The local anodic oxidation (LAO) by the tip of atomic force microscope (AFM) is used for fabrication of nanometer-scaled structures and devices. We study the technology of LAO applied to semiconductor heterostructures, theoretically and experimentally as well. The goal is to improve the LAO process itself, i.e., to create narrow LAO lines that form high-energy barriers in the plane with the 2D electron gas. In the first part we show the electric field distribution in the system tip-sample during LAO. For samples with low-conductive cap layer the maximum electric field is shifted apart the tip apex, which leads to wide oxide lines. Our Monte Carlo (MC) calculations show how the height of the energy barrier in the system depends on the geometry of the created lines (trenches), and on voltage applied to the structure. Based on the calculations, we have proposed a novel LAO technology and applied it to InGaP/AlGaAs/GaAs heterostructure with doping layer only 6 nm beneath the surface. The doping layer can be oxidized easily by the AFM tip in this case, and the oxide objects can be removed by several etchants. This approach to the LAO technology leads to narrow LAO trenches (approximately 60 nm) and to energy barriers high enough for room- and low-temperature applications.