The requirements on dimensional control of contact holes scale with the technology node and are reaching values of only a few nanometers. The allowed 3 sigma variation of the diameter is typically 10%. In traditional optical lithography, cross section variations occur mainly on a global scale as a result of slowly varying image or process parameters. For electron beam lithography and extreme ultraviolet (EUV) lithography, local variations need more attention. The authors have developed a model for the critical dimension (CD) variations resulting from shot noise and checked the results with Monte Carlo simulations. The model predicts that the necessary number of particles to write a contact is independent of the contact diameter, when both the requirements, the resolution, and resist's acid diffusion length scale with the size of the contacts. The minimum number of particles required under ideal circumstances is about 500 per contact, but under more realistic circumstances, e.g., for electron beam lithography, at low voltages, a typical number of electrons per contact is 3900. This means that contact holes at the "32 nm node" (45 nm diameter at 90 nm pitch with 3 sigma of 4.5 nm) require a dose of about 30 mu C/cm(2) and at the "22 nm node" about 60 mu C/cm(2). If the molecular size of the resist molecules contributes to a size variance, or if high energy electrons or EUV photons are used, the required dose may be substantially higher. (c) 2006 American Vacuum Society.