Simulation of Fowler-Nordheim Emission for Scanning Probe Lithography

Field-emission scanning probe lithography based on a Fowler-Nordheim type electron emission from a nanotip enables cost-effective technology for nanodevices. Thereby, the emitted electrons expose directly a ultrathin resist film (below 50nm). The electron energies are in the range of a few tens of electron volts, which is close to the binding energies of resist molecules. During the patterning process the resist molecules are converted into volatile compounds causing a direct patterning. So far, the mechanisms and conditions underlying the patterning process are not completely understood. Therefore, we simulate the emission process using a 2D (based on [1]) as well as 3D models. Both models are compared with experimentally obtained Fowler-Nordheim plots in order to determine the dependency of the electron current on the bias voltage. Hereby, different tip-sample distances, work functions, tip radii and opening angles of the nanotip are considered. The effect of the resist material on the electric field, the electron emission, the electron distribution on the sample surface and, thus, on the lithographic process is studied. To gain insights of the physical processes occuring in the resist layer we carried out Monte-Carlo simulations attributed to questions like the electron distribution inside the resist and the stopping distance of the electrons, i.e. the depth, at which the electrons transferred their energy completely to the resist molecules.