Revisiting multiple trapping and release charge transport in amorphous semiconductors exemplified by hydrogenated amorphous silicon

• Conventional mobility edge model of amorphous semiconductors is inaccurate. • A more reliable depiction of the multiple trapping and release transport is derived. • Measured mobility edge does not differentiate localized and extended states. • Extracted extended-state mobility is higher than the actual free carrier mobility. • Our modified transport model will be extended to nanoscales. Multiple trapping and release (MTR) is a typical charge transport mechanism associated with localized states in technologically important disordered semiconductors such as hydrogenated amorphous silicon ( a -Si:H) and many amorphous oxides. However, till now the analysis of MTR has been built on an “abrupt” mobility edge model. Using electron transport as an example, the abrupt mobility edge model assumes that: (i) states above the conduction band (CB) mobility edge ( E C ) are extended and any of them is omnipresent in space, whereas states below E C are localized and they exist in the energy-space diagram as pointlike sites; (ii) all states are evenly distributed in space. The prequel to this paper [Y. Luo and A. Flewitt, Phys. Rev. B 109 , 104203 (2024)] demonstrates that neither of these simplifications is valid. Hence, this paper reinvestigates MTR transport. Through a probabilistic analysis of the microscopic charge transport details, this paper rigorously achieves two critical conclusions that challenge previous beliefs. First, the mobility edge, which is characterizable through activation energy measurement of conductivity, is an effective quantity associated with carrier relaxation dynamics; it does not demarcate the extended states and localized states of an amorphous semiconductor. Second, the extended-state mobility, which is extractable from time-of-flight experiments, is also an effective quantity that is higher than the mobility of free carriers in the material.