We present the measurements of the cross sections for the two main production modes of single top quarks at the Tevatron with 9.7/fb of data collected by the D0 detector. The analysis employs three different multivariate techniques which are combined to extract the small signal from the large backgrounds in the W+jets final state. We measure independently the t-channel (tqb) and the s-channel (tb), and obtain a lower limit on the CKM matrix element |Vtb|>0.92 at 95% CL. The results are compared with physics beyond the SM. The presence of the s-channel production is established in the D0 data with a significance of more than 3 standard deviations for the first time.