  The kinetic theory of $\mathrm{sech}^2 x$-type electron holes is studied. The
potential of the electron holes is solved in the weak amplitude limit by the
pseudo-potential method. We investigate the existence condition of the
$\mathrm{sech}^2 x$ electron holes. It indicates that the derivatives of
trapped and untrapped distributions at the separatrix play significant roles in
determining the potential profile. The theory is then applied to the
Kappa-distributed plasmas. The amplitude and width of the $\mathrm{sech}^2 x$
electron holes are analyzed. Finally, the theoretical results are verified by
numerical calculations.
