The CDF II experiment and the Tevatron proton-antiproton collider are parts of the Fermi National Laboratories (Fermilab). The Fermilab is located in the vicinity of Chicago, USA. Today, the Tevatron is the only collider which is able to produce the heaviest known elementary particle, the top quark. The top quark was discovered at the Tevatron by the CDF and the D0 collaborations in 1995. So far, all the top quarks found are produced via the strong interaction as top-antitop pairs. The Standard Model of elementary particle physics also predicts single-top quark production via the electroweak interaction. This production mode has not yet been observed. The CDF and the D0 collaborations have set upper limits on the cross section for that process in Run I and improved those results in Run II. Single-top quark production is one of the major interests in Run II of the Tevatron as it offers several ways to test the Standard Model and to search for potential physics beyond the Standard Model. The measurement of the cross section of singly produced top quarks via the electroweak interaction offers the possibility to determine the Cabbibo-Kobayashi-Maskawa (CKM) matrix element V(sub tb) directly. The CKM matrix defines the transformation from the eigenstates of the electroweak interactions to the mass eigenstates of the quarks. V(sub tb) gives the strength of the coupling at the Wtb vertex.