Resonant tunnelling of electrons through parabolic quantum wells: an analytical calculation of the transmission coefficient
The transmission coefficient for tunnelling through a GaAs/GaAlAs parabolic quantum well has been calculated using a transfer matrix model. In this work the one-dimensional effective-mass equation has been first solved analytically by means of confluent hypergeometric functions and airy functions as envelope functions. It is found that barrier width affects significantly the quantum tunnelling current through a parabolic quantum well.