Spin coherence and relaxation of natural quantum dots at the Si/SiO$_2$ interface*

While electron spins confined in quantum dots in silicon heterostructures are good candidates to make qubits, little is known about the coherence of electrons at the Si/SiO$_2$ interface. We perform pulsed electron spin resonance on a Metal-Oxide-Silicon transistor and report the spin relaxation (T$_{1}$) and coherence (T$_{2}$) times for mobile two-dimensional electrons as well as electrons isolated in natural quantum dots at the Si/SiO$_2$ interface. Mobile electrons have short T$_1$ and T$_2$ of around 0.3~$\mu$s at 5~K. Upon confining electrons into isolated dots with a few meV binding energy, T$_1$ rises dramatically as temperature is decreased, reaching 1.1~ms at 350~mK. Simultaneously, T$_2$ rises and saturates at 10~$\mu$s below 1~K. The long T$_1$ is consistent with a reduced efficiency of Rashba fluctuations in causing spin relaxation in a quantum dot. However T$_2$ is not controlled by T$_1$ below 1~K, but is instead caused by an unknown extrinsic mechanism.