A clean tungsten (W) tip apex with a robust atomic plane is required for producing a stable tunneling electron emission under strong electric fields. Because a tip apex fabricated from a wire by aqueous chemical etching is covered by impurity layers, heating treatment in ultra-high vacuum is experimentally known to be necessary. However, strong heating frequently melts the tip apex and causes unstable electron emissions. We investigated quantitatively the tip apex and found a useful method to prepare a tip with stable tunneling electron emissions by controlling electron-bombardment heating power. Careful characterizations of the tip structures were performed with combinations of using field emission I-V curves, scanning electron microscopy, X-ray diffraction (transmitted Debye-Scherrer and Laue) with micro-parabola capillary, field ion microscopy, and field emission microscopy. Tips were chemically etched from (1) polycrystalline W wires (grain size ∼1000 nm) and (2) long-time heated W wires (grain size larger than 1 mm). Heating by 10-40 W (10 s) was found to be good enough to remove oxide layers and produced stable electron emission; however, around 60 W (10 s) heating was threshold power to increase the tip radius, typically +10 ± 5 nm (onset of melting). Further, the grain size of ∼1000 nm was necessary to obtain a conical shape tip apex.