Optimal algorithm to improve the calculation accuracy of energy deposition for betavoltaic MEMS batteries design

Aimed at improving the calculation accuracy when calculating the energy deposition of electrons traveling in solids, a method we call optimal subdivision number searching algorithm is proposed. When treating the energy deposition of electrons traveling in solids, large calculation errors are found, we are conscious of that it is the result of dividing and summing when calculating the integral. Based on the results of former research, we propose a further subdividing and summing method. For β particles with the energy in the entire spectrum span, the energy data is set only to be the integral multiple of keV, and the subdivision number is set to be from 1 to 30, then the energy deposition calculation error collections are obtained. Searching for the minimum error in the collections, we can obtain the corresponding energy and subdivision number pairs, as well as the optimal subdivision number. The method is carried out in four kinds of solid materials, Al, Si, Ni and Au to calculate energy deposition. The result shows that the calculation error is reduced by one order with the improved algorithm.