  We studied the exclusive reaction e p --> e' p' phi using the phi --> K^+ K^-
decay mode. The data were collected using a 4.2 GeV incident electron beam and
the CLAS detector at Jefferson Lab. Our experiment covers the range in Q^2 from
0.7 to 2.2 GeV^2, and W from 2.0 to 2.6 GeV. Taken together with all previous
data, we find a consistent picture of phi production on the proton. Our
measurement shows the expected decrease of the t-slope with the vector meson
formation time c Delta tau below 2 fm. At = 0.6 fm, we measure b_phi = 2.27 +-
0.42 GeV^-2. The cross section dependence on W as W^{0.2+-0.1} at Q^2 = 1.3
GeV^2 was determined by comparison with phi production at HERA after correcting
for threshold effects. This is the same dependence as observed in
photoproduction.
