Energy funneling effect and charge transfer behavior of MoS<sub>2</sub> with thickness gradient

ZUO Huiling; SHEN Quan; LI Jing; LIU Jing; DONG Jiansheng

doi:10.7498/aps.74.20250661

Abstract

Energy funneling effect of two-dimensional materials provides an important method for modulating carrier transfer. However, the formation of energy funneling and its influences on the carrier transfer are still relatively uncharacterized. In this work, the energy funneling induced by the layer number gradient effect in MoS₂ is investigated through atomic-bond-relaxation approach and first-principles calculations. It is found that the bandgap of MoS₂ monotonically increases with the decrease of the layer number, leading the conduction band minimum (valence band maximum) of thin layer MoS₂ to be higher than (lower than) that of thick layer MoS₂. Therefore, both dual thickness gradient and triple thickness gradient MoS₂ can achieve the energy funneling effect. As a result, the carriers will be directionally transferred from the thin layer region to the thick layer region. According to Marcus theory, the carrier transfer rate is dependent on drive force caused by the energy level difference with different thicknesses of MoS₂. For the dual thickness gradient MoS₂, when the thickness difference between adjacent layers is the largest, the driving force is the highest, which is 1L/bulk. In addition, owing to the driving force smaller than the reorganization energy in dual thickness gradient MoS₂, a large driving force corresponds to a high carrier transfer rate, resulting in a higher carrier transfer rate of 1L/bulk than those in other dual thickness gradient systems. For the triple thickness gradient MoS₂, there are two consecutive interface energy differences that induce driving forces. However, the carrier transfer rate is exponentially correlated with the driving force. Therefore, the carrier transfer rate of dual thickness gradient MoS₂ will be higher than that of the corresponding triple thickness gradient MoS₂. Our results demonstrate that the energy funneling effect induced by thickness gradient can realize carrier accumulation in the thick layer region without the need for p-n junctions, which is of great benefit in collecting photogenerated carriers. The atomic force microscopy lithography and chemical vapor deposition will be used to engineer thickness-gradient two-dimensional materials with enhanced optoelectronic properties in future.

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Corresponding author: DONG Jiansheng, jsdong@jsu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12364007), the Basic Research Program for Young Students of Natural Science Foundation of Hunan Province, China (Grant No. 2025JJ60929), the Scientific Research Foundation of Hunan Provincial Education Department, China (Grant No. 24A0366), and the Hunan Students’ Platform for Innovation and Entrepreneurship Training Program, China (Grant No. S202310531036).

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Vol. 74, Issue 18 - 2025-09-20

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