Deep-trapping kinematics of charge carriers in amorphous semiconductors: A theoretical and experimental study

There has been much recent interest in the determination of drift-mobility ({μ}) --lifetime ({τ}) products in amorphous semiconductors by various measurement techniques. Although most measurements have utilized time-of-flight types of transient-photoconductivity experiments, xerographic measurements have also been used, since they provide a clear measurement of the residual potential VR, i.e., the electrostatic potential on the surface of a high-resistivity solid, due to trapped charges in the bulk. This paper identifies and critically examines the theoretical problems involved in the determination of {μ}{τ} from such xerographic measurements. The deep-trapping model of Kanazawa and Batra, which relates the residual potential to the {μ}{τ} product, is reformulated by specifically including the effect of the rate of trapping as being proportional to the instantaneous unoccupied density of traps. The latter description had been neglected in previous models of deep-trapping kinematics. A partial differential equation is derived that describes the space and time evolution of the electric field within the material.By numerically solving the differential equation and integrating the electric field, the residual potential VR has been related to the {μ}{τ} product. It is found that VR depends not only on the {μ}{τ} product but also on the capture coefficient to the microscopic mobility ratio, Cₜ/μ₀. Universal curves relating VR to the {μ}{τ} product and parametric in Cₜ/μ₀ have been obtained that clearly show the importance of including the effect of trap filling in the theory. Furthermore, it is shown that the {μ}{τ} product cannot be uniquely determined via xerographic measurements unless ({ε}Cₜ/eμ₀){}1, where {ε} is the permittivity of the material. Xerographic first-cycle residual-potential experiments in conjunction with interrupted-field time-of-flight (IFTOF) transient-photoconductivity measurements have been carried out on vacuum-deposited pure a-Se and chlorine-doped a-Se:0.3 at. % As alloy films to experimentally correlate the residual potential with the {μ}{τ} values.It is shown that the Kanazawa-Batra universal curve is completely inadequate in describing the present experimental VR versus {μ}{τ} data, by as much as a factor of 5, whereas the theory developed herein can account for the experiments, provided that the capture coefficient Cₜ is 1.22×{}10^-7 cm³ s^-1. The limitations of the present model and its implications are also addressed. The simple range-limited transport concept of Warter leading to the expression VR=L²/2{μ}{τ} for the residual potential under weak-trapping conditions has been found to predict the residual voltage surprisingly well and to within a factor of 2. By carrying out cycled-up xerographic residual-potential experiments on the same films for which the deep-trapping times have been determined, the capture radius of deep hole traps in a-Se and chlorinated a-Se:0.3 at. % As films have been determined. Application of ballistic and diffusional trapping models of Street to the IFTOF lifetime and cycled-up residual-potential data imply capture radii of 2--3 {} for both pure a-Se and Cl-doped 0.3 at. % As alloys. The first-cycle residual-potential model developed herein in combination with IFTOF results, however, leads to capture radii of {~}20 and 85 {} for ballistic and diffusional capture, respectively. The results are discussed in terms of valence-alternation-pair (VAP) and intimate-VAP (IVAP) centers in amorphous semiconductors. The energy spectrum of the density of localized midgap states for both a-Se and Cl-doped a-Se:0.3 at. % As films have been obtained via the xerographic-spectroscopy technique of Abkowitz and Markovics.