For the final correction of the surface figure error of aspherical substrates used in the optics of extreme ultraviolet lithography, ion beam figuring (IBF), which is essentially a machining technique, is regarded as the most promising technique for the job. However, one problem with this technique is that it leaves the surface rougher after the IBF treatment than the surface was before the treatment. Moreover, the machined surface becomes positively charged due to the impact of Ar+ ions that constitute the beam for the IBF processing. Therefore, in this research a Si layer was deposited on a Zerodur (R) substrate by an ion beam sputtering process, following this process, the deposited substrate was machined by an Ar+ ion beam with energies in the range of 0.3-3 keV. The high-spatial-frequency roughnesses (HSFR) of the Zerodur (R) substrate and of the deposited Si layer were found to be 0.11 and 0.08 nm rms, respectively. However, the HSFR of the machined Si layer reaching to a depth of 50 nm can be made to go below 0.10 nm rms and below 0.15 nm rms by employing 0.5 and 1 keV Ar+ ion beam energies, respectively. Therefore, the proposed method can be employed by carrying out IBF on the substrates used in extreme ultraviolet lithography projection optics.