The electron conduction through paths of nanometer size in a current-perpendicular-to-plane device is studied. The model of a free electron confined to the square well potential is proposed. The model leads a conductivity discontinuity and a peak of the current spectrum, d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> i/dV <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Several peaks are observed in the current spectra of a CPP-GMR device with current screen layer, of which size of the current path observed by the conductive-AFM is about 6 nm. The peak voltage is on the same level with the estimated value by the model, although the magnetic behavior cannot be understood. There exist several peaks in the current spectra of a tunneling junction broken by an excessive pulse voltage. It is estimated from the model that the size of the pinhole caused by the breakdown is about 1 nm.