The authors develop a theoretical description of the trapping of electrons by voids in a tight-binding solid. A new microscopic model is introduced in which the internal pore surfaces are parametrised by dimensionless ratios R and eta . Critical values Rc and eta c of these ratios exist at which the fraction f of bound states at the pores vanishes. For a small pore embedded in a finite solid, numerical results for the bound state energies and their degree of localisation are presented. For larger pores in an infinite solid analytic results are obtained. On the basis of these results, the authors examine the possibility that field-dependent losses found experimentally in RF sputtered semiconductors are due to the trapping of electrons by voids and suggest that the field effect arises through transitions between bound pore states and nearby localised states.