By means of a series of N-body/SPH simulations we investigate the morphological properties of thick stellar disks formed through minor mergers with, e.g. a range of gas-to-stellar mass ratios. We show that the vertical surface density profile of the post-merger thick disk follows a sech function and has an excess in the regions furthest away from the disk mid-plane (z 2 kpc). This stellar excess also follows a sech function with a larger scale height than the main thick disk component (except at large radii). It is usually dominated by stars from the primary galaxy, but this depends on the orbital configuration. Stars in the excess have a rotational velocity lower than that of stars in the thick disk, and they may thus be confused with stars in the inner galactic halo, which can have a similar lag. Confirming previous results, the thick disk scale height increases with radius and the rate of its increase is smaller for more gas rich primary galaxies. On the contrary, the scale height of the stellar excess is independent of both radius and gas fraction. We also find that the post-merger thick disk has a radial scale length which is 10−50% larger than that of the thin disk. Two consecutive mergers have basically the same effect on heating the stellar disk as a single merger of the same total mass, i.e., the disk heating effect of a few consecutive mergers does not saturate but is cumulative. To investigate how thick disks produced through secular processes may differ from those produced by minor mergers, we also simulated gravitationally unstable gas-rich disks ("clumpy disks"). These clumpy disks do not produce either a stellar excess or a ratio of thick to thin disk scale lengths greater than one. Comparing our simulation results with observations of the Milky Way and nearby galaxies shows that our results for minor mergers are consistent with observations of the ratio of thick to thin disk scale lengths and with the "Toomre diagram" (the sum in quadrature of the vertical and radial versus the rotational kinetic energies) of the Milky Way. The simulations of clumpy disks do not show such agreement. We conclude that minor mergers are a viable mechanism for the creation of galactic thick disks and investigating stars at several kpc above the mid-plane of the Milky Way and other galaxies may provide a quantitative method for studying the (minor) merger history of galaxies.