Transition metal dichalcogenides (TMDCs) are a class of layered materials with the general formula MX2, where M is a transition metal (Mo, W, etc.) and X is a chalcogen (S, Se, Te). Their electronic and vibrational properties are highly sensitive to external perturbations such as strain and chemical doping, making them attractive for tunable optoelectronic applications. This article examines how uniaxial and biaxial strain, as well as substitutional and electrostatic doping, modify these properties, supported by experimental observations and theoretical predictions.

Strain engineering is a powerful tool to tailor the electronic structure of TMDCs. Uniaxial strain, applied along a specific crystal axis, breaks the in-plane symmetry, leading to anisotropic changes in band structure. For example, monolayer MoS2 under uniaxial tensile strain exhibits a redshift in its photoluminescence (PL) peak due to a reduction in the direct bandgap at the K-point. Theoretical calculations using density functional theory (DFT) predict that 2% uniaxial strain can decrease the bandgap by approximately 0.1 eV. The conduction band minimum (CBM) and valence band maximum (VBM) shift asymmetrically, with the CBM being more sensitive to strain than the VBM. This asymmetry arises from the orbital composition of the bands, where the CBM is primarily derived from metal d-orbitals, while the VBM has strong chalcogen p-orbital contributions.

Biaxial strain, applied uniformly in-plane, preserves the crystal symmetry but alters the bandgap more significantly than uniaxial strain. Monolayer WS2 under biaxial tensile strain shows a linear bandgap reduction of about 50 meV per 1% strain. Compressive biaxial strain, however, can induce a direct-to-indirect bandgap transition in some TMDCs. For instance, DFT studies indicate that applying 1-2% compressive strain to MoSe2 shifts the VBM from the K-point to the Γ-point, converting the material into an indirect semiconductor. This transition is accompanied by a quenching of PL intensity, as observed experimentally.

Vibrational properties, probed by Raman spectroscopy, also respond distinctly to strain. The in-plane E2g and out-of-plane A1g phonon modes in MoS2 exhibit opposite shifts under strain. Uniaxial tensile strain softens the E2g mode (redshift) due to elongated bonds, while the A1g mode hardens (blueshift) because of increased interlayer restoring forces. The ratio of these shifts serves as a strain gauge, with a reported sensitivity of ~4 cm-1 per 1% strain. Biaxial strain produces a more pronounced effect, with both modes shifting linearly but at different rates. These trends are consistent across various TMDCs, though the exact coefficients depend on the material’s elastic constants.

Chemical doping introduces additional carriers or defects, further modifying electronic and vibrational properties. Substitutional doping replaces host atoms with foreign elements, creating localized states or shifting the Fermi level. For example, Re-doped MoS2 introduces mid-gap states below the CBM, reducing the effective bandgap by 0.2-0.3 eV, as confirmed by scanning tunneling spectroscopy. Nb doping in WS2 acts as a p-type dopant, lowering the Fermi level into the valence band and increasing hole conductivity. The doping efficiency depends on the electronegativity difference between the dopant and host atoms, with larger differences leading to stronger perturbations.

Electrostatic doping, achieved via gate voltages or charge transfer, offers non-destructive tuning of carrier concentrations. Back-gated monolayer MoS2 devices demonstrate a metal-insulator transition at carrier densities above 10^13 cm-2, accompanied by a broadening and weakening of PL peaks due to enhanced exciton dissociation. The Raman modes also shift under electrostatic doping: the A1g mode hardens with electron doping due to increased electron-phonon coupling, while hole doping softens it. These shifts are reversible and can be quantified using the Fano model, which accounts for coupling between discrete phonons and continuous electronic transitions.

Experimental techniques like PL and Raman spectroscopy are critical for characterizing these effects. PL quenching under strain or doping reflects non-radiative recombination pathways, such as defect-assisted trapping or Auger processes. The PL intensity of strained WSe2 drops by over 80% at 3% biaxial strain, correlating with the emergence of dark excitons. Raman peak shifts provide insights into lattice deformation and electron-phonon interactions. For instance, the separation between E2g and A1g modes in doped MoS2 decreases with electron doping but increases with hole doping, serving as a diagnostic tool for carrier type and concentration.

Theoretical models complement experiments by predicting trends and mechanisms. Tight-binding calculations reveal that strain-induced bandgap changes arise from orbital overlap variations, while DFT simulations quantify doping-induced charge redistribution. For example, electrostatic doping in MoTe2 is predicted to cause a Lifshitz transition at a critical carrier density, altering the Fermi surface topology. Machine learning approaches are increasingly used to map strain-doping-property relationships, accelerating material discovery.

In summary, strain and doping provide versatile knobs to control TMDC properties. Uniaxial and biaxial strain modulate bandgaps and phonon frequencies anisotropically, while substitutional and electrostatic doping alter carrier concentrations and electronic states. These effects are systematically probed via Raman and PL techniques and validated by theoretical models. The ability to precisely engineer these parameters enables tailored TMDC devices for sensors, transistors, and quantum emitters, though challenges remain in achieving uniform strain or doping at large scales. Future work may explore combined strain-doping effects beyond linear regimes or at extreme conditions.