Magnetotunnelling in semiconductor heterostructures - Fromhold, Timothy Mark (1990)
Experimental studies of magnetotunnelling in heterostructures have revealed series of resonances due to electrons tunnelling from a 2DEG in a lightly-doped emitter into magnetoquantised states in the collector contact of a single-barrier structure (Hickmott, 1987 and Snell et al. 1987) or in the quantum well of a double-barrier structure (Eaves et a1., 1988 and Leadbeater et a1., 1989). These experiments are very suitable for theoretical analysis since a transverse magnetic field (parallel to the barrier interfaces) has little effect on the electronic states of the 2DEG, provided the diamagnetic energy is much less than the binding energy of the bound state of the accumulation layer potential. The tunnelling electrons then have a small range of transverse momenta between +PF and -PF, where PF = l'lkF is the Fermi momentum in the 2DEG. This range determines the positions of the orbit centres of the magnetoquantised states into which the electrons are injected after emergence from the tunnel barrier. For the single-barrier heterostructures described in this thesis, these are interfacial Landau states corresponding to classical orbits in which the electron skips along the barrier interface. For double-barrier structures there are interfacial states at high magnetic fields and traversing states at low magnetic fields. Owing to the high electric field in the quantum well, the corresponding classical orbits are cycloidal trajectories which intersect both barrier interfaces (traversing states) or just one barrier interface (skipping states). The variation of the tunnel current I with magnetic field B and voltage V is calculated using the Bardeen transfer-Hamiltonian approach within a WKB approximation. The accumulation layer potential is modelled according to a simple variational solution. This enables a physical interpretation of the experimental results to be given in terms of the effect of the magnetic field on the effect ive barri er hei ght and the ampli tudes of the magnetoquantised wave functions at the barrier interfaces. Both of these effects are required to account for the observed dependence of current on magnetic field I(B) and the amplitudes of the oscillatory structure revealed in the derivative plots of dI/dB and d2I/dB2 accounts for: The model (a) the observation of two series of resonances corresponding to +PF and -PF electrons in experiments on (InGa)As/InP single-barrier structures. (b) the absence of the +PF series of resonances in GaAs/(A1Ga)As single-barrier structures. (c) the changeover from traversing to skipping states in GaAs/(A1Ga)As double-barrier structures and the characteristic decrease in oscillatory amplitudes in the changeover region.