Conductivity of one-dimensional semiconductor with periodic potential

The kinetic equation for the electron distribution function in a one-dimensional semiconductor with a spatial-periodic potential in the presence of a weak pulling electric field was analytically solved in the limiting case of the infinite length of carrier energy relaxation. An explicit expression for the conductivity of the system was derived for a sinusoidal potential profile with an arbitrary amplitude. It was shown that the singularities in the electron distribution function, arising in the asymptotic limit, are smoothed in the region of finite lengths of energy relaxation. A comparison with the results of an opposite (local) mode shows that conductivity in the significantly nonlocal case is lower at any potential amplitude. (C) 2003 MAIK "Nauka/Interperiodica".