Tham khảo tài liệu 'properties and applications of silicon carbide part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 22 Properties and Applications of Silicon Carbide It would seem that one could now neglect the quadratic terms and solve the linear differential equations. In this case we would obtain simple analytic solutions for system 3 in the form of a linear combination of exponentials. While this approximate solution would not be valid for the total range of relaxation times it would be acceptable for the interval within which the fastest-decaying quantities have completed their relaxation. It can be shown that in this case a pair of coupled equations for acceptors and holes has one of the solutions of the secular equation for the decay rates which is equal to zero. This relates to an extremely slow decay of the acceptor concentration. Indeed in an experiment one observes a considerable slowing down of the acceptor EPR signal 1000 min after the switching off the light. In this case the residual acceptor concentration differs from the equilibrium value A0q 0 and the evolution of the EPR signal with time cannot be fitted with one exponential. Moreover when we neglect quadratic terms we actually disregard the electron-hole recombination processes. All this suggests the importance of the quadratic terms on the right-hand side of Eqs. 3 which are actually responsible for the fast EPR signal intensity decay. For this reason the coupled differential equations 3 were solved numerically with inclusion of all the quadratic terms by the finite difference method. In this approach we increase the time by such a small increment At at which in the Taylor expansion of the time dependent functions n t D0 t A0 t and p t one may restrict oneself to three first terms including the term with At 2. The values of n t D0 t A0 t and p t as well as their first and second derivatives with respect to time were assumed to be equal to the values reached at the preceding instant of time. The value of the first derivative was calculated as the right-hand side of rate equations 3 and that of the second .
