Long Spin Relaxation and Coherence Times of Electrons In Gated Si/SiGe Quantum Dots

Single electron spin states in semiconductor quantum dots are promising candidate qubits. We report the measurement of 250 $\mu $s relaxation (T$_{1})$ and coherence (T$_{2})$ times of electron spins in gated Si/SiGe quantum dots at 350 mK. The experiments used conventional X-band (10 GHz) pulsed electron spin resonance (pESR), on a large area (3.5 x 20 mm$^{2})$ dual-gate undoped high mobility Si/SiGe heterostructure sample, which was patterned with 2 x 10$^{8}$ quantum dots using e-beam lithography. Dots having 150 nm radii with a 700 nm period are induced in a natural Si quantum well by the gates. The measured T$_{1}$ and T$_{2}$ at 350 mK are much longer than those of free 2D electrons, for which we measured T$_{1}$ to be 10 $\mu $s and T$_{2 }$to be 6.5 $\mu $s in this gated sample. The results provide direct proof that the effects of a fluctuating Rashba field have been greatly suppressed by confining the electrons in quantum dots. From 0.35 K to 0.8 K, T$_{1}$ of the electron spins in the quantum dots shows little temperature dependence, while their T$_{2}$ decreased to about 150 $\mu $s at 0.8 K. The measured 350 mK spin coherence time is 10 times longer than previously reported for any silicon 2D electron-based structures, including electron spins confined in ``natural quantum dots'' formed by potential disorder at the Si/SiO$_{2}$\footnote{S. Shankar \textit{et al}., Phys. Rev. B 82, 195323 (2010)} or Si/SiGe interface, where the decoherence appears to be controlled by spin exchange.