where N° is the number of vacancy clusters after irradiation, Nv is the number of vacancy clusters as a function of time, Njv is the number of impurity number 1-vacancy complexes as a function of time, N2V is the number of impurity number 2-vacancy complexes as a function of time, tv, t,v, T2v are the annealing time constants for vacancy clusters, impurity number l-vacancy, and impurity number 2-vacancy respectively, and Nj, Np N2 are the number of interstitials, impurity number 1, and impurity number 2 atoms respectively. Then the degradation in short circuit current can be expressed by: where F is the fraction of defects remaining, Isc is the short circuit current as a function of time, Isco is the short circuit current before irradiation, and lsc$ is the short circuit current immediately after irradiation. That the equation (6) can qualitatively describe the annealing process is illustrated by the isothermal annealing data of figures 2, 3, 4, and 5 compared to a calculated curve using equation (6). It is hypothesized that impurity number 1 is oxygen and impurity number 2 is the dopant impurity boron. This hypothesis is supported by comparison of annealing temperatures for each stage to that of neutron annealing data where the defects have been more positively identified. Figures 6 and 7 show the degree to which the power output of the proton damaged cells can be restored. From these data it appears advantageous to anneal at as high a temperature as possible. It was further observed that the cells annealed after 3 x 10^ p/cm^ annealed more rapidly and more completely than those annealed after 3 x 10^ p/cm2. It is further interesting to note that, although the cells had relatively uniform electrical characteristics and degraded in a uniform manner as illustrated in figure 8, the annealing response showed a wide degree of scatter both in recovery times and in degree of recovery. This suggests that the annealing process is governed by parameters which do not strongly affect either initial cell performance or cell radiation resistance. If this is true and the factors yielding faster and more complete recovery can be identified then cells optimized for annealing should be possible. Conclusions that can be drawn are that 1) the annealing can be effective in restoring the performance of proton damaged cells and 2) factors such as silicon starting material, dopant materials, proton energy spectrum, damage level at which anneals are performed, temperature/time profiles, and solar cell junction designs should be considered in order to optimize annealing conditions.
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