In-plane transition metal dichalcogenide quantum wells: Effective Hamiltonian approach

In-plane or Lateral two dimensional (2D) heterostructures, due to its unique optical and transport properties as well as junction feature, are becoming a good candidate for future electronics and photonics devices. In particular, lateral stitched heterostructures of MoS2/WSe2 mostly synthesized by lithographic pattern provides type II band alignment therefore, the possibility of forming a type II lateral quantum well may be considered as a serious research topic. Here, We theoretically obtain energy levels and electron and hole wave functions in a lateral MoS2/WSe2 single and double quantum well (LSQW and LDQW) which is evidenced by experiments. Within effective 2D Dirac Hamiltonian, an analytical expression for energy dispersion in growth direction has been derived. Based on numerical approach, the variation of energy levels, wave function and number of allowed energy levels as a function of the width of the quantum well are discussed for single electron and hole. We observed that by increasing QW the number of energy levels increases similar to conventional semiconductor QW, but surprising behavior is in LSQW of WSe2/MoS2/WSe2 that the number of allowed energy levels inside QW increases by increasing well width. Our study paves the way for the implementation of in-plane quantum wells in electronic and optoelectronic devices such as sensors, detectors and solar cells.