Analytical Calculation of Exciton Binding Energy, Quasi-Particle Band Gap and Optical Gap in Strained Mono-layer MoS₂

Strain in two-dimensional (2D) materials induces shifts in the visible spectrum due to strained binding energies, an accurate study of which is critical for materials engineering in the design of optoelectronic applications. Different from previous studies that employed computationally demanding theoretical approaches, we present an analytical approach, based on the difference method to calculate the impact of strained binding energy on the optical gap in mono-layer \({\hbox {MoS}}_{2}\) by exploiting an existing tight binding (TB) and a fractional Coulomb potential model, for strained band gap and binding energy calculation, respectively. The inclusion of strained binding energy, changing at a rate of \(-8.1 \, \hbox {meV}/\bigtriangleup 1\%\) of biaxial in-plane tensile strain accompanied with a variation of \(-110 \, \hbox {meV}/\bigtriangleup 1\%\) of strain in the TB band gap, causes the optical gap to alter at a rate of \(-105.3 \, \hbox {meV}/\bigtriangleup 1\%\) of strain, supported by first-principles calculations and is benchmarked with reported experimental and theoretical values. The effect of strained binding energies causes a blueshift in the optical gap by a correction factor, increasing from \(\approx 0.5\%\) to \(\approx 12\%\), with an increase in equi-biaxial in-plane tensile strain from 1% to 11%, respectively. Furthermore, binding energy sensitivity to strain decreases linearly with a structural change from a mono-layer to a few layers in the 2D regime and saturates in the bulk regime. The presented framework can be used for the calculation of strained binding energies and optical gaps of other 2D materials and thus allows us to tune optical properties of 2D nanomaterials that are sensitive to lattice deformations.