Improved High Resolution Post-Transit Spectroscopy for Determining the Density of States in Amorphous Semiconductors
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Improved High Resolution Post-Transit Spectroscopy for Determining the Density of States in Amorphous Semiconductors Charlie Main1, Steve Reynolds1, Rashad I. Badran2 and Joe M. Marshall3 1. School of Science and Engineering, University of Abertay Dundee, Dundee DD1 1HG, UK, 2. Department of Physics, The Hashemite University, Zarqa, Jordan, 3. Dept of Materials Engineering, University of Wales Swansea, UK. ABSTRACT We show that the analysis of post-transit photocurrent i(t) in a multi-trapping context to determine the density of trapping states g(E) is capable of resolving features less than kT in width. A commonly used method uses a Laplace inversion of i(t) data giving the well-known result g(E) ~ t i(t) but employs a delta function approximation for trap release times, which results in loss of energy resolution. We show that it is possible to retain the exponential distribution function for trap release time and solve the multi-trapping rate equations directly, giving significantly improved resolution. The analysis is performed on computer generated posttransit data for distributed and discrete traps, and compared with the earlier method and other related Fourier transform methods for determining g(E). In addition, the versatility of the new method in handling cases with either distributed traps or with discrete traps means that it can be applied to disordered materials or to crystalline materials with well-defined defect levels. INTRODUCTION Post-transit spectroscopy has been employed by numerous groups to determine the distribution of localized trapping states (DOS) in amorphous semiconductors, such as amorphous silicon and its alloys [1-5] and in organic semiconductors [6]. The method involves the creation of excess carriers by pulsed illumination in a semiconductor structure (e.g. p-i-n). A high reverse field ensures that excess carriers emitted from any group of states which has a capture time longer than the transit time of free carriers, will transit the structure, to be collected, before retrapping in these states can occur. Since the rate-limiting step is the release of trapped charge, the resulting ‘post-transit ‘ photocurrent decay i(t) then simply follows the release rate with elapsed time t from successively deeper traps in the semiconductor’s energy gap, with distribution reflecting the DOS, g(E). With no re-trapping taking place as in the ‘pre-transit’ photocurrent case, the situation is relatively easier to model and analyze. We also note here the similarity between the post-transit situation in sandwich configuration, and ‘post- recombination’ in coplanar geometry, if one carrier type predominates, and recombination is monomolecular. All reports known to the authors to date, have used an approximate expression g (E ) ∝ t i (t ) to determine the density of states [7], ascribing an energy scale E = kT ln (νt ) , defined by associating the average release time from traps at energy depth E below the mobility edge with the elapsed time t, where ν is the attempt to escape frequency, assumed to be energy
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