Strain-tunable inter-valley scattering defines universal mobility enhancement in n- and p-type 2D TMDs

Abstract

Strain fundamentally alters carrier transport in semiconductors by modifying their band structure and scattering pathways. In transition-metal dichalcogenides (TMDs), an emerging class of 2D semiconductors, we show that mobility modulation under biaxial strain is dictated by changes in inter-valley scattering rather than effective mass renormalization as in bulk silicon. Using a multiscale full-band transport framework that incorporates both intrinsic phonon, extrinsic impurity, and dielectric scattering, we find that tensile strain enhances n-type mobility through K-Q valley separation, while compressive strain improves p-type mobility via Γ-K decoupling. The tuning rates calculated from our full-band model far exceed those achieved by strain engineering in silicon. Both relaxed and strain-modulated carrier mobilities align quantitatively with experimentally verified measurements and are valid across a wide range of practical FET configurations. The enhancement remains robust across variations in temperature, carrier density, impurity level, and dielectric environment. Our results highlight the pivotal role of strain in improving the reliability and performance of 2D TMD-based electronics.

Figures (8)

• Figure 1: Mechanisms of strain-induced electron mobility enhancement in n-type TMDs.a, Schematic illustration of the key parameters governing electron mobility in n-type TMDs, highlighting the functional relationship between mobility enhancement and applied strain. b, Schematic of the conduction band structure showing energy separation between K and Q valleys ($\Delta \mathrm{E}_{\mathrm{QK}}$) under biaxial strain. c, Evolution of the energy separation $\Delta {\mathrm{E_{QK}}}$ under biaxial strain for MoS$_2$ (purple), MoSe$_2$ (orange), and WS$_2$ (green). First-principles calculated density of states versus conduction band energy along the K–Q direction under varying strain for d, MoS$_2$, e, MoSe$_2$, and f, WS$_2$. Computed intrinsic scattering rates versus carrier energy under varying strain for g, MoS$_2$, h, MoSe$_2$, and i, WS$_2$, showing suppression of scattering under tensile strain. In all panels, compressive, unstrained, and tensile strain regimes are represented by blue, black, and red, respectively.
• Figure 2: Enhanced electron mobility in n-type TMDs through strain engineering.a, Intrinsic electron mobility enhancement considering ADP, ODP, POP, IV, and PZ scattering mechanisms. b, Total electron mobility enhancement incorporating both intrinsic and extrinsic effects (CI + SOP scattering). Results are shown for MoS$_2$ (purple), MoSe$_2$ (orange), and WS$_2$ (green) under biaxial strain at $T$ = 300 K, $n = 10^{13}$ cm$^{-2}$, $n_{\text{imp}} = 5 \times 10^{12}$ cm$^{-2}$, and SiO$_2$ dielectric environment. Tensile strain consistently enhances the electron mobility of all n-type TMDs, with WS$_2$ exhibiting the most significant improvement across both intrinsic and extrinsic scattering regimes.
• Figure 3: Parametric analysis of intrinsic and extrinsic factors influencing strain-induced electron mobility enhancement in n-type TMDs. Unstrained initial electron mobility versus a, temperature, b, carrier concentration, c, impurity concentration, and d, dielectric environment. Mobility enhancement factor per percent strain (evaluated at 1% biaxial tensile strain) versus e, temperature, f, carrier concentration, g, impurity concentration, and h, dielectric environment. Unless otherwise specified, analyses are performed at 300 K, with $n = 10^{13}$ cm$^{-2}$, $n_{\text{imp}} = 5 \times 10^{12}$ cm$^{-2}$, and a SiO$_2$ dielectric. Results are shown for MoS$_2$ (purple), MoSe$_2$ (orange), and WS$_2$ (green). The tensile strain-induced electron mobility enhancement trend remains robust across orders-of-magnitude variation in all parameters, with WS$_2$ consistently showing the best performance.
• Figure 4: Mechanisms of strain-induced hole mobility enhancement in p-type TMDs.a, Schematic overview of the key parameters governing hole mobility in p-type TMDs, highlighting the functional relationship between mobility enhancement and applied strain. b, Schematic of the valence band structure showing energy separation between $\Gamma$ and K valleys ($\Delta \mathrm{E}_{\mathrm{\Gamma K}}$) under biaxial strain. c, Evolution of the energy separation $\Delta \mathrm{E}_{\mathrm{\Gamma K}}$ under biaxial strain for MoSe$_2$ (orange), WSe$_2$ (teal), and MoTe$_2$ (brown). First-principles calculated density of states versus valence band energy along the $\Gamma$--K direction under varying strain for d, MoSe$_2$, e, WSe$_2$, and f, MoTe$_2$. Computed intrinsic scattering rates versus carrier energy under varying strain for g, MoSe$_2$, h, WSe$_2$, and i, MoTe$_2$, showing suppression of scattering under compressive strain.
• Figure 5: Enhanced hole mobility in p-type TMDs through strain engineering.a, Intrinsic hole mobility enhancement considering ADP, ODP, POP, IV, and PZ scattering. b, Total hole mobility enhancement incorporating both intrinsic and extrinsic effects (CI + SOP scattering). Results are shown for MoSe$_2$ (orange), WSe$_2$ (teal), and MoTe$_2$ (brown) under biaxial strain at $T$ = 300 K, $p = 10^{13}$ cm$^{-2}$, $n_{\text{imp}} = 5 \times 10^{12}$ cm$^{-2}$, and SiO$_2$ dielectric environment. Compressive strain consistently enhances the hole mobility of all p-type TMDs, with WSe$_2$ exhibiting the most significant improvement across both intrinsic and extrinsic scattering regimes.