Numerical modelling of photovoltaic cells with the meshless radial basis function collocation method

Doping processes are carried out in order to increase the conductivity levels of semiconductor materials. As a result of this process, two different regions are obtained: P and N semiconductor. While the P-type semiconductor is positively charged due to the need for electrons, the N-type semiconductor is negatively charged due to the excess of electrons. These two regions are divided into depletion region (TB) and quasi neutral zone (YNB). P-type semiconductors have fewer electrons than holes, while N-type semiconductors have fewer holes than electrons. These few electrons and holes are called minority carriers. In this thesis, transport equations of minority carriers in the QNR are solved using the radial basis function (RBF) collocation method. In the one-dimensional modelling study, the impacts of two different surface recombination velocities of S=0 and S→∞, two different diffusion lengths of L_n=L_p=10 μm and L_n=L_p→∞, and two different absorption coefficients of α=1/3 μm and α=1 μm the modelling are investigated by comparing the analytical and numerical solutions. Moreover, two different parameters affect the RBF collocation method, including the number of interpolation points and the shape parameter. Root mean square (rms) and maximum error values are calculated and compared using N=100 fixed number of interpolation nodes and 100 different shape parameters in the range 0.05≤c^2≤5. It has been observed that with the increase of c^2 value, the error values decrease continuously until a certain c^2 value, and then oscillations occur. Similarly, rms and maximum error values are calculated and compared using the c^2=1 fixed shape parameter and 97 interpolation node values in the 20≤N≤500. As in the case of c^2, it has been observed that with the increase of N, the error values decrease continuously up to a certain N, and then oscillations occur. In addition, when a comparison is made between RBFs, it is found that the error values decrease with the increase of the β exponent of the multiquadric (MQ), inverse multiquadric (IMQ) and generalized multiquadric (GMQ) functions. On the other hand, it is seen that the Gaussian (GA) does not converge well to the analytical results for small c^2 and N values compared to the range of 0.05≤c^2≤5 and 20≤N≤500, while it converges best in some cases for large c^2 and N values. For small c^2 values in the range of 0.05≤c^2≤5, the best convergence was obtained using the GMQ function with the largest β=2.5 exponent, while the worst convergence was obtained using the GMQ function with the smallest β=-2.5 exponent. For large c^2 values, the best converging function varies depending on used c^2 value and the RBF selection. In the two-dimensional modelling study, to compare the results obtained by the RBF collocation method, the reference solution is obtained using the finite element method (FEM), which is a mesh-based approach. In this method, triangular elements with a maximum mesh length of 10^(-6) are used. With the RBF collocation method, rms and maximum error values are obtained and compared using fifteen nodes per side, thirteen different shape parameters in the range of 0.02≤c^2≤0.08 and seven different functions. Similarly, rms and maximum error values are obtained and compared using four different shape parameters, five different numbers of nodes per side in the range of 10≤N_a≤30 and seven different functions. While it is seen that the function giving the best convergence to the reference solution in the range of 0.02≤c^2≤0.08 and 10≤N_a≤30 was the GA function, it was found that the function with the worst convergence was the GMQ function with the smallest exponent of β=-2.5. It is also seen that the solution time increases exponentially with the number of nodes. With the rms error and solution times obtained, optimum node numbers are obtained for four different shape parameters in the range of 0.02≤c^2≤0.08, seven different functions and nine different choices of weight values. It is observed that while the optimum values increased with the increase of w_1 which is the weight of the accuracy of the numerical solution and β values, the c^2 value changed the optimum values at a negligible level. In brief, one-dimensional and two-dimensional modelling studies are considered. In one-dimensional modelling, the minority carrier concentration in the QNR of both P and N regions is calculated and compared using various parameters. In contrast, in two-dimensional modelling, the minority carrier concentration of a single region is calculated, and optimum values are obtained using the utopia point method, a multi-objective optimization. In the solution of both models, seven different RBF, including MQ, IMQ, GA and GMQ functions which have four different exponents, are used.