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《Chinese Journal of Luminescence》 2001-03
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Development of Curve Fitting Software for Resolving Overlapping Bands in the Luminescence Spectrum and Skill for Undertaking Curve Fitting

LIN Xiu hua 1,2,3 , JIANG Bing xi 1,2,3 , XIE Su yuan 2 , CHEN Li rong 1,3 (1 Department of Physics, Xiamen University; 2 State Key Laboratory for Physical Chemistry of Solid Surface, Xiamen University, Xiamen 361005, China  
At first we stress that a successful fit result is determined by three factors, namely the high resolution spectrum data, effective computer program and skill for correctly undertaking curve fitting. The latter two factors are considered in this article. The algorithm of curve fitting are based on the damped least squares optimization methods. It is programmed in FORTRAN 77.The general principles of a satisfactory optimization routine are given in the context of degree of convergence and the computation time needed to achieve an acceptable fit. The computer programs developed are capable of separating 24 overlapping bands at the most in a composite profile having 500 experimental data points. In the case of a composite profile strongly perturbed by the shot noises, a weighting function must be introduced into the computer program for its effectively running. Corresponding to the shape of a profile (a smooth curve or a curve revealing a high level of noises) and the constraint conditions, one may use a suitable program to undertake curve fitting. The functions of six programs are listed in Table 1. Furthermore, we stress that the mere ability to undertake the required calculations, in terms of rapid data handling capability of the computer, is not the guarantee that meaningful fits will be obtained. It is shown that a preliminary data processing is needed. In order to eliminate "insensible parameters" during the fitting calculations we should make the conversion of the values of original data. The value of abscissa for every point should be converted into the value expressed in the unit of meV. The value of intensity for every experimental point must be converted into a value as the maximum intensity is set at 100 a.u .Curve fitting may be facilitated if the initial estimates of parameters were chosen appropriately. The peak energy position must be accurately fixed. The discrepancy of a fit may be employed to locate any regions of poor fit in conjunction with visual plot. The regions of poor fit are attributed to incorrect choice of the initial estimates of parameters or the incorrect fit model adopted. A successful fit result is determined by the fit model which include the number of peaks, peak energy position and degree of band asymmetry. These factors are discussed in detail.At last we have exemplified the curve fitting of the 25K luminescence spectrum involving NN 1 bound exciton in GaP∶N sample. We have shown how to undertake the curve fitting of the whole composite profile, how to locate the region of poor fit and to change the fit model, and finally achieve a reliable fit.
【Fund】: 福建省自然科学基金 (E0 0 10 0 0 1);; 厦门大学固体表面物理化学国家重点实验室基金资助项目
【CateGory Index】: O433.4
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