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We report the diffusion of boron, arsenic, and phosphorus in silicon isotope multilayer structures at temperatures between $850\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ and $1100\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$. The diffusion of all dopants and self-atoms at a given temperature is modeled with the same setting of all native-point-defect-related parameters. The evaluation of the relative contributions of charged native-point defects to self-diffusion enables us to determine the defect energy levels introduced by the native-point defects in the Si band gap. Making allowance for the fact that the band gap and the energy levels change with temperature, an energy-level diagram of the native-point defects is obtained that shows a reversed level ordering for the donor levels of the self-interstitials. In accord with the general state of knowledge, the diffusion of boron is mainly mediated by self-interstitials whereas the properties of both vacancies and self-interstitials are important to model arsenic and phosphorus diffusion. The simultaneous diffusion of phosphorus and silicon requires the existence of a singly positively charged interstitial phosphorus. It is the diffusion of this defect that strongly affects the shape of the phosphorus diffusion tail and not entirely the supersaturation of self-interstitials argued so far. Taking into account the mechanisms of dopant diffusion and the properties of native-point defects determined from the simultaneous diffusion experiments, let us describe accurately dopant profiles given in the literature. Altogether, this work provides overall consistent data for modeling dopant and self-diffusion in Si for various experimental conditions. A comparison of experimentally and theoretically determined activation enthalpies of self- and dopant diffusion shows excellent agreement for self-interstitial-mediated diffusion but significant differences for vacancy-mediated diffusion in Si. This disagreement either reflects the deficiency of first-principle calculations to accurately predict the energy band gap of Si or points to a still-remaining lack in our understanding of diffusion in Si.