Ultra-thin (2-5 nm thick) aluminum oxide layers were grown on non-functionalized individual single walled carbon nanotubes (SWCNT) and their bundles by atomic layer deposition (ALD) technique in order to investigate the mechanism of the coating process. Transmission electron microscopy (TEM) was used to examine the uniformity and conformality of the coatings grown at different temperatures (80 degrees C or 220 degrees C) and with different precursors for oxidation (water and ozone). We found that bundles of SWCNTs were coated continuously, but at the same time, bare individual nanotubes remained uncoated. The successful coating of bundles was explained by the formation of interstitial pores between the individual SWCNTs constituting the bundle, where the precursor molecules can adhere, initiating the layer growth. Thicker alumina layers (20-35 nm thick) were used for the coating of bottom-gated SWCNT-network based field effect transistors (FETs). ALD layers, grown at different conditions, were found to influence the performance of the SWCNT-network FETs: low temperature ALD layers caused the ambipolarity of the channel and pronounced n-type conduction, whereas high temperature ALD processes resulted in hysteresis suppression in the transfer characteristics of the SWCNT transistors and preserved p-type conduction. Fixed charges in the ALD layer have been considered as the main factor influencing the conduction change of the SWCNT network based transistors.