A new theory is developed for nonideal J-V characteristics of Schottky barriers with an interfacial layer. This theory is based on the model that nonideal characteristics are due to changes of population in the interface states under applied bias and accompanying changes of the barrier height. The population in the interface states is expressed by the Fermi level, which can be determined by analyzing experimental results. The J-V characteristics are obtained from the flow of carriers into and out of the interface. Tunneling through the interfacial layer constitutes the bottleneck for the carrier flow. Under forward bias, the carrier concentration ns at the interface is proved to be in thermal equilibrium with the bulk. Under reverse bias, n s is in local thermal equilibrium with the interface states. This theory is applied to an undoped a-Si:H Schottky barrier without introducing any ambiguous quantities. The experimental ideality factor, its dependence on temperature and voltage, and current density are quantitatively explained. By analyzing experimental results, the following behaviors are disclosed. The Fermi level of the interface states is significantly lower than the bulk Fermi level at low forward bias, but it approaches the bulk Fermi level with increasing forward-bias voltage. As for the reverse characteristics, the decrease of the barrier height is proportional to √V in the present sample for applied voltage V. For electrons in the interface states, the probability of tunnel transition to the metal is small compared with that of communication with the conduction band.