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Energy funneling effect of two-dimensional materials provides an important method to modulate carrier transfer. However, the formation of energy funneling and its influences on the carrier transfer remain relatively uncharacterized. In this work, we investigate the energy funneling induced by the layer number gradient effect in MoS2 through atomic-bond-relaxation approach and first-principles calculations. We find that the bandgap of MoS2 monotonically increasing with decreasing the layer number, resulting in the conduction band minimum (valence band maximum) of thin layer MoS2 is being 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 induced by the energy level difference of 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 of being 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 compared to 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 to the collection of photogenerated carrier. Future studies may leverage atomic force microscopy lithography and chemical vapor deposition to engineer thickness-gradient two-dimensional materials with enhanced optoelectronic properties.
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Keywords:
- MoS2 /
- thickness gradient /
- energy funneling effect
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