| Positron is the antiparticle of electron and is the first kind of antimatter discovered by human, if it collide with an electron, they will annihilate mainly with the production of two gamma photons. These annihilation photons provide a new way for studying the basic physics property in solid materials. In the past more than half a century, a new independent discipline that is positron annihilation spectroscopy has been formed under the unremitting efforts with countless people, it is a non-destructive technique and has been widely used in material science such as point defects in atom level、Fermi surface、elemental specificity et al., medical science, such as positron emission tomography, and many other areas.The success in experiment greatly encourages the theoretical study of positron annihilation. Experimental methods need a comprehensive theory for a deep, quantitative understanding of the experimental results. Only through the theoretical calculations, can we obtain more physical information from the experimental results. Positron calculation is very important and necessary in the research of materials with positron techniques. In fact, with the development of positron experimental techniques, positron theory is also developing.Here, we define that the calculation method which does not involve the consistent calculation process is the non-consistent field method, such as empirical pseudo-potential method, superposed-neutral-atom method and so on, otherwise, it is the consistent field method, such as the first principle pseudo-potential plane wave method.No matter what kind of method, most of them take the self-consistent calculation for electron, but not for positron. Positron and electron, the "two components" are treated separately, this is the so called "conventional scheme", in this thesis, we will introduce the superposed-neutral-atom method and the pseudo-potential plane wave method in detail for calculating the positron quantum state, although many other methods have something different, they have similar calculating process, if we know the above two methods, it is easy to master the other approaches. In this thesis, some positron related calculation systems based on many references and previous works are finished to study the positron thermal and epithermal process, positron lifetime, positron Doppler broadening and so on in solids. Comprehensive test in done with some related crystalloids, these calculation results agree well with experimental ones, indicating the rationality and correctness of the positron calculation systems. In addition, they can also be used to study the positron annihilation behavior in complex solid materials, laying the foundation for better researches of solids. The main achievements of this thesis are as follows:(1) We use the Monte Carlo simulation to study the positron epithermal process, from much simulation of many simple substances, we find that in epithermal process, the positron epithermal time is very small, it can be ignored compared to positron lifetime; the positron stopping profile obey well the form originally suggested by Makhov in1961for electrons, the mean penetration depth depends on the incident positron energy rather accurately as the power which first suggested by Mills and Wilson in1982, this coincidence with the references; however, in some light elements, such as in Silicon, the positron stopping profile does not agree well with the Makhov form. For thermal process, from many calculations, we find that in low material temperature (usually lower than100K), the positron thermal time usually larger than5ps, this could be detected in positron lifetime experiment, that is to say the thermal time should be considered when we analyze the low temperature lifetime spectrum,(2) From our calculations of positron lifetime, we find that in the compounds which have the same crystal structure, the positron bulk lifetime may have rather simple relationship with the lattice constant. This provides a rather easy way to calculate the positron lifetime. Besides, we use the superposed-neutral-atom method (ATSUP) to calculate the positron lifetime of some complex compounds such as AgBiSe2, the lifetime of Ag-mono vacancy is195ps, agree well with our experimental one which is about198ps. This confirms that there are Ag-vacancies in this material, exists of these Ag-vacancies provide a way for the exchange of the positions of Ag and Bi, which is an important mechanism for the p-n-p transition of AgBiSe2.(3) The Generator Coordinate Hartree Fock method could be used to calculate the free atom wave-function of almost all the elements in periodic table. We adopt this method for positron theoretical research, and it can be used to calculate the positron wavefunction parameters of almost all the elements in periodic table, this makes up the serious weakness of MIKA/Doppler software which developed by Finland group; Base on the free atom wave-function, the broadening spectrum could be obtained, we take the semiconductor silicon as an example, the calculation result of Doppler broadening agrees very well with the experimental one; besides, by compared the first principle pseudo-potential calculation result, we find that because of the defect of the theoretical model, the ATSUP calculation results are a little larger than the experimental ones in the low momentum region, but a little smaller in the high momentum range.(4) Based on the band gap correction and the image charge correction, we calculate the mono-vacancy defect formation energy in different charge states of semiconductor Si and AlN. The calculation result of the mono-vacancy defect formation energy in Si agree well with the formation energy obtained form positron lifetime experiment; In AlN, we find that the defect formation energy of N mono-vacancy is very high, and so, the n-type in AlN semiconductor is not caused by N mono-vacancy.In a word, the positron theoretical calculation systems are built. They can be applied to calculate the positron thermal, trapping, annihilation process and so on in many solid materials of different crystal structures. They also provide the theoretical basis for further positron researches. |
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