Investigation of range-energy relationships for low-energy electron beams in silicon and gallium nitride

The electron beam technique of the Scanning Electron Microscopy (SEM) has been widely used for the characterization of bipolar devices and photodiode materials. The resolution of an electron beam technique is affected by the interaction of the beam and the specimen. The size of this interaction volume, commonly termed the generation volume, is usually characterized by what is called the electron penetration range and is measured from the surface. Since there is currently no consensus on the expressions to use in the calculation of the electron range, this paper provides an analysis of the three most commonly used semiempirical expressions. They are the Gruen range, the universal curve of Everhart and Hoff, and the maximum range of Kanaya and Okayama. This analysis is done using data from the statistical method of Monte Carlo simulations. It was found that the Everhart and Hoff universal curve performs better at low beam energies than the equation of Kanaya and Okayama. However, the validity of all the three expressions is questionable below 5 keV. In order to overcome this, fitted expressions based on the extrapolated range are provided for beam energies below 5 keV in the case of Si and GaN materials. The accuracy of these expressions is affected by the physical parameters used in the Monte Carlo simulations.