Boundary conditions for tunneling through potential barriers in nonparabolic semiconductors

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Abstract
A wave equation is formulated by using the energy-wave-vector relation for nonparabolic bands and it is shown that the resultant boundary condition is in agreement with the condition of the continuity of probability current density. The condition is shown to involve the velocity effective mass with the derivatives of the wave function, in place of the energy effective mass, used earlier. Calculated results are also presented for the probability of tunneling through a single rectangular barrier in the Ga0.47In0.53As/InP/Ga0.47In0.53As system, which show that the nonparabolicity reduces significantly the value of the probability from those estimated by using the energy effective mass in the boundary condition.