Low-energy electron microscopy (LEEM) was used to measure the reflectivity of low-energy electrons from graphitized SiC(0001). The reflectivity shows distinct quantized oscillations as a function of the electron energy and graphite thickness. Conduction bands in thin graphite films form discrete energy levels whose wave vectors are normal to the surface. Resonance of the incident electrons with these quantized conduction band states enhances electrons to transmit through the film into the SiC substrate, resulting in dips in the reflectivity. The dip positions are well explained using tight-binding and first-principles calculations. The graphite thickness distribution can be determined microscopically from LEEM reflectivity measurements.Recently, thin graphite films, especially single graphite sheets called graphene, have attracted much attention. This is because they exhibit interesting electronic transport properties, such as field effects and quantum hall effects. 1-3 So far, thin graphite films have been formed in two ways. One is based on processing bulk graphite using oxygen plasma etching, 1,4 but this method cannot provide thin graphite layers with a large area. The other is to anneal SiC surfaces at high temperatures in an ultrahigh vacuum (UHV). Selective sublimation of Si from the substrate results in the graphite films on the surface. 5-10 The graphite films can be processed to fabricate device structures using standard lithographic techniques, and the magnetotransport measurements of the structures have revealed signatures of quantum confinement. 9 This method may provide wide graphite films, which would make it more suitable for device application. However, to use the thin graphite on the SiC substrate for device fabrication, we need a reproducible way of forming graphite films with an intended thickness. For this purpose, it is essential to determine the graphite thickness during various stages of the formation processes. Auger spectroscopy has been used to estimate thickness of graphite formed on SiC. 7 More recently, it has been shown that the number of graphene layers in the graphite film can be determined from the band structure measured using angle-resolved photoemission spectroscopy, 10 but this method also provides only spatially-averaged information. Local thickness distributions are more desirable.Confinement of electrons in thin films creates quantum well (QW) bound states. QW resonant states can form as well at energies above the confinement potential barrier, because the potential discontinuity scatters electrons quantum-mechanically.To date, photoemission spectroscopy has provided the most direct observation of the QW states, both bound and resonance states, below the Fermi level. 11 Photoemission spectroscopy measurements have revealed that the QW states can cause dramatic quantum size effects on the film properties, such as film stability, 12 magnetic interlayer coupling, 13 and superconductivity. 14 The QW states at discrete energy levels produce peaks in the photoemission energy spe...