-induced anharmonic effect was assessed using the self-consistent phonon theory,^58,59 and it was found to have minimal impact on phonon energies (Fig. S8, supplementary material). For el–ph scattering calculations, the EPW package⁶⁰ was employed, leveraging electron and phonon properties computed via Quantum Espresso⁶¹ within the density functional perturbation theory. Using these inputs, the lattice thermal conductivity and phonon-limited transport properties were determined with the FourPhonon⁵⁰ and Perturbo⁶² codes, respectively. It should be noted that el-ph calculations critically depend on the accuracy of both electronic and phonon band structures, which can be affected by the choice of pseudopotentials and computational methods. To ensure reliability, we compare the electronic and phononic band structures obtained from different approaches, and the high consistency observed between them (Sec. B, supplementary material) validates the robustness of our predictions. Further computational details regarding anharmonic IFCs, anharmonic phonon renormalization, the convergence tests for $κ$ and $μ$ are provided in Secs. E and G of the supplementary material.

See the supplementary material for computational details, validation of electronic and phononic band structures of t-TaN, crystal structure and bonding strength analysis of TaX (X=As, P, N), thermodynamic stability, convergence tests for thermal conductivity and carrier mobility of t-TaN, electronic thermal conductivity, temperature-induced phonon renormalization, normal and umklapp scattering processes of t-TaN, and the comparison of phonon transport properties of $θ$-TaN and t-TaN.

This work was supported by the National Natural Science Foundation of China (NSFC, Grant Nos. 12374038, 12204074, 12222402, 11974062, 12147102, 52371212, and 12404045), the Natural Science Foundation of Chongqing (Grant Nos. CSTB2023NSCQ-JQX0024 and CSTB2022NSCQ-MSX0834), the Fundamental Research Funds for the Central Universities of China (Grant Nos. 2024IAIS-ZX002 and 2023CDJKYJH104), and the Science and Technology Research Program of Chongqing Municipal Education Commission (No. KJQN-202400553).

The authors have no conflicts to disclose.

Xianyong Ding and Xin Jin contributed equally to this work.

Xianyong Ding: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Xin Jin: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Writing – review & editing (supporting). Dengfeng Li: Formal analysis (supporting); Writing – review & editing (supporting). Jing Fan: Formal analysis (supporting); Writing – review & editing (supporting). Xiaoyuan Zhou: Formal analysis (supporting); Writing – review & editing (supporting). Xuewei Lv: Formal analysis (supporting); Writing – review & editing (supporting). Xiaolong Yang: Conceptualization (equal); Formal analysis (equal); Project administration (equal); Supervision (equal); Validation (supporting); Visualization (supporting); Writing – original draft (equal); Writing – review & editing (equal). Zhenxiang Cheng: Formal analysis (equal); Project administration (equal); Supervision (equal); Visualization (equal); Writing – review & editing (equal). Rui Wang: Conceptualization (equal); Formal analysis (equal); Project administration (equal); Supervision (equal); Validation (supporting); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.