Theoretical studies of wavepacket propagation in semiconductor quantum well structures
In this thesis a heuristic expression for the current through a GaAs/GaAlAs heterostructure is derived. This expression is shown to give rise to agreement between experiment and theory. The expression itself is derived within the effective mass formalism, which is discussed to show that its use will not generate large errors. This conclusion is contrary to previous work which will be shown to be in error due to misunderstandings concerning effective mass theory. To justify the approach used to obtain the tunnel current expression the behaviour of a wavepacket incident upon a square potential barrier is studied. The study shows that the wavepacket traverses the potential sufficiently rapidly to allow scattering to be neglected, and that the total transmission probability can be calculated from the solution of the time independent Schrodinger equation. The current expression is reduced to a one dimensional integral by assuming parabolic conduction bands, position independent mass and a thermalised electron distribution. The resulting expression is different from the usual Tsu-Esaki formula, a difference which can be seen to arise because the Tsu-Esaki formula does not account for the different velocities on each side of the barrier. The final stage, before any comparison is made to experimental results, is to show that the numerical technique of Vigneron and Lambin is more accurate than the WKB technique. A comparison of experimental results and the results of the numerical integration of the current density expression shows that they can only be reconciled if a resistance or diode is assumed in series with the tunnel barrier. This fitting parameter is then shown to be sufficient for good fits to be obtained between experiment and theory for the first time.