Barrier collimation does not requir

Barrier collimation does not require adiabaticity. For an abrupt barrier, collimation simply results from transverse momentum conservation, as in Fig. 60a, leading directly to Eq. (3.31). (The total external reflection at an abrupt barrier for trajectories outside the collimation cone is similar to the optical effect of total internal reflection at a boundary separating a region of high refractive index from a region of small refractive index; see the end of Section III.D.2.) A related collimation effect resulting from transverse momentum conservation occurs if electrons tunnel through a potential barrier. Since the tunneling probability through a high potential barrier is only weakly dependent on energy, it follows that the strongest collimation is to be expected if the barrier height equals the Fermi energy. On lowering the barrier below EF ballistic transport over the barrier dominates, and the collimation cone widens according to Eq. (3.31). A quantum mechanical calculation of barrier collimation may be found in Ref.363.