Amorphous silicon ($a$-Si) networks have been generated from melted Si with various quenching rates by molecular-dynamics (MD) simulations employing the Tersoff potential. The cooling rates were set between $5\ifmmode\times\else\texttimes\fi{}{10}^{11}$ and $1\ifmmode\times\else\texttimes\fi{}{10}^{14}\mathrm{K}/\mathrm{s};$ the latter is the slowest quenching rate in MD simulations previously performed. Although the atomic configurations formed by the cooling rate of ${10}^{14}\mathrm{K}/\mathrm{s}$ could reproduce the radial distribution function of $a$-Si obtained experimentally, they contained numerous structural defects such as threefold- and fivefold-coordinated atoms. As the cooling rate decreased, the average coordination number became $\ensuremath{\approx}4$ and tetrahedral bonds predominated. The structural and dynamical properties of $a$-Si generated by a cooling rate with $\ensuremath{\sim}{10}^{12}\mathrm{K}/\mathrm{s}$ were in excellent agreement with those of $a$-Si obtained experimentally.