Aims. We have studied the structure and dynamics of the upper photosphere and lower chromosphere of the quiet Sun. Methods. We analyzed a sequence of scans of slit spectra of the Ca II H line at 396.8 nm, with a spectral resolution of 850 000, and a spatial resolution of about one arcsec, taken in the quiet Sun at disk center, with a duration of about 55 min and an area coverage of 185 × 3.5 . We used statistical methods to characterize size, lifetime, and dynamics of emission features of the Fe II line at 396.94 nm. Results. We have identified about 780 distinct features where the Fe II line shows emission stronger than 3% above the local continuum. Their lifetime is on the order of one minute, and the spatial extent is about or less than 2 . On average, Fe II emission features show a significant redshift of 1.3 km s −1 , with respect to the position of the absorption line. The redshift of the Fe II emission is absent close to the solar limb. The Fe II emission is coupled with a strongly enhanced intensity level of the Ca II wings. A time line analysis shows that other photospheric lines show significant redshift one minute before, and a blueshift after, the occurrence of an emission event. A redshift of the Ca II H line core precedes the redshift of the Fe II line by about 30 s. The occurrence of the H2v emissions is strongly reduced before and significantly increased after the Fe II emission events. Conclusions. The temporal behavior of the Fe II emission line and both the Ca II H line core and H2v emission suggest a connection between Fe II emission and chromospheric activity. The presence of a significant redshift during the Fe II emissions and the absence of this redshift near the limb suggest that the observed redshift is indeed caused by a downflow in the line-forming region. From our result concerning the intensity fluctuations in the core of the Fe II line, and from the magnitude of the downflow velocities we conclude that the Fe II emissions at 396.94 nm occur in the photosphere.