Dimensionality-Induced Transition from Degenerate to Nondegenerate States in Nb-Doped WSe₂

Substitutional doping in transition-metal dichalcogenides (TMDCs) is a pivotal strategy for tuning their electronic and optical properties, enabling their integration into next-generation electronic and optoelectronic devices. This study examines the critical doping levels at which doped TMDCs transition from nondegenerate to degenerate semiconductors, comparing three-dimensional (3D) bulk TMDCs with their two-dimensional (2D) counterparts. Through systematic characterization of Nb-doped WSe₂, we demonstrate that, although high Nb-doped WSe₂ bulk samples (Nb density: 3.9 × 10²⁰ cm^-3, 2.3% doping level) exhibit degenerate transport behavior, ambipolar behavior emerges at the monolayer limit. This observation highlights a significant increase in the critical doping level upon transitioning from 3D to 2D systems. To elucidate these phenomena, we develop a semiempirical model that incorporates the enhanced dopant ions' activation energy due to the quantum confinement effect and the modification of the dielectric environment surrounding 2D systems, revealing mechanisms underlying these dimensionality-induced differences. This understanding facilitates the design of doping strategies for high-performance electronic and optoelectronic devices.