Probing localized states distributions in semiconductors by Laplace transform transient photocurrent spectroscopy

  • Mariana Gueorguieva

    Student thesis: Doctoral Thesis


    The structure of the thesis is as follows:

    Chapter I addresses the question of how the disorder of non-crystalline semiconductors influences their electronic properties. The concept of the mobility edge and mobility gap is introduced and a definition of the density of electronic states (DOS) is given. The DOS will be referred to frequently in this work. Also charge transport and photoconductivity in amorphous semiconductors are briefly described.

    In chapter I the Multiple Trapping model (MT), widely used to describe charge transport in amorphous semiconductors, is formulated in the context of the transient photoconductivity (TPC) experiment. A brief review of the existing mathematically approximate methods (Naito H. et al, 1996; Nagase T. et al, 1999; Ogawa N. et al, 2000) based on the Laplace transformation for solving the MT system of equations is given. One of the main objectives of this work was to develop an exact procedure for solving the Fredholm integral equation of the 1st kind arising from the MT system of equations in the context of TPC experiment. The newly developed method is termed Exact Laplace Transform (ELT) method. The method could formally be divided in two parts. The first part is concerned with finding an exact solution of the Fredholm integral equation of the 1st kind. The second part of the method is a semi-analytic procedure based on a polynomial approach for simulation of I-t data from a model DOS distribution. The method has been thoroughly studied by application to computer simulated I-t data. The ELT method is found to have the finest resolution of ~ kT / 6 (when applied to simulated I-t data) which is clearly an improvement over the approximate methods which have resolution of ~ 2-3 kT. Furthermore, it has been shown that the polynomial approach could be used to obtain information on the free carrier recombination lifetime,  τf  and the procedure has been discussed.

    The Tikhonov regularization method (Tikhonov A. N., 1963; Weese J., FTIKREG program, 1992), regarded as one of the most reliable methods for extracting information from noisy experimental data, has been applied to computer simulated data. It has been shown that the newly developed exact method and the Tikhonov regularization method perform equally well in terms of accuracy and resolution when applied to computer simulated, noise free I-t transients. In the same chapter the approximate and exact methods have been applied to simulated I-t data with and with no noise introduced. The reliability of all methods has been discussed.

    At the end, the approximate and exact methods have been used to extract information on DOS in light-soaked plasma enhanced chemical vapour deposition (PECYD) a — Si : H , and on discrete levels in single crystal Tin-doped CdTe . The results have been compared with other publications.

    In chapter II the time-of-flight (TOF) experiment and the mathematics describing it are briefly reviewed. The ELT and the Tikhonov regularization methods have been adapted for the case of the post-transit TOF experiment and applied to computer simulated TOF I-t data. The performance of the exact methods and the widely used approximate txl(t) approach (Seynhaeve et al, 1989) has been studied. In order to simulate post-transit I-t data the polynomial approach has been used with model DOS distributions and under the assumption of near equivalence of post-transit régime in TOF experiment and post-recombination conditions in the context of the TPC experiment. The ELT and the Tikhonov regularization proved superior to the existing txl(t) approach (Seynhaeve et al, 1989). All three methods (the ELT , the Tikhonov and the txl(t) method) have been applied to experimentally obtained TOF data on a — S i : H and the results have been discussed.

    A summary of the principle results from this work is given in the final chapter (Conclusions).
    Date of AwardJun 2005
    Original languageEnglish

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